{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Ethan, Elizabeth, Luke, Noah, and Matthew. According to Alexander, \"Noah is a knave\". Ethan told you that If Luke is a knave then Matthew is a knave. Elizabeth said that Noah is a knight if and only if Matthew is a knave. \"Noah is not a knight,\" Luke mentioned. In a statement by Noah: \"Matthew is not a knave\". Matthew was heard saying, \"Alexander is a knight or Luke is a knave\". So who is a knight and who is a knave?", "names": ["Alexander", "Ethan", "Elizabeth", "Luke", "Noah", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Alexander is a knave, Ethan is a knave, Elizabeth is a knave, Luke is a knave, Noah is a knight, and Matthew is a knight.", "solution_text_format": "(1) Alexander is a knave\n(2) Ethan is a knave\n(3) Elizabeth is a knave\n(4) Luke is a knave\n(5) Noah is a knight\n(6) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Alexander that Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Matthew is not a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Noah that Matthew is not a knave.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight or Luke is a knave.", "We have exhausted all possibilities for Matthew and Noah, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Alexander is a knight or Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Noah is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that If Luke is a knave then Matthew is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Luke is a knave then Matthew is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Noah is a knight if and only if Matthew is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Matthew is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('->', ('lying', 3), ('lying', 5)), ('<=>', ('telling-truth', 4), ('lying', 5)), ('not', ('telling-truth', 4)), ('not', ('lying', 5)), ('or', ('telling-truth', 0), ('lying', 3)))", "index": 100}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Mason, Sophia, Abigail, Daniel, and Michael. \"Sophia is a knight,\" Riley claimed. In a statement by Mason: \"Daniel is a knave or Michael is a knight\". As Sophia put it, \"Mason is a knight if and only if Mason is a knave\". Abigail said that Daniel is a knight or Riley is a knave. Daniel asserted: \"Riley is a knight\". Michael expressed that Riley is a knave if and only if Abigail is a knave. So who is a knight and who is a knave?", "names": ["Riley", "Mason", "Sophia", "Abigail", "Daniel", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false], "solution_text": "Riley is a knave, Mason is a knight, Sophia is a knave, Abigail is a knight, Daniel is a knave, and Michael is a knave.", "solution_text_format": "(1) Riley is a knave\n(2) Mason is a knight\n(3) Sophia is a knave\n(4) Abigail is a knight\n(5) Daniel is a knave\n(6) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Mason is a knight if and only if Mason is a knave.", "Sophia cannot be a knave, because this would contradict the claim of Riley that Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Riley that Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Daniel is a knave or Michael is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Riley is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Riley is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Riley is a knave if and only if Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Michael that Riley is a knave if and only if Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight or Riley is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Daniel is a knight or Riley is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('or', ('lying', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('or', ('telling-truth', 4), ('lying', 0)), ('telling-truth', 0), ('<=>', ('lying', 0), ('lying', 3)))", "index": 101}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Oliver, Lucas, Benjamin, Michael, and Logan. Amelia remarked, \"Michael is a knight if and only if Logan is a knight\". Oliver noted, \"Amelia is a knave or Michael is a knave\". Lucas told you that Michael is not a knave. \"Lucas is a knave and Amelia is a knave\" - Benjamin. \"Benjamin is a knave or Benjamin is a knight,\" Michael claimed. Logan was heard saying, \"Amelia is a knight and Benjamin is a knight\". So who is a knight and who is a knave?", "names": ["Amelia", "Oliver", "Lucas", "Benjamin", "Michael", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false], "solution_text": "Amelia is a knave, Oliver is a knight, Lucas is a knight, Benjamin is a knave, Michael is a knight, and Logan is a knave.", "solution_text_format": "(1) Amelia is a knave\n(2) Oliver is a knight\n(3) Lucas is a knight\n(4) Benjamin is a knave\n(5) Michael is a knight\n(6) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Michael is a knight if and only if Logan is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Benjamin is a knave or Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Amelia is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Lucas is a knave and Amelia is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Michael is not a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Amelia is a knight and Benjamin is a knight.", "Logan cannot be a knave, because this would contradict the claim of Amelia that Michael is a knight if and only if Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Michael is not a knave.", "We have exhausted all possibilities for Lucas and Benjamin, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knave or Benjamin is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Logan is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Benjamin is a knave or Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Lucas is a knave and Amelia is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Benjamin that Lucas is a knave and Amelia is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Michael is not a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Lucas is a knave and Amelia is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Michael is not a knave.", "Logan cannot be a knight, because this would contradict the false claim of Amelia that Michael is a knight if and only if Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Amelia is a knight and Benjamin is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Amelia is a knave or Michael is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 5)), ('or', ('lying', 0), ('lying', 4)), ('not', ('lying', 4)), ('and', ('lying', 2), ('lying', 0)), ('or', ('lying', 3), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('telling-truth', 3)))", "index": 102}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Jacob, Aurora, Matthew, Logan, and Grace. William said, \"Jacob is a knight or Logan is a knight.\" Jacob told you that William is a knight if and only if Matthew is a knight. Aurora stated, \"If Jacob is a knight then Grace is a knight\". Matthew said, \"Jacob is a knave or Grace is a knave.\" Logan remarked, \"If William is a knave then Jacob is a knight\". According to Grace, \"Logan is a knight\". So who is a knight and who is a knave?", "names": ["William", "Jacob", "Aurora", "Matthew", "Logan", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "William is a knave, Jacob is a knave, Aurora is a knight, Matthew is a knight, Logan is a knave, and Grace is a knave.", "solution_text_format": "(1) William is a knave\n(2) Jacob is a knave\n(3) Aurora is a knight\n(4) Matthew is a knight\n(5) Logan is a knave\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Jacob is a knight or Logan is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that William is a knight if and only if Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Jacob is a knave or Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Matthew that Jacob is a knave or Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Logan is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Grace that Logan is a knight.", "Logan cannot be a knave, because this would contradict the false claim of their own that If William is a knave then Jacob is a knight.", "We have exhausted all possibilities for Logan and Grace, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Jacob that William is a knight if and only if Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that William is a knight if and only if Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Jacob that William is a knight if and only if Matthew is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Jacob is a knave or Grace is a knave.", "We have exhausted all possibilities for Matthew and Jacob, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Jacob is a knight or Logan is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of William that Jacob is a knight or Logan is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that William is a knight if and only if Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Jacob is a knave or Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Logan is a knight.", "Logan cannot be a knight, because this would contradict the false claim of William that Jacob is a knight or Logan is a knight.", "Logan cannot be a knave, because this would contradict the claim of Grace that Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Logan is a knight.", "Logan cannot be a knight, because this would contradict the false claim of William that Jacob is a knight or Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that If William is a knave then Jacob is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Jacob is a knight then Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 4)), ('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('->', ('telling-truth', 1), ('telling-truth', 5)), ('or', ('lying', 1), ('lying', 5)), ('->', ('lying', 0), ('telling-truth', 1)), ('telling-truth', 4))", "index": 103}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Lucas, Penelope, Grace, Ella, and Alexander. As Henry put it, \"Penelope is a knight or Ella is a knave\". \"Henry is not a knave,\" Lucas declared. Penelope asserted: \"If Alexander is a knight then Ella is a knight\". In Grace's words: \"Lucas is a knight\". \"Lucas is a knight if and only if Grace is a knave\" - Ella. Alexander was heard saying, \"Henry is a knave\". So who is a knight and who is a knave?", "names": ["Henry", "Lucas", "Penelope", "Grace", "Ella", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Henry is a knight, Lucas is a knight, Penelope is a knight, Grace is a knight, Ella is a knave, and Alexander is a knave.", "solution_text_format": "(1) Henry is a knight\n(2) Lucas is a knight\n(3) Penelope is a knight\n(4) Grace is a knight\n(5) Ella is a knave\n(6) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Penelope is a knight or Ella is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Alexander is a knight then Ella is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Henry is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Grace is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Henry is not a knave.", "Grace cannot be a knight, because this would contradict the claim of Ella that Lucas is a knight if and only if Grace is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Henry is not a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Grace is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Henry is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 4)), ('not', ('lying', 0)), ('->', ('telling-truth', 5), ('telling-truth', 4)), ('telling-truth', 1), ('<=>', ('telling-truth', 1), ('lying', 3)), ('lying', 0))", "index": 104}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Zoey, Samuel, Matthew, Chloe, and David. Benjamin was heard saying, \"Zoey is a knight if and only if Chloe is a knave\". \"Samuel is not a knight,\" Zoey declared. Samuel remarked, \"Samuel is a knight if and only if Chloe is a knave\". Matthew expressed that If Samuel is a knave then Chloe is a knave. Chloe said, \"Matthew is a knight if and only if Benjamin is a knight.\" David commented, \"Benjamin is a knight and Chloe is a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Zoey", "Samuel", "Matthew", "Chloe", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Benjamin is a knave, Zoey is a knave, Samuel is a knight, Matthew is a knight, Chloe is a knave, and David is a knave.", "solution_text_format": "(1) Benjamin is a knave\n(2) Zoey is a knave\n(3) Samuel is a knight\n(4) Matthew is a knight\n(5) Chloe is a knave\n(6) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Chloe is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Zoey that Samuel is not a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Benjamin that Zoey is a knight if and only if Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Benjamin is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Chloe that Matthew is a knight if and only if Benjamin is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that If Samuel is a knave then Chloe is a knave.", "We have exhausted all possibilities for Matthew, Chloe, and Samuel, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Samuel that Samuel is a knight if and only if Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the claim of Benjamin that Zoey is a knight if and only if Chloe is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of Zoey that Samuel is not a knight.", "We have exhausted all possibilities for Samuel and Zoey, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Chloe is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Zoey that Samuel is not a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Samuel that Samuel is a knight if and only if Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of Benjamin that Zoey is a knight if and only if Chloe is a knave.", "We have exhausted all possibilities for Chloe and Samuel, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Benjamin that Zoey is a knight if and only if Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Benjamin is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Samuel is a knave then Chloe is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight and Chloe is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Benjamin is a knight and Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 4)), ('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('lying', 4)), ('->', ('lying', 2), ('lying', 4)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('lying', 4)))", "index": 105}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Michael, Mason, Matthew, Benjamin, and Liam. \"Benjamin is not a knave\" - Daniel. Michael said, \"If Matthew is a knave then Mason is a knave.\" \"Michael is a knight\" - Mason. \"Daniel is not a knight,\" Matthew declared. \"Mason is a knave and Mason is a knight,\" Benjamin mentioned. Liam said that Mason is a knave and Daniel is a knave. So who is a knight and who is a knave?", "names": ["Daniel", "Michael", "Mason", "Matthew", "Benjamin", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Daniel is a knave, Michael is a knight, Mason is a knight, Matthew is a knight, Benjamin is a knave, and Liam is a knave.", "solution_text_format": "(1) Daniel is a knave\n(2) Michael is a knight\n(3) Mason is a knight\n(4) Matthew is a knight\n(5) Benjamin is a knave\n(6) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Mason is a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Daniel that Benjamin is not a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Daniel that Benjamin is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Mason is a knave and Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Matthew is a knave then Mason is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Daniel is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Mason is a knave and Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('->', ('lying', 3), ('lying', 2)), ('telling-truth', 1), ('not', ('telling-truth', 0)), ('and', ('lying', 2), ('telling-truth', 2)), ('and', ('lying', 2), ('lying', 0)))", "index": 106}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Abigail, Harper, Scarlett, Ava, and Oliver. According to Ethan, \"If Oliver is a knave then Harper is a knight\". \"Scarlett is a knave if and only if Ethan is a knave,\" Abigail claimed. Harper told you that Abigail is a knave. Scarlett noted, \"Ethan is not a knight\". \"Ethan is a knave or Harper is a knave,\" Ava mentioned. In Oliver's words: \"Abigail is a knight if and only if Ava is a knave\". So who is a knight and who is a knave?", "names": ["Ethan", "Abigail", "Harper", "Scarlett", "Ava", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Ethan is a knight, Abigail is a knave, Harper is a knight, Scarlett is a knave, Ava is a knave, and Oliver is a knave.", "solution_text_format": "(1) Ethan is a knight\n(2) Abigail is a knave\n(3) Harper is a knight\n(4) Scarlett is a knave\n(5) Ava is a knave\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that If Oliver is a knave then Harper is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Ava is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Ethan is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Ethan is not a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Abigail that Scarlett is a knave if and only if Ethan is a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Ethan is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Abigail that Scarlett is a knave if and only if Ethan is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Ethan is a knave or Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of Ava that Ethan is a knave or Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that Abigail is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Oliver that Abigail is a knight if and only if Ava is a knave.", "We have exhausted all possibilities for Ava, Scarlett, and Abigail, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Ava is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Ethan is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Ethan is not a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Abigail that Scarlett is a knave if and only if Ethan is a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Ethan is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Abigail that Scarlett is a knave if and only if Ethan is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Ava cannot be a knight, because this would contradict the false claim of Oliver that Abigail is a knight if and only if Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Ethan is a knave or Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 2)), ('<=>', ('lying', 3), ('lying', 0)), ('lying', 1), ('not', ('telling-truth', 0)), ('or', ('lying', 0), ('lying', 2)), ('<=>', ('telling-truth', 1), ('lying', 4)))", "index": 107}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Jack, Mason, Aurora, Jackson, and James. Evelyn expressed that Mason is not a knight. In Jack's words: \"Aurora is a knight or James is a knight\". Mason commented, \"James is a knight and Aurora is a knave\". In a statement by Aurora: \"Evelyn is a knave if and only if Jackson is a knave\". Jackson commented, \"Aurora is a knave\". As James put it, \"Mason is a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "Jack", "Mason", "Aurora", "Jackson", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Evelyn is a knave, Jack is a knight, Mason is a knight, Aurora is a knave, Jackson is a knight, and James is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Jack is a knight\n(3) Mason is a knight\n(4) Aurora is a knave\n(5) Jackson is a knight\n(6) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Mason is not a knight.", "Mason cannot be a knight, because this would contradict the claim of Evelyn that Mason is not a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that James is a knight and Aurora is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Mason is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Mason is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Aurora is a knave.", "Jackson cannot be a knave, because this would contradict the claim of Aurora that Evelyn is a knave if and only if Jackson is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Aurora that Evelyn is a knave if and only if Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Aurora is a knave.", "We have exhausted all possibilities for Jackson, Aurora, James, and Mason, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Mason is not a knight.", "Assume Mason is a knight. No contradiction is found in their claim that James is a knight and Aurora is a knave.", "Assume James is a knight. No contradiction is found in their claim that Mason is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Mason that James is a knight and Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Aurora is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Aurora is a knight or James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('or', ('telling-truth', 3), ('telling-truth', 5)), ('and', ('telling-truth', 5), ('lying', 3)), ('<=>', ('lying', 0), ('lying', 4)), ('lying', 3), ('telling-truth', 2))", "index": 108}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Joseph, Matthew, Chloe, Avery, and Ethan. \"If Avery is a knight then Joseph is a knight,\" Harper declared. Joseph was heard saying, \"Ethan is a knight\". \"If Harper is a knave then Matthew is a knight,\" Matthew mentioned. Chloe commented, \"Matthew is a knight and Ethan is a knight\". In a statement by Avery: \"Chloe is not a knight\". Ethan was heard saying, \"Chloe is a knave or Harper is a knight\". So who is a knight and who is a knave?", "names": ["Harper", "Joseph", "Matthew", "Chloe", "Avery", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Harper is a knight, Joseph is a knight, Matthew is a knight, Chloe is a knight, Avery is a knave, and Ethan is a knight.", "solution_text_format": "(1) Harper is a knight\n(2) Joseph is a knight\n(3) Matthew is a knight\n(4) Chloe is a knight\n(5) Avery is a knave\n(6) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that If Avery is a knight then Joseph is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of Avery that Chloe is not a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Matthew is a knight and Ethan is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Harper is a knave then Matthew is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Chloe that Matthew is a knight and Ethan is a knight.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave or Harper is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of their own that If Harper is a knave then Matthew is a knight.", "We have exhausted all possibilities for Matthew and Chloe, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Matthew is a knight and Ethan is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Harper is a knave then Matthew is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Chloe is a knave or Harper is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('telling-truth', 1)), ('telling-truth', 5), ('->', ('lying', 0), ('telling-truth', 2)), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('telling-truth', 3)), ('or', ('lying', 3), ('telling-truth', 0)))", "index": 109}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Zoey, Liam, Abigail, Aria, and Charlotte. According to Sofia, \"Liam is a knave or Zoey is a knave\". Zoey told you that Abigail is not a knight. In Liam's words: \"Sofia is not a knave\". Abigail noted, \"Liam is a knight\". \"Liam is a knave if and only if Liam is a knight\" - Aria. As Charlotte put it, \"Abigail is a knight if and only if Sofia is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Zoey", "Liam", "Abigail", "Aria", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false], "solution_text": "Sofia is a knight, Zoey is a knave, Liam is a knight, Abigail is a knight, Aria is a knave, and Charlotte is a knave.", "solution_text_format": "(1) Sofia is a knight\n(2) Zoey is a knave\n(3) Liam is a knight\n(4) Abigail is a knight\n(5) Aria is a knave\n(6) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Liam is a knave or Zoey is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Zoey cannot be a knight, because this would contradict the claim of Sofia that Liam is a knave or Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Liam is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Liam is a knave if and only if Liam is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Liam is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Abigail is a knight if and only if Sofia is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('lying', 1)), ('not', ('telling-truth', 3)), ('not', ('lying', 0)), ('telling-truth', 2), ('<=>', ('lying', 2), ('telling-truth', 2)), ('<=>', ('telling-truth', 3), ('lying', 0)))", "index": 110}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Samuel, Sofia, Avery, Daniel, and Owen. Jackson asserted: \"Avery is a knave if and only if Samuel is a knight\". \"If Sofia is a knave then Daniel is a knight,\" Samuel declared. Sofia expressed that Samuel is not a knight. Avery expressed that Daniel is a knave if and only if Sofia is a knave. In Daniel's words: \"Avery is a knave or Jackson is a knave\". Owen told you that Jackson is not a knight. So who is a knight and who is a knave?", "names": ["Jackson", "Samuel", "Sofia", "Avery", "Daniel", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false], "solution_text": "Jackson is a knight, Samuel is a knight, Sofia is a knave, Avery is a knave, Daniel is a knight, and Owen is a knave.", "solution_text_format": "(1) Jackson is a knight\n(2) Samuel is a knight\n(3) Sofia is a knave\n(4) Avery is a knave\n(5) Daniel is a knight\n(6) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Avery is a knave if and only if Samuel is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Sofia is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Avery is a knave or Jackson is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Avery is a knave or Jackson is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Avery that Daniel is a knave if and only if Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Jackson that Avery is a knave if and only if Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of Sofia that Samuel is not a knight.", "We have exhausted all possibilities for Samuel, Sofia, and Daniel, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Sofia is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Avery is a knave or Jackson is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Avery that Daniel is a knave if and only if Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Sofia is a knave then Daniel is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Jackson is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Jackson is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 1)), ('->', ('lying', 2), ('telling-truth', 4)), ('not', ('telling-truth', 1)), ('<=>', ('lying', 4), ('lying', 2)), ('or', ('lying', 3), ('lying', 0)), ('not', ('telling-truth', 0)))", "index": 111}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Abigail, Elizabeth, Daniel, Lucas, and Aria. In Matthew's words: \"If Aria is a knight then Lucas is a knave\". Abigail remarked, \"Elizabeth is a knave if and only if Matthew is a knight\". Elizabeth asserted: \"Matthew is not a knight\". Daniel told you that Lucas is a knave or Abigail is a knight. Lucas said, \"Matthew is a knight and Lucas is a knight.\" According to Aria, \"Daniel is a knight if and only if Elizabeth is a knave\". So who is a knight and who is a knave?", "names": ["Matthew", "Abigail", "Elizabeth", "Daniel", "Lucas", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Matthew is a knight, Abigail is a knight, Elizabeth is a knave, Daniel is a knight, Lucas is a knave, and Aria is a knight.", "solution_text_format": "(1) Matthew is a knight\n(2) Abigail is a knight\n(3) Elizabeth is a knave\n(4) Daniel is a knight\n(5) Lucas is a knave\n(6) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that If Aria is a knight then Lucas is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Elizabeth is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Lucas is a knave or Abigail is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Matthew that If Aria is a knight then Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Matthew is a knight and Lucas is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if Matthew is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Abigail that Elizabeth is a knave if and only if Matthew is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Matthew is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 4)), ('<=>', ('lying', 2), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('or', ('lying', 4), ('telling-truth', 1)), ('and', ('telling-truth', 0), ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('lying', 2)))", "index": 112}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Sofia, James, Noah, Alexander, and David. According to Grace, \"James is a knight or David is a knave\". \"Alexander is not a knight,\" Sofia declared. \"Grace is a knave and David is a knight,\" James declared. Noah stated, \"Grace is not a knave\". \"Noah is a knight and Grace is a knave\" - Alexander. \"Sofia is a knave,\" David mentioned. So who is a knight and who is a knave?", "names": ["Grace", "Sofia", "James", "Noah", "Alexander", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Grace is a knight, Sofia is a knight, James is a knave, Noah is a knight, Alexander is a knave, and David is a knave.", "solution_text_format": "(1) Grace is a knight\n(2) Sofia is a knight\n(3) James is a knave\n(4) Noah is a knight\n(5) Alexander is a knave\n(6) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that James is a knight or David is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Grace is a knave and David is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Grace is a knave and David is a knight.", "David cannot be a knight, because this would contradict the claim of Grace that James is a knight or David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Sofia that Alexander is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Noah is a knight and Grace is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Grace is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 5)), ('not', ('telling-truth', 4)), ('and', ('lying', 0), ('telling-truth', 5)), ('not', ('lying', 0)), ('and', ('telling-truth', 3), ('lying', 0)), ('lying', 1))", "index": 113}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Sofia, Riley, Chloe, William, and Evelyn. \"Riley is a knight if and only if William is a knave,\" Luke claimed. According to Sofia, \"Chloe is not a knave\". In Riley's words: \"Riley is a knight if and only if Chloe is a knave\". In Chloe's words: \"Evelyn is not a knight\". William noted, \"Evelyn is a knave\". Evelyn noted, \"Evelyn is a knight if and only if Luke is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Sofia", "Riley", "Chloe", "William", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true], "solution_text": "Luke is a knave, Sofia is a knave, Riley is a knave, Chloe is a knave, William is a knave, and Evelyn is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Sofia is a knave\n(3) Riley is a knave\n(4) Chloe is a knave\n(5) William is a knave\n(6) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Riley is a knight if and only if William is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight if and only if Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Riley that Riley is a knight if and only if Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight if and only if Luke is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of Chloe that Evelyn is not a knight.", "We have exhausted all possibilities for Evelyn and Chloe, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Riley that Riley is a knight if and only if Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight if and only if Luke is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of Chloe that Evelyn is not a knight.", "We have exhausted all possibilities for Evelyn, Chloe, and Riley, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Riley is a knight if and only if William is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight if and only if Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Riley that Riley is a knight if and only if Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Luke is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave.", "William cannot be a knave, because this would contradict the false claim of Luke that Riley is a knight if and only if William is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of Chloe that Evelyn is not a knight.", "We have exhausted all possibilities for Evelyn and Chloe, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Riley that Riley is a knight if and only if Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Luke is a knave.", "William cannot be a knight, because this would contradict the false claim of Luke that Riley is a knight if and only if William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Chloe is not a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Chloe is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 4)), ('not', ('lying', 3)), ('<=>', ('telling-truth', 2), ('lying', 3)), ('not', ('telling-truth', 5)), ('lying', 5), ('<=>', ('telling-truth', 5), ('lying', 0)))", "index": 114}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, Jackson, Avery, Victoria, Charlotte, and Aurora. Penelope remarked, \"Victoria is a knight or Jackson is a knave\". \"If Avery is a knight then Aurora is a knave\" - Jackson. According to Avery, \"Penelope is a knight if and only if Aurora is a knave\". Victoria noted, \"Victoria is a knight\". Charlotte noted, \"Avery is a knave if and only if Penelope is a knave\". As Aurora put it, \"Avery is a knight\". So who is a knight and who is a knave?", "names": ["Penelope", "Jackson", "Avery", "Victoria", "Charlotte", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "Penelope is a knave, Jackson is a knight, Avery is a knave, Victoria is a knave, Charlotte is a knight, and Aurora is a knave.", "solution_text_format": "(1) Penelope is a knave\n(2) Jackson is a knight\n(3) Avery is a knave\n(4) Victoria is a knave\n(5) Charlotte is a knight\n(6) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Victoria is a knight or Jackson is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Avery is a knight then Aurora is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Jackson that If Avery is a knight then Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Avery is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Avery is a knight.", "Aurora cannot be a knave, because this would contradict the false claim of Avery that Penelope is a knight if and only if Aurora is a knave.", "We have exhausted all possibilities for Aurora and Avery, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Avery is a knight then Aurora is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Avery that Penelope is a knight if and only if Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of Jackson that If Avery is a knight then Aurora is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the false claim of Jackson that If Avery is a knight then Aurora is a knave.", "We have exhausted all possibilities for Avery and Jackson, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Victoria is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Penelope that Victoria is a knight or Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Avery is a knight then Aurora is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Avery that Penelope is a knight if and only if Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of Jackson that If Avery is a knight then Aurora is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the false claim of Jackson that If Avery is a knight then Aurora is a knave.", "We have exhausted all possibilities for Avery, Jackson, and Victoria, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Victoria is a knight or Jackson is a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Penelope that Victoria is a knight or Jackson is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Victoria is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Avery is a knight then Aurora is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Jackson that If Avery is a knight then Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the claim of Avery that Penelope is a knight if and only if Aurora is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Avery that Penelope is a knight if and only if Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Avery is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Avery is a knave if and only if Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('lying', 1)), ('->', ('telling-truth', 2), ('lying', 5)), ('<=>', ('telling-truth', 0), ('lying', 5)), ('telling-truth', 3), ('<=>', ('lying', 2), ('lying', 0)), ('telling-truth', 2))", "index": 115}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Grace, Penelope, Riley, Liam, and Benjamin. In a statement by Daniel: \"Riley is a knave or Riley is a knight\". \"Penelope is not a knave,\" Grace declared. According to Penelope, \"Riley is a knave and Riley is a knight\". Riley noted, \"Penelope is a knight and Benjamin is a knave\". Liam said that If Grace is a knave then Daniel is a knight. Benjamin stated, \"Liam is a knave\". So who is a knight and who is a knave?", "names": ["Daniel", "Grace", "Penelope", "Riley", "Liam", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false], "solution_text": "Daniel is a knight, Grace is a knave, Penelope is a knave, Riley is a knave, Liam is a knight, and Benjamin is a knave.", "solution_text_format": "(1) Daniel is a knight\n(2) Grace is a knave\n(3) Penelope is a knave\n(4) Riley is a knave\n(5) Liam is a knight\n(6) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Riley is a knave or Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Penelope is a knight and Benjamin is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Riley is a knight.", "Penelope cannot be a knave, because this would contradict the claim of Riley that Penelope is a knight and Benjamin is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Penelope is a knight and Benjamin is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Riley is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Riley is a knave and Riley is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Benjamin that Liam is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that If Grace is a knave then Daniel is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Grace is a knave then Daniel is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Penelope is not a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Penelope is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 3)), ('not', ('lying', 2)), ('and', ('lying', 3), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('lying', 5)), ('->', ('lying', 1), ('telling-truth', 0)), ('lying', 4))", "index": 116}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Jackson, Evelyn, Aiden, Emily, and Amelia. Charlotte stated, \"Evelyn is not a knight\". \"Charlotte is a knave or Evelyn is a knight,\" Jackson claimed. Evelyn expressed that If Jackson is a knave then Charlotte is a knight. Aiden said that Aiden is a knight and Jackson is a knave. \"Charlotte is not a knave\" - Emily. Amelia told you that Emily is a knight and Amelia is a knight. So who is a knight and who is a knave?", "names": ["Charlotte", "Jackson", "Evelyn", "Aiden", "Emily", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Charlotte is a knave, Jackson is a knight, Evelyn is a knight, Aiden is a knave, Emily is a knave, and Amelia is a knave.", "solution_text_format": "(1) Charlotte is a knave\n(2) Jackson is a knight\n(3) Evelyn is a knight\n(4) Aiden is a knave\n(5) Emily is a knave\n(6) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Charlotte that Evelyn is not a knight.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knave then Charlotte is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Jackson is a knave then Charlotte is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Charlotte is a knave or Evelyn is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Jackson is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aiden is a knight and Jackson is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Charlotte is not a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Emily is a knight and Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('or', ('lying', 0), ('telling-truth', 2)), ('->', ('lying', 1), ('telling-truth', 0)), ('and', ('telling-truth', 3), ('lying', 1)), ('not', ('lying', 0)), ('and', ('telling-truth', 4), ('telling-truth', 5)))", "index": 117}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Zoey, Emily, Penelope, Charlotte, and Samuel. \"Penelope is not a knight\" - Jackson. Zoey asserted: \"Emily is a knave\". According to Emily, \"Penelope is a knight\". Penelope told you that Jackson is a knave or Charlotte is a knave. Charlotte stated, \"Jackson is a knight if and only if Emily is a knight\". Samuel said, \"Jackson is a knight.\" So who is a knight and who is a knave?", "names": ["Jackson", "Zoey", "Emily", "Penelope", "Charlotte", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Jackson is a knave, Zoey is a knave, Emily is a knight, Penelope is a knight, Charlotte is a knave, and Samuel is a knave.", "solution_text_format": "(1) Jackson is a knave\n(2) Zoey is a knave\n(3) Emily is a knight\n(4) Penelope is a knight\n(5) Charlotte is a knave\n(6) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Jackson that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jackson is a knave or Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Penelope is a knight.", "Emily cannot be a knave, because this would contradict the claim of Charlotte that Jackson is a knight if and only if Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the false claim of Penelope that Jackson is a knave or Charlotte is a knave.", "We have exhausted all possibilities for Charlotte and Penelope, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Jackson is a knave or Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of Charlotte that Jackson is a knight if and only if Emily is a knight.", "Emily cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Penelope is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Emily is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Emily is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Jackson is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('lying', 2), ('telling-truth', 3), ('or', ('lying', 0), ('lying', 4)), ('<=>', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 0))", "index": 118}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Abigail, James, Noah, Ava, and Owen. Michael said, \"If Ava is a knight then James is a knave.\" Abigail asserted: \"Owen is a knave if and only if Ava is a knave\". According to James, \"Michael is not a knight\". \"James is a knave or Ava is a knave\" - Noah. Ava expressed that Michael is a knight if and only if Michael is a knave. Owen commented, \"Michael is not a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Abigail", "James", "Noah", "Ava", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Michael is a knight, Abigail is a knight, James is a knave, Noah is a knight, Ava is a knave, and Owen is a knave.", "solution_text_format": "(1) Michael is a knight\n(2) Abigail is a knight\n(3) James is a knave\n(4) Noah is a knight\n(5) Ava is a knave\n(6) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that If Ava is a knight then James is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Michael is a knight if and only if Michael is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Michael is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Owen is a knave if and only if Ava is a knave.", "Owen cannot be a knight, because this would contradict the claim of Abigail that Owen is a knave if and only if Ava is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that James is a knave or Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 2)), ('<=>', ('lying', 5), ('lying', 4)), ('not', ('telling-truth', 0)), ('or', ('lying', 2), ('lying', 4)), ('<=>', ('telling-truth', 0), ('lying', 0)), ('not', ('telling-truth', 0)))", "index": 119}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Owen, Henry, Emily, Mason, and Penelope. In Luke's words: \"Emily is a knave or Owen is a knave\". \"Mason is a knight if and only if Luke is a knight\" - Owen. As Henry put it, \"Mason is a knave\". As Emily put it, \"Mason is a knight if and only if Mason is a knave\". Mason remarked, \"Luke is a knight and Emily is a knight\". Penelope stated, \"Luke is a knight or Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Owen", "Henry", "Emily", "Mason", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Luke is a knight, Owen is a knave, Henry is a knight, Emily is a knave, Mason is a knave, and Penelope is a knight.", "solution_text_format": "(1) Luke is a knight\n(2) Owen is a knave\n(3) Henry is a knight\n(4) Emily is a knave\n(5) Mason is a knave\n(6) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Emily is a knave or Owen is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Mason is a knight if and only if Mason is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Luke is a knight and Emily is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Luke is a knight and Emily is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Mason is a knight if and only if Luke is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Luke is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Mason is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Luke is a knight or Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 1)), ('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('lying', 4), ('<=>', ('telling-truth', 4), ('lying', 4)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('telling-truth', 5)))", "index": 120}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Riley, Alexander, James, Lucas, and Michael. \"Alexander is a knave,\" Luke claimed. In Riley's words: \"James is a knight\". Alexander said, \"Riley is a knight if and only if Riley is a knave.\" James said that Michael is a knight. Lucas asserted: \"Riley is a knave and Michael is a knight\". In a statement by Michael: \"James is a knave if and only if Riley is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Riley", "Alexander", "James", "Lucas", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Luke is a knight, Riley is a knight, Alexander is a knave, James is a knight, Lucas is a knave, and Michael is a knight.", "solution_text_format": "(1) Luke is a knight\n(2) Riley is a knight\n(3) Alexander is a knave\n(4) James is a knight\n(5) Lucas is a knave\n(6) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Luke that Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that James is a knave if and only if Riley is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Michael is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Riley is a knave and Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('telling-truth', 3), ('<=>', ('telling-truth', 1), ('lying', 1)), ('telling-truth', 5), ('and', ('lying', 1), ('telling-truth', 5)), ('<=>', ('lying', 3), ('lying', 1)))", "index": 121}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Henry, Abigail, Amelia, Sophia, and Jacob. David noted, \"Henry is a knight and Amelia is a knave\". Henry stated, \"Sophia is a knight and Abigail is a knave\". According to Abigail, \"Henry is a knight and Sophia is a knight\". \"Henry is not a knight,\" Amelia claimed. \"If Henry is a knave then David is a knight,\" Sophia mentioned. \"If Jacob is a knight then Sophia is a knave,\" Jacob declared. So who is a knight and who is a knave?", "names": ["David", "Henry", "Abigail", "Amelia", "Sophia", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "David is a knave, Henry is a knave, Abigail is a knave, Amelia is a knight, Sophia is a knave, and Jacob is a knight.", "solution_text_format": "(1) David is a knave\n(2) Henry is a knave\n(3) Abigail is a knave\n(4) Amelia is a knight\n(5) Sophia is a knave\n(6) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Henry is a knight and Amelia is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Sophia is a knight and Abigail is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Henry is a knave then David is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Henry that Sophia is a knight and Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Henry is a knight and Sophia is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Henry that Sophia is a knight and Abigail is a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of David that Henry is a knight and Amelia is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Henry is a knight and Amelia is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Sophia is a knight and Abigail is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Henry is a knave then David is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Henry that Sophia is a knight and Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Henry is a knight and Sophia is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Henry that Sophia is a knight and Abigail is a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Sophia is a knight and Abigail is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that If Henry is a knave then David is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Henry is a knave then David is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Sophia is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Henry is a knight and Sophia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Henry is not a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Jacob is a knight then Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 3)), ('and', ('telling-truth', 4), ('lying', 2)), ('and', ('telling-truth', 1), ('telling-truth', 4)), ('not', ('telling-truth', 1)), ('->', ('lying', 1), ('telling-truth', 0)), ('->', ('telling-truth', 5), ('lying', 4)))", "index": 122}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Henry, William, Sophia, Evelyn, and James. In a statement by Michael: \"If Sophia is a knight then Evelyn is a knave\". In Henry's words: \"Michael is not a knight\". William expressed that Evelyn is a knight or William is a knight. Sophia said, \"Michael is a knave and Henry is a knave.\" \"Michael is a knight,\" Evelyn declared. James remarked, \"Sophia is not a knave\". So who is a knight and who is a knave?", "names": ["Michael", "Henry", "William", "Sophia", "Evelyn", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false], "solution_text": "Michael is a knight, Henry is a knave, William is a knight, Sophia is a knave, Evelyn is a knight, and James is a knave.", "solution_text_format": "(1) Michael is a knight\n(2) Henry is a knave\n(3) William is a knight\n(4) Sophia is a knave\n(5) Evelyn is a knight\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that If Sophia is a knight then Evelyn is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Henry is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Michael is a knave and Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume William is a knight. No contradiction is found in their claim that Evelyn is a knight or William is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Sophia is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Sophia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 4)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('and', ('lying', 0), ('lying', 1)), ('telling-truth', 0), ('not', ('lying', 3)))", "index": 123}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, David, James, Mia, Noah, and Scarlett. Penelope noted, \"James is a knight or Scarlett is a knave\". \"If Noah is a knight then Penelope is a knight,\" David mentioned. \"If Mia is a knight then Penelope is a knave\" - James. Mia remarked, \"Noah is not a knave\". \"Scarlett is a knave and Mia is a knave,\" Noah declared. In a statement by Scarlett: \"Mia is not a knight\". So who is a knight and who is a knave?", "names": ["Penelope", "David", "James", "Mia", "Noah", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Penelope is a knight, David is a knight, James is a knight, Mia is a knave, Noah is a knave, and Scarlett is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) David is a knight\n(3) James is a knight\n(4) Mia is a knave\n(5) Noah is a knave\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that James is a knight or Scarlett is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Mia is a knight then Penelope is a knave.", "Mia cannot be a knight, because this would contradict the claim of James that If Mia is a knight then Penelope is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Noah is not a knave.", "Noah cannot be a knight, because this would contradict the false claim of Mia that Noah is not a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Scarlett is a knave and Mia is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Mia is not a knight.", "Assume David is a knight. No contradiction is found in their claim that If Noah is a knight then Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 5)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('lying', 0)), ('not', ('lying', 4)), ('and', ('lying', 5), ('lying', 3)), ('not', ('telling-truth', 3)))", "index": 124}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Isabella, Ella, Daniel, Logan, and James. Joseph commented, \"Daniel is a knave or Logan is a knave\". In a statement by Isabella: \"Daniel is a knave\". According to Ella, \"Logan is a knave if and only if Logan is a knight\". In a statement by Daniel: \"Logan is a knave and Ella is a knight\". In Logan's words: \"Daniel is a knight\". As James put it, \"If Joseph is a knight then Logan is a knave\". So who is a knight and who is a knave?", "names": ["Joseph", "Isabella", "Ella", "Daniel", "Logan", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true], "solution_text": "Joseph is a knight, Isabella is a knight, Ella is a knave, Daniel is a knave, Logan is a knave, and James is a knight.", "solution_text_format": "(1) Joseph is a knight\n(2) Isabella is a knight\n(3) Ella is a knave\n(4) Daniel is a knave\n(5) Logan is a knave\n(6) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Daniel is a knave or Logan is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Logan is a knave and Ella is a knight.", "Logan cannot be a knight, because this would contradict the claim of Joseph that Daniel is a knave or Logan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Logan is a knave and Ella is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Daniel is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Logan is a knave if and only if Logan is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Logan is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Daniel is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Joseph is a knight then Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 4)), ('lying', 3), ('<=>', ('lying', 4), ('telling-truth', 4)), ('and', ('lying', 4), ('telling-truth', 2)), ('telling-truth', 3), ('->', ('telling-truth', 0), ('lying', 4)))", "index": 125}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Lucas, Mason, Ethan, Amelia, and Liam. In a statement by Jack: \"Mason is not a knight\". In a statement by Lucas: \"Liam is a knight or Jack is a knight\". In Mason's words: \"Amelia is a knight\". \"If Liam is a knight then Amelia is a knight,\" Ethan declared. Amelia was heard saying, \"Mason is a knight if and only if Jack is a knave\". Liam said, \"Mason is a knight if and only if Jack is a knight.\" So who is a knight and who is a knave?", "names": ["Jack", "Lucas", "Mason", "Ethan", "Amelia", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Jack is a knave, Lucas is a knave, Mason is a knight, Ethan is a knight, Amelia is a knight, and Liam is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Lucas is a knave\n(3) Mason is a knight\n(4) Ethan is a knight\n(5) Amelia is a knight\n(6) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Mason is not a knight.", "Mason cannot be a knight, because this would contradict the claim of Jack that Mason is not a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Mason that Amelia is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Mason is a knight if and only if Jack is a knave.", "We have exhausted all possibilities for Amelia and Mason, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Mason is not a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Mason is a knight if and only if Jack is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Liam is a knight or Jack is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Mason is a knight if and only if Jack is a knight.", "Liam cannot be a knave, because this would contradict the claim of Lucas that Liam is a knight or Jack is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Liam is a knight or Jack is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Lucas that Liam is a knight or Jack is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Jack is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Liam is a knight then Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('telling-truth', 4), ('->', ('telling-truth', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)))", "index": 126}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Jackson, Emily, Daniel, Michael, and Matthew. Henry commented, \"Jackson is a knight\". Jackson was heard saying, \"Emily is not a knight\". Emily stated, \"If Matthew is a knave then Matthew is a knight\". Daniel expressed that Henry is a knight and Michael is a knight. Michael asserted: \"Michael is a knight and Daniel is a knight\". In a statement by Matthew: \"Daniel is a knight and Emily is a knave\". So who is a knight and who is a knave?", "names": ["Henry", "Jackson", "Emily", "Daniel", "Michael", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Henry is a knight, Jackson is a knight, Emily is a knave, Daniel is a knave, Michael is a knave, and Matthew is a knave.", "solution_text_format": "(1) Henry is a knight\n(2) Jackson is a knight\n(3) Emily is a knave\n(4) Daniel is a knave\n(5) Michael is a knave\n(6) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Emily is not a knight.", "Emily cannot be a knight, because this would contradict the claim of Jackson that Emily is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that If Matthew is a knave then Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Emily that If Matthew is a knave then Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Daniel is a knight and Emily is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Matthew that Daniel is a knight and Emily is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Henry is a knight and Michael is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Daniel that Henry is a knight and Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Michael is a knight and Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('not', ('telling-truth', 2)), ('->', ('lying', 5), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('telling-truth', 4)), ('and', ('telling-truth', 4), ('telling-truth', 3)), ('and', ('telling-truth', 3), ('lying', 2)))", "index": 127}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Harper, Jacob, Charlotte, Ella, and Noah. Ava was heard saying, \"Charlotte is a knave or Jacob is a knave\". \"Jacob is a knight or Charlotte is a knave,\" Harper mentioned. \"Ella is a knight and Charlotte is a knight,\" Jacob claimed. In a statement by Charlotte: \"Ava is not a knight\". Ella noted, \"Ava is a knight and Harper is a knight\". Noah asserted: \"If Ava is a knave then Jacob is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Harper", "Jacob", "Charlotte", "Ella", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "Ava is a knight, Harper is a knight, Jacob is a knave, Charlotte is a knave, Ella is a knight, and Noah is a knight.", "solution_text_format": "(1) Ava is a knight\n(2) Harper is a knight\n(3) Jacob is a knave\n(4) Charlotte is a knave\n(5) Ella is a knight\n(6) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Charlotte is a knave or Jacob is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Ava is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Charlotte is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Ella is a knight and Charlotte is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Ava is a knight and Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Jacob is a knight or Charlotte is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Ava is a knave then Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 2)), ('or', ('telling-truth', 2), ('lying', 3)), ('and', ('telling-truth', 4), ('telling-truth', 3)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('lying', 0), ('telling-truth', 2)))", "index": 128}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Liam, Emily, Abigail, Chloe, and Sophia. Isabella remarked, \"Abigail is not a knave\". According to Liam, \"Abigail is a knight or Abigail is a knave\". Emily asserted: \"Abigail is a knight or Abigail is a knave\". Abigail said, \"If Emily is a knave then Chloe is a knave.\" In a statement by Chloe: \"Liam is not a knave\". Sophia remarked, \"Isabella is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Liam", "Emily", "Abigail", "Chloe", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Isabella is a knight, Liam is a knight, Emily is a knight, Abigail is a knight, Chloe is a knight, and Sophia is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Liam is a knight\n(3) Emily is a knight\n(4) Abigail is a knight\n(5) Chloe is a knight\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Emily is a knave then Chloe is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Abigail is a knight or Abigail is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Abigail is a knight or Abigail is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('or', ('telling-truth', 3), ('lying', 3)), ('or', ('telling-truth', 3), ('lying', 3)), ('->', ('lying', 2), ('lying', 4)), ('not', ('lying', 1)), ('telling-truth', 0))", "index": 129}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Grace, Jackson, Liam, Henry, and Joseph. \"Liam is not a knave,\" Victoria claimed. Grace noted, \"If Henry is a knight then Victoria is a knight\". Jackson asserted: \"If Victoria is a knave then Henry is a knave\". Liam said, \"Joseph is a knight.\" \"Jackson is not a knight,\" Henry claimed. Joseph said that Liam is a knave or Grace is a knight. So who is a knight and who is a knave?", "names": ["Victoria", "Grace", "Jackson", "Liam", "Henry", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Victoria is a knight, Grace is a knight, Jackson is a knight, Liam is a knight, Henry is a knave, and Joseph is a knight.", "solution_text_format": "(1) Victoria is a knight\n(2) Grace is a knight\n(3) Jackson is a knight\n(4) Liam is a knight\n(5) Henry is a knave\n(6) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Liam is a knave or Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Henry is a knight then Victoria is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Henry that Jackson is not a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that If Victoria is a knave then Henry is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Victoria is a knave then Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('->', ('lying', 0), ('lying', 4)), ('telling-truth', 5), ('not', ('telling-truth', 2)), ('or', ('lying', 3), ('telling-truth', 1)))", "index": 130}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Aria, Alexander, Isabella, Olivia, and Benjamin. In Jacob's words: \"Olivia is a knight and Olivia is a knave\". \"If Benjamin is a knave then Olivia is a knight,\" Aria mentioned. \"Benjamin is a knave if and only if Alexander is a knight,\" Alexander mentioned. Isabella asserted: \"Alexander is a knave\". Olivia said that If Alexander is a knave then Jacob is a knave. Benjamin asserted: \"If Isabella is a knave then Isabella is a knight\". So who is a knight and who is a knave?", "names": ["Jacob", "Aria", "Alexander", "Isabella", "Olivia", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false], "solution_text": "Jacob is a knave, Aria is a knight, Alexander is a knight, Isabella is a knave, Olivia is a knight, and Benjamin is a knave.", "solution_text_format": "(1) Jacob is a knave\n(2) Aria is a knight\n(3) Alexander is a knight\n(4) Isabella is a knave\n(5) Olivia is a knight\n(6) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Jacob cannot be a knight, because this would contradict the claim of their own that Olivia is a knight and Olivia is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Olivia is a knight and Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Alexander is a knave then Jacob is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Alexander is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Alexander that Benjamin is a knave if and only if Alexander is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If Isabella is a knave then Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Alexander is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Benjamin is a knave then Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 4)), ('->', ('lying', 5), ('telling-truth', 4)), ('<=>', ('lying', 5), ('telling-truth', 2)), ('lying', 2), ('->', ('lying', 2), ('lying', 0)), ('->', ('lying', 3), ('telling-truth', 3)))", "index": 131}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, William, Evelyn, Samuel, Victoria, and Sophia. Abigail commented, \"Victoria is a knave if and only if Victoria is a knight\". William asserted: \"Sophia is a knave\". Evelyn expressed that Victoria is a knave if and only if Samuel is a knave. Samuel said, \"Evelyn is a knave and William is a knight.\" Victoria stated, \"Samuel is a knave and Victoria is a knight\". Sophia remarked, \"Evelyn is a knave or William is a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "William", "Evelyn", "Samuel", "Victoria", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Abigail is a knave, William is a knave, Evelyn is a knave, Samuel is a knave, Victoria is a knight, and Sophia is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) William is a knave\n(3) Evelyn is a knave\n(4) Samuel is a knave\n(5) Victoria is a knight\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Abigail cannot be a knight, because this would contradict the claim of their own that Victoria is a knave if and only if Victoria is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Samuel is a knave and Victoria is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Victoria that Samuel is a knave and Victoria is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Evelyn is a knave and William is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Victoria is a knave if and only if Samuel is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Samuel is a knave.", "William cannot be a knight, because this would contradict the false claim of Samuel that Evelyn is a knave and William is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Evelyn is a knave or William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('telling-truth', 4)), ('lying', 5), ('<=>', ('lying', 4), ('lying', 3)), ('and', ('lying', 2), ('telling-truth', 1)), ('and', ('lying', 3), ('telling-truth', 4)), ('or', ('lying', 2), ('telling-truth', 1)))", "index": 132}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Sebastian, Joseph, Lily, Scarlett, and James. \"If James is a knave then Joseph is a knight,\" Luke mentioned. Sebastian expressed that Lily is not a knight. Joseph commented, \"If Scarlett is a knave then Lily is a knave\". Lily remarked, \"Joseph is a knave and Luke is a knight\". Scarlett stated, \"James is a knave and Joseph is a knave\". \"Scarlett is a knight and Sebastian is a knight,\" James declared. So who is a knight and who is a knave?", "names": ["Luke", "Sebastian", "Joseph", "Lily", "Scarlett", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Luke is a knight, Sebastian is a knight, Joseph is a knight, Lily is a knave, Scarlett is a knave, and James is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Sebastian is a knight\n(3) Joseph is a knight\n(4) Lily is a knave\n(5) Scarlett is a knave\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that If James is a knave then Joseph is a knight.", "Assume James is a knight. No contradiction is found in their claim that Scarlett is a knight and Sebastian is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that James is a knave and Joseph is a knave.", "Scarlett cannot be a knave, because this would contradict the claim of James that Scarlett is a knight and Sebastian is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Scarlett is a knight and Sebastian is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that James is a knave and Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Scarlett that James is a knave and Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the claim of Luke that If James is a knave then Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that James is a knave and Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Scarlett is a knave then Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Joseph that If Scarlett is a knave then Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Joseph is a knave and Luke is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Lily is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 2)), ('not', ('telling-truth', 3)), ('->', ('lying', 4), ('lying', 3)), ('and', ('lying', 2), ('telling-truth', 0)), ('and', ('lying', 5), ('lying', 2)), ('and', ('telling-truth', 4), ('telling-truth', 1)))", "index": 133}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Jack, Daniel, Evelyn, Ella, and Mia. Grace told you that If Evelyn is a knight then Ella is a knave. \"Ella is not a knight,\" Jack claimed. Daniel noted, \"Daniel is a knight if and only if Jack is a knave\". \"Mia is a knave if and only if Mia is a knight,\" Evelyn claimed. \"Daniel is not a knight,\" Ella mentioned. Mia stated, \"Jack is a knave or Daniel is a knight\". So who is a knight and who is a knave?", "names": ["Grace", "Jack", "Daniel", "Evelyn", "Ella", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true], "solution_text": "Grace is a knight, Jack is a knave, Daniel is a knave, Evelyn is a knave, Ella is a knight, and Mia is a knight.", "solution_text_format": "(1) Grace is a knight\n(2) Jack is a knave\n(3) Daniel is a knave\n(4) Evelyn is a knave\n(5) Ella is a knight\n(6) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that If Evelyn is a knight then Ella is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Mia is a knave if and only if Mia is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Jack is a knave or Daniel is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Ella is not a knight.", "Ella cannot be a knight, because this would contradict the claim of Jack that Ella is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Jack is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight if and only if Jack is a knave.", "We have exhausted all possibilities for Daniel and Ella, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of Ella that Daniel is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 4)), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 2), ('lying', 1)), ('<=>', ('lying', 5), ('telling-truth', 5)), ('not', ('telling-truth', 2)), ('or', ('lying', 1), ('telling-truth', 2)))", "index": 134}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Joseph, Michael, Jacob, Elizabeth, and Mason. Liam remarked, \"Joseph is a knight and Michael is a knight\". \"If Liam is a knave then Liam is a knight,\" Joseph claimed. Michael stated, \"Joseph is a knight if and only if Jacob is a knave\". In Jacob's words: \"Jacob is a knight if and only if Michael is a knave\". Elizabeth expressed that Liam is not a knight. \"Joseph is a knight if and only if Jacob is a knave,\" Mason claimed. So who is a knight and who is a knave?", "names": ["Liam", "Joseph", "Michael", "Jacob", "Elizabeth", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false], "solution_text": "Liam is a knave, Joseph is a knave, Michael is a knave, Jacob is a knave, Elizabeth is a knight, and Mason is a knave.", "solution_text_format": "(1) Liam is a knave\n(2) Joseph is a knave\n(3) Michael is a knave\n(4) Jacob is a knave\n(5) Elizabeth is a knight\n(6) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Joseph is a knight and Michael is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Liam is a knave then Liam is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Michael that Joseph is a knight if and only if Jacob is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Jacob is a knight if and only if Michael is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Liam that Joseph is a knight and Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Liam that Joseph is a knight and Michael is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Joseph is a knight and Michael is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that If Liam is a knave then Liam is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Liam is a knave then Liam is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Jacob is a knight if and only if Michael is a knave.", "Jacob cannot be a knave, because this would contradict the claim of Michael that Joseph is a knight if and only if Jacob is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Michael that Joseph is a knight if and only if Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Michael is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Liam is not a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Joseph is a knight if and only if Jacob is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('lying', 0), ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('lying', 3)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('not', ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('lying', 3)))", "index": 135}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Evelyn, Isabella, Jackson, Aiden, and Sofia. Liam expressed that Evelyn is a knight. Evelyn remarked, \"Evelyn is a knight and Isabella is a knave\". As Isabella put it, \"If Sofia is a knave then Liam is a knight\". As Jackson put it, \"Evelyn is a knave and Sofia is a knight\". In Aiden's words: \"Jackson is a knave and Evelyn is a knight\". \"If Liam is a knight then Jackson is a knight\" - Sofia. So who is a knight and who is a knave?", "names": ["Liam", "Evelyn", "Isabella", "Jackson", "Aiden", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Liam is a knave, Evelyn is a knave, Isabella is a knight, Jackson is a knight, Aiden is a knave, and Sofia is a knight.", "solution_text_format": "(1) Liam is a knave\n(2) Evelyn is a knave\n(3) Isabella is a knight\n(4) Jackson is a knight\n(5) Aiden is a knave\n(6) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight and Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Evelyn that Evelyn is a knight and Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that If Sofia is a knave then Liam is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Liam that Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Liam that Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Evelyn is a knight and Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Sofia is a knave then Liam is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Liam is a knight then Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Evelyn is a knave and Sofia is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Jackson is a knave and Evelyn is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Jackson is a knave and Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('and', ('telling-truth', 1), ('lying', 2)), ('->', ('lying', 5), ('telling-truth', 0)), ('and', ('lying', 1), ('telling-truth', 5)), ('and', ('lying', 3), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('telling-truth', 3)))", "index": 136}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Riley, Ava, Charlotte, Amelia, and Olivia. According to Alexander, \"If Riley is a knave then Amelia is a knave\". Riley asserted: \"Ava is a knight if and only if Charlotte is a knight\". As Ava put it, \"Charlotte is not a knave\". In a statement by Charlotte: \"Amelia is not a knight\". \"Olivia is a knight or Ava is a knave,\" Amelia mentioned. Olivia asserted: \"Riley is a knave or Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Alexander", "Riley", "Ava", "Charlotte", "Amelia", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "Alexander is a knight, Riley is a knight, Ava is a knave, Charlotte is a knave, Amelia is a knight, and Olivia is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Riley is a knight\n(3) Ava is a knave\n(4) Charlotte is a knave\n(5) Amelia is a knight\n(6) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that If Riley is a knave then Amelia is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Ava is a knight if and only if Charlotte is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of Charlotte that Amelia is not a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Olivia is a knight or Ava is a knave.", "Olivia cannot be a knight, because this would contradict the false claim of Amelia that Olivia is a knight or Ava is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Riley is a knave or Alexander is a knight.", "We have exhausted all possibilities for Olivia and Amelia, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Riley that Ava is a knight if and only if Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Charlotte is not a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Riley that Ava is a knight if and only if Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Amelia is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Olivia is a knight or Ava is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Riley is a knave or Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('lying', 4)), ('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('lying', 3)), ('not', ('telling-truth', 4)), ('or', ('telling-truth', 5), ('lying', 2)), ('or', ('lying', 1), ('telling-truth', 0)))", "index": 137}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Zoey, Grace, Lily, Lucas, and Sophia. \"If Lily is a knave then Lily is a knight,\" Owen declared. Zoey commented, \"Lily is a knave\". In Grace's words: \"Lucas is a knave or Zoey is a knave\". \"Lucas is a knave if and only if Lily is a knight,\" Lily mentioned. Lucas commented, \"If Owen is a knave then Owen is a knight\". Sophia asserted: \"Lily is not a knight\". So who is a knight and who is a knave?", "names": ["Owen", "Zoey", "Grace", "Lily", "Lucas", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Owen is a knave, Zoey is a knight, Grace is a knight, Lily is a knave, Lucas is a knave, and Sophia is a knight.", "solution_text_format": "(1) Owen is a knave\n(2) Zoey is a knight\n(3) Grace is a knight\n(4) Lily is a knave\n(5) Lucas is a knave\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that If Lily is a knave then Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Lily is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Lily that Lucas is a knave if and only if Lily is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of their own that If Owen is a knave then Owen is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Owen that If Lily is a knave then Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that If Lily is a knave then Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Owen that If Lily is a knave then Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Lily is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Lily that Lucas is a knave if and only if Lily is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Owen is a knave then Owen is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Lily is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Lucas is a knave or Zoey is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Lily is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 3)), ('lying', 3), ('or', ('lying', 4), ('lying', 1)), ('<=>', ('lying', 4), ('telling-truth', 3)), ('->', ('lying', 0), ('telling-truth', 0)), ('not', ('telling-truth', 3)))", "index": 138}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Sophia, Riley, Henry, Jackson, and Penelope. In James's words: \"If Sophia is a knight then Riley is a knave\". \"Penelope is not a knight\" - Sophia. \"James is not a knave,\" Riley claimed. \"Riley is a knight\" - Henry. \"Henry is a knave and Sophia is a knight\" - Jackson. Penelope stated, \"Sophia is a knight if and only if Riley is a knave\". So who is a knight and who is a knave?", "names": ["James", "Sophia", "Riley", "Henry", "Jackson", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "James is a knight, Sophia is a knave, Riley is a knight, Henry is a knight, Jackson is a knave, and Penelope is a knight.", "solution_text_format": "(1) James is a knight\n(2) Sophia is a knave\n(3) Riley is a knight\n(4) Henry is a knight\n(5) Jackson is a knave\n(6) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that If Sophia is a knight then Riley is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Sophia that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of James that If Sophia is a knight then Riley is a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that James is not a knave.", "We have exhausted all possibilities for Riley and Penelope, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that James is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Riley is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Sophia is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Henry is a knave and Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('lying', 2)), ('not', ('telling-truth', 5)), ('not', ('lying', 0)), ('telling-truth', 2), ('and', ('lying', 3), ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('lying', 2)))", "index": 139}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Isabella, Aiden, Alexander, William, and Joseph. In Scarlett's words: \"Alexander is a knight if and only if William is a knave\". \"William is a knave if and only if William is a knight\" - Isabella. \"Isabella is a knight,\" Aiden claimed. In a statement by Alexander: \"Scarlett is a knave or William is a knave\". William noted, \"Aiden is not a knave\". \"Aiden is not a knight\" - Joseph. So who is a knight and who is a knave?", "names": ["Scarlett", "Isabella", "Aiden", "Alexander", "William", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true], "solution_text": "Scarlett is a knight, Isabella is a knave, Aiden is a knave, Alexander is a knight, William is a knave, and Joseph is a knight.", "solution_text_format": "(1) Scarlett is a knight\n(2) Isabella is a knave\n(3) Aiden is a knave\n(4) Alexander is a knight\n(5) William is a knave\n(6) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Alexander is a knight if and only if William is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Scarlett is a knave or William is a knave.", "William cannot be a knight, because this would contradict the claim of Scarlett that Alexander is a knight if and only if William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Aiden is not a knave.", "Aiden cannot be a knight, because this would contradict the false claim of William that Aiden is not a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that William is a knave if and only if William is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that William is a knave if and only if William is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Aiden is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 4)), ('<=>', ('lying', 4), ('telling-truth', 4)), ('telling-truth', 1), ('or', ('lying', 0), ('lying', 4)), ('not', ('lying', 2)), ('not', ('telling-truth', 2)))", "index": 140}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Lily, Sophia, Luke, Noah, and Avery. In a statement by Daniel: \"Luke is a knight or Noah is a knave\". \"Daniel is a knave or Sophia is a knave,\" Lily declared. Sophia said that Noah is a knight or Luke is a knight. Luke noted, \"Avery is a knight and Noah is a knave\". In Noah's words: \"Luke is a knight\". As Avery put it, \"Daniel is a knave or Sophia is a knight\". So who is a knight and who is a knave?", "names": ["Daniel", "Lily", "Sophia", "Luke", "Noah", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Daniel is a knight, Lily is a knight, Sophia is a knave, Luke is a knave, Noah is a knave, and Avery is a knave.", "solution_text_format": "(1) Daniel is a knight\n(2) Lily is a knight\n(3) Sophia is a knave\n(4) Luke is a knave\n(5) Noah is a knave\n(6) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Luke is a knight or Noah is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Avery is a knight and Noah is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Daniel is a knave or Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Noah is a knight or Luke is a knight.", "Noah cannot be a knight, because this would contradict the claim of Luke that Avery is a knight and Noah is a knave.", "Noah cannot be a knave, because this would contradict the false claim of their own that Luke is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Noah is a knight or Luke is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Luke that Avery is a knight and Noah is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Avery is a knight and Noah is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Daniel is a knave or Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Noah is a knight or Luke is a knight.", "Noah cannot be a knight, because this would contradict the claim of Daniel that Luke is a knight or Noah is a knave.", "Noah cannot be a knave, because this would contradict the claim of Sophia that Noah is a knight or Luke is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Avery that Daniel is a knave or Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Daniel is a knave or Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Avery that Daniel is a knave or Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Noah is a knight or Luke is a knight.", "Noah cannot be a knight, because this would contradict the claim of Daniel that Luke is a knight or Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Luke is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Daniel is a knave or Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('lying', 4)), ('or', ('lying', 0), ('lying', 2)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('and', ('telling-truth', 5), ('lying', 4)), ('telling-truth', 3), ('or', ('lying', 0), ('telling-truth', 2)))", "index": 141}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Harper, Alexander, James, Lily, and Oliver. Victoria stated, \"Alexander is a knave or James is a knight\". According to Harper, \"Lily is a knave\". Alexander said, \"Oliver is a knave.\" James stated, \"James is a knight and Oliver is a knight\". \"Oliver is a knight and Victoria is a knave\" - Lily. Oliver expressed that Alexander is a knight or James is a knight. So who is a knight and who is a knave?", "names": ["Victoria", "Harper", "Alexander", "James", "Lily", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Victoria is a knight, Harper is a knight, Alexander is a knave, James is a knight, Lily is a knave, and Oliver is a knight.", "solution_text_format": "(1) Victoria is a knight\n(2) Harper is a knight\n(3) Alexander is a knave\n(4) James is a knight\n(5) Lily is a knave\n(6) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Alexander is a knave or James is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Alexander that Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight or James is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Alexander is a knight or James is a knight.", "Assume James is a knight. No contradiction is found in their claim that James is a knight and Oliver is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Harper that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Oliver is a knight and Victoria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 3)), ('lying', 4), ('lying', 5), ('and', ('telling-truth', 3), ('telling-truth', 5)), ('and', ('telling-truth', 5), ('lying', 0)), ('or', ('telling-truth', 2), ('telling-truth', 3)))", "index": 142}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Ella, Sofia, Owen, Michael, and Mason. In Liam's words: \"Sofia is a knave or Liam is a knight\". In Ella's words: \"Sofia is a knight\". According to Sofia, \"Liam is not a knave\". Owen asserted: \"Michael is not a knight\". \"Liam is not a knave\" - Michael. Mason said that Michael is a knave or Michael is a knight. So who is a knight and who is a knave?", "names": ["Liam", "Ella", "Sofia", "Owen", "Michael", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Liam is a knight, Ella is a knight, Sofia is a knight, Owen is a knave, Michael is a knight, and Mason is a knight.", "solution_text_format": "(1) Liam is a knight\n(2) Ella is a knight\n(3) Sofia is a knight\n(4) Owen is a knave\n(5) Michael is a knight\n(6) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Sofia is a knave or Liam is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Sofia is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Owen that Michael is not a knight.", "Michael cannot be a knave, because this would contradict the false claim of their own that Liam is not a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Michael is a knave or Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 0)), ('telling-truth', 2), ('not', ('lying', 0)), ('not', ('telling-truth', 4)), ('not', ('lying', 0)), ('or', ('lying', 4), ('telling-truth', 4)))", "index": 143}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Henry, Olivia, Owen, Sebastian, and Amelia. In a statement by Oliver: \"Olivia is not a knave\". Henry expressed that Olivia is a knave. \"Amelia is a knave and Oliver is a knave,\" Olivia mentioned. Owen told you that Amelia is not a knight. Sebastian stated, \"Owen is a knight if and only if Olivia is a knight\". Amelia asserted: \"Amelia is a knight if and only if Sebastian is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Henry", "Olivia", "Owen", "Sebastian", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true], "solution_text": "Oliver is a knave, Henry is a knight, Olivia is a knave, Owen is a knave, Sebastian is a knight, and Amelia is a knight.", "solution_text_format": "(1) Oliver is a knave\n(2) Henry is a knight\n(3) Olivia is a knave\n(4) Owen is a knave\n(5) Sebastian is a knight\n(6) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Oliver is a knave.", "Olivia cannot be a knave, because this would contradict the claim of Oliver that Olivia is not a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Olivia is not a knave.", "Olivia cannot be a knight, because this would contradict the false claim of Oliver that Olivia is not a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Amelia is a knave and Oliver is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Owen is a knight if and only if Olivia is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Amelia is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Amelia is not a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('lying', 2), ('and', ('lying', 5), ('lying', 0)), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)))", "index": 144}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Chloe, Michael, David, Evelyn, and Sofia. Abigail remarked, \"David is not a knave\". In Chloe's words: \"Abigail is a knight if and only if Sofia is a knight\". Michael commented, \"Sofia is a knight or Chloe is a knave\". \"Chloe is not a knave,\" David claimed. Evelyn said, \"David is a knave if and only if Sofia is a knave.\" In a statement by Sofia: \"David is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Chloe", "Michael", "David", "Evelyn", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true], "solution_text": "Abigail is a knave, Chloe is a knave, Michael is a knight, David is a knave, Evelyn is a knave, and Sofia is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Chloe is a knave\n(3) Michael is a knight\n(4) David is a knave\n(5) Evelyn is a knave\n(6) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that David is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that David is a knave.", "Sofia cannot be a knave, because this would contradict the claim of Chloe that Abigail is a knight if and only if Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of David that Chloe is not a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Abigail that David is not a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that David is not a knave.", "David cannot be a knight, because this would contradict the false claim of Abigail that David is not a knave.", "Assume David is a knave. No contradiction is found in their false claim that Chloe is not a knave.", "Chloe cannot be a knight, because this would contradict the false claim of David that Chloe is not a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that David is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Sofia is a knight or Chloe is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that David is a knave if and only if Sofia is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that David is a knave if and only if Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('<=>', ('telling-truth', 0), ('telling-truth', 5)), ('or', ('telling-truth', 5), ('lying', 1)), ('not', ('lying', 1)), ('<=>', ('lying', 3), ('lying', 5)), ('lying', 3))", "index": 145}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Emily, Alexander, Benjamin, Aria, and Evelyn. In a statement by Luke: \"Benjamin is a knight\". Emily was heard saying, \"Evelyn is a knight or Alexander is a knave\". \"If Luke is a knight then Luke is a knave\" - Alexander. According to Benjamin, \"If Luke is a knight then Emily is a knight\". Aria said that Luke is not a knave. As Evelyn put it, \"Emily is not a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Emily", "Alexander", "Benjamin", "Aria", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "Luke is a knight, Emily is a knight, Alexander is a knave, Benjamin is a knight, Aria is a knight, and Evelyn is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Emily is a knight\n(3) Alexander is a knave\n(4) Benjamin is a knight\n(5) Aria is a knight\n(6) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Luke is a knight then Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Evelyn is a knight or Alexander is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Emily is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Emily is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Emily that Evelyn is a knight or Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Luke is a knight then Luke is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Luke is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('or', ('telling-truth', 5), ('lying', 2)), ('->', ('telling-truth', 0), ('lying', 0)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('lying', 0)), ('not', ('telling-truth', 1)))", "index": 146}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Ella, Chloe, Aria, Owen, and Charlotte. Ethan remarked, \"Aria is a knight or Ethan is a knight\". Ella was heard saying, \"Charlotte is not a knave\". Chloe remarked, \"Ethan is a knight or Aria is a knight\". In Aria's words: \"Chloe is a knave and Ella is a knave\". In a statement by Owen: \"Chloe is not a knight\". As Charlotte put it, \"Chloe is not a knave\". So who is a knight and who is a knave?", "names": ["Ethan", "Ella", "Chloe", "Aria", "Owen", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Ethan is a knight, Ella is a knight, Chloe is a knight, Aria is a knave, Owen is a knave, and Charlotte is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Ella is a knight\n(3) Chloe is a knight\n(4) Aria is a knave\n(5) Owen is a knave\n(6) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Aria is a knight or Ethan is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Chloe is a knave and Ella is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Aria that Chloe is a knave and Ella is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight or Aria is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Chloe is a knave and Ella is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Ethan is a knight or Aria is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Chloe is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Chloe is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 0)), ('not', ('lying', 5)), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('and', ('lying', 2), ('lying', 1)), ('not', ('telling-truth', 2)), ('not', ('lying', 2)))", "index": 147}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, William, Liam, Logan, Luke, and Penelope. \"Liam is not a knave,\" Aurora claimed. William told you that Logan is a knave or Luke is a knight. Liam remarked, \"Luke is a knave or Aurora is a knave\". Logan asserted: \"Aurora is a knight or Liam is a knight\". Luke commented, \"Luke is a knight if and only if Liam is a knight\". In a statement by Penelope: \"Liam is not a knight\". So who is a knight and who is a knave?", "names": ["Aurora", "William", "Liam", "Logan", "Luke", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false], "solution_text": "Aurora is a knight, William is a knave, Liam is a knight, Logan is a knight, Luke is a knave, and Penelope is a knave.", "solution_text_format": "(1) Aurora is a knight\n(2) William is a knave\n(3) Liam is a knight\n(4) Logan is a knight\n(5) Luke is a knave\n(6) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Luke is a knave or Aurora is a knave.", "Luke cannot be a knight, because this would contradict the claim of Liam that Luke is a knave or Aurora is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Liam is a knight.", "Assume William is a knight. No contradiction is found in their claim that Logan is a knave or Luke is a knight.", "Logan cannot be a knight, because this would contradict the claim of William that Logan is a knave or Luke is a knight.", "Logan cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight or Liam is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Logan is a knave or Luke is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Aurora is a knight or Liam is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Liam is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Liam is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('or', ('lying', 3), ('telling-truth', 4)), ('or', ('lying', 4), ('lying', 0)), ('or', ('telling-truth', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 2)), ('not', ('telling-truth', 2)))", "index": 148}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Charlotte, Jack, Sebastian, Abigail, and Mia. In a statement by Grace: \"If Jack is a knave then Abigail is a knave\". \"Sebastian is not a knave,\" Charlotte mentioned. Jack noted, \"Mia is a knight\". Sebastian said that Abigail is a knight if and only if Grace is a knight. Abigail commented, \"Charlotte is a knave or Charlotte is a knight\". According to Mia, \"Abigail is a knight or Grace is a knight\". So who is a knight and who is a knave?", "names": ["Grace", "Charlotte", "Jack", "Sebastian", "Abigail", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Grace is a knight, Charlotte is a knight, Jack is a knight, Sebastian is a knight, Abigail is a knight, and Mia is a knight.", "solution_text_format": "(1) Grace is a knight\n(2) Charlotte is a knight\n(3) Jack is a knight\n(4) Sebastian is a knight\n(5) Abigail is a knight\n(6) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that If Jack is a knave then Abigail is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Abigail is a knight or Grace is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Charlotte is a knave or Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 4)), ('not', ('lying', 3)), ('telling-truth', 5), ('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('lying', 1), ('telling-truth', 1)), ('or', ('telling-truth', 4), ('telling-truth', 0)))", "index": 149}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Benjamin, Lucas, Joseph, Aria, and James. Aiden remarked, \"James is a knight or Benjamin is a knight\". Benjamin stated, \"Aiden is a knave\". Lucas noted, \"James is a knight or James is a knave\". \"Benjamin is not a knave\" - Joseph. Aria was heard saying, \"If Lucas is a knight then Joseph is a knave\". James stated, \"Joseph is a knave if and only if Aiden is a knight\". So who is a knight and who is a knave?", "names": ["Aiden", "Benjamin", "Lucas", "Joseph", "Aria", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Aiden is a knight, Benjamin is a knave, Lucas is a knight, Joseph is a knave, Aria is a knight, and James is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Benjamin is a knave\n(3) Lucas is a knight\n(4) Joseph is a knave\n(5) Aria is a knight\n(6) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that James is a knight or Benjamin is a knight.", "Assume James is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Aiden is a knight.", "Joseph cannot be a knight, because this would contradict the claim of James that Joseph is a knave if and only if Aiden is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Aiden is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Aiden is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that James is a knight or James is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Lucas is a knight then Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 1)), ('lying', 0), ('or', ('telling-truth', 5), ('lying', 5)), ('not', ('lying', 1)), ('->', ('telling-truth', 2), ('lying', 3)), ('<=>', ('lying', 3), ('telling-truth', 0)))", "index": 150}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Emily, Luke, Lucas, Harper, and Ella. In Ava's words: \"Luke is a knight if and only if Ella is a knave\". Emily stated, \"If Emily is a knight then Luke is a knave\". Luke asserted: \"Ella is a knight and Ella is a knave\". \"Harper is a knave and Luke is a knave,\" Lucas claimed. As Harper put it, \"Lucas is a knave if and only if Ava is a knight\". Ella was heard saying, \"If Emily is a knight then Harper is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Emily", "Luke", "Lucas", "Harper", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "Ava is a knight, Emily is a knight, Luke is a knave, Lucas is a knave, Harper is a knight, and Ella is a knight.", "solution_text_format": "(1) Ava is a knight\n(2) Emily is a knight\n(3) Luke is a knave\n(4) Lucas is a knave\n(5) Harper is a knight\n(6) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Luke is a knight if and only if Ella is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Ella is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Ella is a knight and Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Emily is a knight then Harper is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Emily is a knight then Luke is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Ava is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Luke is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Harper is a knave and Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 5)), ('->', ('telling-truth', 1), ('lying', 2)), ('and', ('telling-truth', 5), ('lying', 5)), ('and', ('lying', 4), ('lying', 2)), ('<=>', ('lying', 3), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('telling-truth', 4)))", "index": 151}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Lily, Ella, Emily, Sofia, and Logan. Abigail noted, \"Sofia is not a knave\". Lily expressed that Ella is a knight or Logan is a knight. \"Sofia is a knave and Sofia is a knight,\" Ella claimed. In Emily's words: \"Abigail is a knight\". As Sofia put it, \"If Sofia is a knight then Lily is a knight\". As Logan put it, \"Sofia is not a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Lily", "Ella", "Emily", "Sofia", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Abigail is a knight, Lily is a knight, Ella is a knave, Emily is a knight, Sofia is a knight, and Logan is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) Lily is a knight\n(3) Ella is a knave\n(4) Emily is a knight\n(5) Sofia is a knight\n(6) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Sofia is a knight then Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Ella is a knight or Logan is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Sofia is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Sofia is a knave and Sofia is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('or', ('telling-truth', 2), ('telling-truth', 5)), ('and', ('lying', 4), ('telling-truth', 4)), ('telling-truth', 0), ('->', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('lying', 4)))", "index": 152}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Avery, William, Matthew, Scarlett, and Ethan. Emma commented, \"Emma is a knight or William is a knight\". As Avery put it, \"Emma is a knave and William is a knave\". William said, \"Ethan is a knave.\" \"Avery is a knave or William is a knave,\" Matthew claimed. In Scarlett's words: \"Matthew is a knave and Ethan is a knight\". Ethan said, \"Emma is a knight.\" So who is a knight and who is a knave?", "names": ["Emma", "Avery", "William", "Matthew", "Scarlett", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true], "solution_text": "Emma is a knight, Avery is a knave, William is a knave, Matthew is a knight, Scarlett is a knave, and Ethan is a knight.", "solution_text_format": "(1) Emma is a knight\n(2) Avery is a knave\n(3) William is a knave\n(4) Matthew is a knight\n(5) Scarlett is a knave\n(6) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Emma is a knight or William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of William that Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Emma is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Emma is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Emma is a knave and William is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Emma is a knave and William is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Avery is a knave or William is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Matthew is a knave and Ethan is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Matthew is a knave and Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 2)), ('and', ('lying', 0), ('lying', 2)), ('lying', 5), ('or', ('lying', 1), ('lying', 2)), ('and', ('lying', 3), ('telling-truth', 5)), ('telling-truth', 0))", "index": 153}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Abigail, Ella, Noah, Avery, and Matthew. Jackson remarked, \"Abigail is a knave and Abigail is a knight\". Abigail noted, \"Avery is a knave and Avery is a knight\". \"Matthew is a knave or Matthew is a knight,\" Ella declared. \"If Avery is a knight then Ella is a knight\" - Noah. Avery remarked, \"Matthew is a knight\". \"If Jackson is a knight then Ella is a knight,\" Matthew claimed. So who is a knight and who is a knave?", "names": ["Jackson", "Abigail", "Ella", "Noah", "Avery", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Jackson is a knave, Abigail is a knave, Ella is a knight, Noah is a knight, Avery is a knight, and Matthew is a knight.", "solution_text_format": "(1) Jackson is a knave\n(2) Abigail is a knave\n(3) Ella is a knight\n(4) Noah is a knight\n(5) Avery is a knight\n(6) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Jackson cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Abigail is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Abigail is a knave and Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Avery is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Avery is a knave and Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Jackson is a knight then Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Matthew is a knave or Matthew is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Avery is a knight then Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 1)), ('and', ('lying', 4), ('telling-truth', 4)), ('or', ('lying', 5), ('telling-truth', 5)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('telling-truth', 5), ('->', ('telling-truth', 0), ('telling-truth', 2)))", "index": 154}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Luke, Penelope, Mia, Riley, and Noah. In Scarlett's words: \"Luke is a knight if and only if Scarlett is a knight\". As Luke put it, \"Scarlett is a knight\". In Penelope's words: \"Riley is a knave or Luke is a knave\". Mia stated, \"Noah is a knight or Luke is a knave\". Riley noted, \"Mia is a knight if and only if Luke is a knave\". Noah expressed that Mia is a knight if and only if Riley is a knight. So who is a knight and who is a knave?", "names": ["Scarlett", "Luke", "Penelope", "Mia", "Riley", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false], "solution_text": "Scarlett is a knight, Luke is a knight, Penelope is a knave, Mia is a knave, Riley is a knight, and Noah is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Luke is a knight\n(3) Penelope is a knave\n(4) Mia is a knave\n(5) Riley is a knight\n(6) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Luke is a knight if and only if Scarlett is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Riley is a knave or Luke is a knave.", "Riley cannot be a knight, because this would contradict the claim of Penelope that Riley is a knave or Luke is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Luke is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Noah is a knight or Luke is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Mia is a knight if and only if Riley is a knight.", "Noah cannot be a knave, because this would contradict the claim of Mia that Noah is a knight or Luke is a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of Riley that Mia is a knight if and only if Luke is a knave.", "We have exhausted all possibilities for Mia and Riley, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Riley is a knave or Luke is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Mia is a knight if and only if Luke is a knave.", "Mia cannot be a knight, because this would contradict the claim of Riley that Mia is a knight if and only if Luke is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Noah is a knight or Luke is a knave.", "Noah cannot be a knight, because this would contradict the false claim of Mia that Noah is a knight or Luke is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('telling-truth', 0), ('or', ('lying', 4), ('lying', 1)), ('or', ('telling-truth', 5), ('lying', 1)), ('<=>', ('telling-truth', 3), ('lying', 1)), ('<=>', ('telling-truth', 3), ('telling-truth', 4)))", "index": 155}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Mason, David, Owen, Chloe, and Zoey. Harper noted, \"Zoey is not a knave\". Mason said that Owen is a knave or Zoey is a knight. David remarked, \"If Chloe is a knight then Harper is a knight\". Owen noted, \"Harper is a knight and Chloe is a knight\". As Chloe put it, \"Mason is a knight and Harper is a knave\". Zoey was heard saying, \"Zoey is a knight and Chloe is a knight\". So who is a knight and who is a knave?", "names": ["Harper", "Mason", "David", "Owen", "Chloe", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "Harper is a knave, Mason is a knight, David is a knave, Owen is a knave, Chloe is a knight, and Zoey is a knave.", "solution_text_format": "(1) Harper is a knave\n(2) Mason is a knight\n(3) David is a knave\n(4) Owen is a knave\n(5) Chloe is a knight\n(6) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight and Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Harper is a knave.", "Chloe cannot be a knave, because this would contradict the claim of Zoey that Zoey is a knight and Chloe is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of Harper that Zoey is not a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Harper that Zoey is not a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Zoey is a knight and Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Mason is a knight and Harper is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Owen is a knave or Zoey is a knight.", "Owen cannot be a knight, because this would contradict the claim of Mason that Owen is a knave or Zoey is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Harper is a knight and Chloe is a knight.", "David cannot be a knight, because this would contradict the claim of their own that If Chloe is a knight then Harper is a knight.", "Assume David is a knave. No contradiction is found in their false claim that If Chloe is a knight then Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('or', ('lying', 3), ('telling-truth', 5)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('telling-truth', 4)), ('and', ('telling-truth', 1), ('lying', 0)), ('and', ('telling-truth', 5), ('telling-truth', 4)))", "index": 156}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Alexander, Aurora, Owen, Mason, and Logan. Evelyn asserted: \"Mason is a knight and Logan is a knave\". Alexander asserted: \"Logan is a knave and Evelyn is a knight\". Aurora told you that If Alexander is a knight then Logan is a knight. \"Logan is a knave and Aurora is a knave,\" Owen claimed. \"Alexander is a knave if and only if Owen is a knight,\" Mason mentioned. Logan asserted: \"Aurora is not a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "Alexander", "Aurora", "Owen", "Mason", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false], "solution_text": "Evelyn is a knave, Alexander is a knave, Aurora is a knight, Owen is a knave, Mason is a knave, and Logan is a knave.", "solution_text_format": "(1) Evelyn is a knave\n(2) Alexander is a knave\n(3) Aurora is a knight\n(4) Owen is a knave\n(5) Mason is a knave\n(6) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Mason is a knight and Logan is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Owen is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Logan is a knave and Evelyn is a knight.", "Logan cannot be a knight, because this would contradict the claim of Evelyn that Mason is a knight and Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that If Alexander is a knight then Logan is a knight.", "Aurora cannot be a knave, because this would contradict the false claim of Logan that Aurora is not a knight.", "We have exhausted all possibilities for Aurora and Logan, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Logan is a knave and Evelyn is a knight.", "Logan cannot be a knight, because this would contradict the claim of Evelyn that Mason is a knight and Logan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of Alexander that Logan is a knave and Evelyn is a knight.", "We have exhausted all possibilities for Logan and Alexander, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Evelyn that Mason is a knight and Logan is a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Mason is a knight and Logan is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Owen is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Evelyn is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Logan is a knave and Evelyn is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Aurora is not a knight.", "Aurora cannot be a knight, because this would contradict the claim of Logan that Aurora is not a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knight then Logan is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of Evelyn that Mason is a knight and Logan is a knave.", "We have exhausted all possibilities for Logan and Alexander, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Alexander is a knave if and only if Owen is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Evelyn is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Logan is a knave and Evelyn is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Aurora is not a knight.", "Aurora cannot be a knight, because this would contradict the claim of Logan that Aurora is not a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knight then Logan is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Alexander is a knight then Logan is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Aurora is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Logan is a knave and Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 5)), ('and', ('lying', 5), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('telling-truth', 5)), ('and', ('lying', 5), ('lying', 2)), ('<=>', ('lying', 1), ('telling-truth', 3)), ('not', ('telling-truth', 2)))", "index": 157}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Aria, Evelyn, Ethan, Sophia, and Aurora. \"Aurora is a knight or Evelyn is a knave\" - Michael. In a statement by Aria: \"Sophia is a knight and Ethan is a knight\". Evelyn was heard saying, \"Michael is a knight\". \"Sophia is a knight and Aria is a knight\" - Ethan. Sophia told you that If Michael is a knight then Aurora is a knave. Aurora asserted: \"Sophia is a knave or Michael is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Aria", "Evelyn", "Ethan", "Sophia", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Michael is a knight, Aria is a knave, Evelyn is a knight, Ethan is a knave, Sophia is a knave, and Aurora is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Aria is a knave\n(3) Evelyn is a knight\n(4) Ethan is a knave\n(5) Sophia is a knave\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Aurora is a knight or Evelyn is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Sophia is a knave or Michael is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that If Michael is a knight then Aurora is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Michael is a knight then Aurora is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Michael is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Ethan is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Sophia is a knight and Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Aria is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Sophia is a knight and Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('lying', 2)), ('and', ('telling-truth', 4), ('telling-truth', 3)), ('telling-truth', 0), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('lying', 5)), ('or', ('lying', 4), ('telling-truth', 0)))", "index": 158}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, James, Noah, Samuel, Chloe, and Abigail. Penelope remarked, \"Noah is not a knight\". \"Samuel is a knave or Samuel is a knight,\" James declared. Noah said, \"Chloe is not a knight.\" Samuel remarked, \"Noah is a knave if and only if Penelope is a knight\". Chloe said, \"Penelope is a knight or Penelope is a knave.\" \"Noah is a knight if and only if James is a knave,\" Abigail declared. So who is a knight and who is a knave?", "names": ["Penelope", "James", "Noah", "Samuel", "Chloe", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Penelope is a knight, James is a knight, Noah is a knave, Samuel is a knight, Chloe is a knight, and Abigail is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) James is a knight\n(3) Noah is a knave\n(4) Samuel is a knight\n(5) Chloe is a knight\n(6) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Noah is not a knight.", "Noah cannot be a knight, because this would contradict the claim of Penelope that Noah is not a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Penelope is a knight or Penelope is a knave.", "Assume James is a knight. No contradiction is found in their claim that Samuel is a knave or Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Noah is a knave if and only if Penelope is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Noah is a knight if and only if James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('or', ('lying', 3), ('telling-truth', 3)), ('not', ('telling-truth', 4)), ('<=>', ('lying', 2), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 0)), ('<=>', ('telling-truth', 2), ('lying', 1)))", "index": 159}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Oliver, Sofia, Joseph, Olivia, and Mia. Samuel commented, \"Joseph is a knight and Oliver is a knave\". According to Oliver, \"If Joseph is a knave then Oliver is a knight\". Sofia expressed that Olivia is a knight if and only if Joseph is a knave. \"Mia is a knight,\" Joseph claimed. Olivia told you that Joseph is a knight and Samuel is a knight. In Mia's words: \"Olivia is a knave\". So who is a knight and who is a knave?", "names": ["Samuel", "Oliver", "Sofia", "Joseph", "Olivia", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Samuel is a knave, Oliver is a knight, Sofia is a knight, Joseph is a knight, Olivia is a knave, and Mia is a knight.", "solution_text_format": "(1) Samuel is a knave\n(2) Oliver is a knight\n(3) Sofia is a knight\n(4) Joseph is a knight\n(5) Olivia is a knave\n(6) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Joseph is a knight and Oliver is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Mia that Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight and Samuel is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Joseph that Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Samuel that Joseph is a knight and Oliver is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Joseph is a knight and Oliver is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Samuel is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Joseph is a knight and Samuel is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Joseph is a knave then Oliver is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 1)), ('->', ('lying', 3), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('lying', 3)), ('telling-truth', 5), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('lying', 4))", "index": 160}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, David, Sophia, Aurora, Amelia, and Scarlett. \"David is a knave or Scarlett is a knight,\" Ava mentioned. David expressed that If David is a knight then Amelia is a knight. Sophia was heard saying, \"Scarlett is not a knave\". Aurora stated, \"Ava is a knave and Scarlett is a knave\". \"Sophia is a knight,\" Amelia claimed. Scarlett noted, \"If Sophia is a knave then Ava is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "David", "Sophia", "Aurora", "Amelia", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Ava is a knight, David is a knight, Sophia is a knight, Aurora is a knave, Amelia is a knight, and Scarlett is a knight.", "solution_text_format": "(1) Ava is a knight\n(2) David is a knight\n(3) Sophia is a knight\n(4) Aurora is a knave\n(5) Amelia is a knight\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that David is a knave or Scarlett is a knight.", "Assume David is a knight. No contradiction is found in their claim that If David is a knight then Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Sophia is a knave then Ava is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Ava is a knave and Scarlett is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Ava is a knave and Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 5)), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('not', ('lying', 5)), ('and', ('lying', 0), ('lying', 5)), ('telling-truth', 2), ('->', ('lying', 2), ('telling-truth', 0)))", "index": 161}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Emma, Emily, Evelyn, Aiden, and Lily. Luke stated, \"Aiden is a knave or Emily is a knight\". Emma remarked, \"Emily is a knight if and only if Aiden is a knave\". Emily expressed that Luke is a knave or Evelyn is a knave. \"If Evelyn is a knight then Luke is a knight\" - Evelyn. \"Lily is a knave or Aiden is a knight\" - Aiden. \"Emily is a knave and Evelyn is a knight,\" Lily claimed. So who is a knight and who is a knave?", "names": ["Luke", "Emma", "Emily", "Evelyn", "Aiden", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true], "solution_text": "Luke is a knight, Emma is a knave, Emily is a knave, Evelyn is a knight, Aiden is a knave, and Lily is a knight.", "solution_text_format": "(1) Luke is a knight\n(2) Emma is a knave\n(3) Emily is a knave\n(4) Evelyn is a knight\n(5) Aiden is a knave\n(6) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Aiden is a knave or Emily is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Lily is a knave or Aiden is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Emily is a knave and Evelyn is a knight.", "Emily cannot be a knight, because this would contradict the claim of Lily that Emily is a knave and Evelyn is a knight.", "Emily cannot be a knave, because this would contradict the claim of Luke that Aiden is a knave or Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Emily is a knave and Evelyn is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Luke is a knave or Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Emily that Luke is a knave or Evelyn is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that If Evelyn is a knight then Luke is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Luke that Aiden is a knave or Emily is a knight.", "We have exhausted all possibilities for Emily and Lily, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Lily is a knave or Aiden is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Emily is a knave and Evelyn is a knight.", "Emily cannot be a knight, because this would contradict the claim of Lily that Emily is a knave and Evelyn is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Luke is a knave or Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Evelyn is a knight then Luke is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Emily is a knight if and only if Aiden is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('lying', 4)), ('or', ('lying', 0), ('lying', 3)), ('->', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('lying', 5), ('telling-truth', 4)), ('and', ('lying', 2), ('telling-truth', 3)))", "index": 162}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Logan, Penelope, Elizabeth, Zoey, and Riley. Avery remarked, \"If Penelope is a knight then Zoey is a knight\". Logan was heard saying, \"Riley is a knave if and only if Zoey is a knight\". Penelope said, \"Zoey is a knight if and only if Logan is a knight.\" Elizabeth said, \"Zoey is not a knave.\" \"Penelope is not a knight,\" Zoey declared. In a statement by Riley: \"Logan is a knight and Zoey is a knight\". So who is a knight and who is a knave?", "names": ["Avery", "Logan", "Penelope", "Elizabeth", "Zoey", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false], "solution_text": "Avery is a knave, Logan is a knave, Penelope is a knight, Elizabeth is a knave, Zoey is a knave, and Riley is a knave.", "solution_text_format": "(1) Avery is a knave\n(2) Logan is a knave\n(3) Penelope is a knight\n(4) Elizabeth is a knave\n(5) Zoey is a knave\n(6) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that If Penelope is a knight then Zoey is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Logan is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Penelope is not a knight.", "Zoey cannot be a knave, because this would contradict the claim of Avery that If Penelope is a knight then Zoey is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Logan is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Logan cannot be a knight, because this would contradict the false claim of Penelope that Zoey is a knight if and only if Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Zoey is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Zoey is a knight.", "Riley cannot be a knave, because this would contradict the false claim of Logan that Riley is a knave if and only if Zoey is a knight.", "We have exhausted all possibilities for Riley and Logan, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Penelope is not a knight.", "We have exhausted all possibilities for Zoey and Penelope, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Penelope is a knight then Zoey is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Logan is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Avery that If Penelope is a knight then Zoey is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Logan cannot be a knight, because this would contradict the claim of Penelope that Zoey is a knight if and only if Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Zoey is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Logan that Riley is a knave if and only if Zoey is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Logan is a knight and Zoey is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Zoey is not a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Zoey is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('lying', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('lying', 4)), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 1), ('telling-truth', 4)))", "index": 163}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Noah, James, Mason, Ava, and Emily. \"Emily is a knave and Noah is a knight,\" Harper claimed. In Noah's words: \"James is a knave if and only if Harper is a knave\". According to James, \"Noah is a knave if and only if Harper is a knave\". According to Mason, \"James is not a knave\". In Ava's words: \"Emily is a knight or Harper is a knight\". \"James is not a knave,\" Emily mentioned. So who is a knight and who is a knave?", "names": ["Harper", "Noah", "James", "Mason", "Ava", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Harper is a knave, Noah is a knave, James is a knight, Mason is a knight, Ava is a knight, and Emily is a knight.", "solution_text_format": "(1) Harper is a knave\n(2) Noah is a knave\n(3) James is a knight\n(4) Mason is a knight\n(5) Ava is a knight\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Emily is a knave and Noah is a knight.", "Emily cannot be a knight, because this would contradict the claim of Harper that Emily is a knave and Noah is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that James is not a knave.", "James cannot be a knight, because this would contradict the false claim of Emily that James is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Harper is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that James is a knave if and only if Harper is a knave.", "Noah cannot be a knave, because this would contradict the claim of Harper that Emily is a knave and Noah is a knight.", "We have exhausted all possibilities for Noah, James, and Emily, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Emily is a knave and Noah is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that James is not a knave.", "Assume James is a knight. No contradiction is found in their claim that Noah is a knave if and only if Harper is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that James is a knave if and only if Harper is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that James is a knave if and only if Harper is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that James is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Emily is a knight or Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 1)), ('<=>', ('lying', 2), ('lying', 0)), ('<=>', ('lying', 1), ('lying', 0)), ('not', ('lying', 2)), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('not', ('lying', 2)))", "index": 164}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Jack, Victoria, Olivia, Emma, and Sofia. James noted, \"Sofia is a knave or Victoria is a knave\". Jack stated, \"Emma is a knight if and only if Sofia is a knight\". In a statement by Victoria: \"James is a knight if and only if Emma is a knave\". \"Jack is a knight\" - Olivia. Emma remarked, \"Victoria is a knight and Sofia is a knight\". Sofia expressed that Olivia is a knight and Victoria is a knave. So who is a knight and who is a knave?", "names": ["James", "Jack", "Victoria", "Olivia", "Emma", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "James is a knight, Jack is a knight, Victoria is a knight, Olivia is a knight, Emma is a knave, and Sofia is a knave.", "solution_text_format": "(1) James is a knight\n(2) Jack is a knight\n(3) Victoria is a knight\n(4) Olivia is a knight\n(5) Emma is a knave\n(6) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Sofia is a knave or Victoria is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Olivia is a knight and Victoria is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Emma is a knight if and only if Sofia is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Victoria is a knight and Sofia is a knight.", "Victoria cannot be a knight, because this would contradict the claim of James that Sofia is a knave or Victoria is a knave.", "Victoria cannot be a knave, because this would contradict the claim of Emma that Victoria is a knight and Sofia is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Jack that Emma is a knight if and only if Sofia is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Olivia that Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the claim of Sofia that Olivia is a knight and Victoria is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Olivia is a knight and Victoria is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Emma is a knight if and only if Sofia is a knight.", "Emma cannot be a knight, because this would contradict the claim of Jack that Emma is a knight if and only if Sofia is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Victoria is a knight and Sofia is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that James is a knight if and only if Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('lying', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 0), ('lying', 4)), ('telling-truth', 1), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('and', ('telling-truth', 3), ('lying', 2)))", "index": 165}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Zoey, Ava, William, Emma, and Ethan. Harper asserted: \"William is a knave or Ethan is a knave\". As Zoey put it, \"Ava is a knight and Harper is a knight\". According to Ava, \"Ethan is a knave and William is a knight\". \"Ethan is a knave and Zoey is a knave,\" William declared. Emma stated, \"Ethan is a knave if and only if Zoey is a knave\". Ethan said, \"Ethan is a knight.\" So who is a knight and who is a knave?", "names": ["Harper", "Zoey", "Ava", "William", "Emma", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true], "solution_text": "Harper is a knight, Zoey is a knave, Ava is a knave, William is a knave, Emma is a knave, and Ethan is a knight.", "solution_text_format": "(1) Harper is a knight\n(2) Zoey is a knave\n(3) Ava is a knave\n(4) William is a knave\n(5) Emma is a knave\n(6) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that William is a knave or Ethan is a knave.", "Assume William is a knight. No contradiction is found in their claim that Ethan is a knave and Zoey is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Harper that William is a knave or Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Zoey cannot be a knight, because this would contradict the claim of William that Ethan is a knave and Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ava is a knight and Harper is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Zoey that Ava is a knight and Harper is a knight.", "Ava cannot be a knave, because this would contradict the false claim of their own that Ethan is a knave and William is a knight.", "We have exhausted all possibilities for Ava, Zoey, and Ethan, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Ethan is a knave and Zoey is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Ava is a knight and Harper is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Ethan is a knave and William is a knight.", "Ava cannot be a knave, because this would contradict the claim of Zoey that Ava is a knight and Harper is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ava is a knight and Harper is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Zoey that Ava is a knight and Harper is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Ethan is a knave and William is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Ethan is a knave if and only if Zoey is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 5)), ('and', ('telling-truth', 2), ('telling-truth', 0)), ('and', ('lying', 5), ('telling-truth', 3)), ('and', ('lying', 5), ('lying', 1)), ('<=>', ('lying', 5), ('lying', 1)), ('telling-truth', 5))", "index": 166}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Lucas, Aiden, Chloe, James, and Harper. \"Chloe is a knave,\" Victoria declared. \"If Harper is a knight then Lucas is a knight,\" Lucas declared. Aiden said, \"Chloe is a knave if and only if James is a knight.\" Chloe said that Victoria is a knave or James is a knight. In a statement by James: \"If Victoria is a knight then Chloe is a knave\". Harper noted, \"James is a knave if and only if Chloe is a knight\". So who is a knight and who is a knave?", "names": ["Victoria", "Lucas", "Aiden", "Chloe", "James", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Victoria is a knave, Lucas is a knight, Aiden is a knave, Chloe is a knight, James is a knight, and Harper is a knave.", "solution_text_format": "(1) Victoria is a knave\n(2) Lucas is a knight\n(3) Aiden is a knave\n(4) Chloe is a knight\n(5) James is a knight\n(6) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Victoria that Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Victoria is a knave or James is a knight.", "James cannot be a knight, because this would contradict the false claim of Chloe that Victoria is a knave or James is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that If Victoria is a knight then Chloe is a knave.", "We have exhausted all possibilities for James and Chloe, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Victoria is a knave or James is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Victoria is a knight then Chloe is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Harper is a knight then Lucas is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that James is a knave if and only if Chloe is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that James is a knave if and only if Chloe is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Chloe is a knave if and only if James is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Chloe is a knave if and only if James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('<=>', ('lying', 3), ('telling-truth', 4)), ('or', ('lying', 0), ('telling-truth', 4)), ('->', ('telling-truth', 0), ('lying', 3)), ('<=>', ('lying', 4), ('telling-truth', 3)))", "index": 167}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Zoey, Isabella, Logan, Michael, and William. Samuel noted, \"Isabella is a knave if and only if Michael is a knight\". Zoey told you that Isabella is a knave if and only if William is a knave. In a statement by Isabella: \"Zoey is a knight or Samuel is a knight\". Logan said that If Zoey is a knave then Logan is a knight. According to Michael, \"Isabella is a knight and Michael is a knight\". William commented, \"Michael is a knight if and only if William is a knight\". So who is a knight and who is a knave?", "names": ["Samuel", "Zoey", "Isabella", "Logan", "Michael", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Samuel is a knave, Zoey is a knight, Isabella is a knight, Logan is a knight, Michael is a knight, and William is a knight.", "solution_text_format": "(1) Samuel is a knave\n(2) Zoey is a knight\n(3) Isabella is a knight\n(4) Logan is a knight\n(5) Michael is a knight\n(6) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Michael is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Zoey is a knight or Samuel is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Isabella is a knave if and only if William is a knave.", "Assume William is a knight. No contradiction is found in their claim that Michael is a knight if and only if William is a knight.", "Michael cannot be a knight, because this would contradict the claim of Samuel that Isabella is a knave if and only if Michael is a knight.", "Michael cannot be a knave, because this would contradict the claim of William that Michael is a knight if and only if William is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Zoey that Isabella is a knave if and only if William is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if William is a knave.", "William cannot be a knight, because this would contradict the false claim of Zoey that Isabella is a knave if and only if William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Michael is a knight if and only if William is a knight.", "Michael cannot be a knight, because this would contradict the claim of Samuel that Isabella is a knave if and only if Michael is a knight.", "Michael cannot be a knave, because this would contradict the false claim of William that Michael is a knight if and only if William is a knight.", "We have exhausted all possibilities for Michael, William, and Zoey, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Zoey is a knight or Samuel is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Michael is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Zoey is a knight or Samuel is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Isabella is a knave if and only if William is a knave.", "Assume William is a knight. No contradiction is found in their claim that Michael is a knight if and only if William is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Isabella is a knight and Michael is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Zoey is a knave then Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 4)), ('<=>', ('lying', 2), ('lying', 5)), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('lying', 1), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('telling-truth', 5)))", "index": 168}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Sophia, James, Isabella, Jacob, and Evelyn. Matthew asserted: \"Evelyn is a knight and Isabella is a knave\". \"James is a knight or James is a knave,\" Sophia mentioned. James stated, \"Matthew is a knight and Jacob is a knight\". \"If Jacob is a knave then Sophia is a knave,\" Isabella declared. Jacob told you that Jacob is a knight. Evelyn said, \"Matthew is not a knight.\" So who is a knight and who is a knave?", "names": ["Matthew", "Sophia", "James", "Isabella", "Jacob", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Matthew is a knave, Sophia is a knight, James is a knave, Isabella is a knight, Jacob is a knight, and Evelyn is a knight.", "solution_text_format": "(1) Matthew is a knave\n(2) Sophia is a knight\n(3) James is a knave\n(4) Isabella is a knight\n(5) Jacob is a knight\n(6) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Evelyn is a knight and Isabella is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Matthew is not a knight.", "Evelyn cannot be a knave, because this would contradict the claim of Matthew that Evelyn is a knight and Isabella is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Evelyn is a knight and Isabella is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Jacob is a knave then Sophia is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Jacob is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that James is a knight or James is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Matthew is a knight and Jacob is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Matthew is a knight and Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 3)), ('or', ('telling-truth', 2), ('lying', 2)), ('and', ('telling-truth', 0), ('telling-truth', 4)), ('->', ('lying', 4), ('lying', 1)), ('telling-truth', 4), ('not', ('telling-truth', 0)))", "index": 169}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Ava, Oliver, William, Chloe, and David. Jacob expressed that If David is a knave then Ava is a knave. Ava asserted: \"David is a knight and David is a knave\". Oliver remarked, \"If William is a knave then David is a knave\". William asserted: \"Jacob is a knave and Oliver is a knight\". According to Chloe, \"Oliver is a knight\". David told you that Ava is a knave. So who is a knight and who is a knave?", "names": ["Jacob", "Ava", "Oliver", "William", "Chloe", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true], "solution_text": "Jacob is a knight, Ava is a knave, Oliver is a knave, William is a knave, Chloe is a knave, and David is a knight.", "solution_text_format": "(1) Jacob is a knight\n(2) Ava is a knave\n(3) Oliver is a knave\n(4) William is a knave\n(5) Chloe is a knave\n(6) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that If David is a knave then Ava is a knave.", "Assume David is a knight. No contradiction is found in their claim that Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that David is a knight and David is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that David is a knight and David is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If William is a knave then David is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Jacob is a knave and Oliver is a knight.", "William cannot be a knave, because this would contradict the claim of Oliver that If William is a knave then David is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that If William is a knave then David is a knave.", "William cannot be a knight, because this would contradict the false claim of Oliver that If William is a knave then David is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Jacob is a knave and Oliver is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Oliver is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 1)), ('and', ('telling-truth', 5), ('lying', 5)), ('->', ('lying', 3), ('lying', 5)), ('and', ('lying', 0), ('telling-truth', 2)), ('telling-truth', 2), ('lying', 1))", "index": 170}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Mason, Jacob, Penelope, Harper, and Emma. James commented, \"Penelope is a knave or Jacob is a knight\". In Mason's words: \"Harper is a knight\". Jacob told you that If Mason is a knave then Mason is a knight. Penelope was heard saying, \"Harper is a knave and Emma is a knave\". According to Harper, \"Emma is a knight or James is a knight\". Emma expressed that If Harper is a knight then James is a knight. So who is a knight and who is a knave?", "names": ["James", "Mason", "Jacob", "Penelope", "Harper", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "James is a knight, Mason is a knight, Jacob is a knight, Penelope is a knave, Harper is a knight, and Emma is a knight.", "solution_text_format": "(1) James is a knight\n(2) Mason is a knight\n(3) Jacob is a knight\n(4) Penelope is a knave\n(5) Harper is a knight\n(6) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Penelope is a knave or Jacob is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Harper is a knave and Emma is a knave.", "Harper cannot be a knight, because this would contradict the claim of Penelope that Harper is a knave and Emma is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that Emma is a knight or James is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Harper is a knave and Emma is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Emma is a knight or James is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Harper is a knight then James is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Mason is a knave then Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 2)), ('telling-truth', 4), ('->', ('lying', 1), ('telling-truth', 1)), ('and', ('lying', 4), ('lying', 5)), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('->', ('telling-truth', 4), ('telling-truth', 0)))", "index": 171}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Mia, Ava, Oliver, Riley, and Jackson. In Olivia's words: \"Mia is a knave if and only if Oliver is a knave\". According to Mia, \"Ava is a knight or Mia is a knight\". According to Ava, \"Riley is a knave or Oliver is a knight\". Oliver said that Mia is a knight or Ava is a knight. In a statement by Riley: \"If Jackson is a knave then Jackson is a knight\". Jackson noted, \"Olivia is a knight if and only if Olivia is a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Mia", "Ava", "Oliver", "Riley", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Olivia is a knight, Mia is a knight, Ava is a knight, Oliver is a knight, Riley is a knave, and Jackson is a knave.", "solution_text_format": "(1) Olivia is a knight\n(2) Mia is a knight\n(3) Ava is a knight\n(4) Oliver is a knight\n(5) Riley is a knave\n(6) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Mia is a knave if and only if Oliver is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Ava is a knight or Mia is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Riley is a knave or Oliver is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Jackson is a knave then Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Olivia is a knight if and only if Olivia is a knave.", "Jackson cannot be a knave, because this would contradict the claim of Riley that If Jackson is a knave then Jackson is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that If Jackson is a knave then Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Riley that If Jackson is a knave then Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Olivia is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Mia is a knight or Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 3)), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('lying', 4), ('telling-truth', 3)), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('lying', 5), ('telling-truth', 5)), ('<=>', ('telling-truth', 0), ('lying', 0)))", "index": 172}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Ava, Aurora, Ella, Logan, and Luke. David told you that Luke is a knight if and only if Ava is a knave. \"If Luke is a knave then Logan is a knight,\" Ava mentioned. Aurora expressed that If David is a knight then Ava is a knight. Ella expressed that Logan is a knave or Luke is a knight. \"Ava is a knight or David is a knight,\" Logan claimed. Luke asserted: \"Aurora is a knave or Logan is a knave\". So who is a knight and who is a knave?", "names": ["David", "Ava", "Aurora", "Ella", "Logan", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "David is a knight, Ava is a knight, Aurora is a knight, Ella is a knave, Logan is a knight, and Luke is a knave.", "solution_text_format": "(1) David is a knight\n(2) Ava is a knight\n(3) Aurora is a knight\n(4) Ella is a knave\n(5) Logan is a knight\n(6) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Luke is a knight if and only if Ava is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Aurora is a knave or Logan is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If David is a knight then Ava is a knight.", "Ava cannot be a knight, because this would contradict the claim of David that Luke is a knight if and only if Ava is a knave.", "Ava cannot be a knave, because this would contradict the false claim of their own that If Luke is a knave then Logan is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that If David is a knight then Ava is a knight.", "Ava cannot be a knight, because this would contradict the claim of David that Luke is a knight if and only if Ava is a knave.", "Ava cannot be a knave, because this would contradict the false claim of their own that If Luke is a knave then Logan is a knight.", "We have exhausted all possibilities for Ava and Aurora, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Aurora is a knave or Logan is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If David is a knight then Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Luke is a knave then Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Ava is a knight or David is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Logan is a knave or Luke is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Logan is a knave or Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 1)), ('->', ('lying', 5), ('telling-truth', 4)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('lying', 4), ('telling-truth', 5)), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('lying', 2), ('lying', 4)))", "index": 173}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Aria, Sebastian, Henry, Ava, and Benjamin. As Abigail put it, \"Aria is a knight if and only if Benjamin is a knave\". Aria told you that Aria is a knight or Benjamin is a knave. \"Ava is a knave or Henry is a knight,\" Sebastian declared. Henry was heard saying, \"Ava is a knight and Benjamin is a knight\". Ava said, \"Benjamin is a knave and Abigail is a knight.\" Benjamin said, \"If Abigail is a knight then Ava is a knight.\" So who is a knight and who is a knave?", "names": ["Abigail", "Aria", "Sebastian", "Henry", "Ava", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Abigail is a knave, Aria is a knight, Sebastian is a knight, Henry is a knave, Ava is a knave, and Benjamin is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Aria is a knight\n(3) Sebastian is a knight\n(4) Henry is a knave\n(5) Ava is a knave\n(6) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Aria is a knight if and only if Benjamin is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Aria is a knight or Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Abigail that Aria is a knight if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If Abigail is a knight then Ava is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Benjamin that If Abigail is a knight then Ava is a knight.", "Ava cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knave and Abigail is a knight.", "We have exhausted all possibilities for Ava and Benjamin, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Aria is a knight or Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Abigail is a knight then Ava is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Abigail is a knight.", "Ava cannot be a knave, because this would contradict the claim of Benjamin that If Abigail is a knight then Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of Abigail that Aria is a knight if and only if Benjamin is a knave.", "We have exhausted all possibilities for Benjamin and Aria, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Benjamin is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Aria is a knight or Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Abigail is a knight then Ava is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Abigail is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Benjamin is a knave and Abigail is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Ava is a knave or Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Ava is a knight and Benjamin is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Ava is a knight and Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 5)), ('or', ('telling-truth', 1), ('lying', 5)), ('or', ('lying', 4), ('telling-truth', 3)), ('and', ('telling-truth', 4), ('telling-truth', 5)), ('and', ('lying', 5), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('telling-truth', 4)))", "index": 174}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Mason, Benjamin, Sofia, Harper, and Aria. Samuel noted, \"Aria is a knight\". Mason noted, \"Benjamin is a knave if and only if Aria is a knight\". According to Benjamin, \"Samuel is a knight or Sofia is a knight\". Sofia commented, \"Aria is a knight or Harper is a knave\". Harper was heard saying, \"Harper is a knight\". Aria was heard saying, \"If Benjamin is a knight then Benjamin is a knave\". So who is a knight and who is a knave?", "names": ["Samuel", "Mason", "Benjamin", "Sofia", "Harper", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Samuel is a knave, Mason is a knight, Benjamin is a knight, Sofia is a knight, Harper is a knave, and Aria is a knave.", "solution_text_format": "(1) Samuel is a knave\n(2) Mason is a knight\n(3) Benjamin is a knight\n(4) Sofia is a knight\n(5) Harper is a knave\n(6) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Benjamin is a knight then Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Aria that If Benjamin is a knight then Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight or Sofia is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Samuel that Aria is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Aria is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Samuel that Aria is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Samuel is a knight or Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Aria is a knight or Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of Sofia that Aria is a knight or Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Harper is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('<=>', ('lying', 2), ('telling-truth', 5)), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('telling-truth', 5), ('lying', 4)), ('telling-truth', 4), ('->', ('telling-truth', 2), ('lying', 2)))", "index": 175}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, William, Aria, Samuel, Lucas, and Mason. As Harper put it, \"Lucas is a knave and Samuel is a knave\". William said that Mason is a knave and Samuel is a knight. Aria expressed that Harper is a knight and Mason is a knight. Samuel stated, \"Aria is not a knave\". Lucas expressed that Mason is a knave or William is a knave. Mason told you that Harper is not a knave. So who is a knight and who is a knave?", "names": ["Harper", "William", "Aria", "Samuel", "Lucas", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false], "solution_text": "Harper is a knave, William is a knave, Aria is a knave, Samuel is a knave, Lucas is a knight, and Mason is a knave.", "solution_text_format": "(1) Harper is a knave\n(2) William is a knave\n(3) Aria is a knave\n(4) Samuel is a knave\n(5) Lucas is a knight\n(6) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Lucas is a knave and Samuel is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Harper that Lucas is a knave and Samuel is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Mason is a knave or William is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Harper is not a knave.", "William cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Samuel is a knight.", "William cannot be a knave, because this would contradict the false claim of Lucas that Mason is a knave or William is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the false claim of Lucas that Mason is a knave or William is a knave.", "We have exhausted all possibilities for Mason and Lucas, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Lucas is a knave and Samuel is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Mason is a knave or William is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Harper is not a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Assume William is a knight. No contradiction is found in their claim that Mason is a knave and Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Mason is a knight.", "Aria cannot be a knave, because this would contradict the claim of Samuel that Aria is not a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the claim of William that Mason is a knave and Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Mason is a knave and Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of William that Mason is a knave and Samuel is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Mason is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Harper is a knight and Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 3)), ('and', ('lying', 5), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('not', ('lying', 2)), ('or', ('lying', 5), ('lying', 1)), ('not', ('lying', 0)))", "index": 176}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Emma, Chloe, Zoey, Alexander, and Ella. In a statement by Michael: \"If Zoey is a knight then Chloe is a knave\". Emma noted, \"Chloe is a knave or Zoey is a knave\". Chloe told you that Michael is a knave or Emma is a knave. As Zoey put it, \"Michael is not a knave\". Alexander stated, \"Chloe is a knave\". According to Ella, \"Chloe is a knight or Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Emma", "Chloe", "Zoey", "Alexander", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Michael is a knight, Emma is a knight, Chloe is a knave, Zoey is a knight, Alexander is a knight, and Ella is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Emma is a knight\n(3) Chloe is a knave\n(4) Zoey is a knight\n(5) Alexander is a knight\n(6) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that If Zoey is a knight then Chloe is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Michael is not a knave.", "Chloe cannot be a knight, because this would contradict the claim of Michael that If Zoey is a knight then Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Michael is a knave or Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Chloe is a knave or Zoey is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Chloe is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Chloe is a knight or Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 2)), ('or', ('lying', 2), ('lying', 3)), ('or', ('lying', 0), ('lying', 1)), ('not', ('lying', 0)), ('lying', 2), ('or', ('telling-truth', 2), ('telling-truth', 4)))", "index": 177}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Chloe, David, Charlotte, Elizabeth, and Olivia. Mia stated, \"Mia is a knight or Olivia is a knave\". Chloe said that Charlotte is a knight. David stated, \"Elizabeth is a knave\". Charlotte said, \"Chloe is a knight if and only if Mia is a knave.\" \"Mia is a knight or Olivia is a knight,\" Elizabeth declared. Olivia was heard saying, \"Charlotte is a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Chloe", "David", "Charlotte", "Elizabeth", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Mia is a knave, Chloe is a knight, David is a knave, Charlotte is a knight, Elizabeth is a knight, and Olivia is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Chloe is a knight\n(3) David is a knave\n(4) Charlotte is a knight\n(5) Elizabeth is a knight\n(6) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Mia is a knight or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Mia is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Charlotte that Chloe is a knight if and only if Mia is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Olivia that Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Olivia that Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Mia is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of Charlotte that Chloe is a knight if and only if Mia is a knave.", "We have exhausted all possibilities for Chloe, Charlotte, and Olivia, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Mia is a knight or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Mia is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume David is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of David that Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Mia is a knight or Olivia is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Mia is a knight or Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('lying', 5)), ('telling-truth', 3), ('lying', 4), ('<=>', ('telling-truth', 1), ('lying', 0)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('telling-truth', 3))", "index": 178}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Lucas, Daniel, Scarlett, Grace, and Samuel. According to Luke, \"If Scarlett is a knave then Luke is a knight\". Lucas asserted: \"If Grace is a knight then Scarlett is a knave\". Daniel was heard saying, \"Lucas is a knave or Luke is a knight\". Scarlett remarked, \"Daniel is a knave\". In a statement by Grace: \"Scarlett is a knight\". \"If Luke is a knight then Daniel is a knave,\" Samuel mentioned. So who is a knight and who is a knave?", "names": ["Luke", "Lucas", "Daniel", "Scarlett", "Grace", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Luke is a knight, Lucas is a knight, Daniel is a knight, Scarlett is a knave, Grace is a knave, and Samuel is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Lucas is a knight\n(3) Daniel is a knight\n(4) Scarlett is a knave\n(5) Grace is a knave\n(6) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that If Scarlett is a knave then Luke is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Scarlett that Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Lucas is a knave or Luke is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Lucas is a knave or Luke is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Grace is a knight then Scarlett is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that If Luke is a knight then Daniel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that If Luke is a knight then Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 0)), ('->', ('telling-truth', 4), ('lying', 3)), ('or', ('lying', 1), ('telling-truth', 0)), ('lying', 2), ('telling-truth', 3), ('->', ('telling-truth', 0), ('lying', 2)))", "index": 179}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Owen, Mia, Benjamin, Matthew, and Isabella. Emily said, \"If Mia is a knave then Isabella is a knave.\" Owen commented, \"Benjamin is a knave\". \"Owen is not a knight,\" Mia claimed. According to Benjamin, \"Matthew is a knave or Benjamin is a knight\". Matthew said, \"If Benjamin is a knave then Isabella is a knight.\" Isabella was heard saying, \"If Owen is a knight then Owen is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Owen", "Mia", "Benjamin", "Matthew", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Emily is a knight, Owen is a knave, Mia is a knight, Benjamin is a knight, Matthew is a knight, and Isabella is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Owen is a knave\n(3) Mia is a knight\n(4) Benjamin is a knight\n(5) Matthew is a knight\n(6) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that If Mia is a knave then Isabella is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of Mia that Owen is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Matthew is a knave or Benjamin is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Benjamin is a knave then Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Owen is a knight then Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 5)), ('lying', 3), ('not', ('telling-truth', 1)), ('or', ('lying', 4), ('telling-truth', 3)), ('->', ('lying', 3), ('telling-truth', 5)), ('->', ('telling-truth', 1), ('lying', 1)))", "index": 180}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Charlotte, James, Lucas, Evelyn, and Amelia. According to Emily, \"If Amelia is a knight then Lucas is a knave\". Charlotte asserted: \"Amelia is a knave\". In James's words: \"Charlotte is not a knight\". Lucas stated, \"Amelia is a knight and Charlotte is a knight\". In Evelyn's words: \"Charlotte is a knight\". In Amelia's words: \"Emily is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Charlotte", "James", "Lucas", "Evelyn", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false], "solution_text": "Emily is a knight, Charlotte is a knight, James is a knave, Lucas is a knave, Evelyn is a knight, and Amelia is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Charlotte is a knight\n(3) James is a knave\n(4) Lucas is a knave\n(5) Evelyn is a knight\n(6) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that If Amelia is a knight then Lucas is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Emily is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Emily is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Amelia is a knight and Charlotte is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Amelia is a knight and Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Amelia is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 3)), ('lying', 5), ('not', ('telling-truth', 1)), ('and', ('telling-truth', 5), ('telling-truth', 1)), ('telling-truth', 1), ('lying', 0))", "index": 181}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Sofia, Ava, Amelia, Abigail, and Liam. In Joseph's words: \"If Ava is a knight then Joseph is a knight\". Sofia expressed that Abigail is a knight or Amelia is a knave. Ava expressed that Abigail is a knave and Amelia is a knight. Amelia stated, \"Joseph is a knave and Liam is a knave\". According to Abigail, \"Ava is a knave if and only if Sofia is a knave\". \"Amelia is not a knave,\" Liam claimed. So who is a knight and who is a knave?", "names": ["Joseph", "Sofia", "Ava", "Amelia", "Abigail", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Joseph is a knight, Sofia is a knight, Ava is a knave, Amelia is a knave, Abigail is a knave, and Liam is a knave.", "solution_text_format": "(1) Joseph is a knight\n(2) Sofia is a knight\n(3) Ava is a knave\n(4) Amelia is a knave\n(5) Abigail is a knave\n(6) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that If Ava is a knight then Joseph is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Abigail is a knave and Amelia is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Ava that Abigail is a knave and Amelia is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Abigail that Ava is a knave if and only if Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Abigail is a knight or Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Joseph is a knave and Liam is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of Sofia that Abigail is a knight or Amelia is a knave.", "We have exhausted all possibilities for Amelia, Sofia, and Abigail, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Abigail is a knave and Amelia is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Ava is a knave if and only if Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Abigail that Ava is a knave if and only if Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Abigail is a knight or Amelia is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Abigail is a knight or Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Sofia that Abigail is a knight or Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Joseph is a knave and Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Amelia is not a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Amelia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('telling-truth', 4), ('lying', 3)), ('and', ('lying', 4), ('telling-truth', 3)), ('and', ('lying', 0), ('lying', 5)), ('<=>', ('lying', 2), ('lying', 1)), ('not', ('lying', 3)))", "index": 182}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Penelope, Mia, Lucas, Sophia, and Michael. According to Oliver, \"Lucas is a knave and Penelope is a knight\". As Penelope put it, \"If Penelope is a knight then Oliver is a knight\". Mia asserted: \"Lucas is not a knight\". Lucas said that Sophia is a knight and Oliver is a knight. \"Michael is a knight or Sophia is a knight\" - Sophia. Michael told you that Oliver is a knight and Penelope is a knave. So who is a knight and who is a knave?", "names": ["Oliver", "Penelope", "Mia", "Lucas", "Sophia", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Oliver is a knight, Penelope is a knight, Mia is a knight, Lucas is a knave, Sophia is a knave, and Michael is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) Penelope is a knight\n(3) Mia is a knight\n(4) Lucas is a knave\n(5) Sophia is a knave\n(6) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Lucas is a knave and Penelope is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Oliver that Lucas is a knave and Penelope is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Sophia is a knight and Oliver is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Lucas that Sophia is a knight and Oliver is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Michael is a knight or Sophia is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Sophia that Michael is a knight or Sophia is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Oliver is a knight and Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Penelope is a knight then Oliver is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Lucas is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 1)), ('->', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('telling-truth', 5), ('telling-truth', 4)), ('and', ('telling-truth', 0), ('lying', 1)))", "index": 183}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Emily, Logan, Daniel, Aiden, and Emma. \"Daniel is a knave if and only if Logan is a knight,\" Abigail claimed. Emily remarked, \"Logan is a knight\". \"If Aiden is a knight then Daniel is a knave\" - Logan. Daniel remarked, \"Logan is not a knight\". Aiden was heard saying, \"Abigail is a knave\". In Emma's words: \"Aiden is a knave and Logan is a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Emily", "Logan", "Daniel", "Aiden", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Abigail is a knight, Emily is a knight, Logan is a knight, Daniel is a knave, Aiden is a knave, and Emma is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) Emily is a knight\n(3) Logan is a knight\n(4) Daniel is a knave\n(5) Aiden is a knave\n(6) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Logan is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Logan is not a knight.", "Logan cannot be a knight, because this would contradict the claim of Abigail that Daniel is a knave if and only if Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that If Aiden is a knight then Daniel is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of Logan that If Aiden is a knight then Daniel is a knave.", "We have exhausted all possibilities for Aiden and Logan, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Logan is not a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Aiden is a knight then Daniel is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Aiden is a knave and Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 2)), ('telling-truth', 2), ('->', ('telling-truth', 4), ('lying', 3)), ('not', ('telling-truth', 2)), ('lying', 0), ('and', ('lying', 4), ('telling-truth', 2)))", "index": 184}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Alexander, Samuel, Noah, Luke, and David. Ella noted, \"Alexander is not a knight\". Alexander commented, \"Ella is a knight or Luke is a knave\". Samuel stated, \"Luke is a knave\". \"If Ella is a knave then Luke is a knave,\" Noah mentioned. \"Noah is a knight and Samuel is a knave\" - Luke. \"Ella is a knave and Ella is a knight,\" David claimed. So who is a knight and who is a knave?", "names": ["Ella", "Alexander", "Samuel", "Noah", "Luke", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Ella is a knave, Alexander is a knight, Samuel is a knight, Noah is a knight, Luke is a knave, and David is a knave.", "solution_text_format": "(1) Ella is a knave\n(2) Alexander is a knight\n(3) Samuel is a knight\n(4) Noah is a knight\n(5) Luke is a knave\n(6) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Ella that Alexander is not a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Luke is a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Ella is a knight or Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Alexander that Ella is a knight or Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Noah is a knight and Samuel is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Ella is a knave then Luke is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Luke is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Ella is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Ella is a knave and Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('or', ('telling-truth', 0), ('lying', 4)), ('lying', 4), ('->', ('lying', 0), ('lying', 4)), ('and', ('telling-truth', 3), ('lying', 2)), ('and', ('lying', 0), ('telling-truth', 0)))", "index": 185}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Zoey, Daniel, Lucas, Ava, Owen, and Amelia. Zoey remarked, \"If Amelia is a knight then Ava is a knight\". Daniel told you that Owen is a knave or Daniel is a knight. In Lucas's words: \"Daniel is not a knight\". Ava stated, \"Zoey is a knave\". According to Owen, \"Owen is a knight or Zoey is a knight\". According to Amelia, \"Daniel is a knight and Zoey is a knight\". So who is a knight and who is a knave?", "names": ["Zoey", "Daniel", "Lucas", "Ava", "Owen", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false], "solution_text": "Zoey is a knight, Daniel is a knave, Lucas is a knight, Ava is a knave, Owen is a knight, and Amelia is a knave.", "solution_text_format": "(1) Zoey is a knight\n(2) Daniel is a knave\n(3) Lucas is a knight\n(4) Ava is a knave\n(5) Owen is a knight\n(6) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that If Amelia is a knight then Ava is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Daniel is a knight and Zoey is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Owen is a knave or Daniel is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Owen is a knight or Zoey is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Ava cannot be a knave, because this would contradict the claim of Zoey that If Amelia is a knight then Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of their own that Owen is a knight or Zoey is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Amelia that Daniel is a knight and Zoey is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Daniel is a knight and Zoey is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Amelia that Daniel is a knight and Zoey is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Owen is a knave or Daniel is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Owen is a knight or Zoey is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Daniel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('telling-truth', 3)), ('or', ('lying', 4), ('telling-truth', 1)), ('not', ('telling-truth', 1)), ('lying', 0), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('telling-truth', 0)))", "index": 186}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Luke, Abigail, Mason, Victoria, and Zoey. In a statement by James: \"Luke is a knight and Mason is a knave\". Luke stated, \"Victoria is a knave or Abigail is a knave\". Abigail expressed that If Victoria is a knight then Abigail is a knight. \"Victoria is a knave or James is a knight,\" Mason claimed. \"If James is a knave then Abigail is a knight,\" Victoria mentioned. \"Luke is a knave and Victoria is a knave\" - Zoey. So who is a knight and who is a knave?", "names": ["James", "Luke", "Abigail", "Mason", "Victoria", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "James is a knave, Luke is a knave, Abigail is a knight, Mason is a knave, Victoria is a knight, and Zoey is a knave.", "solution_text_format": "(1) James is a knave\n(2) Luke is a knave\n(3) Abigail is a knight\n(4) Mason is a knave\n(5) Victoria is a knight\n(6) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Luke is a knight and Mason is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Victoria is a knave or Abigail is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If James is a knave then Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Luke that Victoria is a knave or Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Victoria is a knight then Abigail is a knight.", "Mason cannot be a knight, because this would contradict the claim of James that Luke is a knight and Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that Victoria is a knave or James is a knight.", "We have exhausted all possibilities for Mason and Abigail, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the false claim of their own that If James is a knave then Abigail is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of James that Luke is a knight and Mason is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Luke is a knight and Mason is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Victoria is a knave or Abigail is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If James is a knave then Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Luke that Victoria is a knave or Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the claim of Victoria that If James is a knave then Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that If James is a knave then Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Victoria that If James is a knave then Abigail is a knight.", "Abigail cannot be a knave, because this would contradict the false claim of their own that If Victoria is a knight then Abigail is a knight.", "We have exhausted all possibilities for Abigail and Victoria, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Victoria is a knave or Abigail is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If James is a knave then Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Victoria is a knight then Abigail is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Victoria is a knave or James is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Victoria is a knave or James is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Victoria is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Luke is a knave and Victoria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 3)), ('or', ('lying', 4), ('lying', 2)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('lying', 4), ('telling-truth', 0)), ('->', ('lying', 0), ('telling-truth', 2)), ('and', ('lying', 1), ('lying', 4)))", "index": 187}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Aria, Owen, Evelyn, Benjamin, and Ella. Sophia told you that Sophia is a knight if and only if Evelyn is a knave. In Aria's words: \"Ella is a knave and Aria is a knight\". Owen noted, \"Sophia is a knight\". In a statement by Evelyn: \"Ella is a knight\". Benjamin asserted: \"Sophia is not a knave\". Ella expressed that If Benjamin is a knight then Aria is a knave. So who is a knight and who is a knave?", "names": ["Sophia", "Aria", "Owen", "Evelyn", "Benjamin", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Sophia is a knight, Aria is a knight, Owen is a knight, Evelyn is a knave, Benjamin is a knight, and Ella is a knave.", "solution_text_format": "(1) Sophia is a knight\n(2) Aria is a knight\n(3) Owen is a knight\n(4) Evelyn is a knave\n(5) Benjamin is a knight\n(6) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Sophia that Sophia is a knight if and only if Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Evelyn that Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Aria is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Ella is a knave and Aria is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 3)), ('and', ('lying', 5), ('telling-truth', 1)), ('telling-truth', 0), ('telling-truth', 5), ('not', ('lying', 0)), ('->', ('telling-truth', 4), ('lying', 1)))", "index": 188}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Daniel, Michael, Jacob, Aria, and Benjamin. Alexander said, \"Benjamin is a knight and Jacob is a knight.\" \"If Daniel is a knight then Jacob is a knave,\" Daniel declared. As Michael put it, \"If Jacob is a knight then Alexander is a knave\". \"If Alexander is a knave then Daniel is a knave\" - Jacob. Aria commented, \"Jacob is not a knave\". Benjamin noted, \"Aria is a knave\". So who is a knight and who is a knave?", "names": ["Alexander", "Daniel", "Michael", "Jacob", "Aria", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Alexander is a knave, Daniel is a knight, Michael is a knight, Jacob is a knave, Aria is a knave, and Benjamin is a knight.", "solution_text_format": "(1) Alexander is a knave\n(2) Daniel is a knight\n(3) Michael is a knight\n(4) Jacob is a knave\n(5) Aria is a knave\n(6) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Benjamin is a knight and Jacob is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Benjamin that Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Jacob is not a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Aria that Jacob is not a knave.", "Jacob cannot be a knave, because this would contradict the claim of Alexander that Benjamin is a knight and Jacob is a knight.", "We have exhausted all possibilities for Jacob and Aria, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of Alexander that Benjamin is a knight and Jacob is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Benjamin is a knight and Jacob is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Benjamin that Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Jacob is not a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Alexander that Benjamin is a knight and Jacob is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Alexander is a knave then Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Daniel is a knight then Jacob is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Jacob is a knight then Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('telling-truth', 1), ('lying', 3)), ('->', ('telling-truth', 3), ('lying', 0)), ('->', ('lying', 0), ('lying', 1)), ('not', ('lying', 3)), ('lying', 4))", "index": 189}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Chloe, Victoria, Isabella, Ella, and Emily. Benjamin noted, \"Chloe is not a knight\". Chloe was heard saying, \"Chloe is a knight\". \"Chloe is a knave and Emily is a knave,\" Victoria declared. Isabella told you that Benjamin is a knight. Ella commented, \"Benjamin is not a knave\". Emily asserted: \"Chloe is a knave if and only if Victoria is a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Chloe", "Victoria", "Isabella", "Ella", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true], "solution_text": "Benjamin is a knave, Chloe is a knight, Victoria is a knave, Isabella is a knave, Ella is a knave, and Emily is a knight.", "solution_text_format": "(1) Benjamin is a knave\n(2) Chloe is a knight\n(3) Victoria is a knave\n(4) Isabella is a knave\n(5) Ella is a knave\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of Benjamin that Chloe is not a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Chloe is a knave and Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Victoria that Chloe is a knave and Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave if and only if Victoria is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Chloe is a knave and Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Chloe is a knave if and only if Victoria is a knight.", "Emily cannot be a knave, because this would contradict the false claim of Victoria that Chloe is a knave and Emily is a knave.", "We have exhausted all possibilities for Emily, Victoria, and Chloe, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Chloe is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Emily is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Chloe is a knave and Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Victoria is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Benjamin is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Benjamin is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('telling-truth', 1), ('and', ('lying', 1), ('lying', 5)), ('telling-truth', 0), ('not', ('lying', 0)), ('<=>', ('lying', 1), ('telling-truth', 2)))", "index": 190}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, William, Aria, Elizabeth, Owen, and Lucas. \"If Elizabeth is a knave then Aria is a knave,\" Sophia claimed. \"Owen is a knight or Lucas is a knave,\" William declared. Aria commented, \"Lucas is not a knight\". Elizabeth said that Aria is not a knave. In Owen's words: \"Sophia is a knave if and only if Sophia is a knight\". \"Owen is a knight and Lucas is a knight\" - Lucas. So who is a knight and who is a knave?", "names": ["Sophia", "William", "Aria", "Elizabeth", "Owen", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Sophia is a knight, William is a knight, Aria is a knight, Elizabeth is a knight, Owen is a knave, and Lucas is a knave.", "solution_text_format": "(1) Sophia is a knight\n(2) William is a knight\n(3) Aria is a knight\n(4) Elizabeth is a knight\n(5) Owen is a knave\n(6) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Aria is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Lucas is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of Aria that Lucas is not a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Owen is a knight and Lucas is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Sophia is a knave if and only if Sophia is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Sophia is a knight.", "Assume William is a knight. No contradiction is found in their claim that Owen is a knight or Lucas is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 2)), ('or', ('telling-truth', 4), ('lying', 5)), ('not', ('telling-truth', 5)), ('not', ('lying', 2)), ('<=>', ('lying', 0), ('telling-truth', 0)), ('and', ('telling-truth', 4), ('telling-truth', 5)))", "index": 191}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Benjamin, Sebastian, Grace, Ethan, and Aria. \"Ethan is a knave or Michael is a knight,\" Michael claimed. Benjamin remarked, \"If Michael is a knave then Aria is a knave\". \"Benjamin is a knight\" - Sebastian. According to Grace, \"Sebastian is a knave and Aria is a knight\". Ethan was heard saying, \"Michael is a knight\". As Aria put it, \"Ethan is a knight or Benjamin is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Benjamin", "Sebastian", "Grace", "Ethan", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Michael is a knight, Benjamin is a knight, Sebastian is a knight, Grace is a knave, Ethan is a knight, and Aria is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Benjamin is a knight\n(3) Sebastian is a knight\n(4) Grace is a knave\n(5) Ethan is a knight\n(6) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Ethan is a knave or Michael is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Michael is a knave then Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Ethan is a knight or Benjamin is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Aria is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Sebastian is a knave and Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 0)), ('->', ('lying', 0), ('lying', 5)), ('telling-truth', 1), ('and', ('lying', 2), ('telling-truth', 5)), ('telling-truth', 0), ('or', ('telling-truth', 4), ('telling-truth', 1)))", "index": 192}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Aiden, Sofia, Alexander, Mia, and Zoey. \"If Aiden is a knight then Mia is a knight,\" Lucas declared. Aiden noted, \"Sofia is a knave if and only if Lucas is a knight\". Sofia said that Alexander is a knight or Alexander is a knave. Alexander said, \"Mia is a knave if and only if Sofia is a knave.\" Mia remarked, \"Zoey is not a knight\". Zoey said that Sofia is a knave. So who is a knight and who is a knave?", "names": ["Lucas", "Aiden", "Sofia", "Alexander", "Mia", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Lucas is a knight, Aiden is a knave, Sofia is a knight, Alexander is a knight, Mia is a knight, and Zoey is a knave.", "solution_text_format": "(1) Lucas is a knight\n(2) Aiden is a knave\n(3) Sofia is a knight\n(4) Alexander is a knight\n(5) Mia is a knight\n(6) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that If Aiden is a knight then Mia is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Lucas is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Aiden that Sofia is a knave if and only if Lucas is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight or Alexander is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Lucas is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Alexander is a knight or Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Mia is a knave if and only if Sofia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Mia that Zoey is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('telling-truth', 4)), ('<=>', ('lying', 2), ('telling-truth', 0)), ('or', ('telling-truth', 3), ('lying', 3)), ('<=>', ('lying', 4), ('lying', 2)), ('not', ('telling-truth', 5)), ('lying', 2))", "index": 193}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Ava, Sofia, Sophia, Riley, and David. \"Sofia is not a knight,\" Abigail claimed. \"Sophia is a knave and Ava is a knight,\" Ava mentioned. Sofia said that Riley is not a knight. Sophia noted, \"Sofia is a knave or David is a knave\". Riley asserted: \"Sofia is a knight or Abigail is a knight\". David expressed that Ava is a knave. So who is a knight and who is a knave?", "names": ["Abigail", "Ava", "Sofia", "Sophia", "Riley", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true], "solution_text": "Abigail is a knight, Ava is a knave, Sofia is a knave, Sophia is a knight, Riley is a knight, and David is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) Ava is a knave\n(3) Sofia is a knave\n(4) Sophia is a knight\n(5) Riley is a knight\n(6) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of Abigail that Sofia is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Sofia is a knight or Abigail is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Sophia is a knave and Ava is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Ava that Sophia is a knave and Ava is a knight.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Sofia is a knave or David is a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Sophia is a knave and Ava is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Sofia is a knave or David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('and', ('lying', 3), ('telling-truth', 1)), ('not', ('telling-truth', 4)), ('or', ('lying', 2), ('lying', 5)), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('lying', 1))", "index": 194}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Penelope, Liam, Jacob, Grace, and James. \"Penelope is a knave or Liam is a knave,\" Ella declared. Penelope said that Liam is a knave and James is a knave. Liam commented, \"Penelope is a knave\". \"Grace is a knight or James is a knight,\" Jacob mentioned. In a statement by Grace: \"Ella is a knight or Grace is a knight\". In a statement by James: \"Jacob is a knave or Jacob is a knight\". So who is a knight and who is a knave?", "names": ["Ella", "Penelope", "Liam", "Jacob", "Grace", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Ella is a knight, Penelope is a knave, Liam is a knight, Jacob is a knight, Grace is a knight, and James is a knight.", "solution_text_format": "(1) Ella is a knight\n(2) Penelope is a knave\n(3) Liam is a knight\n(4) Jacob is a knight\n(5) Grace is a knight\n(6) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Penelope is a knave or Liam is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Liam is a knave and James is a knave.", "Liam cannot be a knight, because this would contradict the claim of Ella that Penelope is a knave or Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Penelope is a knave.", "James cannot be a knight, because this would contradict the claim of Penelope that Liam is a knave and James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that Jacob is a knave or Jacob is a knight.", "We have exhausted all possibilities for James and Liam, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Liam is a knave and James is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Penelope is a knave.", "Assume James is a knight. No contradiction is found in their claim that Jacob is a knave or Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Grace is a knight or James is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Ella is a knight or Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('lying', 2)), ('and', ('lying', 2), ('lying', 5)), ('lying', 1), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('or', ('telling-truth', 0), ('telling-truth', 4)), ('or', ('lying', 3), ('telling-truth', 3)))", "index": 195}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, James, Emma, Mason, Ella, and Harper. \"Harper is not a knight,\" Mia mentioned. \"Harper is a knight,\" James claimed. Emma asserted: \"Emma is a knight and Mason is a knight\". Mason stated, \"Emma is a knave if and only if Ella is a knave\". Ella commented, \"Harper is not a knight\". According to Harper, \"Mason is a knight or James is a knave\". So who is a knight and who is a knave?", "names": ["Mia", "James", "Emma", "Mason", "Ella", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true], "solution_text": "Mia is a knave, James is a knight, Emma is a knave, Mason is a knight, Ella is a knave, and Harper is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) James is a knight\n(3) Emma is a knave\n(4) Mason is a knight\n(5) Ella is a knave\n(6) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Harper is not a knight.", "Harper cannot be a knight, because this would contradict the claim of Mia that Harper is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Mason is a knight or James is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Harper that Mason is a knight or James is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Ella is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Mason is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Emma is a knight and Mason is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Harper is not a knight.", "James cannot be a knight, because this would contradict the claim of their own that Harper is a knight.", "James cannot be a knave, because this would contradict the false claim of Harper that Mason is a knight or James is a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of Mason that Emma is a knave if and only if Ella is a knave.", "We have exhausted all possibilities for Ella, Emma, Mason, and Harper, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Harper is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Mason is a knight or James is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Emma is a knave if and only if Ella is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Emma is a knight and Mason is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Harper is not a knight.", "Ella cannot be a knave, because this would contradict the claim of Mason that Emma is a knave if and only if Ella is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Emma is a knight and Mason is a knight.", "Ella cannot be a knight, because this would contradict the claim of Mason that Emma is a knave if and only if Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Harper is not a knight.", "Assume James is a knight. No contradiction is found in their claim that Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('telling-truth', 5), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('lying', 2), ('lying', 4)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 3), ('lying', 1)))", "index": 196}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Samuel, Joseph, Sofia, Olivia, and Zoey. According to Owen, \"Olivia is a knight if and only if Zoey is a knight\". Samuel said that Olivia is not a knave. Joseph said, \"If Zoey is a knight then Sofia is a knave.\" Sofia asserted: \"Olivia is a knave if and only if Joseph is a knave\". As Olivia put it, \"Zoey is a knave\". Zoey asserted: \"Joseph is a knave if and only if Owen is a knight\". So who is a knight and who is a knave?", "names": ["Owen", "Samuel", "Joseph", "Sofia", "Olivia", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true], "solution_text": "Owen is a knave, Samuel is a knave, Joseph is a knight, Sofia is a knave, Olivia is a knave, and Zoey is a knight.", "solution_text_format": "(1) Owen is a knave\n(2) Samuel is a knave\n(3) Joseph is a knight\n(4) Sofia is a knave\n(5) Olivia is a knave\n(6) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Zoey is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Olivia that Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the claim of Owen that Olivia is a knight if and only if Zoey is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Owen that Olivia is a knight if and only if Zoey is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of Olivia that Zoey is a knave.", "We have exhausted all possibilities for Zoey and Olivia, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Zoey is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Owen that Olivia is a knight if and only if Zoey is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Owen is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Zoey that Joseph is a knave if and only if Owen is a knight.", "Joseph cannot be a knave, because this would contradict the false claim of their own that If Zoey is a knight then Sofia is a knave.", "We have exhausted all possibilities for Joseph and Zoey, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Owen is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Zoey is a knight then Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Joseph that If Zoey is a knight then Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Joseph is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Olivia is not a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Olivia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('lying', 4)), ('->', ('telling-truth', 5), ('lying', 3)), ('<=>', ('lying', 4), ('lying', 2)), ('lying', 5), ('<=>', ('lying', 2), ('telling-truth', 0)))", "index": 197}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Chloe, Liam, Joseph, David, and Emma. Ella commented, \"Emma is not a knight\". According to Chloe, \"Joseph is a knave or Chloe is a knight\". \"Joseph is a knight and Ella is a knight,\" Liam claimed. Joseph commented, \"Chloe is not a knave\". David said, \"Emma is a knight and Ella is a knight.\" Emma stated, \"Chloe is a knave\". So who is a knight and who is a knave?", "names": ["Ella", "Chloe", "Liam", "Joseph", "David", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Ella is a knight, Chloe is a knight, Liam is a knight, Joseph is a knight, David is a knave, and Emma is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Chloe is a knight\n(3) Liam is a knight\n(4) Joseph is a knight\n(5) David is a knave\n(6) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Emma is not a knight.", "Emma cannot be a knight, because this would contradict the claim of Ella that Emma is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Joseph is a knave or Chloe is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Joseph is a knight and Ella is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Ella is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Emma is a knight and Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('or', ('lying', 3), ('telling-truth', 1)), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('not', ('lying', 1)), ('and', ('telling-truth', 5), ('telling-truth', 0)), ('lying', 1))", "index": 198}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Noah, Emily, Chloe, David, Luke, and Olivia. In a statement by Noah: \"David is a knight if and only if Emily is a knave\". Emily said, \"Noah is not a knave.\" Chloe stated, \"David is a knave and Emily is a knight\". David noted, \"Noah is not a knave\". Luke stated, \"Olivia is a knave\". Olivia remarked, \"Chloe is not a knight\". So who is a knight and who is a knave?", "names": ["Noah", "Emily", "Chloe", "David", "Luke", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true], "solution_text": "Noah is a knave, Emily is a knave, Chloe is a knave, David is a knave, Luke is a knave, and Olivia is a knight.", "solution_text_format": "(1) Noah is a knave\n(2) Emily is a knave\n(3) Chloe is a knave\n(4) David is a knave\n(5) Luke is a knave\n(6) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that David is a knight if and only if Emily is a knave.", "Assume David is a knight. No contradiction is found in their claim that Noah is not a knave.", "Emily cannot be a knight, because this would contradict the claim of Noah that David is a knight if and only if Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that Noah is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of their own that Noah is not a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that David is a knight if and only if Emily is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Noah is not a knave.", "Assume David is a knave. No contradiction is found in their false claim that Noah is not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Noah that David is a knight if and only if Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Noah is not a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that David is a knave and Emily is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that David is a knave and Emily is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Luke that Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Chloe is not a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Chloe is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 1)), ('not', ('lying', 0)), ('and', ('lying', 3), ('telling-truth', 1)), ('not', ('lying', 0)), ('lying', 5), ('not', ('telling-truth', 2)))", "index": 199}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Ella, Zoey, Emily, Mason, and Olivia. Isabella expressed that Ella is a knave and Emily is a knight. Ella noted, \"Ella is a knight or Emily is a knave\". \"If Ella is a knave then Zoey is a knight,\" Zoey mentioned. In a statement by Emily: \"Mason is a knave if and only if Olivia is a knave\". According to Mason, \"Ella is a knight and Zoey is a knave\". In a statement by Olivia: \"If Isabella is a knave then Ella is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Ella", "Zoey", "Emily", "Mason", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Isabella is a knave, Ella is a knight, Zoey is a knight, Emily is a knight, Mason is a knave, and Olivia is a knave.", "solution_text_format": "(1) Isabella is a knave\n(2) Ella is a knight\n(3) Zoey is a knight\n(4) Emily is a knight\n(5) Mason is a knave\n(6) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Ella is a knave and Emily is a knight.", "Ella cannot be a knight, because this would contradict the claim of Isabella that Ella is a knave and Emily is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Ella is a knight or Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Mason is a knave if and only if Olivia is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Zoey is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Ella is a knight and Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Ella is a knave then Zoey is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Emily that Mason is a knave if and only if Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that If Isabella is a knave then Ella is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Ella is a knave then Zoey is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Emily that Mason is a knave if and only if Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that If Isabella is a knave then Ella is a knave.", "We have exhausted all possibilities for Olivia, Zoey, and Mason, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Isabella that Ella is a knave and Emily is a knight.", "We have exhausted all possibilities for Emily and Ella, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Ella is a knave and Emily is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Ella is a knight or Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Mason is a knave if and only if Olivia is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Ella is a knight and Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Mason that Ella is a knight and Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that If Ella is a knave then Zoey is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Ella is a knight and Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Ella is a knave then Zoey is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Emily that Mason is a knave if and only if Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that If Isabella is a knave then Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 3)), ('or', ('telling-truth', 1), ('lying', 3)), ('->', ('lying', 1), ('telling-truth', 2)), ('<=>', ('lying', 4), ('lying', 5)), ('and', ('telling-truth', 1), ('lying', 2)), ('->', ('lying', 0), ('lying', 1)))", "index": 200}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Emily, Avery, Aurora, Ava, and Sophia. According to Sebastian, \"If Emily is a knave then Ava is a knight\". Emily expressed that Sophia is a knight or Avery is a knave. Avery was heard saying, \"Ava is a knave or Aurora is a knave\". In a statement by Aurora: \"Sophia is a knave and Aurora is a knight\". Ava was heard saying, \"Emily is not a knight\". Sophia was heard saying, \"Avery is a knave or Avery is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "Emily", "Avery", "Aurora", "Ava", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Sebastian is a knight, Emily is a knight, Avery is a knight, Aurora is a knave, Ava is a knave, and Sophia is a knight.", "solution_text_format": "(1) Sebastian is a knight\n(2) Emily is a knight\n(3) Avery is a knight\n(4) Aurora is a knave\n(5) Ava is a knave\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that If Emily is a knave then Ava is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Sophia is a knight or Avery is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Avery is a knave or Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Ava is a knave or Aurora is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Emily is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Emily is not a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Sophia is a knave and Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 4)), ('or', ('telling-truth', 5), ('lying', 2)), ('or', ('lying', 4), ('lying', 3)), ('and', ('lying', 5), ('telling-truth', 3)), ('not', ('telling-truth', 1)), ('or', ('lying', 2), ('telling-truth', 2)))", "index": 201}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Liam, Olivia, Abigail, Henry, and Logan. William expressed that Henry is a knight if and only if William is a knight. In Liam's words: \"Logan is a knight if and only if Olivia is a knight\". \"Logan is a knight or William is a knave\" - Olivia. Abigail stated, \"William is a knight if and only if Olivia is a knave\". Henry said that Liam is a knight and William is a knight. \"Henry is a knight or Olivia is a knight,\" Logan declared. So who is a knight and who is a knave?", "names": ["William", "Liam", "Olivia", "Abigail", "Henry", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "William is a knight, Liam is a knight, Olivia is a knight, Abigail is a knave, Henry is a knight, and Logan is a knight.", "solution_text_format": "(1) William is a knight\n(2) Liam is a knight\n(3) Olivia is a knight\n(4) Abigail is a knave\n(5) Henry is a knight\n(6) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Henry is a knight if and only if William is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Liam is a knight and William is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Logan is a knight if and only if Olivia is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Henry is a knight or Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Logan is a knight or William is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that William is a knight if and only if Olivia is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that William is a knight if and only if Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('<=>', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('telling-truth', 5), ('lying', 0)), ('<=>', ('telling-truth', 0), ('lying', 2)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 4), ('telling-truth', 2)))", "index": 202}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Benjamin, Joseph, Mason, Ava, and David. Emma told you that Benjamin is a knight. Benjamin was heard saying, \"David is a knight\". \"Joseph is a knight or David is a knight,\" Joseph mentioned. According to Mason, \"Benjamin is a knight and Emma is a knave\". \"If Ava is a knight then Joseph is a knave,\" Ava claimed. David stated, \"Benjamin is a knight and Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Emma", "Benjamin", "Joseph", "Mason", "Ava", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false], "solution_text": "Emma is a knave, Benjamin is a knave, Joseph is a knave, Mason is a knave, Ava is a knight, and David is a knave.", "solution_text_format": "(1) Emma is a knave\n(2) Benjamin is a knave\n(3) Joseph is a knave\n(4) Mason is a knave\n(5) Ava is a knight\n(6) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Benjamin is a knight and Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Joseph is a knight or David is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight and Emma is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Benjamin is a knight and Emma is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that If Ava is a knight then Joseph is a knave.", "Ava cannot be a knave, because this would contradict the false claim of their own that If Ava is a knight then Joseph is a knave.", "We have exhausted all possibilities for Ava and Mason, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight or David is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Benjamin that David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of Emma that Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Emma that Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that David is a knight.", "David cannot be a knight, because this would contradict the false claim of Benjamin that David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Benjamin is a knight and Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Joseph is a knight or David is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight and Emma is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Benjamin is a knight and Emma is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that If Ava is a knight then Joseph is a knave.", "Ava cannot be a knave, because this would contradict the false claim of their own that If Ava is a knight then Joseph is a knave.", "We have exhausted all possibilities for Ava and Mason, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Joseph is a knight or David is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight and Emma is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Benjamin is a knight and Emma is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Ava is a knight then Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('telling-truth', 5), ('or', ('telling-truth', 2), ('telling-truth', 5)), ('and', ('telling-truth', 1), ('lying', 0)), ('->', ('telling-truth', 4), ('lying', 2)), ('and', ('telling-truth', 1), ('telling-truth', 2)))", "index": 203}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Mia, Lily, Ava, Isabella, and Aiden. Alexander commented, \"Isabella is not a knave\". As Mia put it, \"Alexander is a knight if and only if Isabella is a knight\". \"Alexander is a knave,\" Lily mentioned. As Ava put it, \"If Aiden is a knight then Mia is a knave\". \"Aiden is a knight or Aiden is a knave,\" Isabella declared. Aiden asserted: \"Mia is a knight\". So who is a knight and who is a knave?", "names": ["Alexander", "Mia", "Lily", "Ava", "Isabella", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "Alexander is a knight, Mia is a knight, Lily is a knave, Ava is a knave, Isabella is a knight, and Aiden is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Mia is a knight\n(3) Lily is a knave\n(4) Ava is a knave\n(5) Isabella is a knight\n(6) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Aiden is a knight or Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Isabella is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Alexander is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that If Aiden is a knight then Mia is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that If Aiden is a knight then Mia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('lying', 0), ('->', ('telling-truth', 5), ('lying', 1)), ('or', ('telling-truth', 5), ('lying', 5)), ('telling-truth', 1))", "index": 204}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Jacob, Luke, Michael, Owen, and Avery. In a statement by Lily: \"If Jacob is a knave then Avery is a knave\". Jacob stated, \"Lily is not a knight\". Luke said, \"Michael is a knight.\" In Michael's words: \"Lily is not a knave\". Owen remarked, \"Avery is a knight and Lily is a knight\". Avery noted, \"Luke is a knave if and only if Lily is a knight\". So who is a knight and who is a knave?", "names": ["Lily", "Jacob", "Luke", "Michael", "Owen", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false], "solution_text": "Lily is a knight, Jacob is a knave, Luke is a knight, Michael is a knight, Owen is a knave, and Avery is a knave.", "solution_text_format": "(1) Lily is a knight\n(2) Jacob is a knave\n(3) Luke is a knight\n(4) Michael is a knight\n(5) Owen is a knave\n(6) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that If Jacob is a knave then Avery is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Lily is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Lily that If Jacob is a knave then Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Lily is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Lily is not a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Lily is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Avery is a knight and Lily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('lying', 5)), ('not', ('telling-truth', 0)), ('telling-truth', 3), ('not', ('lying', 0)), ('and', ('telling-truth', 5), ('telling-truth', 0)), ('<=>', ('lying', 2), ('telling-truth', 0)))", "index": 205}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Noah, Victoria, Ella, Amelia, and Ethan. Oliver stated, \"Ella is a knave or Amelia is a knight\". In Noah's words: \"Oliver is not a knave\". \"Noah is a knave if and only if Amelia is a knave,\" Victoria mentioned. Ella stated, \"Victoria is a knight or Ella is a knight\". In a statement by Amelia: \"Oliver is a knight and Victoria is a knave\". As Ethan put it, \"Victoria is a knave and Victoria is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Noah", "Victoria", "Ella", "Amelia", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Oliver is a knave, Noah is a knave, Victoria is a knight, Ella is a knight, Amelia is a knave, and Ethan is a knave.", "solution_text_format": "(1) Oliver is a knave\n(2) Noah is a knave\n(3) Victoria is a knight\n(4) Ella is a knight\n(5) Amelia is a knave\n(6) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Ella is a knave or Amelia is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Victoria is a knight or Ella is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Noah is a knave if and only if Amelia is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Oliver is a knight and Victoria is a knave.", "Amelia cannot be a knave, because this would contradict the claim of Oliver that Ella is a knave or Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of their own that Oliver is not a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Amelia is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Victoria that Noah is a knave if and only if Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the claim of Oliver that Ella is a knave or Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of their own that Oliver is not a knave.", "We have exhausted all possibilities for Noah and Victoria, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Victoria is a knight or Ella is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Ella that Victoria is a knight or Ella is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Amelia is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Victoria that Noah is a knave if and only if Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Oliver is a knight and Victoria is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of their own that Oliver is not a knave.", "We have exhausted all possibilities for Noah, Victoria, and Ella, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Ella is a knave or Amelia is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Victoria is a knight or Ella is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Noah is a knave if and only if Amelia is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Oliver is not a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Oliver is not a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Oliver that Ella is a knave or Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Oliver is a knight and Victoria is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Victoria is a knave and Victoria is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Victoria is a knave and Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 4)), ('not', ('lying', 0)), ('<=>', ('lying', 1), ('lying', 4)), ('or', ('telling-truth', 2), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('lying', 2)), ('and', ('lying', 2), ('telling-truth', 2)))", "index": 206}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Charlotte, Ella, Jackson, Owen, and Amelia. Ava stated, \"Charlotte is a knave and Owen is a knave\". \"Ava is not a knave,\" Charlotte claimed. Ella said, \"Amelia is a knave if and only if Jackson is a knave.\" According to Jackson, \"If Charlotte is a knight then Owen is a knave\". Owen expressed that Charlotte is a knave if and only if Ava is a knave. Amelia expressed that Charlotte is not a knight. So who is a knight and who is a knave?", "names": ["Ava", "Charlotte", "Ella", "Jackson", "Owen", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Ava is a knave, Charlotte is a knave, Ella is a knight, Jackson is a knight, Owen is a knight, and Amelia is a knight.", "solution_text_format": "(1) Ava is a knave\n(2) Charlotte is a knave\n(3) Ella is a knight\n(4) Jackson is a knight\n(5) Owen is a knight\n(6) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Charlotte is a knave and Owen is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Ava that Charlotte is a knave and Owen is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Ava is not a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Charlotte is a knave and Owen is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Ava is not a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Ava is not a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Ava is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Jackson is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Charlotte is a knight then Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('lying', 4)), ('not', ('lying', 0)), ('<=>', ('lying', 5), ('lying', 3)), ('->', ('telling-truth', 1), ('lying', 4)), ('<=>', ('lying', 1), ('lying', 0)), ('not', ('telling-truth', 1)))", "index": 207}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Elizabeth, Jackson, Emma, Amelia, and Sebastian. William expressed that Jackson is a knight. In Elizabeth's words: \"Amelia is a knight or Emma is a knave\". In Jackson's words: \"Sebastian is a knight or William is a knave\". According to Emma, \"Elizabeth is a knight or Sebastian is a knave\". Amelia stated, \"Jackson is a knight if and only if Emma is a knight\". As Sebastian put it, \"Elizabeth is a knight or Elizabeth is a knave\". So who is a knight and who is a knave?", "names": ["William", "Elizabeth", "Jackson", "Emma", "Amelia", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "William is a knight, Elizabeth is a knight, Jackson is a knight, Emma is a knight, Amelia is a knight, and Sebastian is a knight.", "solution_text_format": "(1) William is a knight\n(2) Elizabeth is a knight\n(3) Jackson is a knight\n(4) Emma is a knight\n(5) Amelia is a knight\n(6) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Sebastian is a knight or William is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Elizabeth is a knight or Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Amelia is a knight or Emma is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Elizabeth is a knight or Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('or', ('telling-truth', 4), ('lying', 3)), ('or', ('telling-truth', 5), ('lying', 0)), ('or', ('telling-truth', 1), ('lying', 5)), ('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('or', ('telling-truth', 1), ('lying', 1)))", "index": 208}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Benjamin, Victoria, Sophia, Riley, and Isabella. Emily said that Victoria is a knave if and only if Benjamin is a knight. In a statement by Benjamin: \"If Sophia is a knight then Sophia is a knave\". According to Victoria, \"Benjamin is a knave\". Sophia asserted: \"If Emily is a knight then Isabella is a knave\". Riley stated, \"If Emily is a knight then Victoria is a knight\". Isabella stated, \"Emily is not a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Benjamin", "Victoria", "Sophia", "Riley", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true], "solution_text": "Emily is a knight, Benjamin is a knight, Victoria is a knave, Sophia is a knave, Riley is a knave, and Isabella is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Benjamin is a knight\n(3) Victoria is a knave\n(4) Sophia is a knave\n(5) Riley is a knave\n(6) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Benjamin is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Emily that Victoria is a knave if and only if Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If Sophia is a knight then Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Emily is a knight then Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Sophia that If Emily is a knight then Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Emily is not a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the false claim of Benjamin that If Sophia is a knight then Sophia is a knave.", "We have exhausted all possibilities for Sophia and Benjamin, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Sophia is a knight then Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Benjamin that If Sophia is a knight then Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Emily is a knight then Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Emily is not a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that If Emily is a knight then Victoria is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that If Emily is a knight then Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 1)), ('->', ('telling-truth', 3), ('lying', 3)), ('lying', 1), ('->', ('telling-truth', 0), ('lying', 5)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('not', ('lying', 0)))", "index": 209}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Isabella, Avery, Olivia, William, and Noah. Aiden said, \"Noah is a knave and Avery is a knave.\" As Isabella put it, \"Aiden is a knave if and only if Noah is a knave\". In Avery's words: \"Noah is a knight\". Olivia told you that Avery is a knight if and only if Noah is a knave. William asserted: \"If Avery is a knave then Noah is a knave\". In Noah's words: \"William is a knight and Isabella is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Isabella", "Avery", "Olivia", "William", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true], "solution_text": "Aiden is a knave, Isabella is a knave, Avery is a knight, Olivia is a knave, William is a knight, and Noah is a knight.", "solution_text_format": "(1) Aiden is a knave\n(2) Isabella is a knave\n(3) Avery is a knight\n(4) Olivia is a knave\n(5) William is a knight\n(6) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Noah is a knave and Avery is a knave.", "Noah cannot be a knight, because this would contradict the claim of Aiden that Noah is a knave and Avery is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that William is a knight and Isabella is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Avery is a knave then Noah is a knave.", "Avery cannot be a knight, because this would contradict the claim of Aiden that Noah is a knave and Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Noah is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Aiden is a knave if and only if Noah is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of Noah that William is a knight and Isabella is a knave.", "We have exhausted all possibilities for Isabella and Avery, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of their own that If Avery is a knave then Noah is a knave.", "We have exhausted all possibilities for William and Noah, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Noah is a knave and Avery is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that William is a knight and Isabella is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Avery is a knave then Noah is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Noah is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Aiden is a knave if and only if Noah is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Noah is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Avery is a knight if and only if Noah is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('lying', 2)), ('<=>', ('lying', 0), ('lying', 5)), ('telling-truth', 5), ('<=>', ('telling-truth', 2), ('lying', 5)), ('->', ('lying', 2), ('lying', 5)), ('and', ('telling-truth', 4), ('lying', 1)))", "index": 210}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Isabella, Zoey, Sophia, Evelyn, and Samuel. \"Zoey is a knave or Zoey is a knight,\" Michael claimed. Isabella asserted: \"If Sophia is a knight then Evelyn is a knave\". In a statement by Zoey: \"Isabella is a knight or Evelyn is a knave\". Sophia told you that Evelyn is a knave or Samuel is a knave. \"Zoey is not a knight,\" Evelyn declared. Samuel asserted: \"Zoey is a knave\". So who is a knight and who is a knave?", "names": ["Michael", "Isabella", "Zoey", "Sophia", "Evelyn", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Michael is a knight, Isabella is a knight, Zoey is a knight, Sophia is a knight, Evelyn is a knave, and Samuel is a knave.", "solution_text_format": "(1) Michael is a knight\n(2) Isabella is a knight\n(3) Zoey is a knight\n(4) Sophia is a knight\n(5) Evelyn is a knave\n(6) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Zoey is a knave or Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Isabella is a knight or Evelyn is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Sophia is a knight then Evelyn is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Evelyn is a knave or Samuel is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Isabella that If Sophia is a knight then Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 2)), ('->', ('telling-truth', 3), ('lying', 4)), ('or', ('telling-truth', 1), ('lying', 4)), ('or', ('lying', 4), ('lying', 5)), ('not', ('telling-truth', 2)), ('lying', 2))", "index": 211}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Sebastian, Liam, Aiden, Lily, and Scarlett. Grace remarked, \"Scarlett is a knave and Scarlett is a knight\". In a statement by Sebastian: \"Aiden is a knight and Scarlett is a knight\". As Liam put it, \"Liam is a knight or Lily is a knave\". Aiden told you that Scarlett is a knight or Scarlett is a knave. \"Liam is a knight and Sebastian is a knight,\" Lily claimed. Scarlett asserted: \"If Grace is a knave then Aiden is a knight\". So who is a knight and who is a knave?", "names": ["Grace", "Sebastian", "Liam", "Aiden", "Lily", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Grace is a knave, Sebastian is a knight, Liam is a knight, Aiden is a knight, Lily is a knight, and Scarlett is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Sebastian is a knight\n(3) Liam is a knight\n(4) Aiden is a knight\n(5) Lily is a knight\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Grace cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave and Scarlett is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Scarlett is a knave and Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Grace is a knave then Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Scarlett is a knight or Scarlett is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Aiden is a knight and Scarlett is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight or Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Liam is a knight and Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 5)), ('and', ('telling-truth', 3), ('telling-truth', 5)), ('or', ('telling-truth', 2), ('lying', 4)), ('or', ('telling-truth', 5), ('lying', 5)), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('lying', 0), ('telling-truth', 3)))", "index": 212}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Penelope, Benjamin, Sebastian, Riley, and Olivia. In a statement by Mason: \"Riley is a knight\". Penelope commented, \"If Riley is a knight then Mason is a knave\". \"Mason is a knave,\" Benjamin mentioned. According to Sebastian, \"Olivia is not a knight\". Riley asserted: \"If Benjamin is a knight then Sebastian is a knight\". Olivia remarked, \"Penelope is a knave if and only if Sebastian is a knight\". So who is a knight and who is a knave?", "names": ["Mason", "Penelope", "Benjamin", "Sebastian", "Riley", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Mason is a knave, Penelope is a knight, Benjamin is a knight, Sebastian is a knave, Riley is a knave, and Olivia is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Penelope is a knight\n(3) Benjamin is a knight\n(4) Sebastian is a knave\n(5) Riley is a knave\n(6) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Benjamin is a knight then Sebastian is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Mason is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Mason is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Olivia is not a knight.", "Olivia cannot be a knight, because this would contradict the claim of Sebastian that Olivia is not a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Sebastian is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that If Riley is a knight then Mason is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of Olivia that Penelope is a knave if and only if Sebastian is a knight.", "We have exhausted all possibilities for Penelope and Olivia, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Olivia is not a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Sebastian is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that If Riley is a knight then Mason is a knave.", "Penelope cannot be a knave, because this would contradict the claim of Olivia that Penelope is a knave if and only if Sebastian is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of Sebastian that Olivia is not a knight.", "We have exhausted all possibilities for Olivia, Sebastian, and Benjamin, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the claim of Mason that Riley is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Riley is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Mason that Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Sebastian is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Mason is a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Riley that If Benjamin is a knight then Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Olivia is not a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Sebastian is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Riley is a knight then Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('->', ('telling-truth', 4), ('lying', 0)), ('lying', 0), ('not', ('telling-truth', 5)), ('->', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('lying', 1), ('telling-truth', 3)))", "index": 213}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Harper, Avery, Olivia, Matthew, and Amelia. In Lily's words: \"If Avery is a knight then Amelia is a knight\". Harper told you that Lily is not a knight. Avery noted, \"Harper is a knave or Olivia is a knave\". Olivia told you that If Lily is a knave then Amelia is a knight. Matthew told you that Olivia is a knight if and only if Amelia is a knight. Amelia stated, \"Avery is not a knave\". So who is a knight and who is a knave?", "names": ["Lily", "Harper", "Avery", "Olivia", "Matthew", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Lily is a knight, Harper is a knave, Avery is a knight, Olivia is a knight, Matthew is a knight, and Amelia is a knight.", "solution_text_format": "(1) Lily is a knight\n(2) Harper is a knave\n(3) Avery is a knight\n(4) Olivia is a knight\n(5) Matthew is a knight\n(6) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that If Avery is a knight then Amelia is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Harper is a knave or Olivia is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Lily is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Lily is a knave then Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Avery is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('telling-truth', 0)), ('or', ('lying', 1), ('lying', 3)), ('->', ('lying', 0), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('telling-truth', 5)), ('not', ('lying', 2)))", "index": 214}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Isabella, Ethan, Amelia, Mason, and William. \"William is a knave or Mason is a knave,\" Aria declared. \"William is a knight,\" Isabella mentioned. In Ethan's words: \"Mason is a knight\". \"Ethan is a knave\" - Amelia. \"Aria is a knave and William is a knave\" - Mason. William said that Isabella is a knave or Isabella is a knight. So who is a knight and who is a knave?", "names": ["Aria", "Isabella", "Ethan", "Amelia", "Mason", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Aria is a knight, Isabella is a knight, Ethan is a knave, Amelia is a knight, Mason is a knave, and William is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) Isabella is a knight\n(3) Ethan is a knave\n(4) Amelia is a knight\n(5) Mason is a knave\n(6) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that William is a knave or Mason is a knave.", "Assume William is a knight. No contradiction is found in their claim that Isabella is a knave or Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that William is a knight.", "Mason cannot be a knight, because this would contradict the claim of Aria that William is a knave or Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Aria is a knave and William is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Mason is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Mason is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('lying', 4)), ('telling-truth', 5), ('telling-truth', 4), ('lying', 2), ('and', ('lying', 0), ('lying', 5)), ('or', ('lying', 1), ('telling-truth', 1)))", "index": 215}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Liam, Zoey, Isabella, Mason, and Henry. Joseph asserted: \"Isabella is a knight and Henry is a knave\". In a statement by Liam: \"Zoey is a knight\". As Zoey put it, \"Isabella is not a knave\". \"If Henry is a knight then Mason is a knight,\" Isabella mentioned. Mason commented, \"Joseph is a knight\". Henry said, \"If Mason is a knave then Liam is a knave.\" So who is a knight and who is a knave?", "names": ["Joseph", "Liam", "Zoey", "Isabella", "Mason", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true], "solution_text": "Joseph is a knave, Liam is a knave, Zoey is a knave, Isabella is a knave, Mason is a knave, and Henry is a knight.", "solution_text_format": "(1) Joseph is a knave\n(2) Liam is a knave\n(3) Zoey is a knave\n(4) Isabella is a knave\n(5) Mason is a knave\n(6) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Isabella is a knight and Henry is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Henry is a knight then Mason is a knight.", "Henry cannot be a knight, because this would contradict the claim of Joseph that Isabella is a knight and Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that If Mason is a knave then Liam is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Henry that If Mason is a knave then Liam is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight.", "We have exhausted all possibilities for Mason and Henry, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Joseph that Isabella is a knight and Henry is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Isabella is a knight and Henry is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Henry is a knight then Mason is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Mason is a knave then Liam is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Joseph is a knight.", "Mason cannot be a knave, because this would contradict the claim of Isabella that If Henry is a knight then Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the false claim of Joseph that Isabella is a knight and Henry is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Henry is a knight then Mason is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Mason is a knave then Liam is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Isabella that If Henry is a knight then Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Liam cannot be a knight, because this would contradict the claim of Henry that If Mason is a knave then Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Zoey is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Liam that Zoey is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Isabella is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 5)), ('telling-truth', 2), ('not', ('lying', 3)), ('->', ('telling-truth', 5), ('telling-truth', 4)), ('telling-truth', 0), ('->', ('lying', 4), ('lying', 1)))", "index": 216}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Grace, Penelope, Michael, Noah, and Evelyn. Aiden said, \"Noah is a knight.\" In a statement by Grace: \"Noah is not a knight\". According to Penelope, \"Noah is not a knave\". \"Penelope is not a knight,\" Michael mentioned. Noah expressed that If Aiden is a knight then Penelope is a knight. Evelyn was heard saying, \"Evelyn is a knight and Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Grace", "Penelope", "Michael", "Noah", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false], "solution_text": "Aiden is a knight, Grace is a knave, Penelope is a knight, Michael is a knave, Noah is a knight, and Evelyn is a knave.", "solution_text_format": "(1) Aiden is a knight\n(2) Grace is a knave\n(3) Penelope is a knight\n(4) Michael is a knave\n(5) Noah is a knight\n(6) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Aiden is a knight then Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Noah is not a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Noah is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Penelope is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight and Penelope is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Evelyn is a knight and Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('not', ('telling-truth', 4)), ('not', ('lying', 4)), ('not', ('telling-truth', 2)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('and', ('telling-truth', 5), ('lying', 2)))", "index": 217}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Amelia, Joseph, Riley, Victoria, and James. Isabella told you that If Amelia is a knave then Joseph is a knave. Amelia was heard saying, \"Victoria is a knave\". Joseph said that Isabella is a knight or James is a knight. Riley told you that Isabella is a knight and Joseph is a knight. Victoria commented, \"Riley is not a knight\". James expressed that Amelia is a knave and Isabella is a knight. So who is a knight and who is a knave?", "names": ["Isabella", "Amelia", "Joseph", "Riley", "Victoria", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Isabella is a knight, Amelia is a knight, Joseph is a knight, Riley is a knight, Victoria is a knave, and James is a knave.", "solution_text_format": "(1) Isabella is a knight\n(2) Amelia is a knight\n(3) Joseph is a knight\n(4) Riley is a knight\n(5) Victoria is a knave\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that If Amelia is a knave then Joseph is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Amelia that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Isabella is a knight and Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Isabella is a knight or James is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Isabella is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Amelia is a knave and Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('lying', 2)), ('lying', 4), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('telling-truth', 2)), ('not', ('telling-truth', 3)), ('and', ('lying', 1), ('telling-truth', 0)))", "index": 218}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Emily, Owen, Ella, Aria, and Riley. As Logan put it, \"Owen is a knight\". \"Logan is a knave and Logan is a knight,\" Emily claimed. In a statement by Owen: \"Logan is a knave and Riley is a knight\". According to Ella, \"Riley is a knight if and only if Emily is a knave\". Aria expressed that Logan is not a knave. Riley said that Emily is a knight or Riley is a knight. So who is a knight and who is a knave?", "names": ["Logan", "Emily", "Owen", "Ella", "Aria", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false], "solution_text": "Logan is a knave, Emily is a knave, Owen is a knave, Ella is a knave, Aria is a knave, and Riley is a knave.", "solution_text_format": "(1) Logan is a knave\n(2) Emily is a knave\n(3) Owen is a knave\n(4) Ella is a knave\n(5) Aria is a knave\n(6) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Riley is a knight.", "Owen cannot be a knave, because this would contradict the claim of Logan that Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Owen is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Logan that Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Logan is a knave and Riley is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Owen that Logan is a knave and Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Emily is a knight or Riley is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Logan is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Logan is a knave and Logan is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Emily is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Emily is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Logan is not a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Logan is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('and', ('lying', 0), ('telling-truth', 0)), ('and', ('lying', 0), ('telling-truth', 5)), ('<=>', ('telling-truth', 5), ('lying', 1)), ('not', ('lying', 0)), ('or', ('telling-truth', 1), ('telling-truth', 5)))", "index": 219}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Henry, Jack, Jacob, Evelyn, and Benjamin. Ethan asserted: \"Benjamin is a knight and Evelyn is a knave\". Henry noted, \"If Jacob is a knight then Jack is a knight\". \"If Benjamin is a knave then Henry is a knight,\" Jack declared. Jacob was heard saying, \"Jack is a knave if and only if Jack is a knight\". \"If Jacob is a knight then Jack is a knight\" - Evelyn. Benjamin expressed that If Jack is a knight then Jack is a knave. So who is a knight and who is a knave?", "names": ["Ethan", "Henry", "Jack", "Jacob", "Evelyn", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false], "solution_text": "Ethan is a knave, Henry is a knight, Jack is a knight, Jacob is a knave, Evelyn is a knight, and Benjamin is a knave.", "solution_text_format": "(1) Ethan is a knave\n(2) Henry is a knight\n(3) Jack is a knight\n(4) Jacob is a knave\n(5) Evelyn is a knight\n(6) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Benjamin is a knight and Evelyn is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Jack is a knight then Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Benjamin that If Jack is a knight then Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that If Benjamin is a knave then Henry is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of Ethan that Benjamin is a knight and Evelyn is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Benjamin is a knight and Evelyn is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Jack is a knight then Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Benjamin that If Jack is a knight then Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that If Benjamin is a knave then Henry is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If Jack is a knight then Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Benjamin is a knave then Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Jacob is a knight then Jack is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Jack is a knave if and only if Jack is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Jack is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Jacob is a knight then Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 4)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('->', ('lying', 5), ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 2)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('->', ('telling-truth', 2), ('lying', 2)))", "index": 220}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Mia, Oliver, Avery, Michael, and Olivia. Daniel noted, \"Olivia is a knave if and only if Olivia is a knight\". \"Michael is a knave if and only if Olivia is a knave,\" Mia mentioned. \"Olivia is a knave,\" Oliver claimed. \"Mia is a knave\" - Avery. Michael said, \"Oliver is a knight.\" Olivia asserted: \"Avery is a knave\". So who is a knight and who is a knave?", "names": ["Daniel", "Mia", "Oliver", "Avery", "Michael", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Daniel is a knave, Mia is a knave, Oliver is a knight, Avery is a knight, Michael is a knight, and Olivia is a knave.", "solution_text_format": "(1) Daniel is a knave\n(2) Mia is a knave\n(3) Oliver is a knight\n(4) Avery is a knight\n(5) Michael is a knight\n(6) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Daniel cannot be a knight, because this would contradict the claim of their own that Olivia is a knave if and only if Olivia is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Olivia that Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Michael is a knave if and only if Olivia is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Oliver cannot be a knave, because this would contradict the claim of Michael that Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Mia that Michael is a knave if and only if Olivia is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of Avery that Mia is a knave.", "We have exhausted all possibilities for Mia and Avery, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of Avery that Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Olivia is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('telling-truth', 5)), ('<=>', ('lying', 4), ('lying', 5)), ('lying', 5), ('lying', 1), ('telling-truth', 2), ('lying', 3))", "index": 221}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Noah, Charlotte, Aurora, Isabella, and Luke. Grace expressed that Charlotte is a knave and Aurora is a knight. \"Grace is a knight and Grace is a knave,\" Noah declared. \"Aurora is a knave or Luke is a knight,\" Charlotte claimed. Aurora expressed that Charlotte is a knave or Isabella is a knight. \"Noah is a knave,\" Isabella declared. \"Isabella is a knight\" - Luke. So who is a knight and who is a knave?", "names": ["Grace", "Noah", "Charlotte", "Aurora", "Isabella", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Grace is a knave, Noah is a knave, Charlotte is a knight, Aurora is a knight, Isabella is a knight, and Luke is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Noah is a knave\n(3) Charlotte is a knight\n(4) Aurora is a knight\n(5) Isabella is a knight\n(6) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Charlotte is a knave and Aurora is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Grace that Charlotte is a knave and Aurora is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Aurora is a knave or Luke is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Charlotte is a knave or Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Grace is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Grace is a knight and Grace is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Charlotte that Aurora is a knave or Luke is a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that Isabella is a knight.", "We have exhausted all possibilities for Luke and Noah, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Grace is a knave.", "Noah cannot be a knave, because this would contradict the false claim of Isabella that Noah is a knave.", "We have exhausted all possibilities for Noah and Isabella, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Grace that Charlotte is a knave and Aurora is a knight.", "We have exhausted all possibilities for Aurora and Charlotte, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Charlotte is a knave and Aurora is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Aurora is a knave or Luke is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Charlotte is a knave or Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Grace is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Grace is a knight and Grace is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('lying', 0)), ('or', ('lying', 3), ('telling-truth', 5)), ('or', ('lying', 2), ('telling-truth', 4)), ('lying', 1), ('telling-truth', 4))", "index": 222}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Jacob, William, Harper, Amelia, and Liam. In a statement by Charlotte: \"If Liam is a knave then William is a knave\". As Jacob put it, \"Charlotte is a knave and Liam is a knave\". William expressed that Amelia is a knave or Charlotte is a knight. \"William is not a knight\" - Harper. In a statement by Amelia: \"William is not a knave\". Liam expressed that If Jacob is a knave then Liam is a knight. So who is a knight and who is a knave?", "names": ["Charlotte", "Jacob", "William", "Harper", "Amelia", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Charlotte is a knight, Jacob is a knave, William is a knight, Harper is a knave, Amelia is a knight, and Liam is a knight.", "solution_text_format": "(1) Charlotte is a knight\n(2) Jacob is a knave\n(3) William is a knight\n(4) Harper is a knave\n(5) Amelia is a knight\n(6) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that If Liam is a knave then William is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Jacob is a knave then Liam is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave and Liam is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Charlotte is a knave and Liam is a knave.", "Assume William is a knight. No contradiction is found in their claim that Amelia is a knave or Charlotte is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that William is not a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that William is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that William is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 2)), ('and', ('lying', 0), ('lying', 5)), ('or', ('lying', 4), ('telling-truth', 0)), ('not', ('telling-truth', 2)), ('not', ('lying', 2)), ('->', ('lying', 1), ('telling-truth', 5)))", "index": 223}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Zoey, Sebastian, Luke, Sofia, and Noah. As Joseph put it, \"Sebastian is a knave or Luke is a knight\". According to Zoey, \"If Noah is a knight then Sofia is a knave\". Sebastian said that If Joseph is a knight then Luke is a knave. Luke told you that Joseph is a knight or Zoey is a knight. Sofia said that Zoey is a knight and Zoey is a knave. In Noah's words: \"Sofia is a knight and Sebastian is a knave\". So who is a knight and who is a knave?", "names": ["Joseph", "Zoey", "Sebastian", "Luke", "Sofia", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Joseph is a knight, Zoey is a knight, Sebastian is a knave, Luke is a knight, Sofia is a knave, and Noah is a knave.", "solution_text_format": "(1) Joseph is a knight\n(2) Zoey is a knight\n(3) Sebastian is a knave\n(4) Luke is a knight\n(5) Sofia is a knave\n(6) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Sebastian is a knave or Luke is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Joseph is a knight then Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Sebastian that If Joseph is a knight then Luke is a knave.", "Luke cannot be a knave, because this would contradict the claim of Joseph that Sebastian is a knave or Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Joseph is a knight then Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Joseph is a knight or Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Noah is a knight then Sofia is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Sofia is a knight and Sebastian is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Zoey that If Noah is a knight then Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the claim of Noah that Sofia is a knight and Sebastian is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Sofia is a knight and Sebastian is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Zoey is a knight and Zoey is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Zoey is a knight and Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 3)), ('->', ('telling-truth', 5), ('lying', 4)), ('->', ('telling-truth', 0), ('lying', 3)), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('and', ('telling-truth', 1), ('lying', 1)), ('and', ('telling-truth', 4), ('lying', 2)))", "index": 224}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Emma, Lily, Jack, Daniel, and Charlotte. Aiden commented, \"Emma is not a knave\". Emma asserted: \"Aiden is a knave or Jack is a knight\". \"Daniel is not a knave,\" Lily mentioned. \"Jack is a knight or Charlotte is a knight,\" Jack declared. Daniel said that Charlotte is a knight if and only if Lily is a knave. Charlotte said, \"Daniel is a knave.\" So who is a knight and who is a knave?", "names": ["Aiden", "Emma", "Lily", "Jack", "Daniel", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Aiden is a knight, Emma is a knight, Lily is a knight, Jack is a knight, Daniel is a knight, and Charlotte is a knave.", "solution_text_format": "(1) Aiden is a knight\n(2) Emma is a knight\n(3) Lily is a knight\n(4) Jack is a knight\n(5) Daniel is a knight\n(6) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Emma is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Aiden is a knave or Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Jack is a knight or Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Charlotte that Daniel is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Daniel is not a knave.", "Lily cannot be a knave, because this would contradict the false claim of Daniel that Charlotte is a knight if and only if Lily is a knave.", "We have exhausted all possibilities for Lily and Daniel, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Daniel is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('or', ('lying', 0), ('telling-truth', 3)), ('not', ('lying', 4)), ('or', ('telling-truth', 3), ('telling-truth', 5)), ('<=>', ('telling-truth', 5), ('lying', 2)), ('lying', 4))", "index": 225}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Chloe, Avery, Charlotte, Emily, and Aurora. Aiden remarked, \"Emily is not a knight\". Chloe was heard saying, \"Aurora is a knight or Aiden is a knight\". \"If Emily is a knave then Emily is a knight,\" Avery claimed. \"Aurora is a knight or Aiden is a knave,\" Charlotte mentioned. As Emily put it, \"Chloe is not a knave\". Aurora stated, \"If Avery is a knight then Charlotte is a knight\". So who is a knight and who is a knave?", "names": ["Aiden", "Chloe", "Avery", "Charlotte", "Emily", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Aiden is a knave, Chloe is a knight, Avery is a knight, Charlotte is a knight, Emily is a knight, and Aurora is a knight.", "solution_text_format": "(1) Aiden is a knave\n(2) Chloe is a knight\n(3) Avery is a knight\n(4) Charlotte is a knight\n(5) Emily is a knight\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Emily is not a knight.", "Emily cannot be a knight, because this would contradict the claim of Aiden that Emily is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Chloe is not a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Emily that Chloe is not a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight or Aiden is a knight.", "We have exhausted all possibilities for Chloe and Emily, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Emily is not a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Aurora is a knight or Aiden is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Avery is a knight then Charlotte is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Emily is a knave then Emily is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Aurora is a knight or Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('->', ('lying', 4), ('telling-truth', 4)), ('or', ('telling-truth', 5), ('lying', 0)), ('not', ('lying', 1)), ('->', ('telling-truth', 2), ('telling-truth', 3)))", "index": 226}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Lily, Ethan, Sofia, Sophia, and Isabella. As James put it, \"Lily is a knave\". \"Ethan is a knight,\" Lily claimed. Ethan noted, \"Ethan is a knight and Isabella is a knight\". \"Lily is a knave and Ethan is a knave,\" Sofia declared. According to Sophia, \"Ethan is a knave\". \"If Sophia is a knave then Lily is a knave\" - Isabella. So who is a knight and who is a knave?", "names": ["James", "Lily", "Ethan", "Sofia", "Sophia", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true], "solution_text": "James is a knight, Lily is a knave, Ethan is a knave, Sofia is a knight, Sophia is a knight, and Isabella is a knight.", "solution_text_format": "(1) James is a knight\n(2) Lily is a knave\n(3) Ethan is a knave\n(4) Sofia is a knight\n(5) Sophia is a knight\n(6) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of James that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Lily that Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Ethan is a knight and Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Sophia is a knave then Lily is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Ethan is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Lily is a knave and Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('telling-truth', 2), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('and', ('lying', 1), ('lying', 2)), ('lying', 2), ('->', ('lying', 4), ('lying', 1)))", "index": 227}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Sofia, Joseph, Ethan, Evelyn, and Lily. \"If Ethan is a knave then Joseph is a knight,\" James declared. Sofia asserted: \"If Evelyn is a knight then Lily is a knight\". Joseph was heard saying, \"Joseph is a knight and Sofia is a knave\". As Ethan put it, \"If Sofia is a knight then Sofia is a knave\". Evelyn stated, \"Ethan is a knave or Lily is a knight\". Lily stated, \"Joseph is not a knight\". So who is a knight and who is a knave?", "names": ["James", "Sofia", "Joseph", "Ethan", "Evelyn", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true], "solution_text": "James is a knave, Sofia is a knight, Joseph is a knave, Ethan is a knave, Evelyn is a knight, and Lily is a knight.", "solution_text_format": "(1) James is a knave\n(2) Sofia is a knight\n(3) Joseph is a knave\n(4) Ethan is a knave\n(5) Evelyn is a knight\n(6) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that If Ethan is a knave then Joseph is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Sofia is a knight then Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Ethan that If Sofia is a knight then Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Lily is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Ethan is a knave or Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Sofia that If Evelyn is a knight then Lily is a knight.", "Lily cannot be a knave, because this would contradict the claim of Evelyn that Ethan is a knave or Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of Sofia that If Evelyn is a knight then Lily is a knight.", "We have exhausted all possibilities for Evelyn and Sofia, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Sofia is a knight then Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Evelyn is a knight then Lily is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Ethan is a knave or Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Sofia is a knave.", "Joseph cannot be a knave, because this would contradict the claim of James that If Ethan is a knave then Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Sofia that If Evelyn is a knight then Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Ethan is a knave or Lily is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the false claim of Ethan that If Sofia is a knight then Sofia is a knave.", "We have exhausted all possibilities for Sofia and Ethan, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that If Ethan is a knave then Joseph is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of James that If Ethan is a knave then Joseph is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Sofia is a knight then Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Evelyn is a knight then Lily is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Ethan is a knave or Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the false claim of James that If Ethan is a knave then Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Joseph is a knight and Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 2)), ('->', ('telling-truth', 4), ('telling-truth', 5)), ('and', ('telling-truth', 2), ('lying', 1)), ('->', ('telling-truth', 1), ('lying', 1)), ('or', ('lying', 3), ('telling-truth', 5)), ('not', ('telling-truth', 2)))", "index": 228}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Matthew, Samuel, Joseph, William, and Charlotte. Isabella was heard saying, \"Matthew is a knave or Charlotte is a knight\". In Matthew's words: \"Samuel is a knave and Joseph is a knave\". Samuel said that Isabella is a knight or Isabella is a knave. In a statement by Joseph: \"William is not a knave\". \"Samuel is a knave,\" William declared. \"Matthew is a knight if and only if Samuel is a knight,\" Charlotte declared. So who is a knight and who is a knave?", "names": ["Isabella", "Matthew", "Samuel", "Joseph", "William", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Isabella is a knight, Matthew is a knave, Samuel is a knight, Joseph is a knave, William is a knave, and Charlotte is a knave.", "solution_text_format": "(1) Isabella is a knight\n(2) Matthew is a knave\n(3) Samuel is a knight\n(4) Joseph is a knave\n(5) William is a knave\n(6) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Matthew is a knave or Charlotte is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Samuel is a knave and Joseph is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Matthew that Samuel is a knave and Joseph is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Isabella is a knight or Isabella is a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Samuel is a knave and Joseph is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Isabella is a knight or Isabella is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that William is not a knave.", "William cannot be a knight, because this would contradict the claim of their own that Samuel is a knave.", "William cannot be a knave, because this would contradict the claim of Joseph that William is not a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that William is not a knave.", "William cannot be a knight, because this would contradict the false claim of Joseph that William is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Matthew is a knight if and only if Samuel is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 5)), ('and', ('lying', 2), ('lying', 3)), ('or', ('telling-truth', 0), ('lying', 0)), ('not', ('lying', 4)), ('lying', 2), ('<=>', ('telling-truth', 1), ('telling-truth', 2)))", "index": 229}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Mason, Benjamin, Aurora, Lucas, and Jacob. According to Ella, \"Aurora is a knight or Benjamin is a knight\". Mason commented, \"Benjamin is a knight or Lucas is a knight\". Benjamin said that Mason is a knight or Aurora is a knight. As Aurora put it, \"Ella is a knight or Lucas is a knight\". Lucas asserted: \"If Ella is a knave then Mason is a knave\". \"Aurora is a knave if and only if Benjamin is a knight,\" Jacob mentioned. So who is a knight and who is a knave?", "names": ["Ella", "Mason", "Benjamin", "Aurora", "Lucas", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Ella is a knight, Mason is a knight, Benjamin is a knight, Aurora is a knight, Lucas is a knight, and Jacob is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Mason is a knight\n(3) Benjamin is a knight\n(4) Aurora is a knight\n(5) Lucas is a knight\n(6) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Aurora is a knight or Benjamin is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Ella is a knight or Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Ella is a knave then Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Benjamin is a knight or Lucas is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Mason is a knight or Aurora is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Aurora is a knave if and only if Benjamin is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 2)), ('or', ('telling-truth', 2), ('telling-truth', 4)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('telling-truth', 4)), ('->', ('lying', 0), ('lying', 1)), ('<=>', ('lying', 3), ('telling-truth', 2)))", "index": 230}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Penelope, Victoria, Amelia, Henry, and Jacob. In a statement by Mia: \"Penelope is a knight\". Penelope noted, \"If Amelia is a knight then Victoria is a knave\". Victoria noted, \"Mia is a knave if and only if Henry is a knave\". \"Jacob is not a knave\" - Amelia. \"Jacob is not a knave\" - Henry. \"Victoria is not a knave,\" Jacob claimed. So who is a knight and who is a knave?", "names": ["Mia", "Penelope", "Victoria", "Amelia", "Henry", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Mia is a knight, Penelope is a knight, Victoria is a knave, Amelia is a knave, Henry is a knave, and Jacob is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Penelope is a knight\n(3) Victoria is a knave\n(4) Amelia is a knave\n(5) Henry is a knave\n(6) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Amelia is a knight then Victoria is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Jacob is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the claim of Penelope that If Amelia is a knight then Victoria is a knave.", "Victoria cannot be a knave, because this would contradict the claim of Jacob that Victoria is not a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Amelia that Jacob is not a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Jacob is not a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Amelia that Jacob is not a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Jacob that Victoria is not a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Henry is a knave.", "Henry cannot be a knight, because this would contradict the false claim of Victoria that Mia is a knave if and only if Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Jacob is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('->', ('telling-truth', 3), ('lying', 2)), ('<=>', ('lying', 0), ('lying', 4)), ('not', ('lying', 5)), ('not', ('lying', 5)), ('not', ('lying', 2)))", "index": 231}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Aurora, Luke, Benjamin, Emily, and Mason. According to Aiden, \"If Mason is a knave then Mason is a knight\". Aurora expressed that Benjamin is a knight. Luke noted, \"Mason is a knight and Mason is a knave\". \"Mason is a knave and Benjamin is a knight,\" Benjamin claimed. As Emily put it, \"If Mason is a knave then Luke is a knave\". In Mason's words: \"Aurora is a knight and Luke is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Aurora", "Luke", "Benjamin", "Emily", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false], "solution_text": "Aiden is a knave, Aurora is a knave, Luke is a knave, Benjamin is a knave, Emily is a knight, and Mason is a knave.", "solution_text_format": "(1) Aiden is a knave\n(2) Aurora is a knave\n(3) Luke is a knave\n(4) Benjamin is a knave\n(5) Emily is a knight\n(6) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that If Mason is a knave then Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Aurora is a knight and Luke is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Benjamin is a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Aurora that Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Mason that Aurora is a knight and Luke is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Aiden that If Mason is a knave then Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Mason is a knave then Mason is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Aiden that If Mason is a knave then Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Aurora is a knight and Luke is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Mason is a knave and Benjamin is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Mason is a knave.", "Luke cannot be a knave, because this would contradict the false claim of Mason that Aurora is a knight and Luke is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the claim of Aurora that Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Aurora that Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Mason is a knave and Benjamin is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Mason is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Mason is a knight and Mason is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Mason is a knave then Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 5)), ('telling-truth', 3), ('and', ('telling-truth', 5), ('lying', 5)), ('and', ('lying', 5), ('telling-truth', 3)), ('->', ('lying', 5), ('lying', 2)), ('and', ('telling-truth', 1), ('lying', 2)))", "index": 232}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, James, Scarlett, Lucas, Emma, and Lily. \"James is a knave if and only if Logan is a knight\" - Logan. James was heard saying, \"If Lucas is a knave then Logan is a knight\". As Scarlett put it, \"Emma is a knave and Lily is a knight\". \"Scarlett is a knight if and only if James is a knave\" - Lucas. Emma said, \"If Lily is a knave then Lucas is a knight.\" Lily said, \"Logan is a knight and Lily is a knight.\" So who is a knight and who is a knave?", "names": ["Logan", "James", "Scarlett", "Lucas", "Emma", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false], "solution_text": "Logan is a knave, James is a knave, Scarlett is a knave, Lucas is a knave, Emma is a knave, and Lily is a knave.", "solution_text_format": "(1) Logan is a knave\n(2) James is a knave\n(3) Scarlett is a knave\n(4) Lucas is a knave\n(5) Emma is a knave\n(6) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that James is a knave if and only if Logan is a knight.", "James cannot be a knight, because this would contradict the claim of Logan that James is a knave if and only if Logan is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that If Lucas is a knave then Logan is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that James is a knave if and only if Logan is a knight.", "James cannot be a knight, because this would contradict the false claim of Logan that James is a knave if and only if Logan is a knight.", "Assume James is a knave. No contradiction is found in their false claim that If Lucas is a knave then Logan is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of James that If Lucas is a knave then Logan is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if James is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Lucas that Scarlett is a knight if and only if James is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Emma is a knave and Lily is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Lily is a knave then Lucas is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Lily is a knight.", "Lily cannot be a knave, because this would contradict the claim of Emma that If Lily is a knave then Lucas is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that If Lily is a knave then Lucas is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Scarlett that Emma is a knave and Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Logan is a knight and Lily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 0)), ('->', ('lying', 3), ('telling-truth', 0)), ('and', ('lying', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 2), ('lying', 1)), ('->', ('lying', 5), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('telling-truth', 5)))", "index": 233}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Jackson, Scarlett, Abigail, Oliver, and Daniel. Harper stated, \"Scarlett is a knight and Daniel is a knight\". Jackson noted, \"Abigail is a knight and Abigail is a knave\". In Scarlett's words: \"Jackson is not a knight\". According to Abigail, \"If Oliver is a knight then Harper is a knight\". In a statement by Oliver: \"Jackson is a knave and Daniel is a knight\". Daniel expressed that Scarlett is a knight. So who is a knight and who is a knave?", "names": ["Harper", "Jackson", "Scarlett", "Abigail", "Oliver", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Harper is a knight, Jackson is a knave, Scarlett is a knight, Abigail is a knight, Oliver is a knight, and Daniel is a knight.", "solution_text_format": "(1) Harper is a knight\n(2) Jackson is a knave\n(3) Scarlett is a knight\n(4) Abigail is a knight\n(5) Oliver is a knight\n(6) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Scarlett is a knight and Daniel is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Abigail is a knight and Abigail is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Abigail is a knight and Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Oliver is a knight then Harper is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Jackson is a knave and Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 5)), ('and', ('telling-truth', 3), ('lying', 3)), ('not', ('telling-truth', 1)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('lying', 1), ('telling-truth', 5)), ('telling-truth', 2))", "index": 234}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Aurora, Ava, David, Penelope, and William. Sophia stated, \"William is a knave\". Aurora stated, \"Ava is a knight and Penelope is a knight\". Ava was heard saying, \"David is a knight if and only if David is a knave\". David asserted: \"If William is a knave then Aurora is a knight\". \"Sophia is a knight and Aurora is a knight,\" Penelope declared. William said, \"David is a knight and Penelope is a knight.\" So who is a knight and who is a knave?", "names": ["Sophia", "Aurora", "Ava", "David", "Penelope", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false], "solution_text": "Sophia is a knight, Aurora is a knave, Ava is a knave, David is a knave, Penelope is a knave, and William is a knave.", "solution_text_format": "(1) Sophia is a knight\n(2) Aurora is a knave\n(3) Ava is a knave\n(4) David is a knave\n(5) Penelope is a knave\n(6) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Sophia that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that David is a knight and Penelope is a knight.", "Assume David is a knight. No contradiction is found in their claim that If William is a knave then Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Ava is a knight and Penelope is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that David is a knight if and only if David is a knave.", "Ava cannot be a knave, because this would contradict the claim of Aurora that Ava is a knight and Penelope is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of David that If William is a knave then Aurora is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that If William is a knave then Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of David that If William is a knave then Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Ava is a knight and Penelope is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that David is a knight if and only if David is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that David is a knight if and only if David is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Aurora is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sophia is a knight and Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('and', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('->', ('lying', 5), ('telling-truth', 1)), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('and', ('telling-truth', 3), ('telling-truth', 4)))", "index": 235}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Aria, Ava, Olivia, Benjamin, and Charlotte. Sebastian said that Benjamin is a knave or Aria is a knave. Aria expressed that Ava is a knave. Ava was heard saying, \"Charlotte is a knight if and only if Benjamin is a knight\". Olivia told you that Aria is a knave if and only if Aria is a knight. \"Charlotte is not a knight,\" Benjamin claimed. Charlotte expressed that Olivia is a knight. So who is a knight and who is a knave?", "names": ["Sebastian", "Aria", "Ava", "Olivia", "Benjamin", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "Sebastian is a knave, Aria is a knight, Ava is a knave, Olivia is a knave, Benjamin is a knight, and Charlotte is a knave.", "solution_text_format": "(1) Sebastian is a knave\n(2) Aria is a knight\n(3) Ava is a knave\n(4) Olivia is a knave\n(5) Benjamin is a knight\n(6) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Benjamin is a knave or Aria is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Benjamin that Charlotte is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Aria is a knave if and only if Aria is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Aria is a knight.", "Aria cannot be a knight, because this would contradict the claim of Sebastian that Benjamin is a knave or Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight if and only if Benjamin is a knight.", "Ava cannot be a knave, because this would contradict the false claim of Aria that Ava is a knave.", "We have exhausted all possibilities for Ava, Aria, Olivia, and Charlotte, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Aria is a knave if and only if Aria is a knight.", "Olivia cannot be a knave, because this would contradict the claim of Charlotte that Olivia is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the false claim of Benjamin that Charlotte is not a knight.", "We have exhausted all possibilities for Charlotte and Benjamin, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Benjamin is a knave or Aria is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Benjamin that Charlotte is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Aria is a knave if and only if Aria is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Aria that Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('lying', 1)), ('lying', 2), ('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('<=>', ('lying', 1), ('telling-truth', 1)), ('not', ('telling-truth', 5)), ('telling-truth', 3))", "index": 236}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Oliver, Aurora, Sophia, Sebastian, and Olivia. According to Grace, \"If Grace is a knight then Aurora is a knave\". According to Oliver, \"Aurora is a knave\". Aurora noted, \"Aurora is a knight if and only if Sebastian is a knight\". \"Oliver is a knave\" - Sophia. \"Aurora is a knave or Aurora is a knight,\" Sebastian mentioned. Olivia noted, \"Sebastian is not a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Oliver", "Aurora", "Sophia", "Sebastian", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "Grace is a knight, Oliver is a knight, Aurora is a knave, Sophia is a knave, Sebastian is a knight, and Olivia is a knight.", "solution_text_format": "(1) Grace is a knight\n(2) Oliver is a knight\n(3) Aurora is a knave\n(4) Sophia is a knave\n(5) Sebastian is a knight\n(6) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that If Grace is a knight then Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Grace that If Grace is a knight then Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Aurora is a knave or Aurora is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Aurora is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Oliver is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Sebastian is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('lying', 2)), ('lying', 2), ('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('lying', 1), ('or', ('lying', 2), ('telling-truth', 2)), ('not', ('lying', 4)))", "index": 237}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Evelyn, Aria, Aiden, Sophia, and Avery. Emma was heard saying, \"Evelyn is a knave if and only if Avery is a knight\". \"Avery is a knight or Avery is a knave,\" Evelyn claimed. Aria said that Emma is a knave and Evelyn is a knight. Aiden commented, \"Sophia is a knight and Avery is a knave\". In a statement by Sophia: \"Aria is not a knave\". Avery expressed that Sophia is a knave and Avery is a knight. So who is a knight and who is a knave?", "names": ["Emma", "Evelyn", "Aria", "Aiden", "Sophia", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Emma is a knight, Evelyn is a knight, Aria is a knave, Aiden is a knave, Sophia is a knave, and Avery is a knave.", "solution_text_format": "(1) Emma is a knight\n(2) Evelyn is a knight\n(3) Aria is a knave\n(4) Aiden is a knave\n(5) Sophia is a knave\n(6) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Avery is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Avery is a knight or Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Emma that Evelyn is a knave if and only if Avery is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Sophia is a knave and Avery is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Evelyn is a knight.", "Aria cannot be a knave, because this would contradict the claim of Sophia that Aria is not a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Evelyn is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Emma is a knave and Evelyn is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Avery is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Sophia is a knight and Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 5)), ('or', ('telling-truth', 5), ('lying', 5)), ('and', ('lying', 0), ('telling-truth', 1)), ('and', ('telling-truth', 4), ('lying', 5)), ('not', ('lying', 2)), ('and', ('lying', 4), ('telling-truth', 5)))", "index": 238}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Aria, Owen, Ethan, Alexander, and Benjamin. Daniel remarked, \"Owen is not a knight\". Aria stated, \"If Owen is a knave then Benjamin is a knave\". In Owen's words: \"Benjamin is a knave\". Ethan stated, \"Owen is a knight\". \"Aria is a knight if and only if Aria is a knave,\" Alexander mentioned. In Benjamin's words: \"Ethan is a knight or Owen is a knave\". So who is a knight and who is a knave?", "names": ["Daniel", "Aria", "Owen", "Ethan", "Alexander", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true], "solution_text": "Daniel is a knight, Aria is a knave, Owen is a knave, Ethan is a knave, Alexander is a knave, and Benjamin is a knight.", "solution_text_format": "(1) Daniel is a knight\n(2) Aria is a knave\n(3) Owen is a knave\n(4) Ethan is a knave\n(5) Alexander is a knave\n(6) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of Daniel that Owen is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Ethan is a knight or Owen is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Owen is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Owen is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that If Owen is a knave then Benjamin is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that If Owen is a knave then Benjamin is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Aria is a knight if and only if Aria is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Aria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('->', ('lying', 2), ('lying', 5)), ('lying', 5), ('telling-truth', 2), ('<=>', ('telling-truth', 1), ('lying', 1)), ('or', ('telling-truth', 3), ('lying', 2)))", "index": 239}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Ava, William, Lucas, Riley, and Lily. Benjamin was heard saying, \"Lily is a knight if and only if Ava is a knight\". In Ava's words: \"Lucas is a knight or Lily is a knave\". William asserted: \"Lucas is a knight if and only if Riley is a knave\". Lucas remarked, \"Riley is a knave and Riley is a knight\". Riley stated, \"Lily is not a knave\". Lily said that William is a knave and William is a knight. So who is a knight and who is a knave?", "names": ["Benjamin", "Ava", "William", "Lucas", "Riley", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false], "solution_text": "Benjamin is a knave, Ava is a knight, William is a knave, Lucas is a knave, Riley is a knave, and Lily is a knave.", "solution_text_format": "(1) Benjamin is a knave\n(2) Ava is a knight\n(3) William is a knave\n(4) Lucas is a knave\n(5) Riley is a knave\n(6) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Lily is a knight if and only if Ava is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that William is a knave and William is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that William is a knave and William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Riley is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Riley is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Riley is a knave and Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Lily is not a knave.", "Riley cannot be a knave, because this would contradict the claim of William that Lucas is a knight if and only if Riley is a knave.", "We have exhausted all possibilities for Riley and Lucas, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Riley is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Riley is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Riley is a knave and Riley is a knight.", "Riley cannot be a knight, because this would contradict the false claim of William that Lucas is a knight if and only if Riley is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Lily is not a knave.", "Ava cannot be a knight, because this would contradict the claim of Benjamin that Lily is a knight if and only if Ava is a knight.", "Ava cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight or Lily is a knave.", "We have exhausted all possibilities for Ava, Riley, Lucas, William, and Lily, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Ava is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that William is a knave and William is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that William is a knave and William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Riley is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Riley is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Riley is a knave and Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Lily is not a knave.", "Riley cannot be a knave, because this would contradict the claim of William that Lucas is a knight if and only if Riley is a knave.", "We have exhausted all possibilities for Riley and Lucas, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Riley is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Riley is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Riley is a knave and Riley is a knight.", "Riley cannot be a knight, because this would contradict the false claim of William that Lucas is a knight if and only if Riley is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Lily is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Lucas is a knight or Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('lying', 5)), ('<=>', ('telling-truth', 3), ('lying', 4)), ('and', ('lying', 4), ('telling-truth', 4)), ('not', ('lying', 5)), ('and', ('lying', 2), ('telling-truth', 2)))", "index": 240}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Lily, Harper, Daniel, Charlotte, and Elizabeth. William told you that Charlotte is a knight. Lily was heard saying, \"William is a knight\". Harper said, \"Elizabeth is a knave and Charlotte is a knight.\" As Daniel put it, \"If Daniel is a knight then William is a knave\". \"Charlotte is a knight and Elizabeth is a knight,\" Charlotte declared. \"Harper is a knave or Harper is a knight,\" Elizabeth declared. So who is a knight and who is a knave?", "names": ["William", "Lily", "Harper", "Daniel", "Charlotte", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "William is a knave, Lily is a knave, Harper is a knave, Daniel is a knight, Charlotte is a knave, and Elizabeth is a knight.", "solution_text_format": "(1) William is a knave\n(2) Lily is a knave\n(3) Harper is a knave\n(4) Daniel is a knight\n(5) Charlotte is a knave\n(6) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Charlotte is a knight and Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Harper is a knave or Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Charlotte is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Charlotte is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that William is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that If Daniel is a knight then William is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knight then William is a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of their own that William is a knight.", "We have exhausted all possibilities for Lily and Harper, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Charlotte that Charlotte is a knight and Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of William that Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of William that Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Charlotte is a knight and Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Harper is a knave or Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Charlotte is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Charlotte is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that William is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that William is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Daniel is a knight then William is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('telling-truth', 0), ('and', ('lying', 5), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('lying', 0)), ('and', ('telling-truth', 4), ('telling-truth', 5)), ('or', ('lying', 2), ('telling-truth', 2)))", "index": 241}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Penelope, Emily, Aiden, David, and Aria. In a statement by Sofia: \"Penelope is a knave\". Penelope stated, \"Penelope is a knight and David is a knight\". Emily told you that David is a knight. Aiden noted, \"Penelope is a knight or Aria is a knave\". David said, \"Aiden is a knave and Aiden is a knight.\" According to Aria, \"Sofia is a knight and David is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Penelope", "Emily", "Aiden", "David", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true], "solution_text": "Sofia is a knight, Penelope is a knave, Emily is a knave, Aiden is a knave, David is a knave, and Aria is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Penelope is a knave\n(3) Emily is a knave\n(4) Aiden is a knave\n(5) David is a knave\n(6) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Sofia that Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Penelope is a knight and David is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Aiden is a knave and Aiden is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Aiden is a knave and Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Penelope is a knight or Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Aiden that Penelope is a knight or Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight and David is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Penelope is a knight or Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Sofia is a knight and David is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that David is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that David is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('and', ('telling-truth', 1), ('telling-truth', 4)), ('telling-truth', 4), ('or', ('telling-truth', 1), ('lying', 5)), ('and', ('lying', 3), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('lying', 4)))", "index": 242}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Daniel, Mason, Sofia, Zoey, and Avery. \"Zoey is a knave and Evelyn is a knight\" - Evelyn. In Daniel's words: \"If Zoey is a knave then Sofia is a knave\". According to Mason, \"Evelyn is a knight\". According to Sofia, \"Avery is a knave or Zoey is a knight\". \"Mason is not a knave,\" Zoey declared. \"Zoey is a knave or Daniel is a knave,\" Avery mentioned. So who is a knight and who is a knave?", "names": ["Evelyn", "Daniel", "Mason", "Sofia", "Zoey", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true], "solution_text": "Evelyn is a knave, Daniel is a knight, Mason is a knave, Sofia is a knave, Zoey is a knave, and Avery is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Daniel is a knight\n(3) Mason is a knave\n(4) Sofia is a knave\n(5) Zoey is a knave\n(6) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Zoey is a knave and Evelyn is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Evelyn that Zoey is a knave and Evelyn is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the false claim of Zoey that Mason is not a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that Evelyn is a knight.", "We have exhausted all possibilities for Mason and Zoey, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Zoey is a knave and Evelyn is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight.", "Mason cannot be a knave, because this would contradict the claim of Zoey that Mason is not a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Mason is not a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Evelyn is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Zoey is a knave then Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Daniel that If Zoey is a knave then Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Avery is a knave or Zoey is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Zoey is a knave or Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 0)), ('->', ('lying', 4), ('lying', 3)), ('telling-truth', 0), ('or', ('lying', 5), ('telling-truth', 4)), ('not', ('lying', 2)), ('or', ('lying', 4), ('lying', 1)))", "index": 243}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Alexander, Jacob, Harper, Scarlett, and Henry. According to Sofia, \"Jacob is a knight and Scarlett is a knight\". According to Alexander, \"Harper is a knave and Jacob is a knave\". Jacob told you that Henry is a knight. \"Sofia is a knight if and only if Alexander is a knight\" - Harper. \"Henry is a knight or Jacob is a knight,\" Scarlett declared. According to Henry, \"Sofia is a knave or Alexander is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Alexander", "Jacob", "Harper", "Scarlett", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Sofia is a knight, Alexander is a knave, Jacob is a knight, Harper is a knave, Scarlett is a knight, and Henry is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Alexander is a knave\n(3) Jacob is a knight\n(4) Harper is a knave\n(5) Scarlett is a knight\n(6) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Jacob is a knight and Scarlett is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Sofia is a knave or Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Jacob is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Harper is a knave and Jacob is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Sofia is a knight if and only if Alexander is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Alexander is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Henry is a knight or Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 4)), ('and', ('lying', 3), ('lying', 2)), ('telling-truth', 5), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('lying', 0), ('lying', 1)))", "index": 244}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Benjamin, Matthew, William, Mia, and Grace. Logan commented, \"If Benjamin is a knave then Matthew is a knight\". \"Grace is a knave or Logan is a knight,\" Benjamin declared. Matthew said, \"Mia is a knave if and only if Grace is a knave.\" William stated, \"If Benjamin is a knave then Grace is a knave\". Mia asserted: \"William is a knave\". Grace remarked, \"Benjamin is not a knight\". So who is a knight and who is a knave?", "names": ["Logan", "Benjamin", "Matthew", "William", "Mia", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Logan is a knight, Benjamin is a knight, Matthew is a knight, William is a knight, Mia is a knave, and Grace is a knave.", "solution_text_format": "(1) Logan is a knight\n(2) Benjamin is a knight\n(3) Matthew is a knight\n(4) William is a knight\n(5) Mia is a knave\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that If Benjamin is a knave then Matthew is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Grace is a knave or Logan is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Mia is a knave if and only if Grace is a knave.", "Mia cannot be a knight, because this would contradict the claim of Matthew that Mia is a knave if and only if Grace is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that William is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Benjamin is a knave then Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 2)), ('or', ('lying', 5), ('telling-truth', 0)), ('<=>', ('lying', 4), ('lying', 5)), ('->', ('lying', 1), ('lying', 5)), ('lying', 3), ('not', ('telling-truth', 1)))", "index": 245}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Aria, Henry, Oliver, Sofia, and Joseph. Amelia remarked, \"If Oliver is a knight then Aria is a knight\". Aria remarked, \"Henry is a knave and Oliver is a knight\". As Henry put it, \"If Sofia is a knave then Joseph is a knight\". Oliver expressed that Henry is a knight if and only if Sofia is a knave. Sofia told you that If Oliver is a knight then Henry is a knight. Joseph asserted: \"Oliver is a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "Aria", "Henry", "Oliver", "Sofia", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Amelia is a knight, Aria is a knave, Henry is a knight, Oliver is a knave, Sofia is a knight, and Joseph is a knight.", "solution_text_format": "(1) Amelia is a knight\n(2) Aria is a knave\n(3) Henry is a knight\n(4) Oliver is a knave\n(5) Sofia is a knight\n(6) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that If Oliver is a knight then Aria is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Henry is a knight if and only if Sofia is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Sofia is a knave then Joseph is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Oliver that Henry is a knight if and only if Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Oliver is a knight then Henry is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that If Sofia is a knave then Joseph is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Henry that If Sofia is a knave then Joseph is a knight.", "Sofia cannot be a knave, because this would contradict the claim of Oliver that Henry is a knight if and only if Sofia is a knave.", "We have exhausted all possibilities for Sofia and Henry, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Sofia is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Sofia is a knave then Joseph is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Oliver is a knight then Henry is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Oliver is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Oliver is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Henry is a knave and Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('telling-truth', 1)), ('and', ('lying', 2), ('telling-truth', 3)), ('->', ('lying', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 2), ('lying', 4)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('lying', 3))", "index": 246}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Avery, Jackson, Sofia, Grace, and Samuel. Victoria said that Sofia is not a knight. Avery expressed that Victoria is not a knight. Jackson told you that Avery is a knave and Sofia is a knave. Sofia stated, \"Avery is a knave and Grace is a knight\". As Grace put it, \"Avery is a knight\". Samuel expressed that Grace is a knave if and only if Jackson is a knight. So who is a knight and who is a knave?", "names": ["Victoria", "Avery", "Jackson", "Sofia", "Grace", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Victoria is a knight, Avery is a knave, Jackson is a knight, Sofia is a knave, Grace is a knave, and Samuel is a knight.", "solution_text_format": "(1) Victoria is a knight\n(2) Avery is a knave\n(3) Jackson is a knight\n(4) Sofia is a knave\n(5) Grace is a knave\n(6) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of Victoria that Sofia is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Avery is a knave and Grace is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Victoria is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Grace cannot be a knight, because this would contradict the false claim of Sofia that Avery is a knave and Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Avery is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Avery is a knave and Sofia is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Grace is a knave if and only if Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('not', ('telling-truth', 0)), ('and', ('lying', 1), ('lying', 3)), ('and', ('lying', 1), ('telling-truth', 4)), ('telling-truth', 1), ('<=>', ('lying', 4), ('telling-truth', 2)))", "index": 247}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Zoey, Ethan, Lily, Harper, and Emma. David told you that Lily is a knave if and only if David is a knight. As Zoey put it, \"Emma is a knight or David is a knave\". Ethan said that Harper is not a knight. In Lily's words: \"If David is a knight then Lily is a knight\". Harper stated, \"Lily is not a knave\". Emma was heard saying, \"Lily is a knight if and only if David is a knight\". So who is a knight and who is a knave?", "names": ["David", "Zoey", "Ethan", "Lily", "Harper", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "David is a knight, Zoey is a knave, Ethan is a knight, Lily is a knave, Harper is a knave, and Emma is a knave.", "solution_text_format": "(1) David is a knight\n(2) Zoey is a knave\n(3) Ethan is a knight\n(4) Lily is a knave\n(5) Harper is a knave\n(6) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Lily is a knave if and only if David is a knight.", "Lily cannot be a knight, because this would contradict the claim of David that Lily is a knave if and only if David is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that If David is a knight then Lily is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Emma is a knight or David is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Lily is a knight if and only if David is a knight.", "Emma cannot be a knave, because this would contradict the claim of Zoey that Emma is a knight or David is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Emma is a knight or David is a knave.", "Emma cannot be a knight, because this would contradict the false claim of Zoey that Emma is a knight or David is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Lily is a knight if and only if David is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Harper is not a knight.", "Harper cannot be a knight, because this would contradict the claim of Ethan that Harper is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Lily is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 0)), ('or', ('telling-truth', 5), ('lying', 0)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 0), ('telling-truth', 3)), ('not', ('lying', 3)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)))", "index": 248}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Aurora, Ella, Charlotte, Abigail, and Isabella. According to Evelyn, \"Abigail is a knight and Charlotte is a knight\". Aurora noted, \"Isabella is not a knight\". Ella stated, \"Evelyn is a knave and Abigail is a knight\". In Charlotte's words: \"Ella is not a knave\". In a statement by Abigail: \"Ella is a knight or Aurora is a knight\". Isabella told you that Evelyn is a knave. So who is a knight and who is a knave?", "names": ["Evelyn", "Aurora", "Ella", "Charlotte", "Abigail", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true], "solution_text": "Evelyn is a knave, Aurora is a knave, Ella is a knave, Charlotte is a knave, Abigail is a knave, and Isabella is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Aurora is a knave\n(3) Ella is a knave\n(4) Charlotte is a knave\n(5) Abigail is a knave\n(6) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Abigail is a knight and Charlotte is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Ella is a knight or Aurora is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Abigail is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Evelyn is a knave and Abigail is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Aurora that Isabella is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.", "Charlotte cannot be a knave, because this would contradict the claim of Evelyn that Abigail is a knight and Charlotte is a knight.", "We have exhausted all possibilities for Charlotte and Isabella, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Abigail that Ella is a knight or Aurora is a knight.", "We have exhausted all possibilities for Aurora and Ella, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Evelyn that Abigail is a knight and Charlotte is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Abigail is a knight and Charlotte is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Ella is a knight or Aurora is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Evelyn is a knave and Abigail is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Aurora that Isabella is not a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Evelyn is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Evelyn is a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Evelyn that Abigail is a knight and Charlotte is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Ella is not a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of Aurora that Isabella is not a knight.", "We have exhausted all possibilities for Isabella and Aurora, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that Evelyn is a knave and Abigail is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Ella is a knight or Aurora is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Abigail is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Evelyn is a knave and Abigail is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Abigail that Ella is a knight or Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Evelyn is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Ella is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('telling-truth', 3)), ('not', ('telling-truth', 5)), ('and', ('lying', 0), ('telling-truth', 4)), ('not', ('lying', 2)), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('lying', 0))", "index": 249}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Matthew, Oliver, Ava, Logan, and Noah. Elizabeth was heard saying, \"If Oliver is a knight then Ava is a knight\". Matthew was heard saying, \"Ava is a knave if and only if Elizabeth is a knave\". In Oliver's words: \"Elizabeth is a knight\". In a statement by Ava: \"Logan is a knight and Ava is a knight\". Logan remarked, \"Ava is a knave if and only if Oliver is a knave\". \"Matthew is not a knave,\" Noah mentioned. So who is a knight and who is a knave?", "names": ["Elizabeth", "Matthew", "Oliver", "Ava", "Logan", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Elizabeth is a knight, Matthew is a knight, Oliver is a knight, Ava is a knight, Logan is a knight, and Noah is a knight.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Matthew is a knight\n(3) Oliver is a knight\n(4) Ava is a knight\n(5) Logan is a knight\n(6) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that If Oliver is a knight then Ava is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Logan is a knight and Ava is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Ava is a knave if and only if Oliver is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Ava is a knave if and only if Elizabeth is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Matthew is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('lying', 3), ('lying', 0)), ('telling-truth', 0), ('and', ('telling-truth', 4), ('telling-truth', 3)), ('<=>', ('lying', 3), ('lying', 2)), ('not', ('lying', 1)))", "index": 250}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Jack, Ethan, Penelope, Sofia, and Luke. In a statement by Sebastian: \"Jack is a knight if and only if Ethan is a knave\". \"Penelope is a knight if and only if Penelope is a knave,\" Jack declared. Ethan remarked, \"Penelope is a knave\". Penelope noted, \"Jack is a knave and Sofia is a knave\". As Sofia put it, \"Sebastian is a knave or Luke is a knight\". \"Penelope is a knave or Jack is a knave,\" Luke claimed. So who is a knight and who is a knave?", "names": ["Sebastian", "Jack", "Ethan", "Penelope", "Sofia", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Sebastian is a knight, Jack is a knave, Ethan is a knight, Penelope is a knave, Sofia is a knight, and Luke is a knight.", "solution_text_format": "(1) Sebastian is a knight\n(2) Jack is a knave\n(3) Ethan is a knight\n(4) Penelope is a knave\n(5) Sofia is a knight\n(6) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Jack is a knight if and only if Ethan is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Penelope is a knight if and only if Penelope is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Jack is a knave and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Penelope that Jack is a knave and Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Sebastian is a knave or Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Sofia that Sebastian is a knave or Luke is a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that Penelope is a knave or Jack is a knave.", "We have exhausted all possibilities for Luke and Sofia, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jack is a knave and Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Sebastian is a knave or Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Penelope is a knave or Jack is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 2)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('lying', 3), ('and', ('lying', 1), ('lying', 4)), ('or', ('lying', 0), ('telling-truth', 5)), ('or', ('lying', 3), ('lying', 1)))", "index": 251}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, William, Emma, Benjamin, Isabella, and Mia. Ethan stated, \"Benjamin is a knave or William is a knave\". William asserted: \"Mia is a knight if and only if Isabella is a knight\". \"Mia is a knave and Isabella is a knight,\" Emma claimed. Benjamin commented, \"William is a knight and Mia is a knight\". Isabella commented, \"If Benjamin is a knight then Emma is a knave\". Mia told you that Isabella is a knight. So who is a knight and who is a knave?", "names": ["Ethan", "William", "Emma", "Benjamin", "Isabella", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Ethan is a knave, William is a knight, Emma is a knave, Benjamin is a knight, Isabella is a knight, and Mia is a knight.", "solution_text_format": "(1) Ethan is a knave\n(2) William is a knight\n(3) Emma is a knave\n(4) Benjamin is a knight\n(5) Isabella is a knight\n(6) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Benjamin is a knave or William is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that William is a knight and Mia is a knight.", "William cannot be a knight, because this would contradict the claim of Ethan that Benjamin is a knave or William is a knave.", "William cannot be a knave, because this would contradict the claim of Benjamin that William is a knight and Mia is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that William is a knight and Mia is a knight.", "Assume William is a knight. No contradiction is found in their claim that Mia is a knight if and only if Isabella is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Benjamin that William is a knight and Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the claim of William that Mia is a knight if and only if Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that If Benjamin is a knight then Emma is a knave.", "We have exhausted all possibilities for Isabella and Mia, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Isabella is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of William that Mia is a knight if and only if Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that If Benjamin is a knight then Emma is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Mia that Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of William that Mia is a knight if and only if Isabella is a knight.", "We have exhausted all possibilities for Isabella, Mia, William, and Benjamin, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Benjamin is a knave or William is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that William is a knight and Mia is a knight.", "Assume William is a knight. No contradiction is found in their claim that Mia is a knight if and only if Isabella is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Benjamin is a knight then Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Isabella is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Mia is a knave and Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 1)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('and', ('lying', 5), ('telling-truth', 4)), ('and', ('telling-truth', 1), ('telling-truth', 5)), ('->', ('telling-truth', 3), ('lying', 2)), ('telling-truth', 4))", "index": 252}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Olivia, Aiden, Charlotte, Jacob, and Zoey. Logan stated, \"Jacob is a knight\". Olivia noted, \"Aiden is a knight or Zoey is a knave\". \"If Logan is a knight then Olivia is a knight\" - Aiden. Charlotte remarked, \"Zoey is a knight or Olivia is a knight\". As Jacob put it, \"Aiden is a knave or Charlotte is a knave\". According to Zoey, \"Jacob is a knave if and only if Logan is a knight\". So who is a knight and who is a knave?", "names": ["Logan", "Olivia", "Aiden", "Charlotte", "Jacob", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Logan is a knave, Olivia is a knight, Aiden is a knight, Charlotte is a knight, Jacob is a knave, and Zoey is a knave.", "solution_text_format": "(1) Logan is a knave\n(2) Olivia is a knight\n(3) Aiden is a knight\n(4) Charlotte is a knight\n(5) Jacob is a knave\n(6) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Aiden is a knave or Charlotte is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Logan is a knight then Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Aiden is a knight or Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Jacob is a knave if and only if Logan is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Logan is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Jacob that Aiden is a knave or Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Zoey is a knight or Olivia is a knight.", "We have exhausted all possibilities for Charlotte and Zoey, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Aiden is a knight or Zoey is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Logan is a knight then Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the false claim of Aiden that If Logan is a knight then Olivia is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aiden is a knight or Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Jacob is a knave if and only if Logan is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of Olivia that Aiden is a knight or Zoey is a knave.", "We have exhausted all possibilities for Zoey, Olivia, and Aiden, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Logan that Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Logan that Jacob is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Aiden is a knave or Charlotte is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Logan is a knight then Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Aiden is a knight or Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Jacob is a knave if and only if Logan is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Logan is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Zoey is a knight or Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('or', ('telling-truth', 2), ('lying', 5)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('telling-truth', 5), ('telling-truth', 1)), ('or', ('lying', 2), ('lying', 3)), ('<=>', ('lying', 4), ('telling-truth', 0)))", "index": 253}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Benjamin, Sebastian, Daniel, James, and Mia. \"If James is a knight then Sebastian is a knave,\" Charlotte declared. Benjamin asserted: \"Sebastian is a knave\". Sebastian stated, \"James is a knight\". Daniel remarked, \"Mia is a knave if and only if Sebastian is a knight\". James stated, \"Mia is a knight\". Mia was heard saying, \"Daniel is a knave or James is a knight\". So who is a knight and who is a knave?", "names": ["Charlotte", "Benjamin", "Sebastian", "Daniel", "James", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true], "solution_text": "Charlotte is a knave, Benjamin is a knave, Sebastian is a knight, Daniel is a knave, James is a knight, and Mia is a knight.", "solution_text_format": "(1) Charlotte is a knave\n(2) Benjamin is a knave\n(3) Sebastian is a knight\n(4) Daniel is a knave\n(5) James is a knight\n(6) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that If James is a knight then Sebastian is a knave.", "Assume James is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Daniel is a knave or James is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Mia is a knave if and only if Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Charlotte that If James is a knight then Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that James is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Charlotte that If James is a knight then Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that James is a knight.", "We have exhausted all possibilities for Sebastian and Daniel, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of James that Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of James that Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Daniel is a knave or James is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Mia is a knave if and only if Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that James is a knight.", "Sebastian cannot be a knave, because this would contradict the claim of Daniel that Mia is a knave if and only if Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of Mia that Daniel is a knave or James is a knight.", "We have exhausted all possibilities for Daniel, Mia, and James, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If James is a knight then Sebastian is a knave.", "Assume James is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Daniel is a knave or James is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Mia is a knave if and only if Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Daniel that Mia is a knave if and only if Sebastian is a knight.", "Sebastian cannot be a knave, because this would contradict the false claim of Charlotte that If James is a knight then Sebastian is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that James is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 2)), ('lying', 2), ('telling-truth', 4), ('<=>', ('lying', 5), ('telling-truth', 2)), ('telling-truth', 5), ('or', ('lying', 3), ('telling-truth', 4)))", "index": 254}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Sophia, Riley, Jackson, Jack, and Benjamin. James told you that If Jackson is a knave then Riley is a knave. As Sophia put it, \"Riley is a knave if and only if James is a knave\". In a statement by Riley: \"Benjamin is a knave or Benjamin is a knight\". Jackson expressed that Benjamin is a knave or Benjamin is a knight. Jack expressed that James is not a knight. Benjamin noted, \"If Sophia is a knight then Jack is a knight\". So who is a knight and who is a knave?", "names": ["James", "Sophia", "Riley", "Jackson", "Jack", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "James is a knight, Sophia is a knight, Riley is a knight, Jackson is a knight, Jack is a knave, and Benjamin is a knave.", "solution_text_format": "(1) James is a knight\n(2) Sophia is a knight\n(3) Riley is a knight\n(4) Jackson is a knight\n(5) Jack is a knave\n(6) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that If Jackson is a knave then Riley is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Benjamin is a knave or Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Sophia is a knight then Jack is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Riley is a knave if and only if James is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Benjamin is a knave or Benjamin is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that James is not a knight.", "Jack cannot be a knave, because this would contradict the claim of Benjamin that If Sophia is a knight then Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the claim of Sophia that Riley is a knave if and only if James is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Riley is a knave if and only if James is a knave.", "Riley cannot be a knight, because this would contradict the false claim of Sophia that Riley is a knave if and only if James is a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knave or Benjamin is a knight.", "We have exhausted all possibilities for Riley and Sophia, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If Sophia is a knight then Jack is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Riley is a knave if and only if James is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Benjamin is a knave or Benjamin is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that James is not a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that James is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 2)), ('<=>', ('lying', 2), ('lying', 0)), ('or', ('lying', 5), ('telling-truth', 5)), ('or', ('lying', 5), ('telling-truth', 5)), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 1), ('telling-truth', 4)))", "index": 255}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Mia, Amelia, Abigail, Scarlett, and Aurora. In Grace's words: \"Scarlett is a knave or Aurora is a knight\". In a statement by Mia: \"Scarlett is a knight if and only if Abigail is a knight\". Amelia stated, \"Abigail is a knave or Grace is a knave\". \"Grace is a knave and Aurora is a knight,\" Abigail claimed. Scarlett noted, \"Aurora is a knave and Grace is a knight\". \"Abigail is a knave\" - Aurora. So who is a knight and who is a knave?", "names": ["Grace", "Mia", "Amelia", "Abigail", "Scarlett", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Grace is a knight, Mia is a knight, Amelia is a knight, Abigail is a knave, Scarlett is a knave, and Aurora is a knight.", "solution_text_format": "(1) Grace is a knight\n(2) Mia is a knight\n(3) Amelia is a knight\n(4) Abigail is a knave\n(5) Scarlett is a knave\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Scarlett is a knave or Aurora is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aurora is a knave and Grace is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Scarlett that Aurora is a knave and Grace is a knight.", "Aurora cannot be a knave, because this would contradict the claim of Grace that Scarlett is a knave or Aurora is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aurora is a knave and Grace is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Aurora is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Grace is a knave and Aurora is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Abigail is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Abigail is a knave or Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 4), ('telling-truth', 3)), ('or', ('lying', 3), ('lying', 0)), ('and', ('lying', 0), ('telling-truth', 5)), ('and', ('lying', 5), ('telling-truth', 0)), ('lying', 3))", "index": 256}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Riley, Lucas, Liam, Jackson, and Scarlett. \"Liam is not a knight\" - Sofia. \"Sofia is a knave or Lucas is a knave,\" Riley declared. Lucas said that If Jackson is a knight then Scarlett is a knight. Liam was heard saying, \"Scarlett is a knave\". Jackson stated, \"If Liam is a knave then Riley is a knight\". According to Scarlett, \"Lucas is a knave if and only if Sofia is a knight\". So who is a knight and who is a knave?", "names": ["Sofia", "Riley", "Lucas", "Liam", "Jackson", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Sofia is a knave, Riley is a knight, Lucas is a knave, Liam is a knight, Jackson is a knight, and Scarlett is a knave.", "solution_text_format": "(1) Sofia is a knave\n(2) Riley is a knight\n(3) Lucas is a knave\n(4) Liam is a knight\n(5) Jackson is a knight\n(6) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Liam is not a knight.", "Liam cannot be a knight, because this would contradict the claim of Sofia that Liam is not a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Sofia is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Scarlett that Lucas is a knave if and only if Sofia is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knight then Scarlett is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of Liam that Scarlett is a knave.", "We have exhausted all possibilities for Scarlett and Liam, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Liam that Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Sofia is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Scarlett that Lucas is a knave if and only if Sofia is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Jackson is a knight then Scarlett is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Liam is a knave then Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Sofia is a knave or Lucas is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('or', ('lying', 0), ('lying', 2)), ('->', ('telling-truth', 4), ('telling-truth', 5)), ('lying', 5), ('->', ('lying', 3), ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 0)))", "index": 257}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Chloe, Daniel, Ava, Aria, and Penelope. Jacob commented, \"Daniel is a knight if and only if Jacob is a knight\". Chloe was heard saying, \"If Penelope is a knight then Jacob is a knave\". Daniel was heard saying, \"If Jacob is a knave then Chloe is a knave\". Ava stated, \"Daniel is a knight and Chloe is a knave\". As Aria put it, \"Penelope is a knave and Penelope is a knight\". Penelope remarked, \"Penelope is a knight if and only if Ava is a knight\". So who is a knight and who is a knave?", "names": ["Jacob", "Chloe", "Daniel", "Ava", "Aria", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "Jacob is a knight, Chloe is a knave, Daniel is a knight, Ava is a knight, Aria is a knave, and Penelope is a knight.", "solution_text_format": "(1) Jacob is a knight\n(2) Chloe is a knave\n(3) Daniel is a knight\n(4) Ava is a knight\n(5) Aria is a knave\n(6) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Jacob is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Jacob is a knave then Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Penelope is a knight then Jacob is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Chloe that If Penelope is a knight then Jacob is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Ava is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Daniel is a knight and Chloe is a knave.", "Ava cannot be a knave, because this would contradict the false claim of Penelope that Penelope is a knight if and only if Ava is a knight.", "We have exhausted all possibilities for Ava and Penelope, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that If Penelope is a knight then Jacob is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Daniel is a knight and Chloe is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Penelope is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Penelope is a knave and Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('telling-truth', 5), ('lying', 0)), ('->', ('lying', 0), ('lying', 1)), ('and', ('telling-truth', 2), ('lying', 1)), ('and', ('lying', 5), ('telling-truth', 5)), ('<=>', ('telling-truth', 5), ('telling-truth', 3)))", "index": 258}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Jack, Elizabeth, Mia, Zoey, and Mason. Jacob noted, \"Jack is not a knave\". Jack was heard saying, \"Zoey is a knave and Jacob is a knave\". \"Mia is a knave,\" Elizabeth claimed. In a statement by Mia: \"Zoey is not a knight\". Zoey was heard saying, \"Elizabeth is a knight\". Mason asserted: \"Zoey is not a knight\". So who is a knight and who is a knave?", "names": ["Jacob", "Jack", "Elizabeth", "Mia", "Zoey", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "Jacob is a knave, Jack is a knave, Elizabeth is a knight, Mia is a knave, Zoey is a knight, and Mason is a knave.", "solution_text_format": "(1) Jacob is a knave\n(2) Jack is a knave\n(3) Elizabeth is a knight\n(4) Mia is a knave\n(5) Zoey is a knight\n(6) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Jack is not a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Zoey is a knave and Jacob is a knave.", "Jack cannot be a knave, because this would contradict the claim of Jacob that Jack is not a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Jack is not a knave.", "Jack cannot be a knight, because this would contradict the false claim of Jacob that Jack is not a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Zoey is a knave and Jacob is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of Elizabeth that Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Zoey is not a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Zoey is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('and', ('lying', 4), ('lying', 0)), ('lying', 3), ('not', ('telling-truth', 4)), ('telling-truth', 2), ('not', ('telling-truth', 4)))", "index": 259}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Oliver, Scarlett, Ella, Isabella, and Ava. \"Scarlett is a knight if and only if Oliver is a knight,\" Emily claimed. As Oliver put it, \"Isabella is a knight if and only if Ava is a knight\". Scarlett noted, \"Oliver is a knight if and only if Isabella is a knight\". Ella noted, \"Emily is a knight and Ella is a knight\". As Isabella put it, \"Oliver is a knave or Ella is a knight\". \"Scarlett is a knave if and only if Isabella is a knight\" - Ava. So who is a knight and who is a knave?", "names": ["Emily", "Oliver", "Scarlett", "Ella", "Isabella", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false], "solution_text": "Emily is a knave, Oliver is a knight, Scarlett is a knave, Ella is a knave, Isabella is a knave, and Ava is a knave.", "solution_text_format": "(1) Emily is a knave\n(2) Oliver is a knight\n(3) Scarlett is a knave\n(4) Ella is a knave\n(5) Isabella is a knave\n(6) Ava is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Oliver is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Isabella is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Ava is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Oliver is a knave or Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Emily is a knight and Ella is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave if and only if Isabella is a knight.", "Ava cannot be a knave, because this would contradict the claim of Oliver that Isabella is a knight if and only if Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Isabella that Oliver is a knave or Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Scarlett that Oliver is a knight if and only if Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Emily that Scarlett is a knight if and only if Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Isabella is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Emily that Scarlett is a knight if and only if Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Ava is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Oliver is a knave or Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Emily is a knight and Ella is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Oliver that Isabella is a knight if and only if Ava is a knight.", "Ava cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knave if and only if Isabella is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Emily is a knight and Ella is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Oliver that Isabella is a knight if and only if Ava is a knight.", "Ava cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knave if and only if Isabella is a knight.", "We have exhausted all possibilities for Ava and Ella, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of Scarlett that Oliver is a knight if and only if Isabella is a knight.", "We have exhausted all possibilities for Isabella, Oliver, and Scarlett, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Oliver is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Isabella is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Emily that Scarlett is a knight if and only if Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Ava is a knight.", "Isabella cannot be a knight, because this would contradict the claim of Scarlett that Oliver is a knight if and only if Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Oliver is a knave or Ella is a knight.", "We have exhausted all possibilities for Isabella and Oliver, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Isabella is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Ava is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Scarlett that Oliver is a knight if and only if Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Oliver is a knave or Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Emily is a knight and Ella is a knight.", "Ava cannot be a knight, because this would contradict the claim of Oliver that Isabella is a knight if and only if Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 1), ('telling-truth', 4)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('lying', 1), ('telling-truth', 3)), ('<=>', ('lying', 2), ('telling-truth', 4)))", "index": 260}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Ella, Alexander, Aiden, Jackson, and Joseph. Charlotte asserted: \"Jackson is a knight or Ella is a knight\". As Ella put it, \"Charlotte is not a knight\". Alexander commented, \"Jackson is a knave if and only if Aiden is a knave\". Aiden noted, \"Alexander is not a knave\". In Jackson's words: \"Alexander is a knight\". As Joseph put it, \"Ella is not a knave\". So who is a knight and who is a knave?", "names": ["Charlotte", "Ella", "Alexander", "Aiden", "Jackson", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Charlotte is a knight, Ella is a knave, Alexander is a knight, Aiden is a knight, Jackson is a knight, and Joseph is a knave.", "solution_text_format": "(1) Charlotte is a knight\n(2) Ella is a knave\n(3) Alexander is a knight\n(4) Aiden is a knight\n(5) Jackson is a knight\n(6) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Jackson is a knight or Ella is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ella is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('<=>', ('lying', 4), ('lying', 3)), ('not', ('lying', 2)), ('telling-truth', 2), ('not', ('lying', 1)))", "index": 261}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Henry, Logan, Avery, Daniel, and Aiden. Evelyn said that Daniel is a knave and Logan is a knight. Henry told you that Logan is a knight if and only if Aiden is a knave. \"Daniel is a knight,\" Logan claimed. Avery was heard saying, \"Henry is not a knave\". \"Henry is not a knave\" - Daniel. In Aiden's words: \"Henry is not a knave\". So who is a knight and who is a knave?", "names": ["Evelyn", "Henry", "Logan", "Avery", "Daniel", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false], "solution_text": "Evelyn is a knave, Henry is a knave, Logan is a knave, Avery is a knave, Daniel is a knave, and Aiden is a knave.", "solution_text_format": "(1) Evelyn is a knave\n(2) Henry is a knave\n(3) Logan is a knave\n(4) Avery is a knave\n(5) Daniel is a knave\n(6) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Daniel is a knave and Logan is a knight.", "Daniel cannot be a knight, because this would contradict the claim of Evelyn that Daniel is a knave and Logan is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Henry is not a knave.", "Henry cannot be a knight, because this would contradict the false claim of Daniel that Henry is not a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Aiden is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Daniel is a knight.", "Logan cannot be a knave, because this would contradict the claim of Evelyn that Daniel is a knave and Logan is a knight.", "We have exhausted all possibilities for Logan, Henry, and Daniel, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Daniel is a knave and Logan is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Henry is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Logan is a knight if and only if Aiden is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Daniel is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Henry that Logan is a knight if and only if Aiden is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Henry is not a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Daniel that Henry is not a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Henry is not a knave.", "Henry cannot be a knight, because this would contradict the false claim of Daniel that Henry is not a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Aiden is a knave.", "Logan cannot be a knight, because this would contradict the false claim of Evelyn that Daniel is a knave and Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Henry that Logan is a knight if and only if Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Henry is not a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Henry is not a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Henry is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('lying', 5)), ('telling-truth', 4), ('not', ('lying', 1)), ('not', ('lying', 1)), ('not', ('lying', 1)))", "index": 262}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, William, Victoria, Mason, Grace, and Amelia. Jacob asserted: \"Mason is a knight\". In William's words: \"William is a knight and Jacob is a knight\". \"Jacob is a knight if and only if Jacob is a knave\" - Victoria. Mason remarked, \"William is a knave\". Grace expressed that Grace is a knight and William is a knight. \"Mason is a knave and Amelia is a knight,\" Amelia mentioned. So who is a knight and who is a knave?", "names": ["Jacob", "William", "Victoria", "Mason", "Grace", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false], "solution_text": "Jacob is a knight, William is a knave, Victoria is a knave, Mason is a knight, Grace is a knave, and Amelia is a knave.", "solution_text_format": "(1) Jacob is a knight\n(2) William is a knave\n(3) Victoria is a knave\n(4) Mason is a knight\n(5) Grace is a knave\n(6) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Mason that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that William is a knight and Jacob is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Jacob is a knight if and only if Jacob is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Jacob is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Grace is a knight and William is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight and William is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Mason is a knave and Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 0), ('lying', 0)), ('lying', 1), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('and', ('lying', 3), ('telling-truth', 5)))", "index": 263}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Olivia, Samuel, Liam, Evelyn, and Mason. Emily told you that Evelyn is not a knave. Olivia said, \"Mason is a knight and Liam is a knight.\" \"Liam is a knave,\" Samuel claimed. Liam said, \"Olivia is not a knave.\" In Evelyn's words: \"Mason is a knave or Liam is a knave\". \"Liam is a knave and Liam is a knight\" - Mason. So who is a knight and who is a knave?", "names": ["Emily", "Olivia", "Samuel", "Liam", "Evelyn", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false], "solution_text": "Emily is a knight, Olivia is a knave, Samuel is a knight, Liam is a knave, Evelyn is a knight, and Mason is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Olivia is a knave\n(3) Samuel is a knight\n(4) Liam is a knave\n(5) Evelyn is a knight\n(6) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Evelyn is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Mason is a knave or Liam is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Liam is a knave and Liam is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Liam is a knave and Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Liam is a knight.", "Olivia cannot be a knave, because this would contradict the claim of Liam that Olivia is not a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Olivia is not a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Liam is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Mason is a knight and Liam is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Liam is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('and', ('telling-truth', 5), ('telling-truth', 3)), ('lying', 3), ('not', ('lying', 1)), ('or', ('lying', 5), ('lying', 3)), ('and', ('lying', 3), ('telling-truth', 3)))", "index": 264}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Samuel, Emily, Charlotte, Victoria, and Harper. Mason asserted: \"If Samuel is a knight then Emily is a knave\". Samuel said, \"Harper is not a knight.\" \"Samuel is a knave if and only if Mason is a knave\" - Emily. Charlotte said that Emily is not a knight. Victoria commented, \"Charlotte is a knight or Samuel is a knight\". \"Victoria is a knight if and only if Harper is a knight,\" Harper declared. So who is a knight and who is a knave?", "names": ["Mason", "Samuel", "Emily", "Charlotte", "Victoria", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true], "solution_text": "Mason is a knight, Samuel is a knave, Emily is a knave, Charlotte is a knight, Victoria is a knight, and Harper is a knight.", "solution_text_format": "(1) Mason is a knight\n(2) Samuel is a knave\n(3) Emily is a knave\n(4) Charlotte is a knight\n(5) Victoria is a knight\n(6) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that If Samuel is a knight then Emily is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Harper is not a knight.", "Harper cannot be a knight, because this would contradict the claim of Samuel that Harper is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Harper is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Charlotte is a knight or Samuel is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Emily is not a knight.", "Emily cannot be a knight, because this would contradict the claim of Mason that If Samuel is a knight then Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that Samuel is a knave if and only if Mason is a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Emily is not a knight.", "Emily cannot be a knight, because this would contradict the claim of Mason that If Samuel is a knight then Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that Samuel is a knave if and only if Mason is a knave.", "We have exhausted all possibilities for Emily and Charlotte, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knight or Samuel is a knight.", "We have exhausted all possibilities for Victoria and Harper, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Harper is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Harper is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Charlotte is a knight or Samuel is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Emily is not a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Samuel is a knave if and only if Mason is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('lying', 2)), ('not', ('telling-truth', 5)), ('<=>', ('lying', 1), ('lying', 0)), ('not', ('telling-truth', 2)), ('or', ('telling-truth', 3), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('telling-truth', 5)))", "index": 265}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Oliver, Ava, Victoria, Zoey, and Olivia. Daniel asserted: \"Olivia is a knave or Oliver is a knight\". Oliver commented, \"Zoey is a knave and Ava is a knave\". Ava asserted: \"Olivia is a knave\". Victoria told you that Olivia is a knight if and only if Daniel is a knight. According to Zoey, \"Olivia is not a knight\". As Olivia put it, \"Daniel is a knight or Olivia is a knight\". So who is a knight and who is a knave?", "names": ["Daniel", "Oliver", "Ava", "Victoria", "Zoey", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Daniel is a knight, Oliver is a knight, Ava is a knave, Victoria is a knight, Zoey is a knave, and Olivia is a knight.", "solution_text_format": "(1) Daniel is a knight\n(2) Oliver is a knight\n(3) Ava is a knave\n(4) Victoria is a knight\n(5) Zoey is a knave\n(6) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Olivia is a knave or Oliver is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Daniel is a knight or Olivia is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Zoey is a knave and Ava is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Oliver that Zoey is a knave and Ava is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Olivia is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Oliver that Zoey is a knave and Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 1)), ('and', ('lying', 4), ('lying', 2)), ('lying', 5), ('<=>', ('telling-truth', 5), ('telling-truth', 0)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 0), ('telling-truth', 5)))", "index": 266}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Mason, Zoey, Alexander, Luke, and Lily. According to Abigail, \"Mason is a knight if and only if Luke is a knave\". Mason said, \"Lily is a knight and Zoey is a knave.\" \"If Zoey is a knight then Luke is a knight,\" Zoey claimed. \"If Mason is a knight then Luke is a knight,\" Alexander declared. Luke commented, \"Zoey is a knave if and only if Alexander is a knave\". \"Abigail is a knave or Mason is a knight,\" Lily mentioned. So who is a knight and who is a knave?", "names": ["Abigail", "Mason", "Zoey", "Alexander", "Luke", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Abigail is a knight, Mason is a knave, Zoey is a knight, Alexander is a knight, Luke is a knight, and Lily is a knave.", "solution_text_format": "(1) Abigail is a knight\n(2) Mason is a knave\n(3) Zoey is a knight\n(4) Alexander is a knight\n(5) Luke is a knight\n(6) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Mason is a knight if and only if Luke is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Lily is a knight and Zoey is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Abigail is a knave or Mason is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Mason that Lily is a knight and Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that If Zoey is a knight then Luke is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Mason that Lily is a knight and Zoey is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Lily is a knight and Zoey is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Abigail is a knave or Mason is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Abigail is a knave or Mason is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Zoey is a knight then Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Mason is a knight then Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 4)), ('and', ('telling-truth', 5), ('lying', 2)), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('<=>', ('lying', 2), ('lying', 3)), ('or', ('lying', 0), ('telling-truth', 1)))", "index": 267}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Logan, Lily, Sofia, Ethan, and Ella. \"Sofia is a knave or Lily is a knight,\" Avery claimed. Logan said that Sofia is a knave if and only if Ethan is a knave. Lily remarked, \"Ella is a knight and Ethan is a knight\". Sofia remarked, \"If Ethan is a knave then Ethan is a knight\". Ethan commented, \"Avery is a knight or Lily is a knave\". \"Logan is a knave and Sofia is a knave\" - Ella. So who is a knight and who is a knave?", "names": ["Avery", "Logan", "Lily", "Sofia", "Ethan", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Avery is a knave, Logan is a knight, Lily is a knave, Sofia is a knight, Ethan is a knight, and Ella is a knave.", "solution_text_format": "(1) Avery is a knave\n(2) Logan is a knight\n(3) Lily is a knave\n(4) Sofia is a knight\n(5) Ethan is a knight\n(6) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Sofia is a knave or Lily is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Ethan is a knave then Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Avery is a knight or Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Ella is a knight and Ethan is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Sofia is a knave.", "Ella cannot be a knave, because this would contradict the claim of Lily that Ella is a knight and Ethan is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Avery that Sofia is a knave or Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Sofia that If Ethan is a knave then Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Ethan is a knave then Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Sofia that If Ethan is a knave then Ethan is a knight.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Avery is a knight or Lily is a knave.", "We have exhausted all possibilities for Ethan and Sofia, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Sofia is a knave or Lily is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Ethan is a knave then Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Avery is a knight or Lily is a knave.", "Lily cannot be a knight, because this would contradict the false claim of Avery that Sofia is a knave or Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Ella is a knight and Ethan is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Lily that Ella is a knight and Ethan is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Logan is a knave and Sofia is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 2)), ('<=>', ('lying', 3), ('lying', 4)), ('and', ('telling-truth', 5), ('telling-truth', 4)), ('->', ('lying', 4), ('telling-truth', 4)), ('or', ('telling-truth', 0), ('lying', 2)), ('and', ('lying', 1), ('lying', 3)))", "index": 268}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Joseph, Emily, James, Sebastian, and Ava. William was heard saying, \"Sebastian is a knave or Ava is a knight\". As Joseph put it, \"William is a knave if and only if Ava is a knave\". In a statement by Emily: \"Ava is a knight if and only if Joseph is a knight\". James stated, \"Sebastian is not a knight\". \"If Joseph is a knight then Ava is a knave,\" Sebastian declared. Ava stated, \"William is a knight and Joseph is a knave\". So who is a knight and who is a knave?", "names": ["William", "Joseph", "Emily", "James", "Sebastian", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "William is a knave, Joseph is a knight, Emily is a knave, James is a knave, Sebastian is a knight, and Ava is a knave.", "solution_text_format": "(1) William is a knave\n(2) Joseph is a knight\n(3) Emily is a knave\n(4) James is a knave\n(5) Sebastian is a knight\n(6) Ava is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Sebastian is a knave or Ava is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Joseph is a knight then Ava is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that William is a knave if and only if Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Sebastian that If Joseph is a knight then Ava is a knave.", "Ava cannot be a knave, because this would contradict the claim of William that Sebastian is a knave or Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that William is a knave if and only if Ava is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Joseph that William is a knave if and only if Ava is a knave.", "Ava cannot be a knave, because this would contradict the claim of William that Sebastian is a knave or Ava is a knight.", "We have exhausted all possibilities for Ava and Joseph, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Joseph is a knight then Ava is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that William is a knave if and only if Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that William is a knight and Joseph is a knave.", "Ava cannot be a knave, because this would contradict the claim of Joseph that William is a knave if and only if Ava is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Sebastian that If Joseph is a knight then Ava is a knave.", "We have exhausted all possibilities for Joseph and Sebastian, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Sebastian is a knave or Ava is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Joseph is a knight then Ava is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that William is a knave if and only if Ava is a knave.", "Ava cannot be a knight, because this would contradict the false claim of William that Sebastian is a knave or Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that William is a knight and Joseph is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Ava is a knight if and only if Joseph is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Joseph is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Sebastian is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 5)), ('<=>', ('lying', 0), ('lying', 5)), ('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 1), ('lying', 5)), ('and', ('telling-truth', 0), ('lying', 1)))", "index": 269}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Aiden, Daniel, Logan, Oliver, and Sebastian. Elizabeth asserted: \"Aiden is not a knight\". Aiden was heard saying, \"Sebastian is a knave if and only if Sebastian is a knight\". As Daniel put it, \"Logan is not a knight\". In a statement by Logan: \"Aiden is not a knight\". Oliver told you that Sebastian is not a knave. In Sebastian's words: \"Aiden is not a knight\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Aiden", "Daniel", "Logan", "Oliver", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true], "solution_text": "Elizabeth is a knight, Aiden is a knave, Daniel is a knave, Logan is a knight, Oliver is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Aiden is a knave\n(3) Daniel is a knave\n(4) Logan is a knight\n(5) Oliver is a knight\n(6) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Aiden is not a knight.", "Aiden cannot be a knight, because this would contradict the claim of Elizabeth that Aiden is not a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Aiden is not a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Logan is not a knight.", "Logan cannot be a knight, because this would contradict the claim of Daniel that Logan is not a knight.", "Logan cannot be a knave, because this would contradict the false claim of their own that Aiden is not a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Logan is not a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Aiden is not a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Sebastian is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('<=>', ('lying', 5), ('telling-truth', 5)), ('not', ('telling-truth', 3)), ('not', ('telling-truth', 1)), ('not', ('lying', 5)), ('not', ('telling-truth', 1)))", "index": 270}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Charlotte, Lucas, Lily, Sofia, and Victoria. \"Charlotte is not a knight,\" Avery mentioned. Charlotte was heard saying, \"Victoria is a knave\". \"If Lily is a knight then Sofia is a knave,\" Lucas mentioned. Lily commented, \"Lucas is not a knight\". Sofia asserted: \"Victoria is a knave if and only if Victoria is a knight\". Victoria remarked, \"If Lucas is a knave then Sofia is a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Charlotte", "Lucas", "Lily", "Sofia", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Avery is a knight, Charlotte is a knave, Lucas is a knight, Lily is a knave, Sofia is a knave, and Victoria is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Charlotte is a knave\n(3) Lucas is a knight\n(4) Lily is a knave\n(5) Sofia is a knave\n(6) Victoria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Avery that Charlotte is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Lucas is a knave then Sofia is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Lily is a knight then Sofia is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Lucas is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Victoria is a knave if and only if Victoria is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('lying', 5), ('->', ('telling-truth', 3), ('lying', 4)), ('not', ('telling-truth', 2)), ('<=>', ('lying', 5), ('telling-truth', 5)), ('->', ('lying', 2), ('lying', 4)))", "index": 271}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Oliver, Jackson, Benjamin, Noah, and Luke. Lucas said that Luke is a knight. In a statement by Oliver: \"Noah is a knave\". Jackson was heard saying, \"If Luke is a knave then Benjamin is a knave\". According to Benjamin, \"Luke is a knave and Lucas is a knave\". Noah said that Oliver is a knave and Noah is a knight. In a statement by Luke: \"Lucas is a knave and Noah is a knight\". So who is a knight and who is a knave?", "names": ["Lucas", "Oliver", "Jackson", "Benjamin", "Noah", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false], "solution_text": "Lucas is a knave, Oliver is a knight, Jackson is a knave, Benjamin is a knight, Noah is a knave, and Luke is a knave.", "solution_text_format": "(1) Lucas is a knave\n(2) Oliver is a knight\n(3) Jackson is a knave\n(4) Benjamin is a knight\n(5) Noah is a knave\n(6) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Noah is a knight.", "Luke cannot be a knave, because this would contradict the claim of Lucas that Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Lucas that Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Lucas is a knave and Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Luke that Lucas is a knave and Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Oliver is a knave and Noah is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Noah is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Luke is a knave then Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Jackson that If Luke is a knave then Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Luke is a knave and Lucas is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Luke is a knave then Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Luke is a knave and Lucas is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('lying', 4), ('->', ('lying', 5), ('lying', 3)), ('and', ('lying', 5), ('lying', 0)), ('and', ('lying', 1), ('telling-truth', 4)), ('and', ('lying', 0), ('telling-truth', 4)))", "index": 272}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Aiden, Samuel, Sofia, Evelyn, and Avery. In Jack's words: \"If Jack is a knight then Avery is a knave\". Aiden commented, \"Jack is a knight\". Samuel said, \"Evelyn is a knight and Aiden is a knave.\" Sofia said, \"Jack is not a knave.\" In a statement by Evelyn: \"Samuel is a knave and Sofia is a knave\". Avery expressed that Samuel is a knight. So who is a knight and who is a knave?", "names": ["Jack", "Aiden", "Samuel", "Sofia", "Evelyn", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Jack is a knight, Aiden is a knight, Samuel is a knave, Sofia is a knight, Evelyn is a knave, and Avery is a knave.", "solution_text_format": "(1) Jack is a knight\n(2) Aiden is a knight\n(3) Samuel is a knave\n(4) Sofia is a knight\n(5) Evelyn is a knave\n(6) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that If Jack is a knight then Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Jack that If Jack is a knight then Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Avery that Samuel is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Evelyn is a knight and Aiden is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Samuel is a knave and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Evelyn that Samuel is a knave and Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Jack is not a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Samuel is a knave and Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('lying', 5)), ('telling-truth', 0), ('and', ('telling-truth', 4), ('lying', 1)), ('not', ('lying', 0)), ('and', ('lying', 2), ('lying', 3)), ('telling-truth', 2))", "index": 273}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, William, Sebastian, Daniel, Emma, and Olivia. Lucas expressed that Sebastian is a knight. William remarked, \"Lucas is not a knight\". Sebastian said, \"Olivia is a knave.\" As Daniel put it, \"Emma is a knight and Sebastian is a knave\". Emma stated, \"Lucas is a knight\". Olivia commented, \"Sebastian is a knight or Lucas is a knave\". So who is a knight and who is a knave?", "names": ["Lucas", "William", "Sebastian", "Daniel", "Emma", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true], "solution_text": "Lucas is a knave, William is a knight, Sebastian is a knave, Daniel is a knave, Emma is a knave, and Olivia is a knight.", "solution_text_format": "(1) Lucas is a knave\n(2) William is a knight\n(3) Sebastian is a knave\n(4) Daniel is a knave\n(5) Emma is a knave\n(6) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Sebastian that Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knight or Lucas is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Lucas that Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Lucas that Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Sebastian is a knight or Lucas is a knave.", "Assume William is a knight. No contradiction is found in their claim that Lucas is not a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Emma is a knight and Sebastian is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Lucas is a knight.", "Emma cannot be a knave, because this would contradict the claim of Daniel that Emma is a knight and Sebastian is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Emma is a knight and Sebastian is a knave.", "Emma cannot be a knight, because this would contradict the false claim of Daniel that Emma is a knight and Sebastian is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('not', ('telling-truth', 0)), ('lying', 5), ('and', ('telling-truth', 4), ('lying', 2)), ('telling-truth', 0), ('or', ('telling-truth', 2), ('lying', 0)))", "index": 274}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Aiden, Scarlett, Avery, Ava, and Benjamin. William noted, \"If Scarlett is a knight then Ava is a knave\". Aiden expressed that If Benjamin is a knave then Benjamin is a knight. In a statement by Scarlett: \"William is not a knight\". Avery stated, \"Aiden is a knave\". Ava said, \"Scarlett is a knight.\" Benjamin expressed that Ava is a knight and Avery is a knight. So who is a knight and who is a knave?", "names": ["William", "Aiden", "Scarlett", "Avery", "Ava", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false], "solution_text": "William is a knight, Aiden is a knave, Scarlett is a knave, Avery is a knight, Ava is a knave, and Benjamin is a knave.", "solution_text_format": "(1) William is a knight\n(2) Aiden is a knave\n(3) Scarlett is a knave\n(4) Avery is a knight\n(5) Ava is a knave\n(6) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that If Scarlett is a knight then Ava is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that William is not a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that William is not a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Benjamin is a knave then Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Ava is a knight and Avery is a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Aiden that If Benjamin is a knave then Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Aiden that If Benjamin is a knave then Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ava is a knight and Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 4)), ('->', ('lying', 5), ('telling-truth', 5)), ('not', ('telling-truth', 0)), ('lying', 1), ('telling-truth', 2), ('and', ('telling-truth', 4), ('telling-truth', 3)))", "index": 275}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Henry, Daniel, Luke, Samuel, and Chloe. \"Daniel is a knave\" - Jackson. Henry noted, \"If Samuel is a knight then Chloe is a knight\". Daniel said that Luke is a knight. \"Chloe is not a knight,\" Luke declared. \"Henry is not a knave,\" Samuel mentioned. Chloe was heard saying, \"Luke is a knave\". So who is a knight and who is a knave?", "names": ["Jackson", "Henry", "Daniel", "Luke", "Samuel", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "Jackson is a knight, Henry is a knight, Daniel is a knave, Luke is a knave, Samuel is a knight, and Chloe is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Henry is a knight\n(3) Daniel is a knave\n(4) Luke is a knave\n(5) Samuel is a knight\n(6) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Jackson that Daniel is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Daniel that Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Luke is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Samuel is a knight then Chloe is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Henry is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('->', ('telling-truth', 4), ('telling-truth', 5)), ('telling-truth', 3), ('not', ('telling-truth', 5)), ('not', ('lying', 1)), ('lying', 3))", "index": 276}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Sophia, Isabella, Elizabeth, Ava, and Lily. In a statement by Jackson: \"Ava is a knight if and only if Ava is a knave\". According to Sophia, \"Ava is a knave and Isabella is a knave\". \"If Ava is a knight then Ava is a knave,\" Isabella claimed. Elizabeth stated, \"Ava is a knave if and only if Sophia is a knave\". According to Ava, \"Isabella is a knight or Sophia is a knave\". In Lily's words: \"Elizabeth is a knight and Ava is a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Sophia", "Isabella", "Elizabeth", "Ava", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false], "solution_text": "Jackson is a knave, Sophia is a knave, Isabella is a knave, Elizabeth is a knave, Ava is a knight, and Lily is a knave.", "solution_text_format": "(1) Jackson is a knave\n(2) Sophia is a knave\n(3) Isabella is a knave\n(4) Elizabeth is a knave\n(5) Ava is a knight\n(6) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Jackson cannot be a knight, because this would contradict the claim of their own that Ava is a knight if and only if Ava is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Isabella is a knight or Sophia is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that If Ava is a knight then Ava is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Ava is a knight then Ava is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Ava is a knave and Isabella is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Ava is a knave and Isabella is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Sophia is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Sophia is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Ava is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('lying', 4)), ('and', ('lying', 4), ('lying', 2)), ('->', ('telling-truth', 4), ('lying', 4)), ('<=>', ('lying', 4), ('lying', 1)), ('or', ('telling-truth', 2), ('lying', 1)), ('and', ('telling-truth', 3), ('telling-truth', 4)))", "index": 277}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Lily, Aria, Avery, Abigail, and Benjamin. Samuel noted, \"Lily is a knight and Aria is a knight\". Lily said, \"Samuel is a knight.\" Aria told you that Abigail is a knight. In a statement by Avery: \"If Benjamin is a knight then Benjamin is a knave\". In Abigail's words: \"Avery is a knave and Lily is a knave\". Benjamin remarked, \"Abigail is a knight or Lily is a knave\". So who is a knight and who is a knave?", "names": ["Samuel", "Lily", "Aria", "Avery", "Abigail", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true], "solution_text": "Samuel is a knave, Lily is a knave, Aria is a knight, Avery is a knave, Abigail is a knight, and Benjamin is a knight.", "solution_text_format": "(1) Samuel is a knave\n(2) Lily is a knave\n(3) Aria is a knight\n(4) Avery is a knave\n(5) Abigail is a knight\n(6) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Lily is a knight and Aria is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Samuel is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Lily is a knave.", "Abigail cannot be a knave, because this would contradict the claim of Aria that Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Samuel that Lily is a knight and Aria is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Samuel that Lily is a knight and Aria is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Lily is a knight and Aria is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Samuel is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Samuel is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Avery is a knave and Lily is a knave.", "Avery cannot be a knight, because this would contradict the claim of Abigail that Avery is a knave and Lily is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Abigail is a knight or Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 2)), ('telling-truth', 0), ('telling-truth', 4), ('->', ('telling-truth', 5), ('lying', 5)), ('and', ('lying', 3), ('lying', 1)), ('or', ('telling-truth', 4), ('lying', 1)))", "index": 278}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Sophia, Ella, Jackson, Luke, and Henry. Isabella remarked, \"If Jackson is a knight then Ella is a knight\". Sophia noted, \"Isabella is not a knave\". Ella commented, \"Henry is a knight and Isabella is a knave\". Jackson asserted: \"Luke is not a knight\". Luke asserted: \"If Isabella is a knave then Sophia is a knight\". As Henry put it, \"Luke is a knight or Luke is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Sophia", "Ella", "Jackson", "Luke", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "Isabella is a knight, Sophia is a knight, Ella is a knave, Jackson is a knave, Luke is a knight, and Henry is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Sophia is a knight\n(3) Ella is a knave\n(4) Jackson is a knave\n(5) Luke is a knight\n(6) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that If Jackson is a knight then Ella is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Jackson that Luke is not a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that If Isabella is a knave then Sophia is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Luke is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Isabella is a knave then Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Isabella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Henry is a knight and Isabella is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Luke is a knight or Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('telling-truth', 2)), ('not', ('lying', 0)), ('and', ('telling-truth', 5), ('lying', 0)), ('not', ('telling-truth', 4)), ('->', ('lying', 0), ('telling-truth', 1)), ('or', ('telling-truth', 4), ('lying', 4)))", "index": 279}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Henry, Elizabeth, Aurora, Joseph, and Jackson. In Charlotte's words: \"Joseph is a knight and Aurora is a knave\". According to Henry, \"Joseph is a knave if and only if Jackson is a knight\". Elizabeth told you that Aurora is not a knave. \"Elizabeth is a knave or Elizabeth is a knight,\" Aurora claimed. \"Aurora is a knave if and only if Charlotte is a knave,\" Joseph declared. Jackson told you that Charlotte is a knight. So who is a knight and who is a knave?", "names": ["Charlotte", "Henry", "Elizabeth", "Aurora", "Joseph", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Charlotte is a knave, Henry is a knave, Elizabeth is a knight, Aurora is a knight, Joseph is a knave, and Jackson is a knave.", "solution_text_format": "(1) Charlotte is a knave\n(2) Henry is a knave\n(3) Elizabeth is a knight\n(4) Aurora is a knight\n(5) Joseph is a knave\n(6) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Joseph is a knight and Aurora is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Charlotte is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Charlotte that Joseph is a knight and Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knave or Elizabeth is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Charlotte that Joseph is a knight and Aurora is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Joseph is a knight and Aurora is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Charlotte is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Joseph that Aurora is a knave if and only if Charlotte is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of Charlotte that Joseph is a knight and Aurora is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Charlotte is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Elizabeth is a knave or Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight.", "Jackson cannot be a knave, because this would contradict the claim of Henry that Joseph is a knave if and only if Jackson is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Henry that Joseph is a knave if and only if Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 3)), ('<=>', ('lying', 4), ('telling-truth', 5)), ('not', ('lying', 3)), ('or', ('lying', 2), ('telling-truth', 2)), ('<=>', ('lying', 3), ('lying', 0)), ('telling-truth', 0))", "index": 280}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Logan, Jackson, Daniel, Aria, and Henry. \"Emma is a knight if and only if Aria is a knave,\" Emma declared. Logan told you that Emma is a knight if and only if Daniel is a knight. According to Jackson, \"Aria is a knave if and only if Henry is a knave\". In a statement by Daniel: \"Aria is not a knight\". Aria noted, \"Daniel is a knight if and only if Henry is a knave\". Henry commented, \"Emma is a knight or Jackson is a knight\". So who is a knight and who is a knave?", "names": ["Emma", "Logan", "Jackson", "Daniel", "Aria", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Emma is a knight, Logan is a knight, Jackson is a knave, Daniel is a knight, Aria is a knave, and Henry is a knight.", "solution_text_format": "(1) Emma is a knight\n(2) Logan is a knight\n(3) Jackson is a knave\n(4) Daniel is a knight\n(5) Aria is a knave\n(6) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Emma is a knight if and only if Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Emma that Emma is a knight if and only if Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Henry is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Aria is not a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Emma is a knight or Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Aria is a knave if and only if Henry is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Henry is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Emma is a knight if and only if Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 4)), ('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('<=>', ('lying', 4), ('lying', 5)), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('lying', 5)), ('or', ('telling-truth', 0), ('telling-truth', 2)))", "index": 281}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Sophia, Victoria, Abigail, Grace, and Luke. \"Sophia is a knight if and only if Luke is a knave\" - Elizabeth. Sophia remarked, \"Elizabeth is a knight or Grace is a knight\". As Victoria put it, \"Grace is a knave and Abigail is a knight\". Abigail said, \"Victoria is a knave or Sophia is a knight.\" Grace said, \"Luke is a knave and Elizabeth is a knight.\" Luke told you that Sophia is a knight and Abigail is a knave. So who is a knight and who is a knave?", "names": ["Elizabeth", "Sophia", "Victoria", "Abigail", "Grace", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "Elizabeth is a knight, Sophia is a knight, Victoria is a knave, Abigail is a knight, Grace is a knight, and Luke is a knave.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Sophia is a knight\n(3) Victoria is a knave\n(4) Abigail is a knight\n(5) Grace is a knight\n(6) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Luke is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Elizabeth is a knight or Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Luke is a knave and Elizabeth is a knight.", "Luke cannot be a knight, because this would contradict the claim of Elizabeth that Sophia is a knight if and only if Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Sophia is a knight and Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Victoria is a knave or Sophia is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Abigail is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Grace is a knave and Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 5)), ('or', ('telling-truth', 0), ('telling-truth', 4)), ('and', ('lying', 4), ('telling-truth', 3)), ('or', ('lying', 2), ('telling-truth', 1)), ('and', ('lying', 5), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('lying', 3)))", "index": 282}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Isabella, Ella, James, Elizabeth, and Sebastian. Lily said, \"James is not a knight.\" Isabella noted, \"Ella is a knight or Ella is a knave\". Ella remarked, \"Lily is a knave and Lily is a knight\". James asserted: \"Elizabeth is a knave or Ella is a knight\". According to Elizabeth, \"If Ella is a knave then Isabella is a knave\". In Sebastian's words: \"Lily is a knight and Elizabeth is a knight\". So who is a knight and who is a knave?", "names": ["Lily", "Isabella", "Ella", "James", "Elizabeth", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false], "solution_text": "Lily is a knave, Isabella is a knight, Ella is a knave, James is a knight, Elizabeth is a knave, and Sebastian is a knave.", "solution_text_format": "(1) Lily is a knave\n(2) Isabella is a knight\n(3) Ella is a knave\n(4) James is a knight\n(5) Elizabeth is a knave\n(6) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that James is not a knight.", "James cannot be a knight, because this would contradict the claim of Lily that James is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Elizabeth is a knave or Ella is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Ella is a knave then Isabella is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Lily is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Lily is a knave and Lily is a knight.", "Isabella cannot be a knight, because this would contradict the claim of Elizabeth that If Ella is a knave then Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Ella is a knave.", "We have exhausted all possibilities for Isabella and Ella, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the false claim of James that Elizabeth is a knave or Ella is a knight.", "We have exhausted all possibilities for Elizabeth and James, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that James is not a knight.", "Assume James is a knight. No contradiction is found in their claim that Elizabeth is a knave or Ella is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Ella is a knave then Isabella is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Lily is a knight.", "Ella cannot be a knave, because this would contradict the claim of James that Elizabeth is a knave or Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that If Ella is a knave then Isabella is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Lily is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Lily is a knave and Lily is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Ella is a knight or Ella is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Elizabeth is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Lily is a knight and Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('or', ('telling-truth', 2), ('lying', 2)), ('and', ('lying', 0), ('telling-truth', 0)), ('or', ('lying', 4), ('telling-truth', 2)), ('->', ('lying', 2), ('lying', 1)), ('and', ('telling-truth', 0), ('telling-truth', 4)))", "index": 283}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Ethan, Aurora, Avery, Abigail, and Lucas. William asserted: \"If Abigail is a knave then Lucas is a knave\". Ethan remarked, \"Avery is a knave or Lucas is a knave\". In a statement by Aurora: \"Abigail is a knight if and only if Lucas is a knight\". In Avery's words: \"If Lucas is a knight then Ethan is a knave\". Abigail said that If Lucas is a knight then Ethan is a knave. Lucas told you that Abigail is a knight. So who is a knight and who is a knave?", "names": ["William", "Ethan", "Aurora", "Avery", "Abigail", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "William is a knight, Ethan is a knave, Aurora is a knight, Avery is a knight, Abigail is a knight, and Lucas is a knight.", "solution_text_format": "(1) William is a knight\n(2) Ethan is a knave\n(3) Aurora is a knight\n(4) Avery is a knight\n(5) Abigail is a knight\n(6) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that If Abigail is a knave then Lucas is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Lucas is a knight then Ethan is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Abigail is a knight.", "Ethan cannot be a knight, because this would contradict the claim of Abigail that If Lucas is a knight then Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Avery is a knave or Lucas is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Lucas is a knight then Ethan is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('lying', 5)), ('or', ('lying', 3), ('lying', 5)), ('<=>', ('telling-truth', 4), ('telling-truth', 5)), ('->', ('telling-truth', 5), ('lying', 1)), ('->', ('telling-truth', 5), ('lying', 1)), ('telling-truth', 4))", "index": 284}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Ethan, Henry, Alexander, Emma, and Isabella. Riley said that Emma is not a knave. Ethan asserted: \"Riley is a knave or Isabella is a knight\". According to Henry, \"Riley is a knave and Emma is a knave\". Alexander commented, \"Ethan is a knave and Henry is a knight\". In Emma's words: \"Ethan is not a knave\". Isabella commented, \"If Emma is a knave then Riley is a knight\". So who is a knight and who is a knave?", "names": ["Riley", "Ethan", "Henry", "Alexander", "Emma", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "Riley is a knight, Ethan is a knight, Henry is a knave, Alexander is a knave, Emma is a knight, and Isabella is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Ethan is a knight\n(3) Henry is a knave\n(4) Alexander is a knave\n(5) Emma is a knight\n(6) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Emma is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Riley is a knave or Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Emma is a knave then Riley is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Emma is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Riley is a knave and Emma is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Ethan is a knave and Henry is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ethan is a knave and Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('or', ('lying', 0), ('telling-truth', 5)), ('and', ('lying', 0), ('lying', 4)), ('and', ('lying', 1), ('telling-truth', 2)), ('not', ('lying', 1)), ('->', ('lying', 4), ('telling-truth', 0)))", "index": 285}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Ava, Olivia, Oliver, Jack, and Avery. \"Avery is a knave and Oliver is a knight,\" Amelia mentioned. In Ava's words: \"Jack is a knight\". Olivia said, \"Oliver is a knight or Amelia is a knight.\" Oliver remarked, \"Ava is a knave or Olivia is a knave\". Jack told you that Oliver is not a knight. Avery told you that Ava is a knight or Olivia is a knave. So who is a knight and who is a knave?", "names": ["Amelia", "Ava", "Olivia", "Oliver", "Jack", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false], "solution_text": "Amelia is a knight, Ava is a knave, Olivia is a knight, Oliver is a knight, Jack is a knave, and Avery is a knave.", "solution_text_format": "(1) Amelia is a knight\n(2) Ava is a knave\n(3) Olivia is a knight\n(4) Oliver is a knight\n(5) Jack is a knave\n(6) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Avery is a knave and Oliver is a knight.", "Avery cannot be a knight, because this would contradict the claim of Amelia that Avery is a knave and Oliver is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Ava is a knight or Olivia is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Avery that Ava is a knight or Olivia is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Ava that Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Oliver is not a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Ava is a knave or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Oliver is a knight or Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 3)), ('telling-truth', 4), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('lying', 1), ('lying', 2)), ('not', ('telling-truth', 3)), ('or', ('telling-truth', 1), ('lying', 2)))", "index": 286}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Ella, Aurora, Harper, Ava, and Emily. Alexander asserted: \"Ella is a knight or Emily is a knave\". \"Harper is a knight and Aurora is a knave,\" Ella declared. Aurora said that Emily is a knight. \"Ava is not a knight\" - Harper. \"Emily is a knave and Aurora is a knave,\" Ava claimed. \"Emily is a knight or Aurora is a knave,\" Emily mentioned. So who is a knight and who is a knave?", "names": ["Alexander", "Ella", "Aurora", "Harper", "Ava", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Alexander is a knave, Ella is a knave, Aurora is a knight, Harper is a knight, Ava is a knave, and Emily is a knight.", "solution_text_format": "(1) Alexander is a knave\n(2) Ella is a knave\n(3) Aurora is a knight\n(4) Harper is a knight\n(5) Ava is a knave\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Ella is a knight or Emily is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Harper is a knight and Aurora is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Harper that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Emily is a knave and Aurora is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Emily is a knight or Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Ella that Harper is a knight and Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Emily is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Emily is a knight or Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Ella that Harper is a knight and Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of Ava that Emily is a knave and Aurora is a knave.", "We have exhausted all possibilities for Aurora, Emily, and Ava, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Ella that Harper is a knight and Aurora is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Harper is a knight and Aurora is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Harper that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Emily is a knave and Aurora is a knave.", "Emily cannot be a knight, because this would contradict the claim of Alexander that Ella is a knight or Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Emily is a knight or Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Emily is a knight.", "Aurora cannot be a knave, because this would contradict the false claim of Ella that Harper is a knight and Aurora is a knave.", "We have exhausted all possibilities for Aurora, Emily, and Ava, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Emily is a knave and Aurora is a knave.", "Emily cannot be a knight, because this would contradict the claim of Alexander that Ella is a knight or Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Emily is a knight or Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Emily is a knight.", "Aurora cannot be a knave, because this would contradict the false claim of Emily that Emily is a knight or Aurora is a knave.", "We have exhausted all possibilities for Aurora and Emily, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of Harper that Ava is not a knight.", "We have exhausted all possibilities for Ava, Harper, and Ella, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ella is a knight or Emily is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Alexander that Ella is a knight or Emily is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Harper is a knight and Aurora is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Harper that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Emily is a knave and Aurora is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Emily is a knight or Aurora is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 5)), ('and', ('telling-truth', 3), ('lying', 2)), ('telling-truth', 5), ('not', ('telling-truth', 4)), ('and', ('lying', 5), ('lying', 2)), ('or', ('telling-truth', 5), ('lying', 2)))", "index": 287}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Jack, Avery, Michael, Sebastian, and Elizabeth. \"Elizabeth is not a knight\" - Chloe. Jack stated, \"Sebastian is a knight if and only if Elizabeth is a knight\". Avery was heard saying, \"Avery is a knight and Sebastian is a knave\". In Michael's words: \"Jack is not a knave\". Sebastian was heard saying, \"Jack is a knave\". Elizabeth noted, \"Sebastian is not a knight\". So who is a knight and who is a knave?", "names": ["Chloe", "Jack", "Avery", "Michael", "Sebastian", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false], "solution_text": "Chloe is a knight, Jack is a knave, Avery is a knave, Michael is a knave, Sebastian is a knight, and Elizabeth is a knave.", "solution_text_format": "(1) Chloe is a knight\n(2) Jack is a knave\n(3) Avery is a knave\n(4) Michael is a knave\n(5) Sebastian is a knight\n(6) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Chloe that Elizabeth is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight if and only if Elizabeth is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Elizabeth is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Sebastian is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Avery is a knight and Sebastian is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Jack is not a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Jack is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 4), ('telling-truth', 5)), ('and', ('telling-truth', 2), ('lying', 4)), ('not', ('lying', 1)), ('lying', 1), ('not', ('telling-truth', 4)))", "index": 288}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Abigail, Sofia, Jacob, Evelyn, and Penelope. \"Sofia is not a knave,\" Ethan declared. Abigail remarked, \"Penelope is not a knave\". Sofia told you that Penelope is a knight or Ethan is a knave. As Jacob put it, \"Ethan is a knave or Ethan is a knight\". Evelyn expressed that Ethan is a knave or Penelope is a knave. In a statement by Penelope: \"Ethan is a knight or Evelyn is a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Abigail", "Sofia", "Jacob", "Evelyn", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Ethan is a knight, Abigail is a knight, Sofia is a knight, Jacob is a knight, Evelyn is a knave, and Penelope is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Abigail is a knight\n(3) Sofia is a knight\n(4) Jacob is a knight\n(5) Evelyn is a knave\n(6) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Penelope is a knight or Ethan is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Ethan is a knight or Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Ethan is a knave or Penelope is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Ethan is a knave or Penelope is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Ethan is a knave or Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('not', ('lying', 5)), ('or', ('telling-truth', 5), ('lying', 0)), ('or', ('lying', 0), ('telling-truth', 0)), ('or', ('lying', 0), ('lying', 5)), ('or', ('telling-truth', 0), ('telling-truth', 4)))", "index": 289}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Jacob, Scarlett, Penelope, Lucas, and Logan. According to Joseph, \"Scarlett is a knave and Penelope is a knight\". Jacob was heard saying, \"Lucas is a knight\". Scarlett said that Joseph is a knight and Penelope is a knave. \"Lucas is a knight or Joseph is a knight\" - Penelope. Lucas said that Joseph is not a knight. Logan said, \"Scarlett is not a knave.\" So who is a knight and who is a knave?", "names": ["Joseph", "Jacob", "Scarlett", "Penelope", "Lucas", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false], "solution_text": "Joseph is a knight, Jacob is a knave, Scarlett is a knave, Penelope is a knight, Lucas is a knave, and Logan is a knave.", "solution_text_format": "(1) Joseph is a knight\n(2) Jacob is a knave\n(3) Scarlett is a knave\n(4) Penelope is a knight\n(5) Lucas is a knave\n(6) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Scarlett is a knave and Penelope is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Joseph that Scarlett is a knave and Penelope is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Joseph is a knight and Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Lucas is a knight or Joseph is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Joseph is not a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Joseph is not a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Lucas is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Scarlett is not a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Scarlett is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('telling-truth', 3)), ('telling-truth', 4), ('and', ('telling-truth', 0), ('lying', 3)), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('not', ('lying', 2)))", "index": 290}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Zoey, Noah, Luke, Sophia, and Amelia. Logan was heard saying, \"Sophia is a knave if and only if Noah is a knave\". According to Zoey, \"Logan is a knave and Luke is a knight\". In a statement by Noah: \"Logan is a knave\". Luke commented, \"If Sophia is a knight then Sophia is a knave\". In Sophia's words: \"Zoey is a knave or Amelia is a knave\". Amelia said, \"Amelia is a knight or Sophia is a knight.\" So who is a knight and who is a knave?", "names": ["Logan", "Zoey", "Noah", "Luke", "Sophia", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Logan is a knave, Zoey is a knight, Noah is a knight, Luke is a knight, Sophia is a knave, and Amelia is a knight.", "solution_text_format": "(1) Logan is a knave\n(2) Zoey is a knight\n(3) Noah is a knight\n(4) Luke is a knight\n(5) Sophia is a knave\n(6) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Noah is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Zoey is a knave or Amelia is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Luke is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Logan is a knave and Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that If Sophia is a knight then Sophia is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that If Sophia is a knight then Sophia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight or Sophia is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Logan is a knave.", "Noah cannot be a knave, because this would contradict the claim of Logan that Sophia is a knave if and only if Noah is a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight or Sophia is a knight.", "We have exhausted all possibilities for Amelia, Luke, and Zoey, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Zoey is a knave or Amelia is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Luke is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of Sophia that Zoey is a knave or Amelia is a knave.", "We have exhausted all possibilities for Zoey and Sophia, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Noah is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Zoey is a knave or Amelia is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Logan is a knave and Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that If Sophia is a knight then Sophia is a knave.", "Luke cannot be a knave, because this would contradict the claim of Zoey that Logan is a knave and Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Logan is a knave and Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Zoey that Logan is a knave and Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that If Sophia is a knight then Sophia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight or Sophia is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Logan that Sophia is a knave if and only if Noah is a knave.", "Noah cannot be a knave, because this would contradict the false claim of their own that Logan is a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight or Sophia is a knight.", "We have exhausted all possibilities for Amelia, Luke, and Zoey, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Zoey is a knave or Amelia is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Logan is a knave and Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Sophia is a knight then Sophia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight or Sophia is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('lying', 2)), ('and', ('lying', 0), ('telling-truth', 3)), ('lying', 0), ('->', ('telling-truth', 4), ('lying', 4)), ('or', ('lying', 1), ('lying', 5)), ('or', ('telling-truth', 5), ('telling-truth', 4)))", "index": 291}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Noah, Isabella, Ava, Samuel, and Jackson. \"If Isabella is a knight then Isabella is a knave,\" Harper mentioned. As Noah put it, \"If Harper is a knight then Isabella is a knight\". Isabella asserted: \"Jackson is a knave if and only if Harper is a knight\". In Ava's words: \"Jackson is a knight\". As Samuel put it, \"If Isabella is a knight then Noah is a knight\". \"Noah is a knight or Samuel is a knave,\" Jackson claimed. So who is a knight and who is a knave?", "names": ["Harper", "Noah", "Isabella", "Ava", "Samuel", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Harper is a knave, Noah is a knight, Isabella is a knight, Ava is a knight, Samuel is a knight, and Jackson is a knight.", "solution_text_format": "(1) Harper is a knave\n(2) Noah is a knight\n(3) Isabella is a knight\n(4) Ava is a knight\n(5) Samuel is a knight\n(6) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that If Isabella is a knight then Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Harper that If Isabella is a knight then Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Harper is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Noah is a knight or Samuel is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that If Harper is a knight then Isabella is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that If Harper is a knight then Isabella is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Jackson that Noah is a knight or Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that If Isabella is a knight then Noah is a knight.", "We have exhausted all possibilities for Samuel and Noah, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the false claim of Isabella that Jackson is a knave if and only if Harper is a knight.", "We have exhausted all possibilities for Jackson and Isabella, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that If Isabella is a knight then Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Harper is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Noah is a knight or Samuel is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Harper is a knight then Isabella is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Isabella is a knight then Noah is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 2)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('<=>', ('lying', 5), ('telling-truth', 0)), ('telling-truth', 5), ('->', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('telling-truth', 1), ('lying', 4)))", "index": 292}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Isabella, Lily, Emma, Samuel, and Elizabeth. Sophia stated, \"Isabella is a knight and Samuel is a knight\". \"Elizabeth is a knight,\" Isabella declared. Lily commented, \"Emma is a knight and Samuel is a knight\". Emma remarked, \"Sophia is a knave or Elizabeth is a knight\". Samuel commented, \"If Sophia is a knight then Elizabeth is a knight\". Elizabeth said that Lily is a knave and Isabella is a knight. So who is a knight and who is a knave?", "names": ["Sophia", "Isabella", "Lily", "Emma", "Samuel", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Sophia is a knave, Isabella is a knave, Lily is a knight, Emma is a knight, Samuel is a knight, and Elizabeth is a knave.", "solution_text_format": "(1) Sophia is a knave\n(2) Isabella is a knave\n(3) Lily is a knight\n(4) Emma is a knight\n(5) Samuel is a knight\n(6) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Isabella is a knight and Samuel is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Lily is a knave and Isabella is a knight.", "Lily cannot be a knight, because this would contradict the claim of Elizabeth that Lily is a knave and Isabella is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Emma is a knight and Samuel is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Sophia is a knave or Elizabeth is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Lily that Emma is a knight and Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the claim of Sophia that Isabella is a knight and Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the false claim of their own that Sophia is a knave or Elizabeth is a knight.", "We have exhausted all possibilities for Emma and Lily, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Isabella that Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Sophia that Isabella is a knight and Samuel is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Isabella is a knight and Samuel is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Lily is a knave and Isabella is a knight.", "Lily cannot be a knight, because this would contradict the claim of Elizabeth that Lily is a knave and Isabella is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Emma is a knight and Samuel is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Sophia is a knave or Elizabeth is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Sophia that Isabella is a knight and Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knight then Elizabeth is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the false claim of their own that Sophia is a knave or Elizabeth is a knight.", "We have exhausted all possibilities for Emma and Lily, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Isabella that Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Isabella that Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Lily is a knave and Isabella is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Emma is a knight and Samuel is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Sophia is a knave or Elizabeth is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Sophia is a knight then Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 4)), ('telling-truth', 5), ('and', ('telling-truth', 3), ('telling-truth', 4)), ('or', ('lying', 0), ('telling-truth', 5)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('lying', 2), ('telling-truth', 1)))", "index": 293}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Luke, Owen, Oliver, Ella, and Sofia. In a statement by Ethan: \"Oliver is not a knave\". Luke said, \"If Sofia is a knave then Luke is a knight.\" \"Luke is a knave,\" Owen claimed. Oliver remarked, \"If Ella is a knight then Owen is a knave\". Ella said that Owen is a knight and Ella is a knight. \"Owen is a knight or Ella is a knave,\" Sofia claimed. So who is a knight and who is a knave?", "names": ["Ethan", "Luke", "Owen", "Oliver", "Ella", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Ethan is a knight, Luke is a knight, Owen is a knave, Oliver is a knight, Ella is a knave, and Sofia is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Luke is a knight\n(3) Owen is a knave\n(4) Oliver is a knight\n(5) Ella is a knave\n(6) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Ella is a knight then Owen is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Owen is a knight and Ella is a knight.", "Owen cannot be a knight, because this would contradict the claim of Oliver that If Ella is a knight then Owen is a knave.", "Owen cannot be a knave, because this would contradict the claim of Ella that Owen is a knight and Ella is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Owen is a knight and Ella is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Owen that Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that If Sofia is a knave then Luke is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Luke that If Sofia is a knave then Luke is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Owen is a knight or Ella is a knave.", "We have exhausted all possibilities for Sofia and Luke, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Sofia is a knave then Luke is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Owen is a knight or Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('->', ('lying', 5), ('telling-truth', 1)), ('lying', 1), ('->', ('telling-truth', 4), ('lying', 2)), ('and', ('telling-truth', 2), ('telling-truth', 4)), ('or', ('telling-truth', 2), ('lying', 4)))", "index": 294}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Benjamin, Penelope, Harper, Mia, and Emily. \"Benjamin is not a knave,\" Ella mentioned. \"If Harper is a knight then Benjamin is a knight,\" Benjamin claimed. Penelope said, \"Ella is not a knave.\" According to Harper, \"Penelope is a knight or Ella is a knight\". \"Emily is a knight or Ella is a knight,\" Mia claimed. Emily said that Harper is a knave or Ella is a knave. So who is a knight and who is a knave?", "names": ["Ella", "Benjamin", "Penelope", "Harper", "Mia", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Ella is a knight, Benjamin is a knight, Penelope is a knight, Harper is a knight, Mia is a knight, and Emily is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Benjamin is a knight\n(3) Penelope is a knight\n(4) Harper is a knight\n(5) Mia is a knight\n(6) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Harper is a knight then Benjamin is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Penelope is a knight or Ella is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Emily is a knight or Ella is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Harper is a knave or Ella is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Harper is a knave or Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('not', ('lying', 0)), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('or', ('lying', 3), ('lying', 0)))", "index": 295}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Amelia, Emily, Emma, Harper, and Scarlett. Luke commented, \"Emily is a knave if and only if Luke is a knight\". In Amelia's words: \"Luke is not a knight\". In a statement by Emily: \"If Scarlett is a knave then Amelia is a knight\". Emma was heard saying, \"Luke is not a knight\". Harper told you that Luke is a knight or Scarlett is a knight. Scarlett stated, \"Harper is a knave or Emily is a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Amelia", "Emily", "Emma", "Harper", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false], "solution_text": "Luke is a knight, Amelia is a knave, Emily is a knave, Emma is a knave, Harper is a knight, and Scarlett is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Amelia is a knave\n(3) Emily is a knave\n(4) Emma is a knave\n(5) Harper is a knight\n(6) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Emily is a knave if and only if Luke is a knight.", "Emily cannot be a knight, because this would contradict the claim of Luke that Emily is a knave if and only if Luke is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that If Scarlett is a knave then Amelia is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Emily that If Scarlett is a knave then Amelia is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Harper is a knave or Emily is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Luke is a knight or Scarlett is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Luke is not a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Luke is not a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Luke is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Luke is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('->', ('lying', 5), ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('or', ('lying', 4), ('telling-truth', 2)))", "index": 296}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Ethan, Emma, Logan, Owen, and Luke. According to Harper, \"Emma is a knave if and only if Logan is a knight\". In a statement by Ethan: \"If Logan is a knave then Owen is a knave\". Emma asserted: \"If Luke is a knight then Owen is a knave\". In a statement by Logan: \"Harper is a knave if and only if Logan is a knight\". \"Luke is a knave and Harper is a knight,\" Owen declared. In Luke's words: \"Emma is a knight or Luke is a knight\". So who is a knight and who is a knave?", "names": ["Harper", "Ethan", "Emma", "Logan", "Owen", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Harper is a knave, Ethan is a knight, Emma is a knight, Logan is a knight, Owen is a knave, and Luke is a knight.", "solution_text_format": "(1) Harper is a knave\n(2) Ethan is a knight\n(3) Emma is a knight\n(4) Logan is a knight\n(5) Owen is a knave\n(6) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Emma is a knave if and only if Logan is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Luke is a knight then Owen is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Emma is a knight or Luke is a knight.", "Owen cannot be a knight, because this would contradict the claim of Emma that If Luke is a knight then Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Luke is a knave and Harper is a knight.", "Logan cannot be a knight, because this would contradict the claim of Harper that Emma is a knave if and only if Logan is a knight.", "Logan cannot be a knave, because this would contradict the false claim of their own that Harper is a knave if and only if Logan is a knight.", "We have exhausted all possibilities for Logan and Owen, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the false claim of their own that Emma is a knight or Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that If Luke is a knight then Owen is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Emma is a knight or Luke is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Harper is a knight.", "Owen cannot be a knave, because this would contradict the false claim of Emma that If Luke is a knight then Owen is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the false claim of Emma that If Luke is a knight then Owen is a knave.", "We have exhausted all possibilities for Luke and Emma, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Logan is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Luke is a knight then Owen is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Emma is a knight or Luke is a knight.", "Owen cannot be a knight, because this would contradict the claim of Emma that If Luke is a knight then Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Luke is a knave and Harper is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Harper is a knave if and only if Logan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Logan is a knave then Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 3)), ('->', ('lying', 3), ('lying', 4)), ('->', ('telling-truth', 5), ('lying', 4)), ('<=>', ('lying', 0), ('telling-truth', 3)), ('and', ('lying', 5), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('telling-truth', 5)))", "index": 297}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Oliver, Chloe, Mason, Liam, and Lily. Aiden asserted: \"Liam is not a knight\". Oliver stated, \"Aiden is not a knave\". Chloe said that Mason is not a knight. \"Aiden is a knight and Chloe is a knight,\" Mason mentioned. According to Liam, \"Aiden is a knave and Lily is a knave\". Lily said that Mason is a knave and Mason is a knight. So who is a knight and who is a knave?", "names": ["Aiden", "Oliver", "Chloe", "Mason", "Liam", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "Aiden is a knave, Oliver is a knave, Chloe is a knight, Mason is a knave, Liam is a knight, and Lily is a knave.", "solution_text_format": "(1) Aiden is a knave\n(2) Oliver is a knave\n(3) Chloe is a knight\n(4) Mason is a knave\n(5) Liam is a knight\n(6) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Liam is not a knight.", "Liam cannot be a knight, because this would contradict the claim of Aiden that Liam is not a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Aiden is a knave and Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Mason is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Mason is a knave and Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Aiden is a knight and Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Mason is not a knight.", "Chloe cannot be a knave, because this would contradict the claim of Mason that Aiden is a knight and Chloe is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Aiden is a knight and Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Mason that Aiden is a knight and Chloe is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Mason is not a knight.", "We have exhausted all possibilities for Chloe, Mason, Lily, and Liam, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Aiden is a knave and Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Liam that Aiden is a knave and Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Mason is a knave and Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Chloe is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Aiden is a knight and Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Mason is not a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Aiden is not a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Aiden is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('not', ('lying', 0)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 0), ('telling-truth', 2)), ('and', ('lying', 0), ('lying', 5)), ('and', ('lying', 3), ('telling-truth', 3)))", "index": 298}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, James, Daniel, Olivia, Mason, and Sophia. \"If James is a knight then Mason is a knave,\" Sebastian mentioned. James expressed that Sebastian is a knave if and only if Olivia is a knight. Daniel said, \"Mason is a knave and Sophia is a knight.\" Olivia said that Sebastian is a knave or Mason is a knave. In a statement by Mason: \"Mason is a knight or Sophia is a knight\". Sophia asserted: \"Daniel is not a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "James", "Daniel", "Olivia", "Mason", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Sebastian is a knave, James is a knight, Daniel is a knave, Olivia is a knight, Mason is a knight, and Sophia is a knight.", "solution_text_format": "(1) Sebastian is a knave\n(2) James is a knight\n(3) Daniel is a knave\n(4) Olivia is a knight\n(5) Mason is a knight\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that If James is a knight then Mason is a knave.", "Assume James is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Olivia is a knight.", "Olivia cannot be a knight, because this would contradict the claim of James that Sebastian is a knave if and only if Olivia is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Sebastian is a knave or Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Sebastian that If James is a knight then Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of Olivia that Sebastian is a knave or Mason is a knave.", "We have exhausted all possibilities for Mason and Olivia, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Sebastian is a knave or Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Olivia that Sebastian is a knave or Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Mason is a knight or Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Mason that Mason is a knight or Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Sophia is a knight.", "Daniel cannot be a knave, because this would contradict the false claim of Sophia that Daniel is not a knight.", "We have exhausted all possibilities for Daniel, Sophia, and Mason, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of James that Sebastian is a knave if and only if Olivia is a knight.", "We have exhausted all possibilities for Olivia and James, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If James is a knight then Mason is a knave.", "Assume James is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Sebastian is a knave or Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Mason is a knight or Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Sophia is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Mason is a knave and Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('lying', 4)), ('<=>', ('lying', 0), ('telling-truth', 3)), ('and', ('lying', 4), ('telling-truth', 5)), ('or', ('lying', 0), ('lying', 4)), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('telling-truth', 2)))", "index": 299}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Noah, Liam, Ava, Aria, Joseph, and Lily. Noah said, \"Joseph is a knave and Joseph is a knight.\" In Liam's words: \"Lily is a knave and Joseph is a knave\". Ava commented, \"Aria is a knight or Liam is a knave\". Aria expressed that Joseph is not a knave. Joseph told you that Noah is a knave. In a statement by Lily: \"Noah is a knave if and only if Ava is a knight\". So who is a knight and who is a knave?", "names": ["Noah", "Liam", "Ava", "Aria", "Joseph", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Noah is a knave, Liam is a knave, Ava is a knight, Aria is a knight, Joseph is a knight, and Lily is a knight.", "solution_text_format": "(1) Noah is a knave\n(2) Liam is a knave\n(3) Ava is a knight\n(4) Aria is a knight\n(5) Joseph is a knight\n(6) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Noah cannot be a knight, because this would contradict the claim of their own that Joseph is a knave and Joseph is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Joseph is a knave and Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Noah is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Joseph is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Lily is a knave and Joseph is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Noah is a knave if and only if Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Aria is a knight or Liam is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Joseph is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 4)), ('and', ('lying', 5), ('lying', 4)), ('or', ('telling-truth', 3), ('lying', 1)), ('not', ('lying', 4)), ('lying', 0), ('<=>', ('lying', 0), ('telling-truth', 2)))", "index": 300}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Jack, Luke, Evelyn, Aurora, and Jackson. Samuel asserted: \"If Jack is a knave then Evelyn is a knave\". Jack asserted: \"Aurora is not a knave\". \"Jackson is a knave and Jackson is a knight\" - Luke. As Evelyn put it, \"Jack is a knave if and only if Aurora is a knight\". \"Luke is a knave\" - Aurora. According to Jackson, \"Jack is a knave and Samuel is a knave\". So who is a knight and who is a knave?", "names": ["Samuel", "Jack", "Luke", "Evelyn", "Aurora", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false], "solution_text": "Samuel is a knight, Jack is a knight, Luke is a knave, Evelyn is a knave, Aurora is a knight, and Jackson is a knave.", "solution_text_format": "(1) Samuel is a knight\n(2) Jack is a knight\n(3) Luke is a knave\n(4) Evelyn is a knave\n(5) Aurora is a knight\n(6) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that If Jack is a knave then Evelyn is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Jackson is a knave and Jackson is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Jackson is a knave and Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Jack is a knave and Samuel is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Jack is a knave and Samuel is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Jack is a knave if and only if Aurora is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('lying', 3)), ('not', ('lying', 4)), ('and', ('lying', 5), ('telling-truth', 5)), ('<=>', ('lying', 1), ('telling-truth', 4)), ('lying', 2), ('and', ('lying', 1), ('lying', 0)))", "index": 301}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Emily, Logan, Charlotte, Lily, and Scarlett. \"Lily is not a knight,\" Lucas claimed. Emily said, \"Charlotte is not a knight.\" Logan remarked, \"Lily is a knight\". According to Charlotte, \"If Lucas is a knight then Charlotte is a knight\". Lily stated, \"Scarlett is a knave\". According to Scarlett, \"Lucas is a knave and Logan is a knave\". So who is a knight and who is a knave?", "names": ["Lucas", "Emily", "Logan", "Charlotte", "Lily", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Lucas is a knave, Emily is a knave, Logan is a knight, Charlotte is a knight, Lily is a knight, and Scarlett is a knave.", "solution_text_format": "(1) Lucas is a knave\n(2) Emily is a knave\n(3) Logan is a knight\n(4) Charlotte is a knight\n(5) Lily is a knight\n(6) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Lucas that Lily is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Logan is a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of Lily that Scarlett is a knave.", "We have exhausted all possibilities for Scarlett and Lily, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Lily that Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Lucas is a knave and Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Emily that Charlotte is not a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Lucas is a knight then Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Lucas is a knight then Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('not', ('telling-truth', 3)), ('telling-truth', 4), ('->', ('telling-truth', 0), ('telling-truth', 3)), ('lying', 5), ('and', ('lying', 0), ('lying', 2)))", "index": 302}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Olivia, Chloe, Aurora, Matthew, and Grace. Charlotte told you that Chloe is a knave or Charlotte is a knight. In a statement by Olivia: \"Matthew is not a knave\". In a statement by Chloe: \"Charlotte is not a knave\". \"Charlotte is a knave\" - Aurora. Matthew said, \"If Aurora is a knave then Chloe is a knight.\" In Grace's words: \"If Aurora is a knave then Matthew is a knight\". So who is a knight and who is a knave?", "names": ["Charlotte", "Olivia", "Chloe", "Aurora", "Matthew", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Charlotte is a knight, Olivia is a knight, Chloe is a knight, Aurora is a knave, Matthew is a knight, and Grace is a knight.", "solution_text_format": "(1) Charlotte is a knight\n(2) Olivia is a knight\n(3) Chloe is a knight\n(4) Aurora is a knave\n(5) Matthew is a knight\n(6) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Chloe is a knave or Charlotte is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Aurora is a knave then Chloe is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Aurora is a knave then Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 0)), ('not', ('lying', 4)), ('not', ('lying', 0)), ('lying', 0), ('->', ('lying', 3), ('telling-truth', 2)), ('->', ('lying', 3), ('telling-truth', 4)))", "index": 303}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, James, Oliver, Benjamin, Liam, and Jacob. Emily commented, \"If Oliver is a knight then Liam is a knave\". James commented, \"Emily is a knight if and only if Emily is a knave\". Oliver commented, \"Emily is a knave and Benjamin is a knave\". Benjamin told you that James is a knight. Liam expressed that Benjamin is a knave if and only if Oliver is a knave. In Jacob's words: \"James is a knight and Oliver is a knight\". So who is a knight and who is a knave?", "names": ["Emily", "James", "Oliver", "Benjamin", "Liam", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false], "solution_text": "Emily is a knight, James is a knave, Oliver is a knave, Benjamin is a knave, Liam is a knight, and Jacob is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) James is a knave\n(3) Oliver is a knave\n(4) Benjamin is a knave\n(5) Liam is a knight\n(6) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that If Oliver is a knight then Liam is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Emily is a knave and Benjamin is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Emily is a knave and Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that James is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Emily is a knight if and only if Emily is a knave.", "James cannot be a knave, because this would contradict the claim of Benjamin that James is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that James is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Emily is a knight if and only if Emily is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Emily is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Oliver is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that James is a knight and Oliver is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that James is a knight and Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 4)), ('<=>', ('telling-truth', 0), ('lying', 0)), ('and', ('lying', 0), ('lying', 3)), ('telling-truth', 1), ('<=>', ('lying', 3), ('lying', 2)), ('and', ('telling-truth', 1), ('telling-truth', 2)))", "index": 304}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, Evelyn, Samuel, Chloe, Elizabeth, and Michael. Penelope remarked, \"Penelope is a knight or Elizabeth is a knave\". \"If Elizabeth is a knave then Elizabeth is a knight,\" Evelyn claimed. Samuel said, \"Elizabeth is a knight.\" In a statement by Chloe: \"Samuel is a knave or Elizabeth is a knight\". Elizabeth told you that Penelope is a knight or Samuel is a knave. Michael stated, \"Chloe is a knave and Elizabeth is a knave\". So who is a knight and who is a knave?", "names": ["Penelope", "Evelyn", "Samuel", "Chloe", "Elizabeth", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Penelope is a knight, Evelyn is a knight, Samuel is a knight, Chloe is a knight, Elizabeth is a knight, and Michael is a knave.", "solution_text_format": "(1) Penelope is a knight\n(2) Evelyn is a knight\n(3) Samuel is a knight\n(4) Chloe is a knight\n(5) Elizabeth is a knight\n(6) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Penelope is a knight or Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Penelope is a knight or Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Elizabeth is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Samuel is a knave or Elizabeth is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Elizabeth is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Chloe is a knave and Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('lying', 4)), ('->', ('lying', 4), ('telling-truth', 4)), ('telling-truth', 4), ('or', ('lying', 2), ('telling-truth', 4)), ('or', ('telling-truth', 0), ('lying', 2)), ('and', ('lying', 3), ('lying', 4)))", "index": 305}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Mason, Henry, Benjamin, Abigail, and Charlotte. As Aria put it, \"Mason is a knight\". Mason expressed that Aria is a knave and Charlotte is a knave. \"Charlotte is not a knight,\" Henry claimed. Benjamin noted, \"Aria is a knave if and only if Mason is a knave\". Abigail commented, \"Benjamin is a knight\". Charlotte noted, \"Charlotte is a knight or Henry is a knave\". So who is a knight and who is a knave?", "names": ["Aria", "Mason", "Henry", "Benjamin", "Abigail", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Aria is a knave, Mason is a knave, Henry is a knave, Benjamin is a knight, Abigail is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Aria is a knave\n(2) Mason is a knave\n(3) Henry is a knave\n(4) Benjamin is a knight\n(5) Abigail is a knight\n(6) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Aria is a knave and Charlotte is a knave.", "Mason cannot be a knave, because this would contradict the claim of Aria that Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Mason is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Aria that Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Aria is a knave and Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Charlotte is a knight or Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Aria is a knave if and only if Mason is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('and', ('lying', 0), ('lying', 5)), ('not', ('telling-truth', 5)), ('<=>', ('lying', 0), ('lying', 1)), ('telling-truth', 3), ('or', ('telling-truth', 5), ('lying', 2)))", "index": 306}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Joseph, Luke, Olivia, Emma, and Ella. In a statement by Michael: \"Ella is not a knight\". Joseph asserted: \"Emma is not a knight\". Luke remarked, \"Ella is a knave and Olivia is a knave\". Olivia asserted: \"If Michael is a knight then Emma is a knave\". \"Olivia is a knight,\" Emma claimed. Ella said that Olivia is a knight and Joseph is a knave. So who is a knight and who is a knave?", "names": ["Michael", "Joseph", "Luke", "Olivia", "Emma", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Michael is a knave, Joseph is a knave, Luke is a knave, Olivia is a knight, Emma is a knight, and Ella is a knight.", "solution_text_format": "(1) Michael is a knave\n(2) Joseph is a knave\n(3) Luke is a knave\n(4) Olivia is a knight\n(5) Emma is a knight\n(6) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Ella is not a knight.", "Ella cannot be a knight, because this would contradict the claim of Michael that Ella is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Olivia is a knight and Joseph is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Michael is a knight then Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Olivia that If Michael is a knight then Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that Olivia is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that If Michael is a knight then Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Olivia is a knight.", "Emma cannot be a knave, because this would contradict the false claim of Olivia that If Michael is a knight then Emma is a knave.", "We have exhausted all possibilities for Emma, Olivia, and Ella, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Olivia is a knight and Joseph is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Michael is a knight then Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Olivia is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Emma is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Olivia is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Ella is a knave and Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('not', ('telling-truth', 4)), ('and', ('lying', 5), ('lying', 3)), ('->', ('telling-truth', 0), ('lying', 4)), ('telling-truth', 3), ('and', ('telling-truth', 3), ('lying', 1)))", "index": 307}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Amelia, Jack, Grace, Aria, and Emily. \"Jack is a knave,\" Olivia declared. Amelia was heard saying, \"Emily is a knight\". Jack stated, \"Emily is a knight\". \"Emily is a knave and Emily is a knight,\" Grace mentioned. Aria said that Jack is a knave. In Emily's words: \"Aria is a knave if and only if Jack is a knight\". So who is a knight and who is a knave?", "names": ["Olivia", "Amelia", "Jack", "Grace", "Aria", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Olivia is a knave, Amelia is a knight, Jack is a knight, Grace is a knave, Aria is a knave, and Emily is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) Amelia is a knight\n(3) Jack is a knight\n(4) Grace is a knave\n(5) Aria is a knave\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Olivia that Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Jack that Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Jack is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Emily that Aria is a knave if and only if Jack is a knight.", "Aria cannot be a knave, because this would contradict the false claim of their own that Jack is a knave.", "We have exhausted all possibilities for Aria, Emily, and Jack, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Aria is a knave if and only if Jack is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Jack is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Jack is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Emily is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Emily is a knave and Emily is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Emily is a knave and Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('telling-truth', 5), ('telling-truth', 5), ('and', ('lying', 5), ('telling-truth', 5)), ('lying', 2), ('<=>', ('lying', 4), ('telling-truth', 2)))", "index": 308}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Jack, Grace, Amelia, Aurora, and Chloe. Owen commented, \"Jack is a knight if and only if Grace is a knight\". Jack said that Aurora is a knave if and only if Chloe is a knave. Grace said that Aurora is a knight if and only if Chloe is a knave. As Amelia put it, \"Jack is a knave\". Aurora commented, \"If Aurora is a knight then Chloe is a knave\". \"Aurora is not a knight,\" Chloe declared. So who is a knight and who is a knave?", "names": ["Owen", "Jack", "Grace", "Amelia", "Aurora", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Owen is a knave, Jack is a knave, Grace is a knight, Amelia is a knight, Aurora is a knight, and Chloe is a knave.", "solution_text_format": "(1) Owen is a knave\n(2) Jack is a knave\n(3) Grace is a knight\n(4) Amelia is a knight\n(5) Aurora is a knight\n(6) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Jack is a knight if and only if Grace is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Chloe is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Aurora is a knight then Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Aurora that If Aurora is a knight then Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the claim of Jack that Aurora is a knave if and only if Chloe is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knight then Chloe is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Chloe is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Aurora is a knight then Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Jack that Aurora is a knave if and only if Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Grace cannot be a knight, because this would contradict the claim of Owen that Jack is a knight if and only if Grace is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight if and only if Chloe is a knave.", "We have exhausted all possibilities for Grace and Chloe, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knight then Chloe is a knave.", "We have exhausted all possibilities for Aurora and Jack, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Jack is a knight if and only if Grace is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Chloe is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Aurora is a knight then Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Aurora that If Aurora is a knight then Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the claim of Jack that Aurora is a knave if and only if Chloe is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knight then Chloe is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Chloe is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Aurora is a knight then Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Jack that Aurora is a knave if and only if Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Chloe is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('<=>', ('lying', 4), ('lying', 5)), ('<=>', ('telling-truth', 4), ('lying', 5)), ('lying', 1), ('->', ('telling-truth', 4), ('lying', 5)), ('not', ('telling-truth', 4)))", "index": 309}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Ethan, James, Jack, Mia, and Henry. Michael said that If James is a knight then Mia is a knight. \"James is a knave if and only if James is a knight,\" Ethan declared. James said that Mia is a knight. Jack noted, \"Henry is a knave or Ethan is a knight\". As Mia put it, \"James is a knight or Henry is a knave\". Henry asserted: \"If Henry is a knight then James is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Ethan", "James", "Jack", "Mia", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Michael is a knight, Ethan is a knave, James is a knight, Jack is a knave, Mia is a knight, and Henry is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Ethan is a knave\n(3) James is a knight\n(4) Jack is a knave\n(5) Mia is a knight\n(6) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that If James is a knight then Mia is a knight.", "Assume James is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that James is a knight or Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Henry is a knight then James is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that James is a knave if and only if James is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that James is a knave if and only if James is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Henry is a knave or Ethan is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Henry is a knave or Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('lying', 2), ('telling-truth', 2)), ('telling-truth', 4), ('or', ('lying', 5), ('telling-truth', 1)), ('or', ('telling-truth', 2), ('lying', 5)), ('->', ('telling-truth', 5), ('telling-truth', 2)))", "index": 310}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Penelope, James, Jackson, Zoey, and Mason. Harper commented, \"James is not a knight\". \"Jackson is not a knave,\" Penelope mentioned. \"James is a knight or Penelope is a knight,\" James mentioned. As Jackson put it, \"If Zoey is a knave then James is a knight\". Zoey noted, \"Harper is a knight if and only if Penelope is a knave\". Mason commented, \"If Mason is a knight then Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Harper", "Penelope", "James", "Jackson", "Zoey", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Harper is a knave, Penelope is a knight, James is a knight, Jackson is a knight, Zoey is a knight, and Mason is a knight.", "solution_text_format": "(1) Harper is a knave\n(2) Penelope is a knight\n(3) James is a knight\n(4) Jackson is a knight\n(5) Zoey is a knight\n(6) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that James is not a knight.", "James cannot be a knight, because this would contradict the claim of Harper that James is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that James is a knight or Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of James that James is a knight or Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jackson is not a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Penelope that Jackson is not a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Zoey is a knave then James is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Jackson that If Zoey is a knave then James is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Harper is a knight if and only if Penelope is a knave.", "We have exhausted all possibilities for Zoey, Jackson, Penelope, and James, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that James is not a knight.", "Assume James is a knight. No contradiction is found in their claim that James is a knight or Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Zoey is a knave then James is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Harper is a knight if and only if Penelope is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Mason is a knight then Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('not', ('lying', 3)), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('lying', 4), ('telling-truth', 2)), ('<=>', ('telling-truth', 0), ('lying', 1)), ('->', ('telling-truth', 5), ('telling-truth', 1)))", "index": 311}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Zoey, Amelia, Elizabeth, Logan, Oliver, and Charlotte. Zoey said, \"Logan is a knight if and only if Amelia is a knight.\" \"Zoey is a knave if and only if Elizabeth is a knight,\" Amelia mentioned. \"Charlotte is a knave and Amelia is a knave\" - Elizabeth. Logan was heard saying, \"Oliver is a knave and Oliver is a knight\". \"Charlotte is not a knight,\" Oliver claimed. Charlotte asserted: \"If Amelia is a knave then Charlotte is a knight\". So who is a knight and who is a knave?", "names": ["Zoey", "Amelia", "Elizabeth", "Logan", "Oliver", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false], "solution_text": "Zoey is a knight, Amelia is a knave, Elizabeth is a knight, Logan is a knave, Oliver is a knight, and Charlotte is a knave.", "solution_text_format": "(1) Zoey is a knight\n(2) Amelia is a knave\n(3) Elizabeth is a knight\n(4) Logan is a knave\n(5) Oliver is a knight\n(6) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Logan is a knight if and only if Amelia is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Oliver is a knave and Oliver is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Oliver is a knave and Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Oliver that Charlotte is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Amelia is a knave then Charlotte is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Zoey that Logan is a knight if and only if Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Charlotte is a knave and Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('telling-truth', 1)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('and', ('lying', 5), ('lying', 1)), ('and', ('lying', 4), ('telling-truth', 4)), ('not', ('telling-truth', 5)), ('->', ('lying', 1), ('telling-truth', 5)))", "index": 312}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Logan, David, Emma, Chloe, and Samuel. As Scarlett put it, \"Chloe is a knight if and only if Scarlett is a knight\". Logan asserted: \"Samuel is not a knave\". David said that Scarlett is a knight or Chloe is a knave. \"David is not a knave,\" Emma mentioned. In Chloe's words: \"Samuel is a knight or Emma is a knave\". Samuel was heard saying, \"David is not a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Logan", "David", "Emma", "Chloe", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true], "solution_text": "Scarlett is a knave, Logan is a knight, David is a knave, Emma is a knave, Chloe is a knight, and Samuel is a knight.", "solution_text_format": "(1) Scarlett is a knave\n(2) Logan is a knight\n(3) David is a knave\n(4) Emma is a knave\n(5) Chloe is a knight\n(6) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Scarlett is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Samuel is a knight or Emma is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that David is not a knight.", "David cannot be a knight, because this would contradict the claim of Samuel that David is not a knight.", "David cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knight or Chloe is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that David is not a knight.", "Assume David is a knight. No contradiction is found in their claim that Scarlett is a knight or Chloe is a knave.", "Emma cannot be a knight, because this would contradict the claim of Chloe that Samuel is a knight or Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that David is not a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knight or Chloe is a knave.", "We have exhausted all possibilities for David and Samuel, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Scarlett that Chloe is a knight if and only if Scarlett is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Scarlett is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Samuel is a knight or Emma is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that David is not a knight.", "David cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight or Chloe is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Scarlett is a knight or Chloe is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that David is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that David is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Samuel is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('not', ('lying', 5)), ('or', ('telling-truth', 0), ('lying', 4)), ('not', ('lying', 2)), ('or', ('telling-truth', 5), ('lying', 3)), ('not', ('telling-truth', 2)))", "index": 313}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Aria, Mason, Isabella, Jackson, and Riley. In a statement by William: \"Isabella is a knight and Aria is a knave\". Aria stated, \"If William is a knight then Riley is a knave\". As Mason put it, \"Jackson is not a knave\". Isabella remarked, \"Mason is a knave if and only if Riley is a knave\". Jackson noted, \"William is a knight and Mason is a knight\". \"William is a knave or Mason is a knave,\" Riley declared. So who is a knight and who is a knave?", "names": ["William", "Aria", "Mason", "Isabella", "Jackson", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true], "solution_text": "William is a knave, Aria is a knight, Mason is a knave, Isabella is a knave, Jackson is a knave, and Riley is a knight.", "solution_text_format": "(1) William is a knave\n(2) Aria is a knight\n(3) Mason is a knave\n(4) Isabella is a knave\n(5) Jackson is a knave\n(6) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Isabella is a knight and Aria is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Mason is a knave if and only if Riley is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that William is a knight and Mason is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that William is a knave or Mason is a knave.", "Riley cannot be a knave, because this would contradict the claim of Isabella that Mason is a knave if and only if Riley is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Mason that Jackson is not a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Jackson is not a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Mason that Jackson is not a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that William is a knight and Mason is a knight.", "Riley cannot be a knight, because this would contradict the claim of Isabella that Mason is a knave if and only if Riley is a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that William is a knave or Mason is a knave.", "We have exhausted all possibilities for Riley, Jackson, and Mason, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of William that Isabella is a knight and Aria is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Isabella is a knight and Aria is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Mason is a knave if and only if Riley is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that William is a knight and Mason is a knight.", "Jackson cannot be a knave, because this would contradict the claim of Mason that Jackson is not a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Jackson is not a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Mason that Jackson is not a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that William is a knight and Mason is a knight.", "Riley cannot be a knight, because this would contradict the claim of Isabella that Mason is a knave if and only if Riley is a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that William is a knave or Mason is a knave.", "We have exhausted all possibilities for Riley, Jackson, and Mason, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Riley is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that William is a knight and Mason is a knight.", "Jackson cannot be a knave, because this would contradict the claim of Mason that Jackson is not a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Jackson is not a knave.", "Jackson cannot be a knight, because this would contradict the false claim of Mason that Jackson is not a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that William is a knight and Mason is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that William is a knave or Mason is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If William is a knight then Riley is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 1)), ('->', ('telling-truth', 0), ('lying', 5)), ('not', ('lying', 4)), ('<=>', ('lying', 2), ('lying', 5)), ('and', ('telling-truth', 0), ('telling-truth', 2)), ('or', ('lying', 0), ('lying', 2)))", "index": 314}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Sebastian, Isabella, Alexander, Aria, and Grace. \"Isabella is a knight and Grace is a knight,\" Charlotte claimed. Sebastian asserted: \"Sebastian is a knight\". Isabella said, \"Charlotte is a knight or Alexander is a knave.\" Alexander said, \"If Grace is a knave then Aria is a knave.\" Aria stated, \"Alexander is a knave if and only if Aria is a knight\". Grace asserted: \"Sebastian is not a knave\". So who is a knight and who is a knave?", "names": ["Charlotte", "Sebastian", "Isabella", "Alexander", "Aria", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "Charlotte is a knave, Sebastian is a knave, Isabella is a knight, Alexander is a knave, Aria is a knight, and Grace is a knave.", "solution_text_format": "(1) Charlotte is a knave\n(2) Sebastian is a knave\n(3) Isabella is a knight\n(4) Alexander is a knave\n(5) Aria is a knight\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Isabella is a knight and Grace is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Charlotte is a knight or Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Grace is a knave then Aria is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Alexander is a knave if and only if Aria is a knight.", "Aria cannot be a knave, because this would contradict the false claim of their own that Alexander is a knave if and only if Aria is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Grace that Sebastian is not a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Charlotte that Isabella is a knight and Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Grace is a knave then Aria is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Alexander that If Grace is a knave then Aria is a knave.", "Grace cannot be a knave, because this would contradict the claim of Charlotte that Isabella is a knight and Grace is a knight.", "We have exhausted all possibilities for Grace and Alexander, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Charlotte that Isabella is a knight and Grace is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Isabella is a knight and Grace is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Charlotte is a knight or Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Isabella that Charlotte is a knight or Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Grace is a knave then Aria is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Charlotte that Isabella is a knight and Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Grace that Sebastian is not a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Sebastian is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 5)), ('telling-truth', 1), ('or', ('telling-truth', 0), ('lying', 3)), ('->', ('lying', 5), ('lying', 4)), ('<=>', ('lying', 3), ('telling-truth', 4)), ('not', ('lying', 1)))", "index": 315}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Luke, Abigail, Samuel, Aiden, and Liam. Owen said, \"If Owen is a knight then Luke is a knave.\" Luke was heard saying, \"Samuel is a knight\". Abigail said that Aiden is a knight if and only if Samuel is a knave. Samuel expressed that Owen is a knave. Aiden commented, \"Luke is not a knave\". \"If Owen is a knight then Aiden is a knave,\" Liam mentioned. So who is a knight and who is a knave?", "names": ["Owen", "Luke", "Abigail", "Samuel", "Aiden", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true], "solution_text": "Owen is a knight, Luke is a knave, Abigail is a knave, Samuel is a knave, Aiden is a knave, and Liam is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Luke is a knave\n(3) Abigail is a knave\n(4) Samuel is a knave\n(5) Aiden is a knave\n(6) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that If Owen is a knight then Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Owen that If Owen is a knight then Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Luke that Samuel is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Owen is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Samuel is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Luke is not a knave.", "Aiden cannot be a knave, because this would contradict the claim of Abigail that Aiden is a knight if and only if Samuel is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Samuel is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Abigail that Aiden is a knight if and only if Samuel is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Luke is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Owen is a knight then Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('lying', 1)), ('telling-truth', 3), ('<=>', ('telling-truth', 4), ('lying', 3)), ('lying', 0), ('not', ('lying', 1)), ('->', ('telling-truth', 0), ('lying', 4)))", "index": 316}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Elizabeth, Sophia, Lily, Mia, and Luke. Oliver noted, \"Sophia is a knave or Luke is a knight\". \"If Lily is a knave then Luke is a knave,\" Elizabeth declared. Sophia said that Sophia is a knight or Luke is a knight. Lily noted, \"Elizabeth is a knave or Oliver is a knave\". Mia commented, \"If Oliver is a knight then Elizabeth is a knight\". In a statement by Luke: \"Lily is not a knave\". So who is a knight and who is a knave?", "names": ["Oliver", "Elizabeth", "Sophia", "Lily", "Mia", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false], "solution_text": "Oliver is a knight, Elizabeth is a knight, Sophia is a knave, Lily is a knave, Mia is a knight, and Luke is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) Elizabeth is a knight\n(3) Sophia is a knave\n(4) Lily is a knave\n(5) Mia is a knight\n(6) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Sophia is a knave or Luke is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Sophia is a knight or Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Lily is not a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Elizabeth is a knave or Oliver is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Lily that Elizabeth is a knave or Oliver is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that If Lily is a knave then Luke is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Luke that Lily is not a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Oliver that Sophia is a knave or Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Sophia is a knight or Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Sophia that Sophia is a knight or Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Lily is not a knave.", "Lily cannot be a knight, because this would contradict the false claim of Luke that Lily is not a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Elizabeth is a knave or Oliver is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Lily is a knave then Luke is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Oliver is a knight then Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 5)), ('->', ('lying', 3), ('lying', 5)), ('or', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('lying', 1), ('lying', 0)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('lying', 3)))", "index": 317}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Ava, Jacob, Samuel, Abigail, and Victoria. Sophia said that Samuel is a knight and Victoria is a knight. Ava noted, \"If Jacob is a knave then Sophia is a knave\". Jacob said, \"Victoria is a knight if and only if Ava is a knight.\" Samuel said, \"Abigail is a knight and Sophia is a knave.\" In Abigail's words: \"Victoria is a knight if and only if Victoria is a knave\". Victoria stated, \"If Sophia is a knight then Ava is a knight\". So who is a knight and who is a knave?", "names": ["Sophia", "Ava", "Jacob", "Samuel", "Abigail", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Sophia is a knave, Ava is a knight, Jacob is a knight, Samuel is a knave, Abigail is a knave, and Victoria is a knight.", "solution_text_format": "(1) Sophia is a knave\n(2) Ava is a knight\n(3) Jacob is a knight\n(4) Samuel is a knave\n(5) Abigail is a knave\n(6) Victoria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Samuel is a knight and Victoria is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Abigail is a knight and Sophia is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Sophia that Samuel is a knight and Victoria is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Samuel is a knight and Victoria is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Abigail is a knight and Sophia is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Victoria is a knight if and only if Victoria is a knave.", "Abigail cannot be a knave, because this would contradict the claim of Samuel that Abigail is a knight and Sophia is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Abigail is a knight and Sophia is a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Samuel that Abigail is a knight and Sophia is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Sophia is a knight then Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Jacob is a knave then Sophia is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('telling-truth', 5)), ('->', ('lying', 2), ('lying', 0)), ('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('and', ('telling-truth', 4), ('lying', 0)), ('<=>', ('telling-truth', 5), ('lying', 5)), ('->', ('telling-truth', 0), ('telling-truth', 1)))", "index": 318}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Jacob, Chloe, Benjamin, Ethan, and Logan. Emma remarked, \"Benjamin is a knave and Chloe is a knave\". Jacob commented, \"If Emma is a knave then Logan is a knight\". Chloe said, \"If Ethan is a knave then Chloe is a knight.\" Benjamin expressed that Emma is a knave if and only if Jacob is a knight. Ethan stated, \"Chloe is a knave\". Logan expressed that Chloe is not a knave. So who is a knight and who is a knave?", "names": ["Emma", "Jacob", "Chloe", "Benjamin", "Ethan", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Emma is a knave, Jacob is a knight, Chloe is a knight, Benjamin is a knight, Ethan is a knave, and Logan is a knight.", "solution_text_format": "(1) Emma is a knave\n(2) Jacob is a knight\n(3) Chloe is a knight\n(4) Benjamin is a knight\n(5) Ethan is a knave\n(6) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Benjamin is a knave and Chloe is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Emma that Benjamin is a knave and Chloe is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Emma is a knave then Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Chloe cannot be a knight, because this would contradict the claim of Emma that Benjamin is a knave and Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the claim of Logan that Chloe is not a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Chloe is not a knave.", "Chloe cannot be a knight, because this would contradict the claim of Emma that Benjamin is a knave and Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that If Ethan is a knave then Chloe is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Chloe that If Ethan is a knave then Chloe is a knight.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave.", "We have exhausted all possibilities for Ethan, Chloe, and Logan, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of their own that If Emma is a knave then Logan is a knight.", "We have exhausted all possibilities for Jacob and Benjamin, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Benjamin is a knave and Chloe is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Emma is a knave if and only if Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Emma is a knave then Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Ethan is a knave then Chloe is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Chloe is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 2)), ('->', ('lying', 0), ('telling-truth', 5)), ('->', ('lying', 4), ('telling-truth', 2)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('lying', 2), ('not', ('lying', 2)))", "index": 319}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Scarlett, Amelia, Aurora, Avery, and Luke. Isabella said that Avery is a knave if and only if Isabella is a knight. Scarlett commented, \"Aurora is not a knave\". \"Scarlett is not a knave\" - Amelia. In a statement by Aurora: \"Isabella is a knave\". Avery stated, \"Amelia is a knave\". In Luke's words: \"Isabella is not a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Scarlett", "Amelia", "Aurora", "Avery", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Isabella is a knave, Scarlett is a knight, Amelia is a knight, Aurora is a knight, Avery is a knave, and Luke is a knight.", "solution_text_format": "(1) Isabella is a knave\n(2) Scarlett is a knight\n(3) Amelia is a knight\n(4) Aurora is a knight\n(5) Avery is a knave\n(6) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Avery is a knave if and only if Isabella is a knight.", "Avery cannot be a knight, because this would contradict the claim of Isabella that Avery is a knave if and only if Isabella is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Isabella is a knave.", "Aurora cannot be a knave, because this would contradict the claim of Scarlett that Aurora is not a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of Amelia that Scarlett is not a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the false claim of Avery that Amelia is a knave.", "We have exhausted all possibilities for Amelia and Avery, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Isabella is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Isabella that Avery is a knave if and only if Isabella is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Isabella is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Isabella is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('telling-truth', 0)), ('not', ('lying', 3)), ('not', ('lying', 1)), ('lying', 0), ('lying', 2), ('not', ('telling-truth', 0)))", "index": 320}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Jack, Liam, Jackson, Luke, and Elizabeth. Henry expressed that Luke is not a knight. Jack commented, \"Henry is a knight\". \"Henry is a knave and Elizabeth is a knave,\" Liam declared. \"Liam is a knave or Elizabeth is a knave,\" Jackson declared. In a statement by Luke: \"Liam is a knave if and only if Elizabeth is a knight\". Elizabeth asserted: \"Luke is a knight or Henry is a knight\". So who is a knight and who is a knave?", "names": ["Henry", "Jack", "Liam", "Jackson", "Luke", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Henry is a knave, Jack is a knave, Liam is a knave, Jackson is a knight, Luke is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Jack is a knave\n(3) Liam is a knave\n(4) Jackson is a knight\n(5) Luke is a knight\n(6) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Henry that Luke is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Elizabeth is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Elizabeth is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Henry is a knave and Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Luke that Liam is a knave if and only if Elizabeth is a knight.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Luke is a knight or Henry is a knight.", "We have exhausted all possibilities for Elizabeth, Liam, and Luke, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Luke is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Liam is a knave if and only if Elizabeth is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Henry is a knave and Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Liam that Henry is a knave and Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Luke is a knight or Henry is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Henry is a knave and Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Luke is a knight or Henry is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Henry is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Henry is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Liam is a knave or Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('telling-truth', 0), ('and', ('lying', 0), ('lying', 5)), ('or', ('lying', 2), ('lying', 5)), ('<=>', ('lying', 2), ('telling-truth', 5)), ('or', ('telling-truth', 4), ('telling-truth', 0)))", "index": 321}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Penelope, Alexander, Scarlett, Sofia, and Chloe. Mia noted, \"If Penelope is a knave then Scarlett is a knave\". Penelope stated, \"If Penelope is a knight then Scarlett is a knight\". Alexander commented, \"Chloe is a knight and Sofia is a knave\". \"Chloe is not a knight,\" Scarlett claimed. Sofia told you that Scarlett is a knight. Chloe expressed that Scarlett is a knight and Mia is a knave. So who is a knight and who is a knave?", "names": ["Mia", "Penelope", "Alexander", "Scarlett", "Sofia", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "Mia is a knight, Penelope is a knight, Alexander is a knave, Scarlett is a knight, Sofia is a knight, and Chloe is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Penelope is a knight\n(3) Alexander is a knave\n(4) Scarlett is a knight\n(5) Sofia is a knight\n(6) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that If Penelope is a knave then Scarlett is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Penelope is a knight then Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of Scarlett that Chloe is not a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Scarlett is a knight and Mia is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Chloe is a knight and Sofia is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Chloe is a knight and Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('lying', 3)), ('->', ('telling-truth', 1), ('telling-truth', 3)), ('and', ('telling-truth', 5), ('lying', 4)), ('not', ('telling-truth', 5)), ('telling-truth', 3), ('and', ('telling-truth', 3), ('lying', 0)))", "index": 322}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Alexander, Luke, Aiden, Aria, and Isabella. Victoria expressed that Alexander is a knight and Luke is a knight. According to Alexander, \"Isabella is a knave and Victoria is a knave\". As Luke put it, \"If Alexander is a knave then Victoria is a knight\". Aiden stated, \"If Luke is a knight then Alexander is a knave\". In Aria's words: \"If Victoria is a knave then Luke is a knave\". Isabella commented, \"Isabella is a knight or Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Victoria", "Alexander", "Luke", "Aiden", "Aria", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Victoria is a knave, Alexander is a knave, Luke is a knave, Aiden is a knight, Aria is a knight, and Isabella is a knight.", "solution_text_format": "(1) Victoria is a knave\n(2) Alexander is a knave\n(3) Luke is a knave\n(4) Aiden is a knight\n(5) Aria is a knight\n(6) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Alexander is a knight and Luke is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Victoria is a knave.", "Alexander cannot be a knave, because this would contradict the claim of Victoria that Alexander is a knight and Luke is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Alexander is a knight and Luke is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Isabella is a knave and Victoria is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Alexander that Isabella is a knave and Victoria is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Isabella is a knight or Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Luke is a knight then Alexander is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Victoria that Alexander is a knight and Luke is a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knave then Victoria is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of Isabella that Isabella is a knight or Aiden is a knave.", "We have exhausted all possibilities for Aiden and Isabella, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Isabella is a knave and Victoria is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Isabella is a knight or Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Luke is a knight then Alexander is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that If Alexander is a knave then Victoria is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that If Alexander is a knave then Victoria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Victoria is a knave then Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('lying', 5), ('lying', 0)), ('->', ('lying', 1), ('telling-truth', 0)), ('->', ('telling-truth', 2), ('lying', 1)), ('->', ('lying', 0), ('lying', 2)), ('or', ('telling-truth', 5), ('lying', 3)))", "index": 323}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Abigail, Riley, David, Michael, and Ava. Benjamin expressed that Michael is a knave and David is a knave. \"Ava is a knight if and only if Michael is a knave,\" Abigail claimed. Riley stated, \"Michael is a knave or Benjamin is a knave\". David told you that Benjamin is not a knight. In Michael's words: \"If Riley is a knight then David is a knave\". \"Michael is a knave,\" Ava mentioned. So who is a knight and who is a knave?", "names": ["Benjamin", "Abigail", "Riley", "David", "Michael", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Benjamin is a knave, Abigail is a knight, Riley is a knight, David is a knight, Michael is a knave, and Ava is a knight.", "solution_text_format": "(1) Benjamin is a knave\n(2) Abigail is a knight\n(3) Riley is a knight\n(4) David is a knight\n(5) Michael is a knave\n(6) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Michael is a knave and David is a knave.", "Michael cannot be a knight, because this would contradict the claim of Benjamin that Michael is a knave and David is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that If Riley is a knight then David is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Michael is a knave or Benjamin is a knave.", "David cannot be a knight, because this would contradict the claim of Benjamin that Michael is a knave and David is a knave.", "David cannot be a knave, because this would contradict the false claim of Michael that If Riley is a knight then David is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of their own that Michael is a knave or Benjamin is a knave.", "We have exhausted all possibilities for Riley and Michael, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Michael is a knave and David is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Riley is a knight then David is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Michael is a knave or Benjamin is a knave.", "David cannot be a knight, because this would contradict the claim of Michael that If Riley is a knight then David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that Benjamin is not a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of their own that Michael is a knave or Benjamin is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that If Riley is a knight then David is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Michael is a knave or Benjamin is a knave.", "Assume David is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Ava is a knight if and only if Michael is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Michael is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 3)), ('<=>', ('telling-truth', 5), ('lying', 4)), ('or', ('lying', 4), ('lying', 0)), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 2), ('lying', 3)), ('lying', 4))", "index": 324}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Noah, Zoey, Amelia, Scarlett, and Benjamin. In Ava's words: \"Zoey is a knave if and only if Scarlett is a knave\". Noah commented, \"If Ava is a knight then Scarlett is a knave\". Zoey remarked, \"Benjamin is a knight if and only if Benjamin is a knave\". Amelia asserted: \"Noah is a knight and Benjamin is a knight\". Scarlett was heard saying, \"Amelia is a knave and Zoey is a knight\". Benjamin asserted: \"Benjamin is a knight and Zoey is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Noah", "Zoey", "Amelia", "Scarlett", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Ava is a knight, Noah is a knight, Zoey is a knave, Amelia is a knave, Scarlett is a knave, and Benjamin is a knave.", "solution_text_format": "(1) Ava is a knight\n(2) Noah is a knight\n(3) Zoey is a knave\n(4) Amelia is a knave\n(5) Scarlett is a knave\n(6) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Scarlett is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Benjamin is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight and Zoey is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Benjamin is a knight and Zoey is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Ava that Zoey is a knave if and only if Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Amelia is a knave and Zoey is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Noah is a knight and Benjamin is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Noah is a knight and Benjamin is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Ava is a knight then Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 4)), ('->', ('telling-truth', 0), ('lying', 4)), ('<=>', ('telling-truth', 5), ('lying', 5)), ('and', ('telling-truth', 1), ('telling-truth', 5)), ('and', ('lying', 3), ('telling-truth', 2)), ('and', ('telling-truth', 5), ('telling-truth', 2)))", "index": 325}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Victoria, Daniel, Henry, William, and Ella. Ava was heard saying, \"William is a knave and Ava is a knight\". Victoria told you that Daniel is a knave and Ella is a knave. Daniel asserted: \"Henry is a knave and Ella is a knave\". Henry noted, \"Daniel is a knight and Henry is a knight\". William noted, \"Ava is not a knave\". Ella expressed that William is not a knave. So who is a knight and who is a knave?", "names": ["Ava", "Victoria", "Daniel", "Henry", "William", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false], "solution_text": "Ava is a knave, Victoria is a knave, Daniel is a knight, Henry is a knave, William is a knave, and Ella is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Victoria is a knave\n(3) Daniel is a knight\n(4) Henry is a knave\n(5) William is a knave\n(6) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that William is a knave and Ava is a knight.", "William cannot be a knight, because this would contradict the claim of Ava that William is a knave and Ava is a knight.", "William cannot be a knave, because this would contradict the false claim of their own that Ava is not a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that William is a knave and Ava is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Ava is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that Ava is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Daniel is a knave and Ella is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Victoria that Daniel is a knave and Ella is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Henry is a knave and Ella is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Daniel is a knight and Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Daniel is a knight and Henry is a knight.", "Ella cannot be a knight, because this would contradict the claim of Victoria that Daniel is a knave and Ella is a knave.", "Ella cannot be a knave, because this would contradict the false claim of Daniel that Henry is a knave and Ella is a knave.", "We have exhausted all possibilities for Ella, Henry, and Daniel, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Daniel is a knave and Ella is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Henry is a knave and Ella is a knave.", "Henry cannot be a knight, because this would contradict the claim of Daniel that Henry is a knave and Ella is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Daniel is a knight and Henry is a knight.", "Ella cannot be a knight, because this would contradict the claim of Daniel that Henry is a knave and Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that William is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 0)), ('and', ('lying', 2), ('lying', 5)), ('and', ('lying', 3), ('lying', 5)), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('lying', 0)), ('not', ('lying', 4)))", "index": 326}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Jackson, Zoey, Mia, Grace, and Aiden. Emily was heard saying, \"Jackson is a knave or Grace is a knight\". \"Mia is a knight and Emily is a knave\" - Jackson. Zoey asserted: \"If Aiden is a knave then Mia is a knight\". Mia was heard saying, \"Emily is not a knight\". \"Mia is a knight,\" Grace mentioned. \"Grace is not a knave,\" Aiden claimed. So who is a knight and who is a knave?", "names": ["Emily", "Jackson", "Zoey", "Mia", "Grace", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false], "solution_text": "Emily is a knight, Jackson is a knave, Zoey is a knave, Mia is a knave, Grace is a knave, and Aiden is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Jackson is a knave\n(3) Zoey is a knave\n(4) Mia is a knave\n(5) Grace is a knave\n(6) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Jackson is a knave or Grace is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Emily is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Mia is a knight and Emily is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Emily is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Emily is not a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Mia is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Mia is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Aiden is a knave then Mia is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Grace is not a knave.", "Aiden cannot be a knave, because this would contradict the claim of Zoey that If Aiden is a knave then Mia is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Aiden is a knave then Mia is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Zoey that If Aiden is a knave then Mia is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Grace is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 4)), ('and', ('telling-truth', 3), ('lying', 0)), ('->', ('lying', 5), ('telling-truth', 3)), ('not', ('telling-truth', 0)), ('telling-truth', 3), ('not', ('lying', 4)))", "index": 327}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Charlotte, Logan, Emily, Evelyn, and Noah. Aurora was heard saying, \"Evelyn is a knave and Emily is a knight\". In a statement by Charlotte: \"If Evelyn is a knight then Aurora is a knight\". Logan expressed that Charlotte is a knave. \"Evelyn is a knight and Charlotte is a knight,\" Emily claimed. Evelyn expressed that If Aurora is a knight then Noah is a knave. Noah was heard saying, \"If Evelyn is a knave then Aurora is a knave\". So who is a knight and who is a knave?", "names": ["Aurora", "Charlotte", "Logan", "Emily", "Evelyn", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true], "solution_text": "Aurora is a knave, Charlotte is a knave, Logan is a knight, Emily is a knave, Evelyn is a knight, and Noah is a knight.", "solution_text_format": "(1) Aurora is a knave\n(2) Charlotte is a knave\n(3) Logan is a knight\n(4) Emily is a knave\n(5) Evelyn is a knight\n(6) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Evelyn is a knave and Emily is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Aurora that Evelyn is a knave and Emily is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Aurora is a knight then Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that If Evelyn is a knave then Aurora is a knave.", "Noah cannot be a knave, because this would contradict the false claim of Evelyn that If Aurora is a knight then Noah is a knave.", "We have exhausted all possibilities for Noah and Evelyn, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Evelyn is a knave and Emily is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Aurora is a knight then Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Evelyn is a knave then Aurora is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Evelyn is a knight and Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that If Evelyn is a knight then Aurora is a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Emily that Evelyn is a knight and Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Evelyn is a knight and Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that If Evelyn is a knight then Aurora is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Aurora is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 3)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('lying', 1), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('lying', 5)), ('->', ('lying', 4), ('lying', 0)))", "index": 328}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Jacob, Benjamin, Scarlett, Henry, and Riley. In David's words: \"Henry is a knight\". Jacob was heard saying, \"David is not a knight\". Benjamin remarked, \"David is a knight and Riley is a knight\". According to Scarlett, \"If David is a knight then Riley is a knight\". \"Benjamin is a knight or Benjamin is a knave,\" Henry declared. \"Henry is a knight,\" Riley claimed. So who is a knight and who is a knave?", "names": ["David", "Jacob", "Benjamin", "Scarlett", "Henry", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "David is a knight, Jacob is a knave, Benjamin is a knight, Scarlett is a knight, Henry is a knight, and Riley is a knight.", "solution_text_format": "(1) David is a knight\n(2) Jacob is a knave\n(3) Benjamin is a knight\n(4) Scarlett is a knight\n(5) Henry is a knight\n(6) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Benjamin is a knight or Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that David is a knight and Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Henry is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that David is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that David is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If David is a knight then Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('or', ('telling-truth', 2), ('lying', 2)), ('telling-truth', 4))", "index": 329}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Mason, Matthew, Charlotte, Henry, and Zoey. Aiden commented, \"If Zoey is a knight then Charlotte is a knave\". \"Charlotte is a knight,\" Mason declared. \"Aiden is a knight or Charlotte is a knave\" - Matthew. Charlotte noted, \"Henry is not a knave\". In Henry's words: \"Aiden is a knave and Henry is a knight\". According to Zoey, \"Henry is not a knight\". So who is a knight and who is a knave?", "names": ["Aiden", "Mason", "Matthew", "Charlotte", "Henry", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Aiden is a knight, Mason is a knave, Matthew is a knight, Charlotte is a knave, Henry is a knave, and Zoey is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Mason is a knave\n(3) Matthew is a knight\n(4) Charlotte is a knave\n(5) Henry is a knave\n(6) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that If Zoey is a knight then Charlotte is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Aiden is a knave and Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Aiden is a knave and Henry is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Aiden that If Zoey is a knight then Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Henry is not a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Aiden is a knight or Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 3)), ('telling-truth', 3), ('or', ('telling-truth', 0), ('lying', 3)), ('not', ('lying', 4)), ('and', ('lying', 0), ('telling-truth', 4)), ('not', ('telling-truth', 4)))", "index": 330}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, William, Charlotte, Chloe, Zoey, and Elizabeth. \"If William is a knight then Chloe is a knave\" - Michael. According to William, \"Charlotte is a knave\". \"If Michael is a knight then Elizabeth is a knight,\" Charlotte claimed. Chloe expressed that William is not a knight. Zoey said that Charlotte is not a knave. As Elizabeth put it, \"Michael is a knight or Charlotte is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "William", "Charlotte", "Chloe", "Zoey", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Michael is a knight, William is a knave, Charlotte is a knight, Chloe is a knight, Zoey is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) William is a knave\n(3) Charlotte is a knight\n(4) Chloe is a knight\n(5) Zoey is a knight\n(6) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that If William is a knight then Chloe is a knave.", "Assume William is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of William that Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Michael is a knight then Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Charlotte that If Michael is a knight then Elizabeth is a knight.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Michael is a knight or Charlotte is a knight.", "We have exhausted all possibilities for Elizabeth and Charlotte, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Michael is a knight then Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Michael is a knight or Charlotte is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that William is not a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Charlotte is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('lying', 3)), ('lying', 2), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('not', ('telling-truth', 1)), ('not', ('lying', 2)), ('or', ('telling-truth', 0), ('telling-truth', 2)))", "index": 331}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Jacob, Harper, Emily, Isabella, and Chloe. \"Owen is a knight if and only if Isabella is a knight,\" Owen mentioned. According to Jacob, \"If Chloe is a knave then Owen is a knight\". In Harper's words: \"Isabella is a knight if and only if Jacob is a knave\". In a statement by Emily: \"Chloe is a knave and Emily is a knight\". Isabella said that If Emily is a knight then Emily is a knave. As Chloe put it, \"Harper is a knight if and only if Chloe is a knight\". So who is a knight and who is a knave?", "names": ["Owen", "Jacob", "Harper", "Emily", "Isabella", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "Owen is a knave, Jacob is a knave, Harper is a knight, Emily is a knave, Isabella is a knight, and Chloe is a knave.", "solution_text_format": "(1) Owen is a knave\n(2) Jacob is a knave\n(3) Harper is a knight\n(4) Emily is a knave\n(5) Isabella is a knight\n(6) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Owen is a knight if and only if Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Emily is a knight then Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Isabella that If Emily is a knight then Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Chloe is a knave and Emily is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Harper is a knight if and only if Chloe is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Harper that Isabella is a knight if and only if Jacob is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of their own that If Chloe is a knave then Owen is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Chloe that Harper is a knight if and only if Chloe is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Chloe is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Harper that Isabella is a knight if and only if Jacob is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of their own that If Chloe is a knave then Owen is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the false claim of Chloe that Harper is a knight if and only if Chloe is a knight.", "We have exhausted all possibilities for Harper, Chloe, and Emily, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Owen that Owen is a knight if and only if Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Emily is a knight then Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Isabella that If Emily is a knight then Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Chloe is a knave and Emily is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Harper is a knight if and only if Chloe is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Harper that Isabella is a knight if and only if Jacob is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of their own that If Chloe is a knave then Owen is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Chloe that Harper is a knight if and only if Chloe is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Chloe is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that If Chloe is a knave then Owen is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Chloe is a knave then Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('->', ('lying', 5), ('telling-truth', 0)), ('<=>', ('telling-truth', 4), ('lying', 1)), ('and', ('lying', 5), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('lying', 3)), ('<=>', ('telling-truth', 2), ('telling-truth', 5)))", "index": 332}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Daniel, Jack, Penelope, Sophia, and Emily. Charlotte expressed that Daniel is a knight. Daniel said that Penelope is a knight and Jack is a knave. \"Sophia is a knave and Jack is a knight\" - Jack. Penelope asserted: \"Emily is a knave and Jack is a knight\". In Sophia's words: \"Daniel is a knave and Charlotte is a knave\". Emily asserted: \"If Daniel is a knight then Sophia is a knave\". So who is a knight and who is a knave?", "names": ["Charlotte", "Daniel", "Jack", "Penelope", "Sophia", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Charlotte is a knave, Daniel is a knave, Jack is a knave, Penelope is a knave, Sophia is a knight, and Emily is a knight.", "solution_text_format": "(1) Charlotte is a knave\n(2) Daniel is a knave\n(3) Jack is a knave\n(4) Penelope is a knave\n(5) Sophia is a knight\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Penelope is a knight and Jack is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Emily is a knave and Jack is a knight.", "Emily cannot be a knight, because this would contradict the claim of Penelope that Emily is a knave and Jack is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that If Daniel is a knight then Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Charlotte is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of Emily that If Daniel is a knight then Sophia is a knave.", "We have exhausted all possibilities for Sophia and Emily, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Daniel that Penelope is a knight and Jack is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Charlotte that Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Charlotte that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Penelope is a knight and Jack is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Emily is a knave and Jack is a knight.", "Emily cannot be a knight, because this would contradict the claim of Penelope that Emily is a knave and Jack is a knight.", "Emily cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knight then Sophia is a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Emily is a knave and Jack is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Daniel is a knight then Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Daniel is a knave and Charlotte is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Sophia is a knave and Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('and', ('telling-truth', 3), ('lying', 2)), ('and', ('lying', 4), ('telling-truth', 2)), ('and', ('lying', 5), ('telling-truth', 2)), ('and', ('lying', 1), ('lying', 0)), ('->', ('telling-truth', 1), ('lying', 4)))", "index": 333}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Harper, James, Michael, Zoey, and Riley. Emily stated, \"Zoey is not a knight\". Harper said that Riley is a knave. As James put it, \"If Michael is a knight then Emily is a knight\". As Michael put it, \"If Zoey is a knave then Riley is a knave\". \"If Michael is a knight then Zoey is a knight,\" Zoey declared. Riley stated, \"Emily is a knight or Zoey is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Harper", "James", "Michael", "Zoey", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Emily is a knave, Harper is a knight, James is a knave, Michael is a knight, Zoey is a knight, and Riley is a knave.", "solution_text_format": "(1) Emily is a knave\n(2) Harper is a knight\n(3) James is a knave\n(4) Michael is a knight\n(5) Zoey is a knight\n(6) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Emily that Zoey is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Michael is a knight then Zoey is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Zoey is a knave then Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of Michael that If Zoey is a knave then Riley is a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that Emily is a knight or Zoey is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the false claim of Zoey that If Michael is a knight then Zoey is a knight.", "We have exhausted all possibilities for Michael and Zoey, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Michael is a knight then Zoey is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Zoey is a knave then Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Emily is a knight or Zoey is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Emily is a knight or Zoey is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Riley is a knave.", "James cannot be a knight, because this would contradict the claim of their own that If Michael is a knight then Emily is a knight.", "Assume James is a knave. No contradiction is found in their false claim that If Michael is a knight then Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('lying', 5), ('->', ('telling-truth', 3), ('telling-truth', 0)), ('->', ('lying', 4), ('lying', 5)), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('or', ('telling-truth', 0), ('lying', 4)))", "index": 334}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Mia, Charlotte, Riley, Ella, and Samuel. \"If Riley is a knight then Charlotte is a knave\" - Sofia. Mia told you that Sofia is a knight or Ella is a knight. Charlotte said that Sofia is a knight. In Riley's words: \"Ella is a knave\". Ella commented, \"Mia is not a knave\". In a statement by Samuel: \"If Ella is a knight then Mia is a knight\". So who is a knight and who is a knave?", "names": ["Sofia", "Mia", "Charlotte", "Riley", "Ella", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Sofia is a knight, Mia is a knight, Charlotte is a knight, Riley is a knave, Ella is a knight, and Samuel is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Mia is a knight\n(3) Charlotte is a knight\n(4) Riley is a knave\n(5) Ella is a knight\n(6) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that If Riley is a knight then Charlotte is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Riley that Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the false claim of Ella that Mia is not a knave.", "Mia cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight or Ella is a knight.", "We have exhausted all possibilities for Mia and Ella, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Mia is not a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Sofia is a knight or Ella is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Sofia is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Ella is a knight then Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 2)), ('or', ('telling-truth', 0), ('telling-truth', 4)), ('telling-truth', 0), ('lying', 4), ('not', ('lying', 1)), ('->', ('telling-truth', 4), ('telling-truth', 1)))", "index": 335}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Emily, Henry, Noah, Aiden, and Mason. Chloe said that If Aiden is a knight then Henry is a knight. In Emily's words: \"Mason is not a knave\". Henry was heard saying, \"If Mason is a knave then Emily is a knave\". Noah expressed that If Henry is a knave then Mason is a knave. Aiden remarked, \"If Chloe is a knight then Noah is a knave\". Mason said, \"Noah is a knave or Chloe is a knight.\" So who is a knight and who is a knave?", "names": ["Chloe", "Emily", "Henry", "Noah", "Aiden", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Chloe is a knight, Emily is a knight, Henry is a knight, Noah is a knight, Aiden is a knave, and Mason is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Emily is a knight\n(3) Henry is a knight\n(4) Noah is a knight\n(5) Aiden is a knave\n(6) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that If Aiden is a knight then Henry is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Chloe is a knight then Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Aiden that If Chloe is a knight then Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that If Henry is a knave then Mason is a knave.", "Henry cannot be a knight, because this would contradict the false claim of Noah that If Henry is a knave then Mason is a knave.", "Henry cannot be a knave, because this would contradict the claim of Chloe that If Aiden is a knight then Henry is a knight.", "We have exhausted all possibilities for Henry and Noah, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Chloe is a knight then Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Henry is a knave then Mason is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Mason is a knave then Emily is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Noah is a knave or Chloe is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Mason is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('telling-truth', 2)), ('not', ('lying', 5)), ('->', ('lying', 5), ('lying', 1)), ('->', ('lying', 2), ('lying', 5)), ('->', ('telling-truth', 0), ('lying', 3)), ('or', ('lying', 3), ('telling-truth', 0)))", "index": 336}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Emma, Lily, Joseph, Henry, and Aiden. Michael told you that Lily is a knave or Joseph is a knight. Emma expressed that Michael is a knight or Joseph is a knight. In a statement by Lily: \"If Henry is a knight then Michael is a knave\". Joseph noted, \"If Henry is a knave then Lily is a knave\". \"Aiden is a knight or Aiden is a knave\" - Henry. Aiden said, \"Michael is not a knave.\" So who is a knight and who is a knave?", "names": ["Michael", "Emma", "Lily", "Joseph", "Henry", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Michael is a knight, Emma is a knight, Lily is a knave, Joseph is a knight, Henry is a knight, and Aiden is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Emma is a knight\n(3) Lily is a knave\n(4) Joseph is a knight\n(5) Henry is a knight\n(6) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Lily is a knave or Joseph is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Henry is a knight then Michael is a knave.", "Henry cannot be a knight, because this would contradict the claim of Lily that If Henry is a knight then Michael is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that Aiden is a knight or Aiden is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that If Henry is a knight then Michael is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Aiden is a knight or Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Michael is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Henry is a knave then Lily is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Michael is a knight or Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('->', ('telling-truth', 4), ('lying', 0)), ('->', ('lying', 4), ('lying', 2)), ('or', ('telling-truth', 5), ('lying', 5)), ('not', ('lying', 0)))", "index": 337}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, William, Amelia, Ella, Aurora, and Grace. \"Amelia is a knave if and only if Grace is a knave,\" Jack claimed. William told you that Aurora is a knight or William is a knight. Amelia stated, \"Aurora is a knight and Ella is a knave\". \"William is a knight and Grace is a knave,\" Ella mentioned. Aurora stated, \"Jack is a knave\". Grace said that Ella is not a knight. So who is a knight and who is a knave?", "names": ["Jack", "William", "Amelia", "Ella", "Aurora", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Jack is a knight, William is a knight, Amelia is a knave, Ella is a knight, Aurora is a knave, and Grace is a knave.", "solution_text_format": "(1) Jack is a knight\n(2) William is a knight\n(3) Amelia is a knave\n(4) Ella is a knight\n(5) Aurora is a knave\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Grace is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Aurora is a knight and Ella is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Jack is a knave.", "Aurora cannot be a knave, because this would contradict the claim of Amelia that Aurora is a knight and Ella is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Aurora is a knight and Ella is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Jack is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Jack is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that William is a knight and Grace is a knave.", "Assume William is a knight. No contradiction is found in their claim that Aurora is a knight or William is a knight.", "Grace cannot be a knight, because this would contradict the claim of Jack that Amelia is a knave if and only if Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Ella is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 5)), ('or', ('telling-truth', 4), ('telling-truth', 1)), ('and', ('telling-truth', 4), ('lying', 3)), ('and', ('telling-truth', 1), ('lying', 5)), ('lying', 0), ('not', ('telling-truth', 3)))", "index": 338}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Sebastian, Ethan, James, Jacob, and Owen. \"If Ethan is a knight then Ethan is a knave\" - Riley. Sebastian asserted: \"Ethan is not a knight\". According to Ethan, \"If Ethan is a knight then Sebastian is a knave\". As James put it, \"If Riley is a knight then Ethan is a knight\". Jacob remarked, \"Owen is a knave and Sebastian is a knight\". Owen expressed that Jacob is not a knight. So who is a knight and who is a knave?", "names": ["Riley", "Sebastian", "Ethan", "James", "Jacob", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Riley is a knave, Sebastian is a knave, Ethan is a knight, James is a knight, Jacob is a knave, and Owen is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Sebastian is a knave\n(3) Ethan is a knight\n(4) James is a knight\n(5) Jacob is a knave\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that If Ethan is a knight then Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Riley that If Ethan is a knight then Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of their own that If Ethan is a knight then Sebastian is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that If Ethan is a knight then Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Ethan is a knight then Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Ethan is not a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Assume James is a knight. No contradiction is found in their claim that If Riley is a knight then Ethan is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Owen is a knave and Sebastian is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Owen is a knave and Sebastian is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Jacob is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 2)), ('not', ('telling-truth', 2)), ('->', ('telling-truth', 2), ('lying', 1)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('and', ('lying', 5), ('telling-truth', 1)), ('not', ('telling-truth', 4)))", "index": 339}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Amelia, Mason, Samuel, Isabella, and Lucas. According to Daniel, \"Samuel is a knight\". As Amelia put it, \"Lucas is a knave\". Mason said that Isabella is a knight or Daniel is a knight. In Samuel's words: \"Samuel is a knight if and only if Daniel is a knight\". Isabella said that Mason is a knave. Lucas asserted: \"Samuel is a knight if and only if Daniel is a knave\". So who is a knight and who is a knave?", "names": ["Daniel", "Amelia", "Mason", "Samuel", "Isabella", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Daniel is a knight, Amelia is a knight, Mason is a knight, Samuel is a knight, Isabella is a knave, and Lucas is a knave.", "solution_text_format": "(1) Daniel is a knight\n(2) Amelia is a knight\n(3) Mason is a knight\n(4) Samuel is a knight\n(5) Isabella is a knave\n(6) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Daniel is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Amelia that Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Daniel is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Isabella is a knight or Daniel is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Mason is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('lying', 5), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('lying', 2), ('<=>', ('telling-truth', 3), ('lying', 0)))", "index": 340}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Emma, Evelyn, Jack, Mason, and Mia. \"If Owen is a knight then Evelyn is a knight,\" Owen mentioned. \"Jack is a knight or Jack is a knave,\" Emma mentioned. \"Mason is a knave\" - Evelyn. \"Emma is a knight if and only if Owen is a knight,\" Jack claimed. As Mason put it, \"Emma is a knave\". \"Evelyn is a knight,\" Mia mentioned. So who is a knight and who is a knave?", "names": ["Owen", "Emma", "Evelyn", "Jack", "Mason", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Owen is a knight, Emma is a knight, Evelyn is a knight, Jack is a knight, Mason is a knave, and Mia is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Emma is a knight\n(3) Evelyn is a knight\n(4) Jack is a knight\n(5) Mason is a knave\n(6) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that If Owen is a knight then Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Evelyn that Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Jack is a knight or Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Emma is a knight if and only if Owen is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 2)), ('or', ('telling-truth', 3), ('lying', 3)), ('lying', 4), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('lying', 1), ('telling-truth', 2))", "index": 341}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Benjamin, Ella, Emily, Alexander, and Luke. In Owen's words: \"Owen is a knight or Emily is a knight\". Benjamin expressed that Luke is a knight or Alexander is a knight. Ella expressed that Alexander is not a knight. \"Owen is a knight if and only if Luke is a knight,\" Emily declared. In Alexander's words: \"Emily is a knave or Owen is a knight\". Luke remarked, \"Alexander is not a knight\". So who is a knight and who is a knave?", "names": ["Owen", "Benjamin", "Ella", "Emily", "Alexander", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false], "solution_text": "Owen is a knight, Benjamin is a knight, Ella is a knave, Emily is a knave, Alexander is a knight, and Luke is a knave.", "solution_text_format": "(1) Owen is a knight\n(2) Benjamin is a knight\n(3) Ella is a knave\n(4) Emily is a knave\n(5) Alexander is a knight\n(6) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Owen is a knight or Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Owen is a knight if and only if Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Luke that Alexander is not a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Emily is a knave or Owen is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Emily that Owen is a knight if and only if Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Emily that Owen is a knight if and only if Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Emily is a knave or Owen is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Luke is a knight or Alexander is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Alexander is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Alexander is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('telling-truth', 5), ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 0), ('telling-truth', 5)), ('or', ('lying', 3), ('telling-truth', 0)), ('not', ('telling-truth', 4)))", "index": 342}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Henry, Avery, Owen, Noah, and David. As Mia put it, \"If Owen is a knight then Noah is a knave\". \"Noah is not a knave,\" Henry mentioned. Avery commented, \"Mia is a knave and Mia is a knight\". Owen commented, \"David is a knave or Avery is a knave\". Noah was heard saying, \"Henry is a knave or Henry is a knight\". \"Mia is a knight\" - David. So who is a knight and who is a knave?", "names": ["Mia", "Henry", "Avery", "Owen", "Noah", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Mia is a knave, Henry is a knight, Avery is a knave, Owen is a knight, Noah is a knight, and David is a knave.", "solution_text_format": "(1) Mia is a knave\n(2) Henry is a knight\n(3) Avery is a knave\n(4) Owen is a knight\n(5) Noah is a knight\n(6) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that If Owen is a knight then Noah is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that David is a knave or Avery is a knave.", "Assume David is a knight. No contradiction is found in their claim that Mia is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Mia is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Mia is a knave and Mia is a knight.", "Noah cannot be a knight, because this would contradict the claim of Mia that If Owen is a knight then Noah is a knave.", "Noah cannot be a knave, because this would contradict the false claim of their own that Henry is a knave or Henry is a knight.", "We have exhausted all possibilities for Noah and Avery, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of their own that Mia is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that David is a knave or Avery is a knave.", "Assume David is a knight. No contradiction is found in their claim that Mia is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Mia is a knight.", "Avery cannot be a knave, because this would contradict the false claim of Owen that David is a knave or Avery is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of Owen that David is a knave or Avery is a knave.", "We have exhausted all possibilities for David and Owen, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that If Owen is a knight then Noah is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that David is a knave or Avery is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Mia is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Mia is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Mia is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Mia is a knave and Mia is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Henry is a knave or Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Noah is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 4)), ('not', ('lying', 4)), ('and', ('lying', 0), ('telling-truth', 0)), ('or', ('lying', 5), ('lying', 2)), ('or', ('lying', 1), ('telling-truth', 1)), ('telling-truth', 0))", "index": 343}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Alexander, Charlotte, Sophia, Oliver, and Lily. \"Lily is a knave if and only if Oliver is a knave,\" Samuel declared. Alexander said, \"Oliver is a knight and Lily is a knave.\" \"Alexander is a knight,\" Charlotte declared. Sophia remarked, \"Oliver is a knave\". \"Lily is not a knave,\" Oliver claimed. In a statement by Lily: \"Charlotte is a knave\". So who is a knight and who is a knave?", "names": ["Samuel", "Alexander", "Charlotte", "Sophia", "Oliver", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true], "solution_text": "Samuel is a knight, Alexander is a knave, Charlotte is a knave, Sophia is a knave, Oliver is a knight, and Lily is a knight.", "solution_text_format": "(1) Samuel is a knight\n(2) Alexander is a knave\n(3) Charlotte is a knave\n(4) Sophia is a knave\n(5) Oliver is a knight\n(6) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Lily is a knave if and only if Oliver is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Lily that Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Oliver is a knight and Lily is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Oliver is a knight and Lily is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Lily is not a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 4)), ('and', ('telling-truth', 4), ('lying', 5)), ('telling-truth', 1), ('lying', 4), ('not', ('lying', 5)), ('lying', 2))", "index": 344}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Michael, Evelyn, Sophia, James, and Jacob. In Benjamin's words: \"If Sophia is a knight then Evelyn is a knight\". Michael asserted: \"Benjamin is a knave or James is a knight\". Evelyn said, \"Sophia is a knight or James is a knave.\" In Sophia's words: \"If Michael is a knave then James is a knight\". James remarked, \"Sophia is a knight or Evelyn is a knight\". \"Benjamin is a knave and Sophia is a knight,\" Jacob declared. So who is a knight and who is a knave?", "names": ["Benjamin", "Michael", "Evelyn", "Sophia", "James", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Benjamin is a knight, Michael is a knight, Evelyn is a knight, Sophia is a knight, James is a knight, and Jacob is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Michael is a knight\n(3) Evelyn is a knight\n(4) Sophia is a knight\n(5) James is a knight\n(6) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that If Sophia is a knight then Evelyn is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Michael is a knave then James is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Benjamin is a knave or James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Sophia is a knight or Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Sophia is a knight or James is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Sophia is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Benjamin is a knave and Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('telling-truth', 2)), ('or', ('lying', 0), ('telling-truth', 4)), ('or', ('telling-truth', 3), ('lying', 4)), ('->', ('lying', 1), ('telling-truth', 4)), ('or', ('telling-truth', 3), ('telling-truth', 2)), ('and', ('lying', 0), ('telling-truth', 3)))", "index": 345}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Luke, Elizabeth, Mason, Owen, and Sebastian. In a statement by Olivia: \"If Sebastian is a knave then Elizabeth is a knave\". \"Olivia is a knave and Luke is a knight,\" Luke claimed. \"Luke is not a knave,\" Elizabeth declared. Mason was heard saying, \"Olivia is not a knight\". As Owen put it, \"Owen is a knight and Mason is a knight\". Sebastian was heard saying, \"Olivia is a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Luke", "Elizabeth", "Mason", "Owen", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false], "solution_text": "Olivia is a knight, Luke is a knave, Elizabeth is a knave, Mason is a knave, Owen is a knave, and Sebastian is a knave.", "solution_text_format": "(1) Olivia is a knight\n(2) Luke is a knave\n(3) Elizabeth is a knave\n(4) Mason is a knave\n(5) Owen is a knave\n(6) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that If Sebastian is a knave then Elizabeth is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Olivia that If Sebastian is a knave then Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Olivia is a knave and Luke is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Olivia is not a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Olivia is not a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Mason is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Owen is a knight and Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 2)), ('and', ('lying', 0), ('telling-truth', 1)), ('not', ('lying', 1)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 4), ('telling-truth', 3)), ('lying', 0))", "index": 346}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Amelia, Abigail, Liam, David, and Lucas. Elizabeth expressed that Lucas is a knave or Abigail is a knight. \"Liam is not a knave\" - Amelia. Abigail said, \"Elizabeth is a knight and Liam is a knight.\" \"Elizabeth is a knave if and only if Elizabeth is a knight,\" Liam declared. David was heard saying, \"Liam is not a knight\". As Lucas put it, \"David is a knave\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Amelia", "Abigail", "Liam", "David", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false], "solution_text": "Elizabeth is a knight, Amelia is a knave, Abigail is a knave, Liam is a knave, David is a knight, and Lucas is a knave.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Amelia is a knave\n(3) Abigail is a knave\n(4) Liam is a knave\n(5) David is a knight\n(6) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Lucas is a knave or Abigail is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Lucas that David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave if and only if Elizabeth is a knight.", "Liam cannot be a knave, because this would contradict the false claim of David that Liam is not a knight.", "We have exhausted all possibilities for Liam and David, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Liam is not a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave if and only if Elizabeth is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Elizabeth is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Liam is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Liam is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Liam is not a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Liam is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 2)), ('not', ('lying', 3)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('<=>', ('lying', 0), ('telling-truth', 0)), ('not', ('telling-truth', 3)), ('lying', 4))", "index": 347}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Owen, Avery, Abigail, David, and Joseph. William stated, \"David is not a knave\". Owen expressed that David is not a knight. Avery asserted: \"Owen is a knight if and only if David is a knight\". \"Avery is a knave if and only if Joseph is a knight,\" Abigail declared. David commented, \"Owen is a knave and Avery is a knight\". In Joseph's words: \"Avery is a knave or Abigail is a knight\". So who is a knight and who is a knave?", "names": ["William", "Owen", "Avery", "Abigail", "David", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true], "solution_text": "William is a knave, Owen is a knight, Avery is a knave, Abigail is a knight, David is a knave, and Joseph is a knight.", "solution_text_format": "(1) William is a knave\n(2) Owen is a knight\n(3) Avery is a knave\n(4) Abigail is a knight\n(5) David is a knave\n(6) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that David is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Owen is a knave and Avery is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that David is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that David is not a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Owen is a knight if and only if David is a knight.", "Avery cannot be a knave, because this would contradict the claim of David that Owen is a knave and Avery is a knight.", "We have exhausted all possibilities for Avery and Owen, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of William that David is not a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that David is not a knave.", "David cannot be a knight, because this would contradict the false claim of William that David is not a knave.", "Assume David is a knave. No contradiction is found in their false claim that Owen is a knave and Avery is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that David is not a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Owen is a knight if and only if David is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Owen is a knight if and only if David is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Avery is a knave if and only if Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Avery is a knave or Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('telling-truth', 4)), ('<=>', ('lying', 2), ('telling-truth', 5)), ('and', ('lying', 1), ('telling-truth', 2)), ('or', ('lying', 2), ('telling-truth', 3)))", "index": 348}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Mason, Jacob, Grace, Avery, and Oliver. \"Jacob is a knave,\" Mia mentioned. Mason expressed that Mia is a knight and Grace is a knave. Jacob noted, \"Mia is a knight if and only if Mason is a knight\". Grace commented, \"Mia is not a knight\". \"Oliver is a knight\" - Avery. Oliver commented, \"Jacob is not a knave\". So who is a knight and who is a knave?", "names": ["Mia", "Mason", "Jacob", "Grace", "Avery", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Mia is a knave, Mason is a knave, Jacob is a knight, Grace is a knight, Avery is a knight, and Oliver is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Mason is a knave\n(3) Jacob is a knight\n(4) Grace is a knight\n(5) Avery is a knight\n(6) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Mia that Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Mason is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Jacob that Mia is a knight if and only if Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Mia is a knight and Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Mia is not a knight.", "Grace cannot be a knave, because this would contradict the false claim of Mason that Mia is a knight and Grace is a knave.", "We have exhausted all possibilities for Grace, Mason, and Jacob, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Mia is a knight if and only if Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Grace is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Mia is a knight and Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Mia is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Jacob is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('and', ('telling-truth', 0), ('lying', 3)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('telling-truth', 5), ('not', ('lying', 2)))", "index": 349}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Aiden, Samuel, Victoria, Charlotte, and Emily. According to Benjamin, \"Aiden is a knight or Samuel is a knight\". Aiden said, \"Emily is a knave and Benjamin is a knave.\" In Samuel's words: \"If Samuel is a knight then Emily is a knave\". Victoria told you that Benjamin is a knave or Aiden is a knave. In a statement by Charlotte: \"Charlotte is a knight or Victoria is a knight\". \"Aiden is a knight,\" Emily declared. So who is a knight and who is a knave?", "names": ["Benjamin", "Aiden", "Samuel", "Victoria", "Charlotte", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Benjamin is a knight, Aiden is a knave, Samuel is a knight, Victoria is a knight, Charlotte is a knight, and Emily is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Aiden is a knave\n(3) Samuel is a knight\n(4) Victoria is a knight\n(5) Charlotte is a knight\n(6) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Aiden is a knight or Samuel is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Emily is a knave and Benjamin is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Emily is a knave and Benjamin is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Aiden is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Aiden is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Samuel is a knight then Emily is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Benjamin is a knave or Aiden is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Charlotte is a knight or Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('lying', 5), ('lying', 0)), ('->', ('telling-truth', 2), ('lying', 5)), ('or', ('lying', 0), ('lying', 1)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('telling-truth', 1))", "index": 350}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Harper, Luke, James, Sebastian, and Alexander. \"Luke is a knave\" - Matthew. Harper stated, \"Alexander is a knight\". Luke was heard saying, \"Harper is a knight or Luke is a knight\". \"Alexander is a knight and Matthew is a knight,\" James claimed. Sebastian said that Luke is a knight if and only if Matthew is a knave. Alexander said, \"Matthew is not a knave.\" So who is a knight and who is a knave?", "names": ["Matthew", "Harper", "Luke", "James", "Sebastian", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "Matthew is a knave, Harper is a knave, Luke is a knight, James is a knave, Sebastian is a knight, and Alexander is a knave.", "solution_text_format": "(1) Matthew is a knave\n(2) Harper is a knave\n(3) Luke is a knight\n(4) James is a knave\n(5) Sebastian is a knight\n(6) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Matthew that Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Harper is a knight or Luke is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Luke that Harper is a knight or Luke is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Harper that Alexander is a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Matthew is not a knave.", "We have exhausted all possibilities for Alexander, Harper, and Luke, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Harper is a knight or Luke is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Matthew is not a knave.", "Alexander cannot be a knave, because this would contradict the claim of Harper that Alexander is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Harper that Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Matthew is not a knave.", "James cannot be a knight, because this would contradict the claim of their own that Alexander is a knight and Matthew is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Alexander is a knight and Matthew is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Luke is a knight if and only if Matthew is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('telling-truth', 5), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('telling-truth', 5), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('not', ('lying', 0)))", "index": 351}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Noah, Luke, Sofia, Emily, Ethan, and Grace. As Noah put it, \"Sofia is a knight\". \"Emily is not a knave,\" Luke mentioned. As Sofia put it, \"Grace is not a knight\". Emily expressed that Ethan is not a knave. Ethan expressed that Noah is not a knave. As Grace put it, \"Ethan is a knave if and only if Noah is a knight\". So who is a knight and who is a knave?", "names": ["Noah", "Luke", "Sofia", "Emily", "Ethan", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Noah is a knight, Luke is a knight, Sofia is a knight, Emily is a knight, Ethan is a knight, and Grace is a knave.", "solution_text_format": "(1) Noah is a knight\n(2) Luke is a knight\n(3) Sofia is a knight\n(4) Emily is a knight\n(5) Ethan is a knight\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Grace is not a knight.", "Grace cannot be a knight, because this would contradict the claim of Sofia that Grace is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Noah is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Noah is not a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Ethan is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('not', ('lying', 3)), ('not', ('telling-truth', 5)), ('not', ('lying', 4)), ('not', ('lying', 0)), ('<=>', ('lying', 4), ('telling-truth', 0)))", "index": 352}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Aiden, Riley, Grace, Scarlett, and Aurora. Sofia noted, \"Aiden is a knave or Grace is a knight\". Aiden stated, \"Sofia is a knight or Aurora is a knight\". Riley said that Aurora is a knight and Sofia is a knight. \"Aiden is a knave if and only if Scarlett is a knight,\" Grace mentioned. In a statement by Scarlett: \"Aiden is a knave if and only if Riley is a knight\". \"Aurora is a knight and Grace is a knave,\" Aurora mentioned. So who is a knight and who is a knave?", "names": ["Sofia", "Aiden", "Riley", "Grace", "Scarlett", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true], "solution_text": "Sofia is a knave, Aiden is a knight, Riley is a knave, Grace is a knave, Scarlett is a knight, and Aurora is a knight.", "solution_text_format": "(1) Sofia is a knave\n(2) Aiden is a knight\n(3) Riley is a knave\n(4) Grace is a knave\n(5) Scarlett is a knight\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Aiden is a knave or Grace is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Sofia is a knight or Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Aurora is a knight and Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Aurora that Aurora is a knight and Grace is a knave.", "Grace cannot be a knave, because this would contradict the claim of Sofia that Aiden is a knave or Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Aurora is a knight and Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Grace that Aiden is a knave if and only if Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Sofia is a knight.", "Riley cannot be a knave, because this would contradict the false claim of Scarlett that Aiden is a knave if and only if Riley is a knight.", "We have exhausted all possibilities for Riley and Scarlett, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Sofia that Aiden is a knave or Grace is a knight.", "We have exhausted all possibilities for Grace and Aurora, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight or Aurora is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Aiden is a knave or Grace is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Sofia is a knight or Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Aurora is a knight and Grace is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Sofia that Aiden is a knave or Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Sofia is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Aurora is a knight and Sofia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('telling-truth', 5), ('telling-truth', 0)), ('<=>', ('lying', 1), ('telling-truth', 4)), ('<=>', ('lying', 1), ('telling-truth', 2)), ('and', ('telling-truth', 5), ('lying', 3)))", "index": 353}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, David, Aria, Emily, Aurora, and Matthew. \"Matthew is a knave if and only if David is a knave,\" Jack mentioned. David noted, \"Jack is not a knight\". \"Aria is a knight or Jack is a knave,\" Aria claimed. Emily commented, \"Aria is a knave or Aurora is a knave\". \"Aria is a knight and Jack is a knight\" - Aurora. Matthew stated, \"David is a knave or Aria is a knave\". So who is a knight and who is a knave?", "names": ["Jack", "David", "Aria", "Emily", "Aurora", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Jack is a knave, David is a knight, Aria is a knight, Emily is a knight, Aurora is a knave, and Matthew is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) David is a knight\n(3) Aria is a knight\n(4) Emily is a knight\n(5) Aurora is a knave\n(6) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Matthew is a knave if and only if David is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that David is a knave or Aria is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Jack is not a knight.", "David cannot be a knave, because this would contradict the claim of Jack that Matthew is a knave if and only if David is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that David is a knave or Aria is a knave.", "David cannot be a knight, because this would contradict the claim of Jack that Matthew is a knave if and only if David is a knave.", "David cannot be a knave, because this would contradict the false claim of Matthew that David is a knave or Aria is a knave.", "We have exhausted all possibilities for David and Matthew, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if David is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that David is a knave or Aria is a knave.", "David cannot be a knight, because this would contradict the false claim of Jack that Matthew is a knave if and only if David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that Jack is not a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that David is a knave or Aria is a knave.", "Assume David is a knight. No contradiction is found in their claim that Jack is not a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Aria is a knight or Jack is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Aria is a knave or Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Emily that Aria is a knave or Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Aria is a knight and Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 1)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 2), ('lying', 0)), ('or', ('lying', 2), ('lying', 4)), ('and', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('lying', 1), ('lying', 2)))", "index": 354}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Ella, Grace, Charlotte, Emily, and Victoria. According to Chloe, \"Grace is a knave\". Ella remarked, \"If Chloe is a knave then Grace is a knight\". Grace commented, \"Chloe is a knave and Charlotte is a knight\". Charlotte told you that Chloe is a knave if and only if Ella is a knave. According to Emily, \"Chloe is a knave and Grace is a knave\". \"Chloe is a knight and Charlotte is a knave,\" Victoria claimed. So who is a knight and who is a knave?", "names": ["Chloe", "Ella", "Grace", "Charlotte", "Emily", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Chloe is a knight, Ella is a knight, Grace is a knave, Charlotte is a knight, Emily is a knave, and Victoria is a knave.", "solution_text_format": "(1) Chloe is a knight\n(2) Ella is a knight\n(3) Grace is a knave\n(4) Charlotte is a knight\n(5) Emily is a knave\n(6) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Chloe that Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Chloe is a knave and Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Chloe is a knave then Grace is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Grace is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Chloe is a knave and Grace is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Chloe is a knight and Charlotte is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Chloe is a knight and Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('->', ('lying', 0), ('telling-truth', 2)), ('and', ('lying', 0), ('telling-truth', 3)), ('<=>', ('lying', 0), ('lying', 1)), ('and', ('lying', 0), ('lying', 2)), ('and', ('telling-truth', 0), ('lying', 3)))", "index": 355}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Avery, Henry, Abigail, Sophia, and Michael. Jack said, \"Abigail is a knave and Henry is a knave.\" Avery remarked, \"Sophia is a knight or Abigail is a knight\". According to Henry, \"Abigail is not a knave\". Abigail said, \"Avery is a knave if and only if Avery is a knight.\" Sophia remarked, \"If Jack is a knight then Abigail is a knight\". According to Michael, \"Avery is a knave if and only if Sophia is a knight\". So who is a knight and who is a knave?", "names": ["Jack", "Avery", "Henry", "Abigail", "Sophia", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false], "solution_text": "Jack is a knight, Avery is a knave, Henry is a knave, Abigail is a knave, Sophia is a knave, and Michael is a knave.", "solution_text_format": "(1) Jack is a knight\n(2) Avery is a knave\n(3) Henry is a knave\n(4) Abigail is a knave\n(5) Sophia is a knave\n(6) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Abigail is a knave and Henry is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Jack that Abigail is a knave and Henry is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Sophia is a knight or Abigail is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that If Jack is a knight then Abigail is a knight.", "Sophia cannot be a knave, because this would contradict the claim of Avery that Sophia is a knight or Abigail is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Sophia is a knight or Abigail is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Avery that Sophia is a knight or Abigail is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Jack is a knight then Abigail is a knight.", "Henry cannot be a knight, because this would contradict the claim of Jack that Abigail is a knave and Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Abigail is not a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Avery is a knave if and only if Sophia is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 2)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('not', ('lying', 3)), ('<=>', ('lying', 1), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('telling-truth', 3)), ('<=>', ('lying', 1), ('telling-truth', 4)))", "index": 356}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Riley, Luke, Matthew, Mason, and Oliver. Victoria noted, \"Luke is a knight and Riley is a knave\". \"Matthew is a knave,\" Riley mentioned. Luke said that Riley is a knave or Victoria is a knight. \"Riley is a knight and Mason is a knave,\" Matthew claimed. Mason was heard saying, \"If Oliver is a knave then Luke is a knight\". Oliver was heard saying, \"Matthew is a knave\". So who is a knight and who is a knave?", "names": ["Victoria", "Riley", "Luke", "Matthew", "Mason", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true], "solution_text": "Victoria is a knave, Riley is a knight, Luke is a knave, Matthew is a knave, Mason is a knight, and Oliver is a knight.", "solution_text_format": "(1) Victoria is a knave\n(2) Riley is a knight\n(3) Luke is a knave\n(4) Matthew is a knave\n(5) Mason is a knight\n(6) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Luke is a knight and Riley is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Riley is a knave or Victoria is a knight.", "Riley cannot be a knight, because this would contradict the claim of Victoria that Luke is a knight and Riley is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Riley is a knight and Mason is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of Riley that Matthew is a knave.", "We have exhausted all possibilities for Matthew and Riley, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Victoria that Luke is a knight and Riley is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Luke is a knight and Riley is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Riley is a knave or Victoria is a knight.", "Riley cannot be a knight, because this would contradict the claim of Luke that Riley is a knave or Victoria is a knight.", "Riley cannot be a knave, because this would contradict the false claim of Victoria that Luke is a knight and Riley is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Riley is a knave or Victoria is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Riley that Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Riley is a knight and Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Oliver is a knave then Luke is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Matthew is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('lying', 1)), ('lying', 3), ('or', ('lying', 1), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('lying', 4)), ('->', ('lying', 5), ('telling-truth', 2)), ('lying', 3))", "index": 357}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Emily, Liam, Benjamin, David, and Riley. Logan remarked, \"Emily is not a knave\". \"Emily is a knight or Logan is a knight,\" Emily mentioned. According to Liam, \"Riley is a knave and David is a knave\". Benjamin told you that Liam is a knight. David expressed that Liam is a knight. Riley commented, \"Riley is a knight and Emily is a knave\". So who is a knight and who is a knave?", "names": ["Logan", "Emily", "Liam", "Benjamin", "David", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true], "solution_text": "Logan is a knave, Emily is a knave, Liam is a knave, Benjamin is a knave, David is a knave, and Riley is a knight.", "solution_text_format": "(1) Logan is a knave\n(2) Emily is a knave\n(3) Liam is a knave\n(4) Benjamin is a knave\n(5) David is a knave\n(6) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Emily is a knight or Logan is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Riley is a knave and David is a knave.", "Riley cannot be a knight, because this would contradict the claim of Liam that Riley is a knave and David is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Riley is a knight and Emily is a knave.", "David cannot be a knight, because this would contradict the claim of Liam that Riley is a knave and David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that Liam is a knight.", "We have exhausted all possibilities for David and Riley, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Riley is a knave and David is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Riley is a knight and Emily is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Riley is a knight and Emily is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Liam is a knight.", "David cannot be a knave, because this would contradict the false claim of Liam that Riley is a knave and David is a knave.", "We have exhausted all possibilities for David, Riley, and Liam, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Logan that Emily is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Logan that Emily is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Emily is a knight or Logan is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Riley is a knave and David is a knave.", "Riley cannot be a knight, because this would contradict the claim of Liam that Riley is a knave and David is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Riley is a knight and Emily is a knave.", "David cannot be a knight, because this would contradict the claim of Liam that Riley is a knave and David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that Liam is a knight.", "We have exhausted all possibilities for David and Riley, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Riley is a knave and David is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight and Emily is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Liam is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Liam is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Liam is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('lying', 5), ('lying', 4)), ('telling-truth', 2), ('telling-truth', 2), ('and', ('telling-truth', 5), ('lying', 1)))", "index": 358}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Emma, Aiden, Elizabeth, Riley, and Oliver. In a statement by Liam: \"Aiden is a knave and Elizabeth is a knave\". As Emma put it, \"Riley is a knight or Liam is a knave\". Aiden told you that Emma is a knave and Riley is a knave. Elizabeth noted, \"Riley is a knave and Elizabeth is a knight\". Riley stated, \"Aiden is a knight and Emma is a knave\". As Oliver put it, \"Aiden is a knight or Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Liam", "Emma", "Aiden", "Elizabeth", "Riley", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true], "solution_text": "Liam is a knave, Emma is a knight, Aiden is a knave, Elizabeth is a knight, Riley is a knave, and Oliver is a knight.", "solution_text_format": "(1) Liam is a knave\n(2) Emma is a knight\n(3) Aiden is a knave\n(4) Elizabeth is a knight\n(5) Riley is a knave\n(6) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Aiden is a knave and Elizabeth is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Liam that Aiden is a knave and Elizabeth is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Emma is a knave and Riley is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Riley is a knight or Liam is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Emma is a knave.", "Riley cannot be a knave, because this would contradict the claim of Emma that Riley is a knight or Liam is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Riley is a knight or Liam is a knave.", "Riley cannot be a knight, because this would contradict the false claim of Emma that Riley is a knight or Liam is a knave.", "Riley cannot be a knave, because this would contradict the false claim of Aiden that Emma is a knave and Riley is a knave.", "We have exhausted all possibilities for Riley, Emma, and Aiden, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Aiden is a knave and Elizabeth is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Emma is a knave and Riley is a knave.", "Emma cannot be a knight, because this would contradict the claim of Aiden that Emma is a knave and Riley is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that Riley is a knight or Liam is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Emma is a knave and Riley is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Riley is a knight or Liam is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Emma is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Aiden is a knight and Emma is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Riley is a knave and Elizabeth is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Aiden is a knight or Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 3)), ('or', ('telling-truth', 4), ('lying', 0)), ('and', ('lying', 1), ('lying', 4)), ('and', ('lying', 4), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('lying', 1)), ('or', ('telling-truth', 2), ('lying', 2)))", "index": 359}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Riley, Ethan, Penelope, Samuel, and Aiden. Scarlett commented, \"Samuel is a knave\". Riley asserted: \"Aiden is not a knave\". \"If Riley is a knight then Samuel is a knight,\" Ethan declared. Penelope remarked, \"Aiden is a knight or Riley is a knave\". \"Aiden is a knave,\" Samuel mentioned. Aiden told you that Aiden is a knight if and only if Samuel is a knave. So who is a knight and who is a knave?", "names": ["Scarlett", "Riley", "Ethan", "Penelope", "Samuel", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Scarlett is a knight, Riley is a knight, Ethan is a knave, Penelope is a knight, Samuel is a knave, and Aiden is a knight.", "solution_text_format": "(1) Scarlett is a knight\n(2) Riley is a knight\n(3) Ethan is a knave\n(4) Penelope is a knight\n(5) Samuel is a knave\n(6) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Scarlett that Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Samuel is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that If Riley is a knight then Samuel is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Riley is a knight then Samuel is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Aiden is a knight or Riley is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('not', ('lying', 5)), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('or', ('telling-truth', 5), ('lying', 1)), ('lying', 5), ('<=>', ('telling-truth', 5), ('lying', 4)))", "index": 360}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Riley, Michael, Emily, Owen, and Grace. According to Lucas, \"If Grace is a knight then Michael is a knave\". \"Emily is a knave,\" Riley mentioned. \"Grace is not a knave\" - Michael. Emily told you that Michael is a knight or Riley is a knight. Owen commented, \"If Grace is a knave then Lucas is a knight\". Grace said, \"Riley is a knave or Riley is a knight.\" So who is a knight and who is a knave?", "names": ["Lucas", "Riley", "Michael", "Emily", "Owen", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Lucas is a knave, Riley is a knave, Michael is a knight, Emily is a knight, Owen is a knight, and Grace is a knight.", "solution_text_format": "(1) Lucas is a knave\n(2) Riley is a knave\n(3) Michael is a knight\n(4) Emily is a knight\n(5) Owen is a knight\n(6) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that If Grace is a knight then Michael is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Riley is a knave or Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Riley that Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that Michael is a knight or Riley is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Michael is a knight or Riley is a knight.", "Michael cannot be a knight, because this would contradict the claim of Lucas that If Grace is a knight then Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that Grace is not a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of Riley that Emily is a knave.", "We have exhausted all possibilities for Emily and Riley, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the false claim of their own that Riley is a knave or Riley is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Grace is a knight then Michael is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Riley is a knave or Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Riley that Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that Michael is a knight or Riley is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Michael is a knight or Riley is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Grace is not a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Grace is a knave then Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 2)), ('lying', 3), ('not', ('lying', 5)), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('lying', 5), ('telling-truth', 0)), ('or', ('lying', 1), ('telling-truth', 1)))", "index": 361}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Sophia, Oliver, Aiden, David, and Matthew. Aurora noted, \"Sophia is a knave or Matthew is a knight\". Sophia said, \"Aiden is a knight or Aiden is a knave.\" As Oliver put it, \"Matthew is a knight or Aurora is a knave\". Aiden told you that Aurora is a knave and Aurora is a knight. David asserted: \"Aurora is not a knight\". Matthew asserted: \"Aiden is a knave or Aurora is a knave\". So who is a knight and who is a knave?", "names": ["Aurora", "Sophia", "Oliver", "Aiden", "David", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Aurora is a knight, Sophia is a knight, Oliver is a knight, Aiden is a knave, David is a knave, and Matthew is a knight.", "solution_text_format": "(1) Aurora is a knight\n(2) Sophia is a knight\n(3) Oliver is a knight\n(4) Aiden is a knave\n(5) David is a knave\n(6) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Sophia is a knave or Matthew is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Aiden is a knight or Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Aurora is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aurora is a knave and Aurora is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Aiden is a knave or Aurora is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Matthew is a knight or Aurora is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Aurora is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that Aurora is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 5)), ('or', ('telling-truth', 3), ('lying', 3)), ('or', ('telling-truth', 5), ('lying', 0)), ('and', ('lying', 0), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('or', ('lying', 3), ('lying', 0)))", "index": 362}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Mia, Daniel, Lucas, David, and Jacob. \"Daniel is not a knight,\" Chloe declared. \"If Chloe is a knave then Jacob is a knight,\" Mia declared. Daniel noted, \"Jacob is a knight or David is a knight\". Lucas noted, \"Mia is a knight if and only if Daniel is a knave\". \"Lucas is a knight,\" David claimed. In Jacob's words: \"David is a knight or David is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Mia", "Daniel", "Lucas", "David", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Chloe is a knave, Mia is a knight, Daniel is a knight, Lucas is a knave, David is a knave, and Jacob is a knight.", "solution_text_format": "(1) Chloe is a knave\n(2) Mia is a knight\n(3) Daniel is a knight\n(4) Lucas is a knave\n(5) David is a knave\n(6) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of Chloe that Daniel is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Jacob is a knight or David is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Daniel that Jacob is a knight or David is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of their own that David is a knight or David is a knave.", "We have exhausted all possibilities for Jacob and Daniel, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Jacob is a knight or David is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that David is a knight or David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Mia is a knight if and only if Daniel is a knave.", "Mia cannot be a knight, because this would contradict the claim of Lucas that Mia is a knight if and only if Daniel is a knave.", "Mia cannot be a knave, because this would contradict the false claim of their own that If Chloe is a knave then Jacob is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of David that Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of David that Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Daniel is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Chloe is a knave then Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('->', ('lying', 0), ('telling-truth', 5)), ('or', ('telling-truth', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('lying', 2)), ('telling-truth', 3), ('or', ('telling-truth', 4), ('lying', 4)))", "index": 363}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Joseph, Harper, Daniel, Grace, and Matthew. According to Isabella, \"Grace is a knight if and only if Matthew is a knight\". Joseph commented, \"If Grace is a knight then Daniel is a knave\". Harper asserted: \"If Isabella is a knight then Matthew is a knight\". In Daniel's words: \"Isabella is a knight if and only if Joseph is a knave\". Grace expressed that Daniel is a knight or Harper is a knave. Matthew said, \"Daniel is a knight and Matthew is a knight.\" So who is a knight and who is a knave?", "names": ["Isabella", "Joseph", "Harper", "Daniel", "Grace", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Isabella is a knight, Joseph is a knave, Harper is a knight, Daniel is a knight, Grace is a knight, and Matthew is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Joseph is a knave\n(3) Harper is a knight\n(4) Daniel is a knight\n(5) Grace is a knight\n(6) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Grace is a knight if and only if Matthew is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Daniel is a knight or Harper is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that If Grace is a knight then Daniel is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Grace is a knight then Daniel is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Isabella is a knight then Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Daniel is a knight and Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 5)), ('->', ('telling-truth', 4), ('lying', 3)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('<=>', ('telling-truth', 0), ('lying', 1)), ('or', ('telling-truth', 3), ('lying', 2)), ('and', ('telling-truth', 3), ('telling-truth', 5)))", "index": 364}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Lucas, Amelia, Matthew, Abigail, and Emily. Aria was heard saying, \"If Lucas is a knave then Amelia is a knight\". Lucas stated, \"Matthew is a knight and Lucas is a knight\". \"Lucas is a knight or Lucas is a knave,\" Amelia mentioned. Matthew asserted: \"Amelia is not a knight\". Abigail noted, \"Aria is a knight or Abigail is a knight\". Emily remarked, \"Amelia is not a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Lucas", "Amelia", "Matthew", "Abigail", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false], "solution_text": "Aria is a knight, Lucas is a knave, Amelia is a knight, Matthew is a knave, Abigail is a knight, and Emily is a knave.", "solution_text_format": "(1) Aria is a knight\n(2) Lucas is a knave\n(3) Amelia is a knight\n(4) Matthew is a knave\n(5) Abigail is a knight\n(6) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that If Lucas is a knave then Amelia is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Matthew is a knight and Lucas is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of Matthew that Amelia is not a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight or Lucas is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Lucas that Matthew is a knight and Lucas is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Matthew is a knight and Lucas is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of Matthew that Amelia is not a knight.", "Amelia cannot be a knave, because this would contradict the claim of Aria that If Lucas is a knave then Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Amelia is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Lucas is a knight or Lucas is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Aria is a knight or Abigail is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Amelia is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Amelia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 2)), ('and', ('telling-truth', 3), ('telling-truth', 1)), ('or', ('telling-truth', 1), ('lying', 1)), ('not', ('telling-truth', 2)), ('or', ('telling-truth', 0), ('telling-truth', 4)), ('not', ('telling-truth', 2)))", "index": 365}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Evelyn, Avery, Amelia, Lucas, and Zoey. Olivia commented, \"Lucas is a knave\". Evelyn expressed that Zoey is a knight. Avery said that Evelyn is a knight and Avery is a knight. As Amelia put it, \"Avery is a knave and Zoey is a knight\". In a statement by Lucas: \"If Zoey is a knave then Amelia is a knave\". Zoey remarked, \"Evelyn is a knight if and only if Avery is a knight\". So who is a knight and who is a knave?", "names": ["Olivia", "Evelyn", "Avery", "Amelia", "Lucas", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Olivia is a knave, Evelyn is a knight, Avery is a knight, Amelia is a knave, Lucas is a knight, and Zoey is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) Evelyn is a knight\n(3) Avery is a knight\n(4) Amelia is a knave\n(5) Lucas is a knight\n(6) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Olivia that Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Zoey is a knave then Amelia is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Lucas that If Zoey is a knave then Amelia is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Avery is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Zoey is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Zoey is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight and Avery is a knight.", "Avery cannot be a knave, because this would contradict the false claim of Zoey that Evelyn is a knight if and only if Avery is a knight.", "We have exhausted all possibilities for Avery, Evelyn, Zoey, and Lucas, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Zoey is a knave then Amelia is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Avery is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Zoey is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Evelyn is a knight and Avery is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Zoey is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Avery is a knave and Zoey is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('telling-truth', 5), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('lying', 2), ('telling-truth', 5)), ('->', ('lying', 5), ('lying', 3)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)))", "index": 366}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Charlotte, Victoria, Mia, Aiden, and Daniel. In Emma's words: \"If Charlotte is a knave then Mia is a knight\". \"Aiden is a knave,\" Charlotte declared. Victoria told you that Mia is a knave if and only if Charlotte is a knight. In Mia's words: \"Charlotte is a knave\". \"Victoria is not a knave,\" Aiden declared. Daniel asserted: \"Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Emma", "Charlotte", "Victoria", "Mia", "Aiden", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Emma is a knight, Charlotte is a knave, Victoria is a knight, Mia is a knight, Aiden is a knight, and Daniel is a knave.", "solution_text_format": "(1) Emma is a knight\n(2) Charlotte is a knave\n(3) Victoria is a knight\n(4) Mia is a knight\n(5) Aiden is a knight\n(6) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that If Charlotte is a knave then Mia is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Charlotte that Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Victoria is not a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Aiden that Victoria is not a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Charlotte is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave.", "Mia cannot be a knave, because this would contradict the false claim of Victoria that Mia is a knave if and only if Charlotte is a knight.", "We have exhausted all possibilities for Mia, Victoria, and Aiden, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Mia is a knave if and only if Charlotte is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Aiden is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 3)), ('lying', 4), ('<=>', ('lying', 3), ('telling-truth', 1)), ('lying', 1), ('not', ('lying', 2)), ('lying', 4))", "index": 367}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Mason, Aurora, Matthew, Evelyn, and Oliver. Aiden commented, \"Matthew is not a knave\". \"Aurora is a knight,\" Mason claimed. As Aurora put it, \"Evelyn is not a knave\". \"Evelyn is a knight and Mason is a knave,\" Matthew claimed. \"Aiden is a knight,\" Evelyn mentioned. According to Oliver, \"Mason is a knight or Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Mason", "Aurora", "Matthew", "Evelyn", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true], "solution_text": "Aiden is a knave, Mason is a knave, Aurora is a knave, Matthew is a knave, Evelyn is a knave, and Oliver is a knight.", "solution_text_format": "(1) Aiden is a knave\n(2) Mason is a knave\n(3) Aurora is a knave\n(4) Matthew is a knave\n(5) Evelyn is a knave\n(6) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Evelyn is a knight and Mason is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Aiden is a knight.", "Mason cannot be a knight, because this would contradict the claim of Matthew that Evelyn is a knight and Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Mason that Aurora is a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Evelyn is not a knave.", "We have exhausted all possibilities for Aurora and Mason, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Matthew that Evelyn is a knight and Mason is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Aiden that Matthew is not a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Matthew is not a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Aiden that Matthew is not a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Evelyn is a knight and Mason is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Aiden is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Aiden is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Evelyn is not a knave.", "Aurora cannot be a knave, because this would contradict the claim of Mason that Aurora is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Mason that Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Evelyn is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Mason is a knight or Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('telling-truth', 2), ('not', ('lying', 4)), ('and', ('telling-truth', 4), ('lying', 1)), ('telling-truth', 0), ('or', ('telling-truth', 1), ('lying', 0)))", "index": 368}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Victoria, Aria, Ava, Matthew, and Zoey. Joseph stated, \"Ava is not a knave\". Victoria said that If Ava is a knave then Matthew is a knave. In Aria's words: \"Joseph is a knave if and only if Ava is a knight\". Ava said, \"Aria is not a knight.\" \"Victoria is a knight and Joseph is a knave,\" Matthew declared. As Zoey put it, \"Matthew is a knave\". So who is a knight and who is a knave?", "names": ["Joseph", "Victoria", "Aria", "Ava", "Matthew", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Joseph is a knight, Victoria is a knight, Aria is a knave, Ava is a knight, Matthew is a knave, and Zoey is a knight.", "solution_text_format": "(1) Joseph is a knight\n(2) Victoria is a knight\n(3) Aria is a knave\n(4) Ava is a knight\n(5) Matthew is a knave\n(6) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Ava is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Aria is not a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Joseph is a knave if and only if Ava is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Ava is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Ava is a knave then Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Joseph is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Victoria is a knight and Joseph is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Matthew is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('->', ('lying', 3), ('lying', 4)), ('<=>', ('lying', 0), ('telling-truth', 3)), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 1), ('lying', 0)), ('lying', 4))", "index": 369}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Joseph, Emily, Zoey, Logan, and Chloe. As Avery put it, \"If Logan is a knight then Chloe is a knight\". As Joseph put it, \"Logan is not a knave\". Emily was heard saying, \"If Zoey is a knave then Emily is a knight\". Zoey asserted: \"Logan is a knave or Chloe is a knight\". Logan expressed that Joseph is a knave and Emily is a knave. In a statement by Chloe: \"Emily is a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Joseph", "Emily", "Zoey", "Logan", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false], "solution_text": "Avery is a knight, Joseph is a knave, Emily is a knight, Zoey is a knight, Logan is a knave, and Chloe is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Joseph is a knave\n(3) Emily is a knight\n(4) Zoey is a knight\n(5) Logan is a knave\n(6) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that If Logan is a knight then Chloe is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Joseph is a knave and Emily is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Logan that Joseph is a knave and Emily is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Logan is not a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Joseph is a knave and Emily is a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Logan is not a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Logan is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Zoey is a knave then Emily is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Logan is a knave or Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Emily is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('lying', 4)), ('->', ('lying', 3), ('telling-truth', 2)), ('or', ('lying', 4), ('telling-truth', 5)), ('and', ('lying', 1), ('lying', 2)), ('lying', 2))", "index": 370}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Samuel, Sofia, Noah, Victoria, and David. Henry commented, \"Victoria is not a knight\". Samuel said, \"Noah is a knight.\" Sofia said that If Noah is a knave then Victoria is a knave. Noah said that Victoria is a knave and Sofia is a knave. Victoria said that If Henry is a knight then Noah is a knave. In David's words: \"Sofia is a knight\". So who is a knight and who is a knave?", "names": ["Henry", "Samuel", "Sofia", "Noah", "Victoria", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false], "solution_text": "Henry is a knave, Samuel is a knave, Sofia is a knave, Noah is a knave, Victoria is a knight, and David is a knave.", "solution_text_format": "(1) Henry is a knave\n(2) Samuel is a knave\n(3) Sofia is a knave\n(4) Noah is a knave\n(5) Victoria is a knight\n(6) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of Henry that Victoria is not a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Henry is a knight then Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Victoria is a knave and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Noah that Victoria is a knave and Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Noah is a knave then Victoria is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of Victoria that If Henry is a knight then Noah is a knave.", "We have exhausted all possibilities for Noah and Victoria, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Henry is a knight then Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Victoria is a knave and Sofia is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Victoria is a knave and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that If Noah is a knave then Victoria is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Noah is a knave then Victoria is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Noah is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Noah is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Sofia is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Sofia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('telling-truth', 3), ('->', ('lying', 3), ('lying', 4)), ('and', ('lying', 4), ('lying', 2)), ('->', ('telling-truth', 0), ('lying', 3)), ('telling-truth', 2))", "index": 371}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Avery, Samuel, Benjamin, Logan, and Sophia. \"If Benjamin is a knight then Samuel is a knight,\" Sebastian claimed. \"Benjamin is a knight if and only if Sophia is a knight\" - Avery. Samuel stated, \"Benjamin is not a knave\". In a statement by Benjamin: \"Sebastian is a knave and Samuel is a knight\". In a statement by Logan: \"Sebastian is a knave\". Sophia was heard saying, \"Benjamin is not a knave\". So who is a knight and who is a knave?", "names": ["Sebastian", "Avery", "Samuel", "Benjamin", "Logan", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Sebastian is a knight, Avery is a knight, Samuel is a knave, Benjamin is a knave, Logan is a knave, and Sophia is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Avery is a knight\n(3) Samuel is a knave\n(4) Benjamin is a knave\n(5) Logan is a knave\n(6) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that If Benjamin is a knight then Samuel is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Samuel is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Sebastian is a knave and Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Avery that Benjamin is a knight if and only if Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('telling-truth', 3), ('telling-truth', 5)), ('not', ('lying', 3)), ('and', ('lying', 0), ('telling-truth', 2)), ('lying', 0), ('not', ('lying', 3)))", "index": 372}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Elizabeth, Olivia, Emma, Benjamin, and Evelyn. As Logan put it, \"Emma is a knight and Evelyn is a knight\". \"Emma is a knight if and only if Olivia is a knave,\" Elizabeth claimed. Olivia said, \"Emma is a knight if and only if Benjamin is a knight.\" In a statement by Emma: \"Logan is a knave and Logan is a knight\". Benjamin commented, \"Olivia is a knave and Olivia is a knight\". As Evelyn put it, \"Benjamin is a knight if and only if Elizabeth is a knight\". So who is a knight and who is a knave?", "names": ["Logan", "Elizabeth", "Olivia", "Emma", "Benjamin", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Logan is a knave, Elizabeth is a knight, Olivia is a knight, Emma is a knave, Benjamin is a knave, and Evelyn is a knave.", "solution_text_format": "(1) Logan is a knave\n(2) Elizabeth is a knight\n(3) Olivia is a knight\n(4) Emma is a knave\n(5) Benjamin is a knave\n(6) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Emma is a knight and Evelyn is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Logan is a knight.", "Emma cannot be a knave, because this would contradict the claim of Logan that Emma is a knight and Evelyn is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Emma is a knight and Evelyn is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Logan is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Logan is a knave and Logan is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Elizabeth is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Olivia is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Olivia is a knave and Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Emma is a knight if and only if Benjamin is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Evelyn that Benjamin is a knight if and only if Elizabeth is a knight.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Emma is a knight if and only if Olivia is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Emma is a knight if and only if Benjamin is a knight.", "We have exhausted all possibilities for Olivia and Benjamin, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Elizabeth is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Olivia is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Olivia is a knave and Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Emma is a knight if and only if Benjamin is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Emma is a knight if and only if Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('<=>', ('telling-truth', 3), ('telling-truth', 4)), ('and', ('lying', 0), ('telling-truth', 0)), ('and', ('lying', 2), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)))", "index": 373}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Benjamin, Lucas, Zoey, Evelyn, and Sophia. \"Benjamin is not a knight,\" James declared. \"Lucas is not a knave,\" Benjamin claimed. Lucas told you that Benjamin is a knight if and only if Zoey is a knight. Zoey remarked, \"Lucas is a knave\". Evelyn stated, \"Lucas is a knight\". Sophia commented, \"Zoey is a knight if and only if James is a knight\". So who is a knight and who is a knave?", "names": ["James", "Benjamin", "Lucas", "Zoey", "Evelyn", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true], "solution_text": "James is a knight, Benjamin is a knave, Lucas is a knave, Zoey is a knight, Evelyn is a knave, and Sophia is a knight.", "solution_text_format": "(1) James is a knight\n(2) Benjamin is a knave\n(3) Lucas is a knave\n(4) Zoey is a knight\n(5) Evelyn is a knave\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of James that Benjamin is not a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Benjamin that Lucas is not a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Lucas is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Lucas is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Zoey is a knight if and only if James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('lying', 2), ('telling-truth', 2), ('<=>', ('telling-truth', 3), ('telling-truth', 0)))", "index": 374}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Matthew, Oliver, Michael, Lucas, and Abigail. \"Lucas is not a knave\" - Sebastian. Matthew remarked, \"Sebastian is not a knave\". \"Sebastian is a knight and Abigail is a knave,\" Oliver mentioned. Michael noted, \"Matthew is a knight and Oliver is a knave\". Lucas was heard saying, \"Matthew is not a knave\". Abigail was heard saying, \"Oliver is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "Matthew", "Oliver", "Michael", "Lucas", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false], "solution_text": "Sebastian is a knave, Matthew is a knave, Oliver is a knave, Michael is a knave, Lucas is a knave, and Abigail is a knave.", "solution_text_format": "(1) Sebastian is a knave\n(2) Matthew is a knave\n(3) Oliver is a knave\n(4) Michael is a knave\n(5) Lucas is a knave\n(6) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Sebastian is a knight and Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Oliver that Sebastian is a knight and Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Oliver is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Sebastian is a knight and Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Oliver is a knight.", "Abigail cannot be a knave, because this would contradict the false claim of Oliver that Sebastian is a knight and Abigail is a knave.", "We have exhausted all possibilities for Abigail and Oliver, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Sebastian is not a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Sebastian that Lucas is not a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Sebastian that Lucas is not a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Matthew is not a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Abigail is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Sebastian is a knight and Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Oliver is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Oliver is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Matthew is a knight and Oliver is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Matthew is a knight and Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('not', ('lying', 0)), ('and', ('telling-truth', 0), ('lying', 5)), ('and', ('telling-truth', 1), ('lying', 2)), ('not', ('lying', 1)), ('telling-truth', 2))", "index": 375}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Liam, David, Ava, Jackson, and William. \"James is a knight if and only if David is a knight,\" James mentioned. Liam was heard saying, \"If David is a knave then Jackson is a knave\". In a statement by David: \"Ava is not a knave\". Ava was heard saying, \"Ava is a knight and James is a knave\". \"James is a knight or Liam is a knave,\" Jackson mentioned. \"If David is a knight then James is a knight,\" William declared. So who is a knight and who is a knave?", "names": ["James", "Liam", "David", "Ava", "Jackson", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "James is a knave, Liam is a knight, David is a knight, Ava is a knight, Jackson is a knave, and William is a knave.", "solution_text_format": "(1) James is a knave\n(2) Liam is a knight\n(3) David is a knight\n(4) Ava is a knight\n(5) Jackson is a knave\n(6) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that James is a knight if and only if David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Ava is not a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Ava is a knight and James is a knave.", "Ava cannot be a knave, because this would contradict the claim of David that Ava is not a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of James that James is a knight if and only if David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that James is a knight if and only if David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Ava is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Ava is a knight and James is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If David is a knave then Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that James is a knight or Liam is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that James is a knight or Liam is a knave.", "William cannot be a knight, because this would contradict the claim of their own that If David is a knight then James is a knight.", "Assume William is a knave. No contradiction is found in their false claim that If David is a knight then James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('telling-truth', 2)), ('->', ('lying', 2), ('lying', 4)), ('not', ('lying', 3)), ('and', ('telling-truth', 3), ('lying', 0)), ('or', ('telling-truth', 0), ('lying', 1)), ('->', ('telling-truth', 2), ('telling-truth', 0)))", "index": 376}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Zoey, Riley, Samuel, Scarlett, and David. Olivia commented, \"Zoey is not a knight\". In Zoey's words: \"Samuel is a knave\". \"Riley is a knight,\" Riley claimed. Samuel commented, \"Riley is a knight and Zoey is a knight\". Scarlett remarked, \"Olivia is a knave\". David told you that If Samuel is a knave then Scarlett is a knave. So who is a knight and who is a knave?", "names": ["Olivia", "Zoey", "Riley", "Samuel", "Scarlett", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "Olivia is a knave, Zoey is a knight, Riley is a knave, Samuel is a knave, Scarlett is a knight, and David is a knave.", "solution_text_format": "(1) Olivia is a knave\n(2) Zoey is a knight\n(3) Riley is a knave\n(4) Samuel is a knave\n(5) Scarlett is a knight\n(6) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Olivia that Zoey is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Riley is a knight and Zoey is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of Zoey that Samuel is a knave.", "We have exhausted all possibilities for Samuel and Zoey, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Zoey that Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Riley is a knight and Zoey is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Samuel that Riley is a knight and Zoey is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Riley is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Olivia is a knave.", "David cannot be a knight, because this would contradict the claim of their own that If Samuel is a knave then Scarlett is a knave.", "Assume David is a knave. No contradiction is found in their false claim that If Samuel is a knave then Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('lying', 3), ('telling-truth', 2), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('lying', 0), ('->', ('lying', 3), ('lying', 4)))", "index": 377}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Sophia, Jackson, Victoria, James, and Emma. Aria said that James is a knight if and only if Aria is a knight. Sophia noted, \"Aria is not a knight\". As Jackson put it, \"James is a knave or Victoria is a knight\". Victoria was heard saying, \"Aria is a knight\". James remarked, \"Jackson is not a knave\". Emma said that If James is a knave then Victoria is a knight. So who is a knight and who is a knave?", "names": ["Aria", "Sophia", "Jackson", "Victoria", "James", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Aria is a knight, Sophia is a knave, Jackson is a knight, Victoria is a knight, James is a knight, and Emma is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) Sophia is a knave\n(3) Jackson is a knight\n(4) Victoria is a knight\n(5) James is a knight\n(6) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that James is a knight if and only if Aria is a knight.", "Assume James is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that James is a knave or Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Aria is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Aria is not a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If James is a knave then Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('or', ('lying', 4), ('telling-truth', 3)), ('telling-truth', 0), ('not', ('lying', 2)), ('->', ('lying', 4), ('telling-truth', 3)))", "index": 378}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Lily, Isabella, Logan, Charlotte, and Owen. David asserted: \"Lily is a knave and Isabella is a knave\". In Lily's words: \"Charlotte is not a knight\". Isabella noted, \"Lily is a knight or Logan is a knave\". According to Logan, \"Logan is a knight and David is a knight\". Charlotte said, \"Owen is a knave if and only if Lily is a knight.\" Owen told you that Isabella is a knave if and only if Charlotte is a knave. So who is a knight and who is a knave?", "names": ["David", "Lily", "Isabella", "Logan", "Charlotte", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true], "solution_text": "David is a knave, Lily is a knave, Isabella is a knight, Logan is a knave, Charlotte is a knight, and Owen is a knight.", "solution_text_format": "(1) David is a knave\n(2) Lily is a knave\n(3) Isabella is a knight\n(4) Logan is a knave\n(5) Charlotte is a knight\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Lily is a knave and Isabella is a knave.", "Lily cannot be a knight, because this would contradict the claim of David that Lily is a knave and Isabella is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Owen is a knave if and only if Lily is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Charlotte is a knave.", "Isabella cannot be a knight, because this would contradict the claim of David that Lily is a knave and Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the claim of Owen that Isabella is a knave if and only if Charlotte is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Charlotte that Owen is a knave if and only if Lily is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the false claim of Lily that Charlotte is not a knight.", "We have exhausted all possibilities for Charlotte and Lily, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Lily is a knave and Isabella is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Lily that Charlotte is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Lily is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Charlotte is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Owen that Isabella is a knave if and only if Charlotte is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Lily is a knight or Logan is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Charlotte that Owen is a knave if and only if Lily is a knight.", "We have exhausted all possibilities for Owen and Charlotte, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Owen is a knave if and only if Lily is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Charlotte is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Lily is a knight or Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Isabella that Lily is a knight or Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Logan is a knight and David is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('lying', 2)), ('not', ('telling-truth', 4)), ('or', ('telling-truth', 1), ('lying', 3)), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('<=>', ('lying', 5), ('telling-truth', 1)), ('<=>', ('lying', 2), ('lying', 4)))", "index": 379}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Sofia, Harper, Charlotte, James, and Olivia. Chloe expressed that James is a knight if and only if Harper is a knave. \"Olivia is a knave and Chloe is a knight,\" Sofia declared. As Harper put it, \"If Chloe is a knave then Sofia is a knight\". In a statement by Charlotte: \"If Sofia is a knave then Olivia is a knave\". \"Harper is a knight if and only if Olivia is a knight,\" James mentioned. As Olivia put it, \"Harper is a knight if and only if Charlotte is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Sofia", "Harper", "Charlotte", "James", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Chloe is a knight, Sofia is a knight, Harper is a knight, Charlotte is a knight, James is a knave, and Olivia is a knave.", "solution_text_format": "(1) Chloe is a knight\n(2) Sofia is a knight\n(3) Harper is a knight\n(4) Charlotte is a knight\n(5) James is a knave\n(6) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that James is a knight if and only if Harper is a knave.", "Assume James is a knight. No contradiction is found in their claim that Harper is a knight if and only if Olivia is a knight.", "Harper cannot be a knight, because this would contradict the claim of Chloe that James is a knight if and only if Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that If Chloe is a knave then Sofia is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Olivia is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Chloe is a knave then Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Olivia is a knave and Chloe is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Sofia that Olivia is a knave and Chloe is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Sofia is a knave then Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('lying', 2)), ('and', ('lying', 5), ('telling-truth', 0)), ('->', ('lying', 0), ('telling-truth', 1)), ('->', ('lying', 1), ('lying', 5)), ('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('<=>', ('telling-truth', 2), ('lying', 3)))", "index": 380}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Isabella, Avery, Lily, Mason, and Scarlett. Aurora said that Aurora is a knight and Scarlett is a knight. Isabella said that Avery is a knight. Avery told you that Lily is a knave if and only if Aurora is a knight. Lily noted, \"Aurora is a knave and Mason is a knight\". Mason stated, \"Scarlett is not a knave\". \"Lily is not a knight,\" Scarlett mentioned. So who is a knight and who is a knave?", "names": ["Aurora", "Isabella", "Avery", "Lily", "Mason", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Aurora is a knight, Isabella is a knight, Avery is a knight, Lily is a knave, Mason is a knight, and Scarlett is a knight.", "solution_text_format": "(1) Aurora is a knight\n(2) Isabella is a knight\n(3) Avery is a knight\n(4) Lily is a knave\n(5) Mason is a knight\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Aurora is a knight and Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Mason is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Aurora is a knave and Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Lily is a knave if and only if Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('telling-truth', 5)), ('telling-truth', 2), ('<=>', ('lying', 3), ('telling-truth', 0)), ('and', ('lying', 0), ('telling-truth', 4)), ('not', ('lying', 5)), ('not', ('telling-truth', 3)))", "index": 381}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Daniel, Sofia, Charlotte, Alexander, and Abigail. Jack said that If Charlotte is a knight then Abigail is a knight. Daniel asserted: \"If Sofia is a knave then Charlotte is a knight\". Sofia remarked, \"Daniel is a knight if and only if Alexander is a knave\". Charlotte stated, \"Abigail is not a knave\". Alexander stated, \"Abigail is not a knight\". Abigail told you that Alexander is not a knight. So who is a knight and who is a knave?", "names": ["Jack", "Daniel", "Sofia", "Charlotte", "Alexander", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Jack is a knight, Daniel is a knight, Sofia is a knight, Charlotte is a knight, Alexander is a knave, and Abigail is a knight.", "solution_text_format": "(1) Jack is a knight\n(2) Daniel is a knight\n(3) Sofia is a knight\n(4) Charlotte is a knight\n(5) Alexander is a knave\n(6) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that If Charlotte is a knight then Abigail is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Sofia is a knave then Charlotte is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('telling-truth', 5)), ('->', ('lying', 2), ('telling-truth', 3)), ('<=>', ('telling-truth', 1), ('lying', 4)), ('not', ('lying', 5)), ('not', ('telling-truth', 5)), ('not', ('telling-truth', 4)))", "index": 382}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Joseph, Chloe, Riley, Ava, and Daniel. Sophia commented, \"Riley is a knave and Joseph is a knave\". According to Joseph, \"Daniel is not a knave\". Chloe commented, \"If Sophia is a knight then Daniel is a knave\". Riley noted, \"Ava is a knave if and only if Daniel is a knight\". \"Sophia is a knave or Joseph is a knave\" - Ava. Daniel asserted: \"Riley is a knave and Chloe is a knave\". So who is a knight and who is a knave?", "names": ["Sophia", "Joseph", "Chloe", "Riley", "Ava", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Sophia is a knave, Joseph is a knave, Chloe is a knight, Riley is a knight, Ava is a knight, and Daniel is a knave.", "solution_text_format": "(1) Sophia is a knave\n(2) Joseph is a knave\n(3) Chloe is a knight\n(4) Riley is a knight\n(5) Ava is a knight\n(6) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Riley is a knave and Joseph is a knave.", "Riley cannot be a knight, because this would contradict the claim of Sophia that Riley is a knave and Joseph is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Daniel is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Sophia is a knave or Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Sophia that Riley is a knave and Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Daniel is not a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Joseph that Daniel is not a knave.", "Daniel cannot be a knave, because this would contradict the false claim of Riley that Ava is a knave if and only if Daniel is a knight.", "We have exhausted all possibilities for Daniel and Joseph, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Sophia is a knave or Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Sophia that Riley is a knave and Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of Ava that Sophia is a knave or Joseph is a knave.", "We have exhausted all possibilities for Joseph, Ava, and Riley, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Riley is a knave and Joseph is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Ava is a knave if and only if Daniel is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Sophia is a knave or Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Daniel cannot be a knight, because this would contradict the claim of Riley that Ava is a knave if and only if Daniel is a knight.", "Daniel cannot be a knave, because this would contradict the claim of Joseph that Daniel is not a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Daniel is not a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Joseph that Daniel is not a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Riley is a knave and Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Sophia is a knight then Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 1)), ('not', ('lying', 5)), ('->', ('telling-truth', 0), ('lying', 5)), ('<=>', ('lying', 4), ('telling-truth', 5)), ('or', ('lying', 0), ('lying', 1)), ('and', ('lying', 3), ('lying', 2)))", "index": 383}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Aria, Samuel, Logan, Oliver, and Luke. \"Aria is a knight and Logan is a knight,\" Aiden declared. According to Aria, \"Aiden is a knight if and only if Aria is a knight\". Samuel said, \"Logan is a knight if and only if Aiden is a knight.\" Logan said that Luke is not a knave. Oliver stated, \"Logan is a knight if and only if Aria is a knight\". Luke remarked, \"Aiden is not a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Aria", "Samuel", "Logan", "Oliver", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Aiden is a knight, Aria is a knight, Samuel is a knight, Logan is a knight, Oliver is a knight, and Luke is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Aria is a knight\n(3) Samuel is a knight\n(4) Logan is a knight\n(5) Oliver is a knight\n(6) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Aria is a knight and Logan is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Aria is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Luke is not a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Logan is a knight if and only if Aiden is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Logan is a knight if and only if Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('not', ('lying', 5)), ('<=>', ('telling-truth', 3), ('telling-truth', 1)), ('not', ('lying', 0)))", "index": 384}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Mia, Scarlett, William, Joseph, and Isabella. \"If Isabella is a knave then Mia is a knight\" - Emma. Mia noted, \"If Scarlett is a knight then William is a knave\". As Scarlett put it, \"Joseph is a knave or Emma is a knave\". William commented, \"Emma is a knave and Isabella is a knight\". \"Mia is a knight and Emma is a knave,\" Joseph claimed. In a statement by Isabella: \"If Scarlett is a knight then Mia is a knight\". So who is a knight and who is a knave?", "names": ["Emma", "Mia", "Scarlett", "William", "Joseph", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Emma is a knight, Mia is a knight, Scarlett is a knight, William is a knave, Joseph is a knave, and Isabella is a knight.", "solution_text_format": "(1) Emma is a knight\n(2) Mia is a knight\n(3) Scarlett is a knight\n(4) William is a knave\n(5) Joseph is a knave\n(6) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that If Isabella is a knave then Mia is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Scarlett is a knight then Mia is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Joseph is a knave or Emma is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Scarlett that Joseph is a knave or Emma is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Mia is a knight and Emma is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Scarlett is a knight then William is a knave.", "William cannot be a knight, because this would contradict the claim of Mia that If Scarlett is a knight then William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Emma is a knave and Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 1)), ('->', ('telling-truth', 2), ('lying', 3)), ('or', ('lying', 4), ('lying', 0)), ('and', ('lying', 0), ('telling-truth', 5)), ('and', ('telling-truth', 1), ('lying', 0)), ('->', ('telling-truth', 2), ('telling-truth', 1)))", "index": 385}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Sofia, Jacob, Henry, Evelyn, and Mason. \"Sofia is a knave,\" Aiden mentioned. Sofia expressed that If Aiden is a knave then Henry is a knight. Jacob was heard saying, \"Mason is a knight and Jacob is a knight\". \"Evelyn is a knight\" - Henry. Evelyn stated, \"If Mason is a knight then Jacob is a knight\". Mason expressed that Jacob is a knave or Evelyn is a knight. So who is a knight and who is a knave?", "names": ["Aiden", "Sofia", "Jacob", "Henry", "Evelyn", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Aiden is a knave, Sofia is a knight, Jacob is a knight, Henry is a knight, Evelyn is a knight, and Mason is a knight.", "solution_text_format": "(1) Aiden is a knave\n(2) Sofia is a knight\n(3) Jacob is a knight\n(4) Henry is a knight\n(5) Evelyn is a knight\n(6) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Aiden that Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knave then Henry is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Aiden is a knave then Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Mason is a knight then Jacob is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Jacob is a knave or Evelyn is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Mason is a knight and Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('->', ('lying', 0), ('telling-truth', 3)), ('and', ('telling-truth', 5), ('telling-truth', 2)), ('telling-truth', 4), ('->', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('lying', 2), ('telling-truth', 4)))", "index": 386}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Aria, Samuel, Isabella, Mason, and Alexander. Scarlett said, \"Alexander is a knight.\" Aria asserted: \"If Alexander is a knight then Mason is a knave\". According to Samuel, \"Alexander is not a knave\". Isabella asserted: \"If Mason is a knight then Samuel is a knave\". \"Alexander is a knight,\" Mason claimed. Alexander remarked, \"Aria is a knave or Isabella is a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Aria", "Samuel", "Isabella", "Mason", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Scarlett is a knight, Aria is a knave, Samuel is a knight, Isabella is a knave, Mason is a knight, and Alexander is a knight.", "solution_text_format": "(1) Scarlett is a knight\n(2) Aria is a knave\n(3) Samuel is a knight\n(4) Isabella is a knave\n(5) Mason is a knight\n(6) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Aria is a knave or Isabella is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Alexander is a knight then Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Aria that If Alexander is a knight then Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that If Alexander is a knight then Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Mason is a knight then Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Isabella that If Mason is a knight then Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Alexander is not a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Mason is a knight then Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Alexander is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('->', ('telling-truth', 5), ('lying', 4)), ('not', ('lying', 5)), ('->', ('telling-truth', 4), ('lying', 2)), ('telling-truth', 5), ('or', ('lying', 1), ('telling-truth', 3)))", "index": 387}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Jacob, Samuel, Abigail, Matthew, and Emma. \"Abigail is not a knight,\" Oliver mentioned. \"Abigail is a knave or Oliver is a knave\" - Jacob. Samuel was heard saying, \"Oliver is not a knave\". In Abigail's words: \"Samuel is a knave and Matthew is a knave\". In a statement by Matthew: \"Emma is a knight or Jacob is a knave\". Emma told you that Jacob is a knight and Abigail is a knight. So who is a knight and who is a knave?", "names": ["Oliver", "Jacob", "Samuel", "Abigail", "Matthew", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Oliver is a knight, Jacob is a knight, Samuel is a knight, Abigail is a knave, Matthew is a knave, and Emma is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) Jacob is a knight\n(3) Samuel is a knight\n(4) Abigail is a knave\n(5) Matthew is a knave\n(6) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of Oliver that Abigail is not a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Samuel is a knave and Matthew is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Emma is a knight or Jacob is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Abigail is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Jacob is a knight and Abigail is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Matthew that Emma is a knight or Jacob is a knave.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Abigail is a knave or Oliver is a knave.", "We have exhausted all possibilities for Jacob and Emma, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Emma is a knight or Jacob is a knave.", "Emma cannot be a knight, because this would contradict the false claim of Matthew that Emma is a knight or Jacob is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Jacob is a knight and Abigail is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Abigail is a knave or Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('or', ('lying', 3), ('lying', 0)), ('not', ('lying', 0)), ('and', ('lying', 2), ('lying', 4)), ('or', ('telling-truth', 5), ('lying', 1)), ('and', ('telling-truth', 1), ('telling-truth', 3)))", "index": 388}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Emma, Sebastian, Samuel, Noah, and Ella. As David put it, \"Ella is a knave or Emma is a knight\". According to Emma, \"Sebastian is a knave and David is a knave\". Sebastian expressed that If Noah is a knave then Ella is a knave. \"Emma is a knave or Noah is a knave,\" Samuel claimed. According to Noah, \"David is a knave or Samuel is a knave\". \"Emma is a knight\" - Ella. So who is a knight and who is a knave?", "names": ["David", "Emma", "Sebastian", "Samuel", "Noah", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false], "solution_text": "David is a knight, Emma is a knave, Sebastian is a knight, Samuel is a knight, Noah is a knave, and Ella is a knave.", "solution_text_format": "(1) David is a knight\n(2) Emma is a knave\n(3) Sebastian is a knight\n(4) Samuel is a knight\n(5) Noah is a knave\n(6) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Ella is a knave or Emma is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Emma is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and David is a knave.", "Emma cannot be a knave, because this would contradict the claim of David that Ella is a knave or Emma is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Emma is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and David is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Sebastian is a knave and David is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Noah is a knave then Ella is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that David is a knave or Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Noah that David is a knave or Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Emma is a knave or Noah is a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that David is a knave or Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Emma is a knave or Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 1)), ('and', ('lying', 2), ('lying', 0)), ('->', ('lying', 4), ('lying', 5)), ('or', ('lying', 1), ('lying', 4)), ('or', ('lying', 0), ('lying', 3)), ('telling-truth', 1))", "index": 389}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Aurora, Samuel, Harper, Ava, and Charlotte. Logan said, \"Harper is not a knight.\" Aurora stated, \"Harper is not a knight\". Samuel noted, \"If Logan is a knight then Logan is a knave\". In a statement by Harper: \"Ava is a knight\". Ava stated, \"Samuel is a knave and Aurora is a knave\". Charlotte told you that Ava is not a knave. So who is a knight and who is a knave?", "names": ["Logan", "Aurora", "Samuel", "Harper", "Ava", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Logan is a knight, Aurora is a knight, Samuel is a knave, Harper is a knave, Ava is a knave, and Charlotte is a knave.", "solution_text_format": "(1) Logan is a knight\n(2) Aurora is a knight\n(3) Samuel is a knave\n(4) Harper is a knave\n(5) Ava is a knave\n(6) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Harper is not a knight.", "Harper cannot be a knight, because this would contradict the claim of Logan that Harper is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Ava is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Harper that Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Samuel is a knave and Aurora is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that If Logan is a knight then Logan is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that If Logan is a knight then Logan is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Harper is not a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Ava is not a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Ava is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('not', ('telling-truth', 3)), ('->', ('telling-truth', 0), ('lying', 0)), ('telling-truth', 4), ('and', ('lying', 2), ('lying', 1)), ('not', ('lying', 4)))", "index": 390}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Scarlett, Sofia, Harper, Daniel, and Matthew. As Sebastian put it, \"Harper is a knight or Matthew is a knight\". According to Scarlett, \"Daniel is not a knight\". Sofia expressed that Matthew is a knave or Sofia is a knight. Harper asserted: \"Sofia is not a knave\". According to Daniel, \"Sebastian is not a knight\". \"Daniel is a knave and Scarlett is a knave\" - Matthew. So who is a knight and who is a knave?", "names": ["Sebastian", "Scarlett", "Sofia", "Harper", "Daniel", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Sebastian is a knight, Scarlett is a knight, Sofia is a knight, Harper is a knight, Daniel is a knave, and Matthew is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Scarlett is a knight\n(3) Sofia is a knight\n(4) Harper is a knight\n(5) Daniel is a knave\n(6) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Harper is a knight or Matthew is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Matthew is a knave or Sofia is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Daniel is a knave and Scarlett is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Matthew that Daniel is a knave and Scarlett is a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that Daniel is not a knight.", "We have exhausted all possibilities for Scarlett and Daniel, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Daniel is a knave and Scarlett is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Daniel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 5)), ('not', ('telling-truth', 4)), ('or', ('lying', 5), ('telling-truth', 2)), ('not', ('lying', 2)), ('not', ('telling-truth', 0)), ('and', ('lying', 4), ('lying', 1)))", "index": 391}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Grace, Benjamin, Emily, Charlotte, and Henry. Amelia was heard saying, \"Emily is a knave and Henry is a knave\". Grace said, \"If Henry is a knight then Benjamin is a knight.\" Benjamin remarked, \"Benjamin is a knight or Charlotte is a knight\". According to Emily, \"If Grace is a knight then Grace is a knave\". Charlotte expressed that Henry is a knight and Benjamin is a knave. Henry asserted: \"Benjamin is a knave and Grace is a knight\". So who is a knight and who is a knave?", "names": ["Amelia", "Grace", "Benjamin", "Emily", "Charlotte", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Amelia is a knight, Grace is a knight, Benjamin is a knight, Emily is a knave, Charlotte is a knave, and Henry is a knave.", "solution_text_format": "(1) Amelia is a knight\n(2) Grace is a knight\n(3) Benjamin is a knight\n(4) Emily is a knave\n(5) Charlotte is a knave\n(6) Henry is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Emily is a knave and Henry is a knave.", "Emily cannot be a knight, because this would contradict the claim of Amelia that Emily is a knave and Henry is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that If Grace is a knight then Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Henry is a knight then Benjamin is a knight.", "Henry cannot be a knight, because this would contradict the claim of Amelia that Emily is a knave and Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Benjamin is a knave and Grace is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Benjamin is a knight or Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Benjamin is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Henry is a knight and Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 5)), ('->', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('telling-truth', 2), ('telling-truth', 4)), ('->', ('telling-truth', 1), ('lying', 1)), ('and', ('telling-truth', 5), ('lying', 2)), ('and', ('lying', 2), ('telling-truth', 1)))", "index": 392}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Aurora, Owen, Evelyn, Jacob, and Sofia. \"Owen is a knight,\" Samuel claimed. As Aurora put it, \"If Sofia is a knight then Jacob is a knave\". As Owen put it, \"Jacob is a knave and Aurora is a knight\". Evelyn expressed that Aurora is not a knight. In Jacob's words: \"Samuel is a knave and Owen is a knave\". Sofia said that If Jacob is a knight then Evelyn is a knave. So who is a knight and who is a knave?", "names": ["Samuel", "Aurora", "Owen", "Evelyn", "Jacob", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Samuel is a knight, Aurora is a knight, Owen is a knight, Evelyn is a knave, Jacob is a knave, and Sofia is a knight.", "solution_text_format": "(1) Samuel is a knight\n(2) Aurora is a knight\n(3) Owen is a knight\n(4) Evelyn is a knave\n(5) Jacob is a knave\n(6) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Jacob is a knave and Aurora is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Owen that Jacob is a knave and Aurora is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Samuel is a knave and Owen is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Sofia is a knight then Jacob is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Jacob is a knight then Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Aurora is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Aurora is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('->', ('telling-truth', 5), ('lying', 4)), ('and', ('lying', 4), ('telling-truth', 1)), ('not', ('telling-truth', 1)), ('and', ('lying', 0), ('lying', 2)), ('->', ('telling-truth', 4), ('lying', 3)))", "index": 393}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Grace, Chloe, Aria, Victoria, and Emma. \"Chloe is a knight or Victoria is a knave,\" Oliver claimed. As Grace put it, \"If Victoria is a knave then Emma is a knight\". Chloe said, \"If Emma is a knight then Emma is a knave.\" Aria commented, \"Aria is a knight if and only if Oliver is a knight\". Victoria stated, \"Grace is a knight or Chloe is a knight\". According to Emma, \"Chloe is a knight and Aria is a knave\". So who is a knight and who is a knave?", "names": ["Oliver", "Grace", "Chloe", "Aria", "Victoria", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Oliver is a knight, Grace is a knight, Chloe is a knight, Aria is a knight, Victoria is a knight, and Emma is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) Grace is a knight\n(3) Chloe is a knight\n(4) Aria is a knight\n(5) Victoria is a knight\n(6) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Chloe is a knight or Victoria is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Emma is a knight then Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Chloe that If Emma is a knight then Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Chloe is a knight and Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Aria is a knight if and only if Oliver is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Grace is a knight or Chloe is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Victoria is a knave then Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 4)), ('->', ('lying', 4), ('telling-truth', 5)), ('->', ('telling-truth', 5), ('lying', 5)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('telling-truth', 2), ('lying', 3)))", "index": 394}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Aiden, Ava, Olivia, Lucas, and Oliver. James was heard saying, \"Ava is a knight or Aiden is a knave\". \"If Ava is a knight then Oliver is a knave,\" Aiden declared. Ava noted, \"James is a knave or Oliver is a knight\". Olivia expressed that Ava is a knight. In Lucas's words: \"Oliver is a knave and Ava is a knight\". In a statement by Oliver: \"If James is a knave then Lucas is a knight\". So who is a knight and who is a knave?", "names": ["James", "Aiden", "Ava", "Olivia", "Lucas", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "James is a knight, Aiden is a knave, Ava is a knight, Olivia is a knight, Lucas is a knave, and Oliver is a knight.", "solution_text_format": "(1) James is a knight\n(2) Aiden is a knave\n(3) Ava is a knight\n(4) Olivia is a knight\n(5) Lucas is a knave\n(6) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Ava is a knight or Aiden is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that James is a knave or Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If James is a knave then Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Oliver is a knave and Ava is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Oliver is a knave and Ava is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that If Ava is a knight then Oliver is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Ava is a knight then Oliver is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 1)), ('->', ('telling-truth', 2), ('lying', 5)), ('or', ('lying', 0), ('telling-truth', 5)), ('telling-truth', 2), ('and', ('lying', 5), ('telling-truth', 2)), ('->', ('lying', 0), ('telling-truth', 4)))", "index": 395}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Aiden, David, Owen, Olivia, and Matthew. \"Olivia is a knight or David is a knight\" - Ethan. Aiden stated, \"Olivia is a knight\". \"David is a knight if and only if Olivia is a knight,\" David claimed. According to Owen, \"Olivia is a knight or Ethan is a knave\". \"Matthew is a knight if and only if Olivia is a knight,\" Olivia mentioned. Matthew commented, \"David is not a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Aiden", "David", "Owen", "Olivia", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Ethan is a knight, Aiden is a knight, David is a knave, Owen is a knight, Olivia is a knight, and Matthew is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Aiden is a knight\n(3) David is a knave\n(4) Owen is a knight\n(5) Olivia is a knight\n(6) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Olivia is a knight or David is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Olivia is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that David is not a knight.", "David cannot be a knight, because this would contradict the claim of Matthew that David is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that David is a knight if and only if Olivia is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Olivia is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Olivia is a knight or Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 2)), ('telling-truth', 4), ('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('or', ('telling-truth', 4), ('lying', 0)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('not', ('telling-truth', 2)))", "index": 396}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Liam, Jacob, Owen, Lucas, and Charlotte. \"Jacob is a knight or Lucas is a knight,\" Alexander claimed. \"Lucas is a knave,\" Liam claimed. \"Lucas is a knave,\" Jacob claimed. In a statement by Owen: \"Alexander is not a knave\". \"If Charlotte is a knave then Lucas is a knight,\" Lucas mentioned. \"Alexander is not a knave,\" Charlotte declared. So who is a knight and who is a knave?", "names": ["Alexander", "Liam", "Jacob", "Owen", "Lucas", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true], "solution_text": "Alexander is a knight, Liam is a knave, Jacob is a knave, Owen is a knight, Lucas is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Liam is a knave\n(3) Jacob is a knave\n(4) Owen is a knight\n(5) Lucas is a knight\n(6) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Jacob is a knight or Lucas is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Jacob that Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Charlotte is a knave then Lucas is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Lucas that If Charlotte is a knave then Lucas is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Alexander is not a knave.", "We have exhausted all possibilities for Charlotte and Lucas, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Charlotte is a knave then Lucas is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Lucas is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Alexander is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 4)), ('lying', 4), ('lying', 4), ('not', ('lying', 0)), ('->', ('lying', 5), ('telling-truth', 4)), ('not', ('lying', 0)))", "index": 397}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Grace, Owen, Jack, James, and Evelyn. \"Evelyn is a knave and Jack is a knight,\" William claimed. Grace told you that Evelyn is a knave or William is a knight. \"James is a knave and Evelyn is a knave,\" Owen declared. Jack asserted: \"If Owen is a knight then Evelyn is a knight\". James was heard saying, \"Owen is not a knight\". Evelyn told you that Jack is a knight if and only if Owen is a knave. So who is a knight and who is a knave?", "names": ["William", "Grace", "Owen", "Jack", "James", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "William is a knave, Grace is a knave, Owen is a knave, Jack is a knight, James is a knight, and Evelyn is a knight.", "solution_text_format": "(1) William is a knave\n(2) Grace is a knave\n(3) Owen is a knave\n(4) Jack is a knight\n(5) James is a knight\n(6) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Evelyn is a knave and Jack is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of William that Evelyn is a knave and Jack is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jack is a knight if and only if Owen is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Owen is a knight then Evelyn is a knight.", "Owen cannot be a knight, because this would contradict the claim of Jack that If Owen is a knight then Evelyn is a knight.", "Owen cannot be a knave, because this would contradict the false claim of Evelyn that Jack is a knight if and only if Owen is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of William that Evelyn is a knave and Jack is a knight.", "We have exhausted all possibilities for Jack and Evelyn, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Evelyn is a knave and Jack is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jack is a knight if and only if Owen is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Owen is a knight then Evelyn is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that James is a knave and Evelyn is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that James is a knave and Evelyn is a knave.", "Assume James is a knight. No contradiction is found in their claim that Owen is not a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave or William is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Evelyn is a knave or William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 3)), ('or', ('lying', 5), ('telling-truth', 0)), ('and', ('lying', 4), ('lying', 5)), ('->', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 3), ('lying', 2)))", "index": 398}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Noah, Joseph, Isabella, Sophia, Emma, and James. \"Emma is a knight or Isabella is a knight,\" Noah declared. In a statement by Joseph: \"Isabella is a knight\". Isabella stated, \"James is a knave\". \"James is a knight\" - Sophia. \"Isabella is a knight,\" Emma declared. \"Sophia is a knight if and only if Noah is a knave,\" James claimed. So who is a knight and who is a knave?", "names": ["Noah", "Joseph", "Isabella", "Sophia", "Emma", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "Noah is a knave, Joseph is a knave, Isabella is a knave, Sophia is a knight, Emma is a knave, and James is a knight.", "solution_text_format": "(1) Noah is a knave\n(2) Joseph is a knave\n(3) Isabella is a knave\n(4) Sophia is a knight\n(5) Emma is a knave\n(6) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Emma is a knight or Isabella is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Isabella that James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Noah is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that James is a knight.", "Sophia cannot be a knave, because this would contradict the false claim of James that Sophia is a knight if and only if Noah is a knave.", "We have exhausted all possibilities for Sophia and James, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Emma that Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Emma that Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the claim of Noah that Emma is a knight or Isabella is a knight.", "We have exhausted all possibilities for Isabella and Emma, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Emma is a knight or Isabella is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Noah that Emma is a knight or Isabella is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Isabella is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Noah that Emma is a knight or Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Noah is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that James is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Isabella is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 2)), ('telling-truth', 2), ('lying', 5), ('telling-truth', 5), ('telling-truth', 2), ('<=>', ('telling-truth', 3), ('lying', 0)))", "index": 399}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Noah, Liam, Mia, Harper, Sebastian, and Jackson. \"Sebastian is a knight,\" Noah mentioned. Liam expressed that Harper is a knight and Harper is a knave. In a statement by Mia: \"Sebastian is a knight and Harper is a knave\". Harper was heard saying, \"Noah is a knave and Mia is a knight\". \"Noah is a knight and Harper is a knight,\" Sebastian mentioned. Jackson commented, \"Liam is a knight and Sebastian is a knave\". So who is a knight and who is a knave?", "names": ["Noah", "Liam", "Mia", "Harper", "Sebastian", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, false], "solution_text": "Noah is a knave, Liam is a knave, Mia is a knave, Harper is a knave, Sebastian is a knave, and Jackson is a knave.", "solution_text_format": "(1) Noah is a knave\n(2) Liam is a knave\n(3) Mia is a knave\n(4) Harper is a knave\n(5) Sebastian is a knave\n(6) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Noah is a knight and Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Noah is a knave and Mia is a knight.", "Harper cannot be a knave, because this would contradict the claim of Sebastian that Noah is a knight and Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Noah that Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Noah that Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Noah is a knight and Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Noah is a knave and Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Harper is a knave.", "Mia cannot be a knave, because this would contradict the claim of Harper that Noah is a knave and Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Noah is a knave and Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Harper is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Sebastian is a knight and Harper is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Harper is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Harper is a knight and Harper is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Liam is a knight and Sebastian is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Liam is a knight and Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('and', ('telling-truth', 3), ('lying', 3)), ('and', ('telling-truth', 4), ('lying', 3)), ('and', ('lying', 0), ('telling-truth', 2)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('and', ('telling-truth', 1), ('lying', 4)))", "index": 400}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, William, Victoria, Michael, Evelyn, and Charlotte. In Liam's words: \"Charlotte is a knight or Evelyn is a knight\". \"If Charlotte is a knave then Michael is a knight\" - William. Victoria noted, \"Liam is a knight\". Michael expressed that William is a knave if and only if Victoria is a knave. \"William is a knight and Liam is a knight,\" Evelyn claimed. Charlotte remarked, \"Victoria is not a knight\". So who is a knight and who is a knave?", "names": ["Liam", "William", "Victoria", "Michael", "Evelyn", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Liam is a knight, William is a knight, Victoria is a knight, Michael is a knight, Evelyn is a knight, and Charlotte is a knave.", "solution_text_format": "(1) Liam is a knight\n(2) William is a knight\n(3) Victoria is a knight\n(4) Michael is a knight\n(5) Evelyn is a knight\n(6) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Charlotte is a knight or Evelyn is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of Charlotte that Victoria is not a knight.", "Victoria cannot be a knave, because this would contradict the false claim of their own that Liam is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Liam is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that William is a knight and Liam is a knight.", "Assume William is a knight. No contradiction is found in their claim that If Charlotte is a knave then Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that William is a knave if and only if Victoria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 4)), ('->', ('lying', 5), ('telling-truth', 3)), ('telling-truth', 0), ('<=>', ('lying', 1), ('lying', 2)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('telling-truth', 2)))", "index": 401}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Abigail, Ethan, Evelyn, Mason, and Alexander. Michael told you that Evelyn is a knave. In a statement by Abigail: \"Evelyn is a knave or Alexander is a knave\". Ethan stated, \"Michael is a knight or Alexander is a knave\". \"Michael is a knight or Mason is a knave,\" Evelyn declared. Mason commented, \"Abigail is a knave if and only if Ethan is a knight\". \"Michael is a knave or Michael is a knight\" - Alexander. So who is a knight and who is a knave?", "names": ["Michael", "Abigail", "Ethan", "Evelyn", "Mason", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "Michael is a knave, Abigail is a knave, Ethan is a knave, Evelyn is a knight, Mason is a knave, and Alexander is a knight.", "solution_text_format": "(1) Michael is a knave\n(2) Abigail is a knave\n(3) Ethan is a knave\n(4) Evelyn is a knight\n(5) Mason is a knave\n(6) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Michael that Evelyn is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Michael is a knight or Mason is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Michael is a knight or Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Evelyn that Michael is a knight or Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Ethan is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Evelyn is a knave or Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Abigail that Evelyn is a knave or Alexander is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Michael is a knave or Michael is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Evelyn is a knave or Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Michael is a knave or Michael is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Michael is a knight or Alexander is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Michael is a knight or Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('or', ('lying', 3), ('lying', 5)), ('or', ('telling-truth', 0), ('lying', 5)), ('or', ('telling-truth', 0), ('lying', 4)), ('<=>', ('lying', 1), ('telling-truth', 2)), ('or', ('lying', 0), ('telling-truth', 0)))", "index": 402}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Elizabeth, Henry, Evelyn, Ethan, and Sophia. Benjamin expressed that Elizabeth is a knight if and only if Benjamin is a knight. Elizabeth was heard saying, \"Evelyn is a knave or Henry is a knight\". In Henry's words: \"If Sophia is a knave then Benjamin is a knight\". Evelyn said that Ethan is a knave if and only if Benjamin is a knight. \"Elizabeth is not a knave,\" Ethan claimed. \"Henry is a knave or Elizabeth is a knave\" - Sophia. So who is a knight and who is a knave?", "names": ["Benjamin", "Elizabeth", "Henry", "Evelyn", "Ethan", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Benjamin is a knight, Elizabeth is a knight, Henry is a knight, Evelyn is a knave, Ethan is a knight, and Sophia is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Elizabeth is a knight\n(3) Henry is a knight\n(4) Evelyn is a knave\n(5) Ethan is a knight\n(6) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if Benjamin is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Evelyn is a knave or Henry is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Benjamin is a knight.", "Ethan cannot be a knight, because this would contradict the claim of Evelyn that Ethan is a knave if and only if Benjamin is a knight.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Elizabeth is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Benjamin is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Elizabeth is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Sophia is a knave then Benjamin is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Henry is a knave or Elizabeth is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Henry is a knave or Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('lying', 3), ('telling-truth', 2)), ('->', ('lying', 5), ('telling-truth', 0)), ('<=>', ('lying', 4), ('telling-truth', 0)), ('not', ('lying', 1)), ('or', ('lying', 2), ('lying', 1)))", "index": 403}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Zoey, Benjamin, Alexander, Lily, and Olivia. \"If Elizabeth is a knight then Olivia is a knight,\" Elizabeth mentioned. Zoey was heard saying, \"Benjamin is not a knave\". \"Alexander is a knight and Olivia is a knave,\" Benjamin mentioned. Alexander stated, \"Benjamin is a knave\". According to Lily, \"Elizabeth is a knight or Olivia is a knave\". Olivia expressed that Olivia is a knight or Elizabeth is a knave. So who is a knight and who is a knave?", "names": ["Elizabeth", "Zoey", "Benjamin", "Alexander", "Lily", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true], "solution_text": "Elizabeth is a knight, Zoey is a knave, Benjamin is a knave, Alexander is a knight, Lily is a knight, and Olivia is a knight.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Zoey is a knave\n(3) Benjamin is a knave\n(4) Alexander is a knight\n(5) Lily is a knight\n(6) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Olivia is a knight or Elizabeth is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Alexander is a knight and Olivia is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Zoey that Benjamin is not a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Zoey that Benjamin is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Alexander is a knight and Olivia is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Elizabeth is a knight or Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 5)), ('not', ('lying', 2)), ('and', ('telling-truth', 3), ('lying', 5)), ('lying', 2), ('or', ('telling-truth', 0), ('lying', 5)), ('or', ('telling-truth', 5), ('lying', 0)))", "index": 404}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, William, Sophia, Benjamin, Jack, and James. Aurora said, \"Sophia is a knave if and only if Jack is a knave.\" In William's words: \"James is a knight if and only if Benjamin is a knight\". Sophia expressed that Benjamin is a knave. In a statement by Benjamin: \"Benjamin is a knight and Aurora is a knight\". As Jack put it, \"If William is a knight then James is a knight\". In James's words: \"If Jack is a knight then Aurora is a knight\". So who is a knight and who is a knave?", "names": ["Aurora", "William", "Sophia", "Benjamin", "Jack", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Aurora is a knight, William is a knave, Sophia is a knight, Benjamin is a knave, Jack is a knight, and James is a knight.", "solution_text_format": "(1) Aurora is a knight\n(2) William is a knave\n(3) Sophia is a knight\n(4) Benjamin is a knave\n(5) Jack is a knight\n(6) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Jack is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Sophia that Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Benjamin is a knight and Aurora is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If William is a knight then James is a knight.", "Assume William is a knight. No contradiction is found in their claim that James is a knight if and only if Benjamin is a knight.", "James cannot be a knight, because this would contradict the claim of William that James is a knight if and only if Benjamin is a knight.", "James cannot be a knave, because this would contradict the claim of Jack that If William is a knight then James is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that James is a knight if and only if Benjamin is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Jack is a knight then Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 3)), ('lying', 3), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('telling-truth', 5)), ('->', ('telling-truth', 4), ('telling-truth', 0)))", "index": 405}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Aurora, Liam, Aiden, Sophia, and Luke. Michael stated, \"Sophia is a knight\". \"Liam is a knave or Aiden is a knave,\" Aurora claimed. Liam said that Luke is a knave and Sophia is a knight. In Aiden's words: \"Aurora is a knight if and only if Liam is a knave\". Sophia told you that Aiden is a knave if and only if Aiden is a knight. Luke expressed that If Michael is a knight then Aurora is a knave. So who is a knight and who is a knave?", "names": ["Michael", "Aurora", "Liam", "Aiden", "Sophia", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true], "solution_text": "Michael is a knave, Aurora is a knight, Liam is a knave, Aiden is a knight, Sophia is a knave, and Luke is a knight.", "solution_text_format": "(1) Michael is a knave\n(2) Aurora is a knight\n(3) Liam is a knave\n(4) Aiden is a knight\n(5) Sophia is a knave\n(6) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Aiden is a knave if and only if Aiden is a knight.", "Sophia cannot be a knave, because this would contradict the claim of Michael that Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Michael that Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Liam is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Liam is a knave or Aiden is a knave.", "Liam cannot be a knight, because this would contradict the claim of Aurora that Liam is a knave or Aiden is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Luke is a knave and Sophia is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Michael is a knight then Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('or', ('lying', 2), ('lying', 3)), ('and', ('lying', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('lying', 2)), ('<=>', ('lying', 3), ('telling-truth', 3)), ('->', ('telling-truth', 0), ('lying', 1)))", "index": 406}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Emma, Sofia, Jacob, Matthew, and Luke. According to Lucas, \"Emma is a knave and Luke is a knight\". \"If Matthew is a knave then Luke is a knight,\" Emma declared. \"Matthew is a knave and Sofia is a knight,\" Sofia mentioned. In a statement by Jacob: \"Jacob is a knight or Sofia is a knave\". In Matthew's words: \"Emma is a knave or Emma is a knight\". \"Lucas is a knave,\" Luke mentioned. So who is a knight and who is a knave?", "names": ["Lucas", "Emma", "Sofia", "Jacob", "Matthew", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Lucas is a knave, Emma is a knight, Sofia is a knave, Jacob is a knight, Matthew is a knight, and Luke is a knight.", "solution_text_format": "(1) Lucas is a knave\n(2) Emma is a knight\n(3) Sofia is a knave\n(4) Jacob is a knight\n(5) Matthew is a knight\n(6) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Emma is a knave and Luke is a knight.", "Emma cannot be a knight, because this would contradict the claim of Lucas that Emma is a knave and Luke is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that If Matthew is a knave then Luke is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Emma that If Matthew is a knave then Luke is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Emma is a knave or Emma is a knight.", "We have exhausted all possibilities for Matthew and Emma, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Emma is a knave and Luke is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Matthew is a knave then Luke is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Emma is a knave or Emma is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Lucas is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Matthew is a knave and Sofia is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Matthew is a knave and Sofia is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Jacob is a knight or Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 5)), ('->', ('lying', 4), ('telling-truth', 5)), ('and', ('lying', 4), ('telling-truth', 2)), ('or', ('telling-truth', 3), ('lying', 2)), ('or', ('lying', 1), ('telling-truth', 1)), ('lying', 0))", "index": 407}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Amelia, Penelope, Scarlett, Elizabeth, and Evelyn. In Jack's words: \"Amelia is a knight if and only if Amelia is a knave\". Amelia expressed that Elizabeth is a knight if and only if Elizabeth is a knave. According to Penelope, \"Scarlett is a knight or Evelyn is a knight\". \"Amelia is a knave,\" Scarlett declared. \"Evelyn is a knave if and only if Penelope is a knight,\" Elizabeth claimed. Evelyn commented, \"Scarlett is a knave\". So who is a knight and who is a knave?", "names": ["Jack", "Amelia", "Penelope", "Scarlett", "Elizabeth", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Jack is a knave, Amelia is a knave, Penelope is a knight, Scarlett is a knight, Elizabeth is a knight, and Evelyn is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Amelia is a knave\n(3) Penelope is a knight\n(4) Scarlett is a knight\n(5) Elizabeth is a knight\n(6) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Jack cannot be a knight, because this would contradict the claim of their own that Amelia is a knight if and only if Amelia is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight if and only if Elizabeth is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Penelope is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Evelyn that Scarlett is a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that Amelia is a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Amelia is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Scarlett is a knight or Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 1)), ('<=>', ('telling-truth', 4), ('lying', 4)), ('or', ('telling-truth', 3), ('telling-truth', 5)), ('lying', 1), ('<=>', ('lying', 5), ('telling-truth', 2)), ('lying', 3))", "index": 408}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Aurora, Logan, Grace, Owen, and Alexander. In Aria's words: \"Logan is a knave and Aurora is a knave\". Aurora said that If Grace is a knave then Owen is a knight. Logan said that If Owen is a knight then Aria is a knave. Grace remarked, \"Alexander is a knight if and only if Aurora is a knight\". \"Aria is a knight,\" Owen mentioned. In Alexander's words: \"Aurora is a knight and Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Aurora", "Logan", "Grace", "Owen", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Aria is a knave, Aurora is a knight, Logan is a knight, Grace is a knight, Owen is a knave, and Alexander is a knight.", "solution_text_format": "(1) Aria is a knave\n(2) Aurora is a knight\n(3) Logan is a knight\n(4) Grace is a knight\n(5) Owen is a knave\n(6) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Logan is a knave and Aurora is a knave.", "Logan cannot be a knight, because this would contradict the claim of Aria that Logan is a knave and Aurora is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that If Owen is a knight then Aria is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Aria is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Aria that Logan is a knave and Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Grace is a knave then Owen is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Logan that If Owen is a knight then Aria is a knave.", "We have exhausted all possibilities for Owen and Logan, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Logan is a knave and Aurora is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that If Owen is a knight then Aria is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Aria is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Aria is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Grace is a knave then Owen is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Aurora is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Aurora is a knight and Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 1)), ('->', ('lying', 3), ('telling-truth', 4)), ('->', ('telling-truth', 4), ('lying', 0)), ('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('telling-truth', 0), ('and', ('telling-truth', 1), ('telling-truth', 5)))", "index": 409}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Liam, Luke, Charlotte, Samuel, and Grace. Victoria remarked, \"Charlotte is a knave or Luke is a knight\". Liam expressed that If Charlotte is a knave then Victoria is a knight. \"If Charlotte is a knave then Grace is a knight,\" Luke declared. As Charlotte put it, \"Luke is a knight\". According to Samuel, \"Victoria is a knave if and only if Charlotte is a knight\". \"Charlotte is a knave if and only if Luke is a knave\" - Grace. So who is a knight and who is a knave?", "names": ["Victoria", "Liam", "Luke", "Charlotte", "Samuel", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Victoria is a knight, Liam is a knight, Luke is a knight, Charlotte is a knight, Samuel is a knave, and Grace is a knight.", "solution_text_format": "(1) Victoria is a knight\n(2) Liam is a knight\n(3) Luke is a knight\n(4) Charlotte is a knight\n(5) Samuel is a knave\n(6) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Charlotte is a knave or Luke is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Charlotte is a knave then Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Luke is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Charlotte is a knave then Victoria is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Victoria is a knave if and only if Charlotte is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 2)), ('->', ('lying', 3), ('telling-truth', 0)), ('->', ('lying', 3), ('telling-truth', 5)), ('telling-truth', 2), ('<=>', ('lying', 0), ('telling-truth', 3)), ('<=>', ('lying', 3), ('lying', 2)))", "index": 410}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Daniel, Ella, Sophia, Evelyn, and Jacob. In a statement by Charlotte: \"If Daniel is a knight then Sophia is a knight\". Daniel asserted: \"Sophia is a knight or Daniel is a knight\". Ella told you that Daniel is a knave and Ella is a knight. \"Charlotte is a knight and Daniel is a knave,\" Sophia claimed. \"If Daniel is a knight then Jacob is a knave,\" Evelyn claimed. Jacob noted, \"Daniel is not a knight\". So who is a knight and who is a knave?", "names": ["Charlotte", "Daniel", "Ella", "Sophia", "Evelyn", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "Charlotte is a knave, Daniel is a knight, Ella is a knave, Sophia is a knave, Evelyn is a knight, and Jacob is a knave.", "solution_text_format": "(1) Charlotte is a knave\n(2) Daniel is a knight\n(3) Ella is a knave\n(4) Sophia is a knave\n(5) Evelyn is a knight\n(6) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that If Daniel is a knight then Sophia is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Sophia is a knight or Daniel is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Daniel is a knave.", "Sophia cannot be a knave, because this would contradict the claim of Charlotte that If Daniel is a knight then Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Sophia is a knight or Daniel is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Daniel that Sophia is a knight or Daniel is a knight.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knight and Daniel is a knave.", "We have exhausted all possibilities for Sophia and Daniel, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Daniel is a knight then Sophia is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Sophia is a knight or Daniel is a knight.", "Sophia cannot be a knight, because this would contradict the false claim of Charlotte that If Daniel is a knight then Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Charlotte is a knight and Daniel is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Daniel is a knave and Ella is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Daniel is a knight then Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Evelyn that If Daniel is a knight then Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Daniel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('telling-truth', 1)), ('and', ('lying', 1), ('telling-truth', 2)), ('and', ('telling-truth', 0), ('lying', 1)), ('->', ('telling-truth', 1), ('lying', 5)), ('not', ('telling-truth', 1)))", "index": 411}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Oliver, Alexander, Victoria, Aiden, and Penelope. Jackson noted, \"Victoria is not a knave\". Oliver commented, \"Jackson is not a knight\". Alexander said, \"Penelope is a knave.\" \"Aiden is a knight,\" Victoria declared. Aiden was heard saying, \"Victoria is a knave or Aiden is a knight\". As Penelope put it, \"Oliver is a knave if and only if Oliver is a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Oliver", "Alexander", "Victoria", "Aiden", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Jackson is a knight, Oliver is a knave, Alexander is a knight, Victoria is a knight, Aiden is a knight, and Penelope is a knave.", "solution_text_format": "(1) Jackson is a knight\n(2) Oliver is a knave\n(3) Alexander is a knight\n(4) Victoria is a knight\n(5) Aiden is a knight\n(6) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Victoria is a knave or Aiden is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Jackson is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Alexander that Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('not', ('telling-truth', 0)), ('lying', 5), ('telling-truth', 4), ('or', ('lying', 3), ('telling-truth', 4)), ('<=>', ('lying', 1), ('telling-truth', 1)))", "index": 412}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Charlotte, Henry, Victoria, Isabella, and Aurora. Emily asserted: \"Charlotte is a knight\". Charlotte said, \"Henry is a knight or Emily is a knave.\" Henry told you that Aurora is a knight. \"Isabella is a knave if and only if Emily is a knight,\" Victoria mentioned. Isabella was heard saying, \"Emily is a knight and Charlotte is a knight\". \"If Charlotte is a knight then Isabella is a knight,\" Aurora mentioned. So who is a knight and who is a knave?", "names": ["Emily", "Charlotte", "Henry", "Victoria", "Isabella", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Emily is a knight, Charlotte is a knight, Henry is a knight, Victoria is a knave, Isabella is a knight, and Aurora is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Charlotte is a knight\n(3) Henry is a knight\n(4) Victoria is a knave\n(5) Isabella is a knight\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Henry is a knight or Emily is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Charlotte is a knight then Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Emily is a knight and Charlotte is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Isabella is a knave if and only if Emily is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('or', ('telling-truth', 2), ('lying', 0)), ('telling-truth', 5), ('<=>', ('lying', 4), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 1), ('telling-truth', 4)))", "index": 413}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Liam, Amelia, Zoey, Ava, and Harper. Sofia noted, \"If Ava is a knave then Amelia is a knight\". \"Zoey is a knave,\" Liam claimed. \"If Sofia is a knave then Zoey is a knave,\" Amelia declared. In a statement by Zoey: \"Liam is a knave and Liam is a knight\". Ava remarked, \"Amelia is a knave and Sofia is a knight\". \"Sofia is a knave\" - Harper. So who is a knight and who is a knave?", "names": ["Sofia", "Liam", "Amelia", "Zoey", "Ava", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Sofia is a knight, Liam is a knight, Amelia is a knight, Zoey is a knave, Ava is a knave, and Harper is a knave.", "solution_text_format": "(1) Sofia is a knight\n(2) Liam is a knight\n(3) Amelia is a knight\n(4) Zoey is a knave\n(5) Ava is a knave\n(6) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that If Ava is a knave then Amelia is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Amelia is a knave and Sofia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Ava that Amelia is a knave and Sofia is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that If Sofia is a knave then Zoey is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Amelia is a knave and Sofia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Sofia is a knave then Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Liam is a knave and Liam is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Liam is a knave and Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Zoey is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Sofia is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('telling-truth', 2)), ('lying', 3), ('->', ('lying', 0), ('lying', 3)), ('and', ('lying', 1), ('telling-truth', 1)), ('and', ('lying', 2), ('telling-truth', 0)), ('lying', 0))", "index": 414}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Sofia, Owen, Jack, Sebastian, and Jackson. Abigail commented, \"Jack is a knave if and only if Owen is a knave\". Sofia was heard saying, \"Abigail is a knight if and only if Sebastian is a knight\". \"Jackson is a knave and Abigail is a knave,\" Owen mentioned. \"Owen is a knight if and only if Owen is a knave,\" Jack claimed. Sebastian said that Jack is a knave. Jackson was heard saying, \"Jackson is a knight or Jack is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Sofia", "Owen", "Jack", "Sebastian", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "Abigail is a knight, Sofia is a knight, Owen is a knave, Jack is a knave, Sebastian is a knight, and Jackson is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) Sofia is a knight\n(3) Owen is a knave\n(4) Jack is a knave\n(5) Sebastian is a knight\n(6) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Jack is a knave if and only if Owen is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Owen is a knight if and only if Owen is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Abigail that Jack is a knave if and only if Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Jackson is a knave and Abigail is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Jackson is a knight or Jack is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 2)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('and', ('lying', 5), ('lying', 0)), ('<=>', ('telling-truth', 2), ('lying', 2)), ('lying', 3), ('or', ('telling-truth', 5), ('lying', 3)))", "index": 415}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Charlotte, Amelia, Grace, Ava, and Jack. Daniel asserted: \"If Charlotte is a knight then Grace is a knave\". Charlotte remarked, \"Jack is a knight\". Amelia said, \"Jack is a knave and Grace is a knave.\" Grace expressed that Amelia is a knave if and only if Jack is a knave. Ava stated, \"Amelia is a knight and Daniel is a knave\". Jack remarked, \"Grace is a knight and Amelia is a knave\". So who is a knight and who is a knave?", "names": ["Daniel", "Charlotte", "Amelia", "Grace", "Ava", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Daniel is a knight, Charlotte is a knave, Amelia is a knight, Grace is a knave, Ava is a knave, and Jack is a knave.", "solution_text_format": "(1) Daniel is a knight\n(2) Charlotte is a knave\n(3) Amelia is a knight\n(4) Grace is a knave\n(5) Ava is a knave\n(6) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that If Charlotte is a knight then Grace is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Grace is a knight and Amelia is a knave.", "Grace cannot be a knight, because this would contradict the claim of Daniel that If Charlotte is a knight then Grace is a knave.", "Grace cannot be a knave, because this would contradict the claim of Jack that Grace is a knight and Amelia is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Charlotte that Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Charlotte that Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Grace is a knight and Amelia is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Jack is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Jack is a knave and Grace is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of Jack that Grace is a knight and Amelia is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Jack is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Jack is a knave and Grace is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Amelia is a knight and Daniel is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Amelia is a knight and Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('lying', 3)), ('telling-truth', 5), ('and', ('lying', 5), ('lying', 3)), ('<=>', ('lying', 2), ('lying', 5)), ('and', ('telling-truth', 2), ('lying', 0)), ('and', ('telling-truth', 3), ('lying', 2)))", "index": 416}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Zoey, Mason, Emma, Abigail, and Samuel. As Mia put it, \"Zoey is not a knave\". \"Abigail is not a knight\" - Zoey. Mason expressed that Samuel is a knave and Mason is a knight. Emma asserted: \"Abigail is a knave or Samuel is a knight\". \"Mia is a knave or Emma is a knight,\" Abigail declared. As Samuel put it, \"If Mia is a knight then Emma is a knave\". So who is a knight and who is a knave?", "names": ["Mia", "Zoey", "Mason", "Emma", "Abigail", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Mia is a knave, Zoey is a knave, Mason is a knave, Emma is a knight, Abigail is a knight, and Samuel is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Zoey is a knave\n(3) Mason is a knave\n(4) Emma is a knight\n(5) Abigail is a knight\n(6) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Zoey is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of Zoey that Abigail is not a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Mia is a knave or Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Abigail that Mia is a knave or Emma is a knight.", "Emma cannot be a knave, because this would contradict the false claim of their own that Abigail is a knave or Samuel is a knight.", "We have exhausted all possibilities for Emma and Abigail, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of Mia that Zoey is not a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Mia that Zoey is not a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Mia is a knave or Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Abigail is a knave or Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Mia is a knight then Emma is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Samuel is a knave and Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Samuel is a knave and Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('not', ('telling-truth', 4)), ('and', ('lying', 5), ('telling-truth', 2)), ('or', ('lying', 4), ('telling-truth', 5)), ('or', ('lying', 0), ('telling-truth', 3)), ('->', ('telling-truth', 0), ('lying', 3)))", "index": 417}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Grace, Ava, Alexander, Emily, and Emma. \"Grace is a knight if and only if Ava is a knight,\" Abigail claimed. \"If Emma is a knave then Emily is a knave,\" Grace declared. \"Grace is a knight\" - Ava. In a statement by Alexander: \"Ava is a knight and Grace is a knave\". Emily told you that Ava is a knight or Alexander is a knave. According to Emma, \"Grace is a knight or Emily is a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Grace", "Ava", "Alexander", "Emily", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Abigail is a knight, Grace is a knight, Ava is a knight, Alexander is a knave, Emily is a knight, and Emma is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) Grace is a knight\n(3) Ava is a knight\n(4) Alexander is a knave\n(5) Emily is a knight\n(6) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Grace is a knight if and only if Ava is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Emma is a knave then Emily is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Grace is a knight or Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Ava is a knight or Alexander is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Grace is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Ava is a knight and Grace is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ava is a knight and Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('lying', 5), ('lying', 4)), ('telling-truth', 1), ('and', ('telling-truth', 2), ('lying', 1)), ('or', ('telling-truth', 2), ('lying', 3)), ('or', ('telling-truth', 1), ('telling-truth', 4)))", "index": 418}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Alexander, David, Emily, Charlotte, and Emma. Daniel was heard saying, \"Emma is a knave or Emily is a knight\". According to Alexander, \"Daniel is not a knight\". \"Emily is a knave,\" David declared. In a statement by Emily: \"Emma is a knave and Charlotte is a knave\". In Charlotte's words: \"Charlotte is a knight if and only if Daniel is a knight\". \"David is a knight\" - Emma. So who is a knight and who is a knave?", "names": ["Daniel", "Alexander", "David", "Emily", "Charlotte", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false], "solution_text": "Daniel is a knight, Alexander is a knave, David is a knave, Emily is a knight, Charlotte is a knave, and Emma is a knave.", "solution_text_format": "(1) Daniel is a knight\n(2) Alexander is a knave\n(3) David is a knave\n(4) Emily is a knight\n(5) Charlotte is a knave\n(6) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Emma is a knave or Emily is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of David that Emily is a knave.", "Emily cannot be a knave, because this would contradict the claim of Daniel that Emma is a knave or Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Emma that David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that David is a knight.", "David cannot be a knight, because this would contradict the false claim of Emma that David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Emma is a knave and Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Emily that Emma is a knave and Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Daniel is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Daniel is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Daniel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 3)), ('not', ('telling-truth', 0)), ('lying', 3), ('and', ('lying', 5), ('lying', 4)), ('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('telling-truth', 2))", "index": 419}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, William, Olivia, Samuel, Chloe, and Ava. Harper was heard saying, \"If Ava is a knave then Ava is a knight\". William noted, \"Ava is not a knight\". Olivia expressed that Chloe is a knight or William is a knight. \"William is not a knave\" - Samuel. Chloe told you that Harper is a knave or Harper is a knight. \"William is a knight and William is a knave\" - Ava. So who is a knight and who is a knave?", "names": ["Harper", "William", "Olivia", "Samuel", "Chloe", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Harper is a knave, William is a knight, Olivia is a knight, Samuel is a knight, Chloe is a knight, and Ava is a knave.", "solution_text_format": "(1) Harper is a knave\n(2) William is a knight\n(3) Olivia is a knight\n(4) Samuel is a knight\n(5) Chloe is a knight\n(6) Ava is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that If Ava is a knave then Ava is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that William is a knight and William is a knave.", "Ava cannot be a knave, because this would contradict the claim of Harper that If Ava is a knave then Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that If Ava is a knave then Ava is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Harper that If Ava is a knave then Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that William is a knight and William is a knave.", "Assume William is a knight. No contradiction is found in their claim that Ava is not a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Chloe is a knight or William is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Harper is a knave or Harper is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that William is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 5)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('lying', 1)), ('or', ('lying', 0), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('lying', 1)))", "index": 420}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Emma, Charlotte, Luke, Sebastian, and Abigail. Riley was heard saying, \"Emma is not a knight\". \"Emma is a knight if and only if Riley is a knave,\" Emma mentioned. Charlotte was heard saying, \"Sebastian is a knight or Riley is a knave\". In a statement by Luke: \"Emma is a knave and Riley is a knave\". \"Sebastian is a knight or Abigail is a knave,\" Sebastian declared. \"Luke is a knight if and only if Emma is a knight,\" Abigail claimed. So who is a knight and who is a knave?", "names": ["Riley", "Emma", "Charlotte", "Luke", "Sebastian", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false], "solution_text": "Riley is a knave, Emma is a knight, Charlotte is a knight, Luke is a knave, Sebastian is a knight, and Abigail is a knave.", "solution_text_format": "(1) Riley is a knave\n(2) Emma is a knight\n(3) Charlotte is a knight\n(4) Luke is a knave\n(5) Sebastian is a knight\n(6) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Emma is not a knight.", "Emma cannot be a knight, because this would contradict the claim of Riley that Emma is not a knight.", "Emma cannot be a knave, because this would contradict the false claim of their own that Emma is a knight if and only if Riley is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Emma is a knight if and only if Riley is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Sebastian is a knight or Riley is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sebastian is a knight or Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Luke is a knight if and only if Emma is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Riley is a knave.", "Luke cannot be a knave, because this would contradict the claim of Abigail that Luke is a knight if and only if Emma is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Emma is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Riley is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Emma is a knave and Riley is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('lying', 0)), ('or', ('telling-truth', 4), ('lying', 0)), ('and', ('lying', 1), ('lying', 0)), ('or', ('telling-truth', 4), ('lying', 5)), ('<=>', ('telling-truth', 3), ('telling-truth', 1)))", "index": 421}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Owen, Samuel, Matthew, Ella, and Jacob. As Joseph put it, \"Joseph is a knight\". Owen remarked, \"Ella is a knight\". Samuel asserted: \"Ella is not a knight\". Matthew asserted: \"Samuel is a knight\". As Ella put it, \"If Ella is a knight then Jacob is a knight\". Jacob commented, \"Joseph is not a knight\". So who is a knight and who is a knave?", "names": ["Joseph", "Owen", "Samuel", "Matthew", "Ella", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true], "solution_text": "Joseph is a knave, Owen is a knight, Samuel is a knave, Matthew is a knave, Ella is a knight, and Jacob is a knight.", "solution_text_format": "(1) Joseph is a knave\n(2) Owen is a knight\n(3) Samuel is a knave\n(4) Matthew is a knave\n(5) Ella is a knight\n(6) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Ella is a knight then Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Joseph is not a knight.", "Jacob cannot be a knave, because this would contradict the claim of Ella that If Ella is a knight then Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Owen that Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Owen that Ella is a knight.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Ella is a knight then Jacob is a knight.", "We have exhausted all possibilities for Ella and Owen, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Ella is a knight then Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Ella is not a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Samuel is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 0), ('telling-truth', 4), ('not', ('telling-truth', 4)), ('telling-truth', 2), ('->', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('telling-truth', 0)))", "index": 422}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Matthew, Noah, Zoey, Sophia, and Elizabeth. Logan asserted: \"Matthew is a knight\". Matthew stated, \"Logan is a knave or Noah is a knave\". Noah said that Matthew is a knave and Elizabeth is a knight. Zoey noted, \"Matthew is a knight\". \"Matthew is a knight or Zoey is a knight,\" Sophia claimed. Elizabeth stated, \"If Logan is a knave then Logan is a knight\". So who is a knight and who is a knave?", "names": ["Logan", "Matthew", "Noah", "Zoey", "Sophia", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Logan is a knight, Matthew is a knight, Noah is a knave, Zoey is a knight, Sophia is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Logan is a knight\n(2) Matthew is a knight\n(3) Noah is a knave\n(4) Zoey is a knight\n(5) Sophia is a knight\n(6) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Logan is a knave or Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Matthew that Logan is a knave or Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Matthew is a knave and Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Logan is a knave then Logan is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Matthew is a knight or Zoey is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('or', ('lying', 0), ('lying', 2)), ('and', ('lying', 1), ('telling-truth', 5)), ('telling-truth', 1), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('->', ('lying', 0), ('telling-truth', 0)))", "index": 423}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Alexander, Owen, Luke, Charlotte, and Joseph. David was heard saying, \"If David is a knight then Charlotte is a knight\". Alexander expressed that Owen is a knave. \"Charlotte is not a knight,\" Owen claimed. According to Luke, \"David is a knight and Joseph is a knave\". Charlotte remarked, \"Owen is a knave or David is a knight\". Joseph asserted: \"Charlotte is a knave\". So who is a knight and who is a knave?", "names": ["David", "Alexander", "Owen", "Luke", "Charlotte", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "David is a knight, Alexander is a knight, Owen is a knave, Luke is a knight, Charlotte is a knight, and Joseph is a knave.", "solution_text_format": "(1) David is a knight\n(2) Alexander is a knight\n(3) Owen is a knave\n(4) Luke is a knight\n(5) Charlotte is a knight\n(6) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that If David is a knight then Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Owen is a knave or David is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Owen is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that David is a knight and Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Luke that David is a knight and Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 4)), ('lying', 2), ('not', ('telling-truth', 4)), ('and', ('telling-truth', 0), ('lying', 5)), ('or', ('lying', 2), ('telling-truth', 0)), ('lying', 4))", "index": 424}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Aiden, Victoria, Harper, Logan, and Riley. Alexander remarked, \"Riley is a knight and Riley is a knave\". Aiden noted, \"Victoria is a knight\". As Victoria put it, \"Aiden is a knave or Riley is a knight\". As Harper put it, \"Riley is not a knave\". In Logan's words: \"Harper is not a knight\". Riley remarked, \"Harper is not a knave\". So who is a knight and who is a knave?", "names": ["Alexander", "Aiden", "Victoria", "Harper", "Logan", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Alexander is a knave, Aiden is a knight, Victoria is a knight, Harper is a knight, Logan is a knave, and Riley is a knight.", "solution_text_format": "(1) Alexander is a knave\n(2) Aiden is a knight\n(3) Victoria is a knight\n(4) Harper is a knight\n(5) Logan is a knave\n(6) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Alexander cannot be a knight, because this would contradict the claim of their own that Riley is a knight and Riley is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Riley is a knight and Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Riley is not a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Aiden is a knave or Riley is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Harper is not a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Harper is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 5)), ('telling-truth', 2), ('or', ('lying', 1), ('telling-truth', 5)), ('not', ('lying', 5)), ('not', ('telling-truth', 3)), ('not', ('lying', 3)))", "index": 425}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Owen, Abigail, Alexander, David, and Evelyn. Sebastian was heard saying, \"Abigail is a knight or Sebastian is a knight\". \"Evelyn is a knight or Sebastian is a knight\" - Owen. As Abigail put it, \"Owen is a knight or Owen is a knave\". Alexander stated, \"David is not a knight\". In a statement by David: \"Evelyn is a knave if and only if Owen is a knight\". \"If Sebastian is a knight then Abigail is a knave,\" Evelyn claimed. So who is a knight and who is a knave?", "names": ["Sebastian", "Owen", "Abigail", "Alexander", "David", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Sebastian is a knight, Owen is a knight, Abigail is a knight, Alexander is a knave, David is a knight, and Evelyn is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Owen is a knight\n(3) Abigail is a knight\n(4) Alexander is a knave\n(5) David is a knight\n(6) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Abigail is a knight or Sebastian is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Owen is a knight or Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Evelyn is a knight or Sebastian is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that If Sebastian is a knight then Abigail is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Abigail is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that David is not a knight.", "David cannot be a knight, because this would contradict the claim of Alexander that David is not a knight.", "David cannot be a knave, because this would contradict the false claim of their own that Evelyn is a knave if and only if Owen is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that David is not a knight.", "Assume David is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('or', ('telling-truth', 1), ('lying', 1)), ('not', ('telling-truth', 4)), ('<=>', ('lying', 5), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('lying', 2)))", "index": 426}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Jackson, Amelia, Harper, Scarlett, and Mason. \"Amelia is a knave or Liam is a knight,\" Liam declared. \"Mason is a knave or Liam is a knight,\" Jackson mentioned. \"Harper is a knight if and only if Harper is a knave,\" Amelia declared. Harper noted, \"Liam is a knight\". Scarlett asserted: \"Mason is a knave or Harper is a knight\". Mason remarked, \"Harper is a knave or Amelia is a knave\". So who is a knight and who is a knave?", "names": ["Liam", "Jackson", "Amelia", "Harper", "Scarlett", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Liam is a knight, Jackson is a knight, Amelia is a knave, Harper is a knight, Scarlett is a knight, and Mason is a knight.", "solution_text_format": "(1) Liam is a knight\n(2) Jackson is a knight\n(3) Amelia is a knave\n(4) Harper is a knight\n(5) Scarlett is a knight\n(6) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Amelia is a knave or Liam is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Harper is a knight if and only if Harper is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Liam is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Mason is a knave or Liam is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Harper is a knave or Amelia is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Mason is a knave or Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 0)), ('or', ('lying', 5), ('telling-truth', 0)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('telling-truth', 0), ('or', ('lying', 5), ('telling-truth', 3)), ('or', ('lying', 3), ('lying', 2)))", "index": 427}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Sofia, Emma, Liam, Elizabeth, and James. Henry expressed that Sofia is not a knight. Sofia said that Emma is a knight or Elizabeth is a knave. Emma said, \"Liam is a knight and Sofia is a knight.\" \"James is a knave,\" Liam claimed. According to Elizabeth, \"Henry is a knave or Emma is a knight\". James said that Sofia is not a knight. So who is a knight and who is a knave?", "names": ["Henry", "Sofia", "Emma", "Liam", "Elizabeth", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Henry is a knave, Sofia is a knight, Emma is a knight, Liam is a knight, Elizabeth is a knight, and James is a knave.", "solution_text_format": "(1) Henry is a knave\n(2) Sofia is a knight\n(3) Emma is a knight\n(4) Liam is a knight\n(5) Elizabeth is a knight\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of Henry that Sofia is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Emma is a knight or Elizabeth is a knave.", "Emma cannot be a knight, because this would contradict the false claim of Sofia that Emma is a knight or Elizabeth is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Liam is a knight and Sofia is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Liam that James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that Sofia is not a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Henry is a knave or Emma is a knight.", "Elizabeth cannot be a knave, because this would contradict the false claim of Sofia that Emma is a knight or Elizabeth is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the false claim of Liam that James is a knave.", "We have exhausted all possibilities for James, Liam, Emma, and Sofia, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Sofia is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Emma is a knight or Elizabeth is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Liam is a knight and Sofia is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Liam that James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Sofia is not a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Henry is a knave or Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('or', ('telling-truth', 2), ('lying', 4)), ('and', ('telling-truth', 3), ('telling-truth', 1)), ('lying', 5), ('or', ('lying', 0), ('telling-truth', 2)), ('not', ('telling-truth', 1)))", "index": 428}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Daniel, Scarlett, Michael, Sofia, and Victoria. \"Sofia is a knave or Scarlett is a knight\" - Ella. In a statement by Daniel: \"Victoria is a knight or Daniel is a knight\". Scarlett commented, \"Victoria is a knight or Daniel is a knave\". Michael asserted: \"Sofia is not a knight\". Sofia noted, \"Scarlett is a knave\". Victoria was heard saying, \"Scarlett is a knave or Michael is a knight\". So who is a knight and who is a knave?", "names": ["Ella", "Daniel", "Scarlett", "Michael", "Sofia", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Ella is a knight, Daniel is a knight, Scarlett is a knight, Michael is a knight, Sofia is a knave, and Victoria is a knight.", "solution_text_format": "(1) Ella is a knight\n(2) Daniel is a knight\n(3) Scarlett is a knight\n(4) Michael is a knight\n(5) Sofia is a knave\n(6) Victoria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Sofia is a knave or Scarlett is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Sofia that Scarlett is a knave.", "Scarlett cannot be a knave, because this would contradict the claim of Ella that Sofia is a knave or Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Victoria is a knight or Daniel is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Scarlett is a knave or Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Victoria is a knight or Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 2)), ('or', ('telling-truth', 5), ('telling-truth', 1)), ('or', ('telling-truth', 5), ('lying', 1)), ('not', ('telling-truth', 4)), ('lying', 2), ('or', ('lying', 2), ('telling-truth', 3)))", "index": 429}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Emma, Joseph, Olivia, Daniel, and William. As Jack put it, \"Joseph is a knave if and only if Olivia is a knave\". Emma expressed that Emma is a knight and Joseph is a knave. Joseph asserted: \"If Joseph is a knight then Emma is a knave\". Olivia said, \"Olivia is a knight if and only if Jack is a knight.\" Daniel stated, \"Olivia is a knave\". In a statement by William: \"If William is a knight then Daniel is a knave\". So who is a knight and who is a knave?", "names": ["Jack", "Emma", "Joseph", "Olivia", "Daniel", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "Jack is a knight, Emma is a knave, Joseph is a knight, Olivia is a knight, Daniel is a knave, and William is a knight.", "solution_text_format": "(1) Jack is a knight\n(2) Emma is a knave\n(3) Joseph is a knight\n(4) Olivia is a knight\n(5) Daniel is a knave\n(6) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Olivia is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Joseph is a knight then Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Joseph is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Emma is a knight and Joseph is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Jack is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Assume William is a knight. No contradiction is found in their claim that If William is a knight then Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 3)), ('and', ('telling-truth', 1), ('lying', 2)), ('->', ('telling-truth', 2), ('lying', 1)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('lying', 3), ('->', ('telling-truth', 5), ('lying', 4)))", "index": 430}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Daniel, Emma, Liam, Amelia, and Emily. William noted, \"Amelia is not a knight\". Daniel remarked, \"Liam is a knave if and only if William is a knight\". Emma stated, \"William is a knight and Emily is a knave\". \"Amelia is not a knave,\" Liam mentioned. Amelia told you that Daniel is not a knight. Emily stated, \"If Amelia is a knight then Daniel is a knight\". So who is a knight and who is a knave?", "names": ["William", "Daniel", "Emma", "Liam", "Amelia", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true], "solution_text": "William is a knight, Daniel is a knight, Emma is a knave, Liam is a knave, Amelia is a knave, and Emily is a knight.", "solution_text_format": "(1) William is a knight\n(2) Daniel is a knight\n(3) Emma is a knave\n(4) Liam is a knave\n(5) Amelia is a knave\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of William that Amelia is not a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Liam is a knave if and only if William is a knight.", "Liam cannot be a knight, because this would contradict the claim of Daniel that Liam is a knave if and only if William is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Amelia is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that William is a knight and Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Emma that William is a knight and Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that If Amelia is a knight then Daniel is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that William is a knight and Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Amelia is a knight then Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('<=>', ('lying', 3), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('lying', 5)), ('not', ('lying', 4)), ('not', ('telling-truth', 1)), ('->', ('telling-truth', 4), ('telling-truth', 1)))", "index": 431}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Jackson, William, Aurora, Penelope, and Aria. \"Penelope is a knight\" - Mia. Jackson remarked, \"Aria is a knight\". \"Mia is a knave or William is a knight\" - William. \"Mia is a knight and Aria is a knight,\" Aurora claimed. Penelope said, \"Jackson is a knight if and only if Aria is a knave.\" Aria expressed that Aurora is not a knight. So who is a knight and who is a knave?", "names": ["Mia", "Jackson", "William", "Aurora", "Penelope", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Mia is a knave, Jackson is a knight, William is a knight, Aurora is a knave, Penelope is a knave, and Aria is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Jackson is a knight\n(3) William is a knight\n(4) Aurora is a knave\n(5) Penelope is a knave\n(6) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Aria is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Aria is a knight.", "Aria cannot be a knight, because this would contradict the claim of Penelope that Jackson is a knight if and only if Aria is a knave.", "Aria cannot be a knave, because this would contradict the claim of Jackson that Aria is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Aria is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Jackson that Aria is a knight.", "Aria cannot be a knave, because this would contradict the claim of Penelope that Jackson is a knight if and only if Aria is a knave.", "We have exhausted all possibilities for Aria and Jackson, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Mia that Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Mia that Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Aria is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Aurora is not a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Aria is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Mia is a knight and Aria is a knight.", "Assume William is a knight. No contradiction is found in their claim that Mia is a knave or William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('telling-truth', 5), ('or', ('lying', 0), ('telling-truth', 2)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('<=>', ('telling-truth', 1), ('lying', 5)), ('not', ('telling-truth', 3)))", "index": 432}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, Olivia, Matthew, Owen, Emily, and Jack. \"Jack is a knight if and only if Olivia is a knight,\" Penelope mentioned. Olivia said, \"If Emily is a knave then Penelope is a knave.\" Matthew said that Matthew is a knight or Emily is a knight. Owen said that Matthew is a knight. According to Emily, \"Jack is a knave if and only if Owen is a knight\". Jack was heard saying, \"Emily is a knave\". So who is a knight and who is a knave?", "names": ["Penelope", "Olivia", "Matthew", "Owen", "Emily", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Penelope is a knave, Olivia is a knight, Matthew is a knight, Owen is a knight, Emily is a knight, and Jack is a knave.", "solution_text_format": "(1) Penelope is a knave\n(2) Olivia is a knight\n(3) Matthew is a knight\n(4) Owen is a knight\n(5) Emily is a knight\n(6) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Jack is a knight if and only if Olivia is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Jack that Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Matthew is a knight or Emily is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that If Emily is a knave then Penelope is a knave.", "Olivia cannot be a knave, because this would contradict the claim of Penelope that Jack is a knight if and only if Olivia is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Owen that Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Emily that Jack is a knave if and only if Owen is a knight.", "We have exhausted all possibilities for Owen and Emily, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Jack is a knave if and only if Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Matthew is a knight or Emily is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Penelope that Jack is a knight if and only if Olivia is a knight.", "Olivia cannot be a knave, because this would contradict the false claim of their own that If Emily is a knave then Penelope is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Matthew is a knight or Emily is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Emily that Jack is a knave if and only if Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the false claim of Jack that Emily is a knave.", "We have exhausted all possibilities for Emily and Jack, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Jack is a knight if and only if Olivia is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Jack that Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Matthew is a knight or Emily is a knight.", "Olivia cannot be a knight, because this would contradict the false claim of Penelope that Jack is a knight if and only if Olivia is a knight.", "Olivia cannot be a knave, because this would contradict the false claim of their own that If Emily is a knave then Penelope is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Owen that Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Emily that Jack is a knave if and only if Owen is a knight.", "We have exhausted all possibilities for Owen and Emily, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Jack is a knave if and only if Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Matthew is a knight or Emily is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Emily is a knave then Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('->', ('lying', 4), ('lying', 0)), ('or', ('telling-truth', 2), ('telling-truth', 4)), ('telling-truth', 2), ('<=>', ('lying', 5), ('telling-truth', 3)), ('lying', 4))", "index": 433}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Sophia, Sebastian, Chloe, Amelia, and Riley. William noted, \"Amelia is a knight or Sebastian is a knight\". Sophia noted, \"If Amelia is a knave then Chloe is a knave\". Sebastian was heard saying, \"Amelia is not a knave\". Chloe was heard saying, \"Amelia is a knave if and only if Amelia is a knight\". Amelia said, \"Chloe is not a knight.\" Riley was heard saying, \"Sebastian is a knave\". So who is a knight and who is a knave?", "names": ["William", "Sophia", "Sebastian", "Chloe", "Amelia", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "William is a knight, Sophia is a knight, Sebastian is a knight, Chloe is a knave, Amelia is a knight, and Riley is a knave.", "solution_text_format": "(1) William is a knight\n(2) Sophia is a knight\n(3) Sebastian is a knight\n(4) Chloe is a knave\n(5) Amelia is a knight\n(6) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Amelia is a knight or Sebastian is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Amelia is a knave if and only if Amelia is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Amelia is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Amelia is a knave then Chloe is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 2)), ('->', ('lying', 4), ('lying', 3)), ('not', ('lying', 4)), ('<=>', ('lying', 4), ('telling-truth', 4)), ('not', ('telling-truth', 3)), ('lying', 2))", "index": 434}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Aria, Evelyn, Daniel, Riley, and Emma. As Harper put it, \"Emma is a knave if and only if Harper is a knight\". In a statement by Aria: \"Daniel is a knave or Harper is a knave\". As Evelyn put it, \"If Harper is a knave then Daniel is a knight\". Daniel said that Daniel is a knight if and only if Riley is a knight. According to Riley, \"Harper is a knight if and only if Daniel is a knight\". According to Emma, \"Harper is a knight and Evelyn is a knight\". So who is a knight and who is a knave?", "names": ["Harper", "Aria", "Evelyn", "Daniel", "Riley", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "Harper is a knave, Aria is a knight, Evelyn is a knave, Daniel is a knave, Riley is a knight, and Emma is a knave.", "solution_text_format": "(1) Harper is a knave\n(2) Aria is a knight\n(3) Evelyn is a knave\n(4) Daniel is a knave\n(5) Riley is a knight\n(6) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Emma is a knave if and only if Harper is a knight.", "Emma cannot be a knight, because this would contradict the claim of Harper that Emma is a knave if and only if Harper is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Harper is a knight and Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Emma that Harper is a knight and Evelyn is a knight.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that If Harper is a knave then Daniel is a knight.", "We have exhausted all possibilities for Evelyn and Emma, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Harper is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Harper that Emma is a knave if and only if Harper is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Harper is a knight and Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Harper is a knave then Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Harper is a knight if and only if Daniel is a knight.", "Riley cannot be a knave, because this would contradict the claim of Daniel that Daniel is a knight if and only if Riley is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Evelyn that If Harper is a knave then Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Harper is a knave then Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Evelyn that If Harper is a knave then Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Harper is a knight if and only if Daniel is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Daniel is a knave or Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('telling-truth', 0)), ('or', ('lying', 3), ('lying', 0)), ('->', ('lying', 0), ('telling-truth', 3)), ('<=>', ('telling-truth', 3), ('telling-truth', 4)), ('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('telling-truth', 2)))", "index": 435}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Aria, Grace, Scarlett, Jackson, and Aiden. According to Isabella, \"If Jackson is a knave then Scarlett is a knight\". Aria was heard saying, \"If Scarlett is a knave then Scarlett is a knight\". Grace was heard saying, \"If Jackson is a knight then Scarlett is a knave\". Scarlett noted, \"Jackson is not a knight\". Jackson said that Grace is a knight. As Aiden put it, \"Jackson is not a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Aria", "Grace", "Scarlett", "Jackson", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Isabella is a knight, Aria is a knave, Grace is a knight, Scarlett is a knave, Jackson is a knight, and Aiden is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Aria is a knave\n(3) Grace is a knight\n(4) Scarlett is a knave\n(5) Jackson is a knight\n(6) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that If Jackson is a knave then Scarlett is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Jackson is a knight then Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Grace that If Jackson is a knight then Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that If Scarlett is a knave then Scarlett is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that If Scarlett is a knave then Scarlett is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Jackson is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('telling-truth', 3)), ('->', ('lying', 3), ('telling-truth', 3)), ('->', ('telling-truth', 4), ('lying', 3)), ('not', ('telling-truth', 4)), ('telling-truth', 2), ('not', ('lying', 4)))", "index": 436}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Mia, James, Liam, Abigail, and Michael. Luke asserted: \"Abigail is a knight and Mia is a knave\". Mia expressed that Michael is a knight and James is a knight. James expressed that Michael is a knight or Mia is a knave. Liam remarked, \"Abigail is a knave\". Abigail was heard saying, \"Mia is a knave\". According to Michael, \"Mia is a knave and Abigail is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Mia", "James", "Liam", "Abigail", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false], "solution_text": "Luke is a knight, Mia is a knave, James is a knight, Liam is a knave, Abigail is a knight, and Michael is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Mia is a knave\n(3) James is a knight\n(4) Liam is a knave\n(5) Abigail is a knight\n(6) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Abigail is a knight and Mia is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of Luke that Abigail is a knight and Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Michael is a knight and James is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Abigail is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Mia is a knave and Abigail is a knave.", "Assume James is a knight. No contradiction is found in their claim that Michael is a knight or Mia is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 1)), ('and', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('telling-truth', 5), ('lying', 1)), ('lying', 4), ('lying', 1), ('and', ('lying', 1), ('lying', 4)))", "index": 437}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Jack, Benjamin, Lucas, Joseph, and Jackson. In Avery's words: \"If Lucas is a knave then Jack is a knave\". According to Jack, \"Joseph is a knave or Joseph is a knight\". \"Joseph is a knave if and only if Lucas is a knave,\" Benjamin mentioned. As Lucas put it, \"Joseph is not a knight\". Joseph commented, \"Jackson is a knight and Jack is a knave\". As Jackson put it, \"Benjamin is not a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Jack", "Benjamin", "Lucas", "Joseph", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Avery is a knight, Jack is a knight, Benjamin is a knave, Lucas is a knight, Joseph is a knave, and Jackson is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Jack is a knight\n(3) Benjamin is a knave\n(4) Lucas is a knight\n(5) Joseph is a knave\n(6) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that If Lucas is a knave then Jack is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of Lucas that Joseph is not a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Jackson is a knight and Jack is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Joseph is a knave if and only if Lucas is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Jackson that Benjamin is not a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Joseph is a knave if and only if Lucas is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Lucas is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Joseph is a knave or Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 1)), ('or', ('lying', 4), ('telling-truth', 4)), ('<=>', ('lying', 4), ('lying', 3)), ('not', ('telling-truth', 4)), ('and', ('telling-truth', 5), ('lying', 1)), ('not', ('lying', 2)))", "index": 438}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Scarlett, James, Penelope, Ella, and Henry. Grace told you that If Ella is a knight then Penelope is a knave. \"If James is a knave then James is a knight,\" Scarlett declared. James was heard saying, \"Henry is a knave\". \"Grace is not a knight,\" Penelope mentioned. In a statement by Ella: \"Henry is a knave\". Henry stated, \"Penelope is a knight or Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Scarlett", "James", "Penelope", "Ella", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true], "solution_text": "Grace is a knight, Scarlett is a knave, James is a knave, Penelope is a knave, Ella is a knave, and Henry is a knight.", "solution_text_format": "(1) Grace is a knight\n(2) Scarlett is a knave\n(3) James is a knave\n(4) Penelope is a knave\n(5) Ella is a knave\n(6) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that If Ella is a knight then Penelope is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Ella that Henry is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight or Penelope is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Penelope is a knight or Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Grace is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If James is a knave then James is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Henry is a knave.", "James cannot be a knave, because this would contradict the claim of Scarlett that If James is a knave then James is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that If James is a knave then James is a knight.", "James cannot be a knight, because this would contradict the false claim of Scarlett that If James is a knave then James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 3)), ('->', ('lying', 2), ('telling-truth', 2)), ('lying', 5), ('not', ('telling-truth', 0)), ('lying', 5), ('or', ('telling-truth', 3), ('lying', 3)))", "index": 439}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Sophia, Aria, David, Scarlett, and James. Liam noted, \"If Scarlett is a knave then Aria is a knave\". Sophia was heard saying, \"Scarlett is a knight\". Aria remarked, \"Liam is a knight if and only if David is a knight\". According to David, \"David is a knight\". In a statement by Scarlett: \"David is a knight if and only if Scarlett is a knight\". James said, \"Liam is a knave and David is a knight.\" So who is a knight and who is a knave?", "names": ["Liam", "Sophia", "Aria", "David", "Scarlett", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Liam is a knight, Sophia is a knight, Aria is a knight, David is a knight, Scarlett is a knight, and James is a knave.", "solution_text_format": "(1) Liam is a knight\n(2) Sophia is a knight\n(3) Aria is a knight\n(4) David is a knight\n(5) Scarlett is a knight\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that If Scarlett is a knave then Aria is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that David is a knight if and only if Scarlett is a knight.", "Assume David is a knight. No contradiction is found in their claim that David is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Liam is a knight if and only if David is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Scarlett is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Liam is a knave and David is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Liam is a knave and David is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('lying', 2)), ('telling-truth', 4), ('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('telling-truth', 3), ('<=>', ('telling-truth', 3), ('telling-truth', 4)), ('and', ('lying', 0), ('telling-truth', 3)))", "index": 440}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Penelope, Joseph, Olivia, Henry, and Liam. Emma commented, \"Penelope is a knave\". Penelope noted, \"Olivia is a knave or Henry is a knight\". Joseph asserted: \"Henry is a knave and Penelope is a knave\". \"Olivia is a knight and Joseph is a knight,\" Olivia declared. As Henry put it, \"If Emma is a knave then Penelope is a knave\". Liam noted, \"If Olivia is a knight then Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Emma", "Penelope", "Joseph", "Olivia", "Henry", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true], "solution_text": "Emma is a knave, Penelope is a knight, Joseph is a knave, Olivia is a knave, Henry is a knave, and Liam is a knight.", "solution_text_format": "(1) Emma is a knave\n(2) Penelope is a knight\n(3) Joseph is a knave\n(4) Olivia is a knave\n(5) Henry is a knave\n(6) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Emma that Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Olivia is a knave or Henry is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Olivia is a knight and Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Henry is a knave and Penelope is a knave.", "Henry cannot be a knight, because this would contradict the false claim of Penelope that Olivia is a knave or Henry is a knight.", "Henry cannot be a knave, because this would contradict the false claim of their own that If Emma is a knave then Penelope is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Olivia that Olivia is a knight and Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of Penelope that Olivia is a knave or Henry is a knight.", "We have exhausted all possibilities for Olivia and Penelope, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Olivia is a knave or Henry is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Olivia is a knight and Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Penelope is a knave.", "Joseph cannot be a knave, because this would contradict the claim of Olivia that Olivia is a knight and Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Olivia is a knight and Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Penelope is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Henry is a knave and Penelope is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that If Emma is a knave then Penelope is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that If Emma is a knave then Penelope is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Olivia is a knight then Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('or', ('lying', 3), ('telling-truth', 4)), ('and', ('lying', 4), ('lying', 1)), ('and', ('telling-truth', 3), ('telling-truth', 2)), ('->', ('lying', 0), ('lying', 1)), ('->', ('telling-truth', 3), ('lying', 1)))", "index": 441}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Lucas, Riley, Ethan, Zoey, and Emily. Oliver commented, \"Ethan is not a knave\". \"If Riley is a knave then Riley is a knight\" - Lucas. According to Riley, \"Ethan is a knave if and only if Emily is a knight\". \"Zoey is a knight and Lucas is a knight,\" Ethan declared. In Zoey's words: \"If Zoey is a knight then Lucas is a knave\". According to Emily, \"Lucas is not a knave\". So who is a knight and who is a knave?", "names": ["Oliver", "Lucas", "Riley", "Ethan", "Zoey", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false], "solution_text": "Oliver is a knave, Lucas is a knave, Riley is a knave, Ethan is a knave, Zoey is a knight, and Emily is a knave.", "solution_text_format": "(1) Oliver is a knave\n(2) Lucas is a knave\n(3) Riley is a knave\n(4) Ethan is a knave\n(5) Zoey is a knight\n(6) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Zoey is a knight and Lucas is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Zoey is a knight then Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Zoey that If Zoey is a knight then Lucas is a knave.", "Lucas cannot be a knave, because this would contradict the claim of Ethan that Zoey is a knight and Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of Ethan that Zoey is a knight and Lucas is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Oliver that Ethan is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Ethan is not a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Oliver that Ethan is not a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Zoey is a knight and Lucas is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Zoey is a knight then Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Ethan that Zoey is a knight and Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Riley is a knave then Riley is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Lucas that If Riley is a knave then Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Riley that Ethan is a knave if and only if Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Lucas is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('->', ('lying', 2), ('telling-truth', 2)), ('<=>', ('lying', 3), ('telling-truth', 5)), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('->', ('telling-truth', 4), ('lying', 1)), ('not', ('lying', 1)))", "index": 442}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Samuel, Elizabeth, Liam, Matthew, and James. Aiden told you that If James is a knave then James is a knight. Samuel remarked, \"Elizabeth is a knight and Samuel is a knight\". Elizabeth commented, \"James is a knight or Matthew is a knight\". Liam expressed that If Matthew is a knave then Samuel is a knight. Matthew was heard saying, \"If Liam is a knight then James is a knave\". According to James, \"Samuel is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Samuel", "Elizabeth", "Liam", "Matthew", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Aiden is a knave, Samuel is a knight, Elizabeth is a knight, Liam is a knight, Matthew is a knight, and James is a knave.", "solution_text_format": "(1) Aiden is a knave\n(2) Samuel is a knight\n(3) Elizabeth is a knight\n(4) Liam is a knight\n(5) Matthew is a knight\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that If James is a knave then James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of James that Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Samuel is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that James is a knight or Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Liam is a knight then James is a knave.", "Liam cannot be a knight, because this would contradict the claim of Matthew that If Liam is a knight then James is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knave then Samuel is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that If Liam is a knight then James is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that If Matthew is a knave then Samuel is a knight.", "Liam cannot be a knave, because this would contradict the false claim of Matthew that If Liam is a knight then James is a knave.", "We have exhausted all possibilities for Liam and Matthew, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that James is a knight or Matthew is a knight.", "We have exhausted all possibilities for Elizabeth and Samuel, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the claim of Aiden that If James is a knave then James is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If James is a knave then James is a knight.", "James cannot be a knight, because this would contradict the false claim of Aiden that If James is a knave then James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Elizabeth is a knight and Samuel is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that James is a knight or Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Liam is a knight then James is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Matthew is a knave then Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 5)), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('telling-truth', 5), ('telling-truth', 4)), ('->', ('lying', 4), ('telling-truth', 1)), ('->', ('telling-truth', 3), ('lying', 5)), ('lying', 1))", "index": 443}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Sophia, Jack, Olivia, Alexander, and Harper. \"Alexander is a knave if and only if Harper is a knave\" - Avery. \"Harper is a knight and Alexander is a knave,\" Sophia declared. Jack commented, \"If Avery is a knave then Harper is a knight\". Olivia remarked, \"Harper is not a knave\". Alexander expressed that If Harper is a knave then Jack is a knight. Harper asserted: \"Jack is not a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Sophia", "Jack", "Olivia", "Alexander", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Avery is a knight, Sophia is a knave, Jack is a knight, Olivia is a knight, Alexander is a knight, and Harper is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Sophia is a knave\n(3) Jack is a knight\n(4) Olivia is a knight\n(5) Alexander is a knight\n(6) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Harper is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Harper is a knave then Jack is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Avery is a knave then Harper is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Alexander is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Harper is a knight and Alexander is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Harper is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('lying', 5)), ('and', ('telling-truth', 5), ('lying', 4)), ('->', ('lying', 0), ('telling-truth', 5)), ('not', ('lying', 5)), ('->', ('lying', 5), ('telling-truth', 2)), ('not', ('lying', 2)))", "index": 444}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Samuel, Henry, Jack, Logan, and Alexander. \"Alexander is a knight or Logan is a knave,\" Isabella declared. Samuel commented, \"Alexander is a knight\". Henry noted, \"Jack is a knave and Logan is a knave\". Jack asserted: \"Samuel is a knight\". Logan stated, \"If Samuel is a knave then Isabella is a knave\". \"Isabella is a knave if and only if Jack is a knight\" - Alexander. So who is a knight and who is a knave?", "names": ["Isabella", "Samuel", "Henry", "Jack", "Logan", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false], "solution_text": "Isabella is a knave, Samuel is a knave, Henry is a knave, Jack is a knave, Logan is a knight, and Alexander is a knave.", "solution_text_format": "(1) Isabella is a knave\n(2) Samuel is a knave\n(3) Henry is a knave\n(4) Jack is a knave\n(5) Logan is a knight\n(6) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Alexander is a knight or Logan is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of Alexander that Isabella is a knave if and only if Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the false claim of Jack that Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight.", "We have exhausted all possibilities for Samuel and Jack, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Alexander is a knight.", "Samuel cannot be a knave, because this would contradict the claim of Jack that Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of Alexander that Isabella is a knave if and only if Jack is a knight.", "We have exhausted all possibilities for Jack and Alexander, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Alexander is a knight or Logan is a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Isabella that Alexander is a knight or Logan is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Alexander that Isabella is a knave if and only if Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Alexander is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Samuel is a knave then Isabella is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Jack is a knave and Logan is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Jack is a knave and Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('lying', 4)), ('telling-truth', 5), ('and', ('lying', 3), ('lying', 4)), ('telling-truth', 1), ('->', ('lying', 1), ('lying', 0)), ('<=>', ('lying', 0), ('telling-truth', 3)))", "index": 445}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Daniel, Olivia, Aurora, Ella, and James. Sophia remarked, \"Daniel is a knight or Olivia is a knave\". Daniel noted, \"Aurora is a knight if and only if Sophia is a knave\". Olivia said, \"Ella is a knave or Aurora is a knave.\" According to Aurora, \"If Sophia is a knave then Ella is a knave\". \"Olivia is a knight if and only if Ella is a knight,\" Ella declared. According to James, \"Daniel is a knight\". So who is a knight and who is a knave?", "names": ["Sophia", "Daniel", "Olivia", "Aurora", "Ella", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "Sophia is a knave, Daniel is a knave, Olivia is a knight, Aurora is a knave, Ella is a knight, and James is a knave.", "solution_text_format": "(1) Sophia is a knave\n(2) Daniel is a knave\n(3) Olivia is a knight\n(4) Aurora is a knave\n(5) Ella is a knight\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Daniel is a knight or Olivia is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Sophia is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Daniel that Aurora is a knight if and only if Sophia is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knave then Ella is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Sophia is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Sophia is a knave then Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Ella is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Sophia that Daniel is a knight or Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the claim of Ella that Olivia is a knight if and only if Ella is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Ella is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Sophia that Daniel is a knight or Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Ella is a knave or Aurora is a knave.", "We have exhausted all possibilities for Olivia and Ella, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of Daniel that Aurora is a knight if and only if Sophia is a knave.", "We have exhausted all possibilities for Aurora and Daniel, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Daniel is a knight or Olivia is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Sophia that Daniel is a knight or Olivia is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Sophia is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Daniel that Aurora is a knight if and only if Sophia is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that If Sophia is a knave then Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Ella is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Ella is a knave or Aurora is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Daniel is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 2)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('or', ('lying', 4), ('lying', 3)), ('->', ('lying', 0), ('lying', 4)), ('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('telling-truth', 1))", "index": 446}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Harper, James, Sofia, Scarlett, and William. According to Amelia, \"Harper is not a knave\". According to Harper, \"James is not a knave\". James said that Scarlett is not a knave. \"William is a knight,\" Sofia claimed. Scarlett expressed that Sofia is not a knight. William was heard saying, \"Harper is a knight or Amelia is a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "Harper", "James", "Sofia", "Scarlett", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "Amelia is a knave, Harper is a knave, James is a knave, Sofia is a knight, Scarlett is a knave, and William is a knight.", "solution_text_format": "(1) Amelia is a knave\n(2) Harper is a knave\n(3) James is a knave\n(4) Sofia is a knight\n(5) Scarlett is a knave\n(6) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that James is not a knave.", "Assume James is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of Scarlett that Sofia is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that William is a knight.", "William cannot be a knight, because this would contradict the false claim of Sofia that William is a knight.", "William cannot be a knave, because this would contradict the false claim of their own that Harper is a knight or Amelia is a knave.", "We have exhausted all possibilities for William and Sofia, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of James that Scarlett is not a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the claim of Harper that James is not a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Amelia that Harper is not a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Amelia that Harper is not a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that James is not a knave.", "James cannot be a knight, because this would contradict the false claim of Harper that James is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of James that Scarlett is not a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Sofia is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Harper is a knight or Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('not', ('lying', 2)), ('not', ('lying', 4)), ('telling-truth', 5), ('not', ('telling-truth', 3)), ('or', ('telling-truth', 1), ('lying', 0)))", "index": 447}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Lucas, James, Jackson, Ava, and Aurora. Victoria told you that Jackson is a knight and Ava is a knave. Lucas asserted: \"Victoria is a knave if and only if Ava is a knight\". James asserted: \"If Ava is a knave then Lucas is a knave\". \"James is a knight and Victoria is a knight\" - Jackson. In Ava's words: \"James is a knight if and only if Jackson is a knight\". As Aurora put it, \"Ava is a knight if and only if James is a knave\". So who is a knight and who is a knave?", "names": ["Victoria", "Lucas", "James", "Jackson", "Ava", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true], "solution_text": "Victoria is a knave, Lucas is a knave, James is a knight, Jackson is a knave, Ava is a knave, and Aurora is a knight.", "solution_text_format": "(1) Victoria is a knave\n(2) Lucas is a knave\n(3) James is a knight\n(4) Jackson is a knave\n(5) Ava is a knave\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Jackson is a knight and Ava is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that James is a knight and Victoria is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Ava is a knave then Lucas is a knave.", "Ava cannot be a knight, because this would contradict the claim of Victoria that Jackson is a knight and Ava is a knave.", "Ava cannot be a knave, because this would contradict the false claim of their own that James is a knight if and only if Jackson is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the claim of Jackson that James is a knight and Victoria is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Victoria that Jackson is a knight and Ava is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Jackson is a knight and Ava is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that James is a knight and Victoria is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that James is a knight and Victoria is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Ava is a knave then Lucas is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that James is a knight if and only if Jackson is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that James is a knight if and only if Jackson is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Victoria is a knave if and only if Ava is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Ava is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Ava is a knight if and only if James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 4)), ('<=>', ('lying', 0), ('telling-truth', 4)), ('->', ('lying', 4), ('lying', 1)), ('and', ('telling-truth', 2), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('telling-truth', 4), ('lying', 2)))", "index": 448}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Liam, Sophia, Jackson, Joseph, and Charlotte. According to Samuel, \"Sophia is a knave or Liam is a knave\". Liam stated, \"If Charlotte is a knave then Joseph is a knave\". \"Charlotte is a knight and Samuel is a knave,\" Sophia declared. \"Sophia is not a knight,\" Jackson mentioned. Joseph told you that Jackson is a knight and Samuel is a knight. According to Charlotte, \"Jackson is a knight and Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Samuel", "Liam", "Sophia", "Jackson", "Joseph", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Samuel is a knight, Liam is a knight, Sophia is a knave, Jackson is a knight, Joseph is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Samuel is a knight\n(2) Liam is a knight\n(3) Sophia is a knave\n(4) Jackson is a knight\n(5) Joseph is a knight\n(6) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Sophia is a knave or Liam is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Samuel is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Charlotte is a knight and Samuel is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Jackson is a knight and Joseph is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Sophia is not a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Jackson is a knight and Samuel is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Charlotte is a knave then Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('lying', 1)), ('->', ('lying', 5), ('lying', 4)), ('and', ('telling-truth', 5), ('lying', 0)), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('and', ('telling-truth', 3), ('telling-truth', 4)))", "index": 449}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Luke, Liam, Abigail, Aurora, and Avery. Ethan said that Ethan is a knight if and only if Luke is a knave. Luke remarked, \"If Liam is a knave then Ethan is a knave\". \"If Ethan is a knight then Ethan is a knave,\" Liam declared. Abigail stated, \"Abigail is a knight or Ethan is a knight\". Aurora said, \"Luke is a knave.\" In Avery's words: \"Aurora is not a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Luke", "Liam", "Abigail", "Aurora", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false], "solution_text": "Ethan is a knight, Luke is a knave, Liam is a knave, Abigail is a knight, Aurora is a knight, and Avery is a knave.", "solution_text_format": "(1) Ethan is a knight\n(2) Luke is a knave\n(3) Liam is a knave\n(4) Abigail is a knight\n(5) Aurora is a knight\n(6) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Luke is a knave.", "Luke cannot be a knight, because this would contradict the claim of Ethan that Ethan is a knight if and only if Luke is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that If Liam is a knave then Ethan is a knave.", "Liam cannot be a knight, because this would contradict the false claim of Luke that If Liam is a knave then Ethan is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that If Ethan is a knight then Ethan is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Abigail is a knight or Ethan is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Luke is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Aurora is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Aurora is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('->', ('lying', 2), ('lying', 0)), ('->', ('telling-truth', 0), ('lying', 0)), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('lying', 1), ('not', ('telling-truth', 4)))", "index": 450}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Lucas, Emily, Ethan, Abigail, and Joseph. \"Lucas is not a knave\" - Lily. As Lucas put it, \"Emily is a knight or Abigail is a knight\". Emily said that Abigail is a knight or Abigail is a knave. In Ethan's words: \"If Lucas is a knave then Lily is a knight\". Abigail expressed that Ethan is a knave and Joseph is a knight. Joseph noted, \"Lucas is a knight if and only if Ethan is a knave\". So who is a knight and who is a knave?", "names": ["Lily", "Lucas", "Emily", "Ethan", "Abigail", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Lily is a knight, Lucas is a knight, Emily is a knight, Ethan is a knight, Abigail is a knave, and Joseph is a knave.", "solution_text_format": "(1) Lily is a knight\n(2) Lucas is a knight\n(3) Emily is a knight\n(4) Ethan is a knight\n(5) Abigail is a knave\n(6) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Emily is a knight or Abigail is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Abigail is a knight or Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Ethan is a knave and Joseph is a knight.", "Ethan cannot be a knight, because this would contradict the claim of Abigail that Ethan is a knave and Joseph is a knight.", "Ethan cannot be a knave, because this would contradict the false claim of their own that If Lucas is a knave then Lily is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Ethan is a knave and Joseph is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Lucas is a knave then Lily is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Lucas is a knight if and only if Ethan is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('or', ('telling-truth', 2), ('telling-truth', 4)), ('or', ('telling-truth', 4), ('lying', 4)), ('->', ('lying', 1), ('telling-truth', 0)), ('and', ('lying', 3), ('telling-truth', 5)), ('<=>', ('telling-truth', 1), ('lying', 3)))", "index": 451}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Luke, Aria, Ella, Alexander, and David. Charlotte said, \"Ella is a knave if and only if Aria is a knight.\" \"If Luke is a knight then Aria is a knave,\" Luke declared. \"Charlotte is not a knight,\" Aria mentioned. According to Ella, \"David is a knight or Aria is a knave\". \"Luke is not a knave\" - Alexander. \"Charlotte is not a knave,\" David mentioned. So who is a knight and who is a knave?", "names": ["Charlotte", "Luke", "Aria", "Ella", "Alexander", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Charlotte is a knight, Luke is a knight, Aria is a knave, Ella is a knight, Alexander is a knight, and David is a knight.", "solution_text_format": "(1) Charlotte is a knight\n(2) Luke is a knight\n(3) Aria is a knave\n(4) Ella is a knight\n(5) Alexander is a knight\n(6) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Ella is a knave if and only if Aria is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that David is a knight or Aria is a knave.", "Assume David is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Aria cannot be a knight, because this would contradict the claim of Charlotte that Ella is a knave if and only if Aria is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Luke is a knight then Aria is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Luke is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('lying', 2)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 5), ('lying', 2)), ('not', ('lying', 1)), ('not', ('lying', 0)))", "index": 452}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Zoey, Noah, Sofia, Riley, and Grace. In Sebastian's words: \"Riley is a knave\". Zoey expressed that Sofia is not a knave. Noah told you that Sofia is a knave. Sofia commented, \"Zoey is a knave or Noah is a knave\". According to Riley, \"Sebastian is a knave or Grace is a knave\". Grace said, \"Sebastian is a knight and Sofia is a knave.\" So who is a knight and who is a knave?", "names": ["Sebastian", "Zoey", "Noah", "Sofia", "Riley", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Sebastian is a knave, Zoey is a knight, Noah is a knave, Sofia is a knight, Riley is a knight, and Grace is a knave.", "solution_text_format": "(1) Sebastian is a knave\n(2) Zoey is a knight\n(3) Noah is a knave\n(4) Sofia is a knight\n(5) Riley is a knight\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of Sebastian that Riley is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Sebastian is a knave or Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Sebastian is a knight and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Grace that Sebastian is a knight and Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Zoey is a knave or Noah is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Sofia is not a knave.", "Zoey cannot be a knave, because this would contradict the false claim of Sofia that Zoey is a knave or Noah is a knave.", "We have exhausted all possibilities for Zoey and Sofia, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the false claim of Riley that Sebastian is a knave or Grace is a knave.", "We have exhausted all possibilities for Grace and Riley, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Sebastian is a knave or Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Sofia is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Sebastian is a knight and Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Zoey is a knave or Noah is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Sofia is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('not', ('lying', 3)), ('lying', 3), ('or', ('lying', 1), ('lying', 2)), ('or', ('lying', 0), ('lying', 5)), ('and', ('telling-truth', 0), ('lying', 3)))", "index": 453}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Matthew, Ethan, Amelia, Henry, and Harper. Avery asserted: \"Amelia is a knave if and only if Henry is a knave\". \"Ethan is a knight or Avery is a knave,\" Matthew mentioned. \"Henry is a knave if and only if Amelia is a knave,\" Ethan claimed. Amelia commented, \"Ethan is a knave if and only if Matthew is a knave\". \"Ethan is a knight and Amelia is a knight,\" Henry declared. Harper told you that Amelia is a knight. So who is a knight and who is a knave?", "names": ["Avery", "Matthew", "Ethan", "Amelia", "Henry", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Avery is a knight, Matthew is a knight, Ethan is a knight, Amelia is a knight, Henry is a knight, and Harper is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Matthew is a knight\n(3) Ethan is a knight\n(4) Amelia is a knight\n(5) Henry is a knight\n(6) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Henry is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Matthew is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Henry is a knave if and only if Amelia is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Ethan is a knight and Amelia is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Ethan is a knight or Avery is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 4)), ('or', ('telling-truth', 2), ('lying', 0)), ('<=>', ('lying', 4), ('lying', 3)), ('<=>', ('lying', 2), ('lying', 1)), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('telling-truth', 3))", "index": 454}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Oliver, Logan, Jackson, Sebastian, and Luke. Owen expressed that Jackson is a knave. \"Owen is a knave or Logan is a knight\" - Oliver. \"If Oliver is a knight then Owen is a knave,\" Logan claimed. \"If Luke is a knight then Oliver is a knave,\" Jackson declared. Sebastian commented, \"If Owen is a knave then Luke is a knave\". \"Jackson is not a knight,\" Luke claimed. So who is a knight and who is a knave?", "names": ["Owen", "Oliver", "Logan", "Jackson", "Sebastian", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Owen is a knave, Oliver is a knight, Logan is a knight, Jackson is a knight, Sebastian is a knight, and Luke is a knave.", "solution_text_format": "(1) Owen is a knave\n(2) Oliver is a knight\n(3) Logan is a knight\n(4) Jackson is a knight\n(5) Sebastian is a knight\n(6) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Owen that Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Luke is a knight then Oliver is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Owen is a knave or Logan is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that If Oliver is a knight then Owen is a knave.", "Logan cannot be a knave, because this would contradict the claim of Oliver that Owen is a knave or Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the false claim of Jackson that If Luke is a knight then Oliver is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the false claim of Jackson that If Luke is a knight then Oliver is a knave.", "We have exhausted all possibilities for Luke and Jackson, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Luke is a knight then Oliver is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Jackson is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Owen is a knave or Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Oliver is a knight then Owen is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Owen is a knave then Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('or', ('lying', 0), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('lying', 0)), ('->', ('telling-truth', 5), ('lying', 1)), ('->', ('lying', 0), ('lying', 5)), ('not', ('telling-truth', 3)))", "index": 455}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Liam, Lily, Sophia, Mia, and Jack. In a statement by Chloe: \"Jack is a knight and Liam is a knave\". Liam said, \"Sophia is a knave and Chloe is a knight.\" Lily was heard saying, \"Chloe is a knight\". Sophia expressed that If Chloe is a knave then Liam is a knave. \"Liam is a knave or Lily is a knight\" - Mia. Jack expressed that Chloe is a knight if and only if Lily is a knight. So who is a knight and who is a knave?", "names": ["Chloe", "Liam", "Lily", "Sophia", "Mia", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Chloe is a knight, Liam is a knave, Lily is a knight, Sophia is a knight, Mia is a knight, and Jack is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Liam is a knave\n(3) Lily is a knight\n(4) Sophia is a knight\n(5) Mia is a knight\n(6) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Jack is a knight and Liam is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Chloe is a knight.", "Liam cannot be a knight, because this would contradict the claim of Chloe that Jack is a knight and Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Sophia is a knave and Chloe is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Chloe is a knave then Liam is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Liam is a knave or Lily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 1)), ('and', ('lying', 3), ('telling-truth', 0)), ('telling-truth', 0), ('->', ('lying', 0), ('lying', 1)), ('or', ('lying', 1), ('telling-truth', 2)), ('<=>', ('telling-truth', 0), ('telling-truth', 2)))", "index": 456}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Daniel, Jack, Aiden, Sofia, and Elizabeth. Chloe remarked, \"Elizabeth is not a knight\". In a statement by Daniel: \"Jack is a knave\". Jack was heard saying, \"If Sofia is a knave then Chloe is a knave\". In a statement by Aiden: \"Elizabeth is a knight if and only if Sofia is a knave\". \"If Elizabeth is a knight then Chloe is a knight,\" Sofia mentioned. Elizabeth noted, \"Jack is a knight or Sofia is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Daniel", "Jack", "Aiden", "Sofia", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Chloe is a knave, Daniel is a knave, Jack is a knight, Aiden is a knight, Sofia is a knave, and Elizabeth is a knight.", "solution_text_format": "(1) Chloe is a knave\n(2) Daniel is a knave\n(3) Jack is a knight\n(4) Aiden is a knight\n(5) Sofia is a knave\n(6) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Chloe that Elizabeth is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Jack is a knight or Sofia is a knave.", "Jack cannot be a knight, because this would contradict the false claim of Elizabeth that Jack is a knight or Sofia is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that If Sofia is a knave then Chloe is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Jack that If Sofia is a knave then Chloe is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Elizabeth is a knight then Chloe is a knight.", "We have exhausted all possibilities for Sofia, Jack, and Elizabeth, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Elizabeth is not a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Jack is a knight or Sofia is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that If Sofia is a knave then Chloe is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that If Elizabeth is a knight then Chloe is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Elizabeth is a knight then Chloe is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Jack is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Jack is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('lying', 2), ('->', ('lying', 4), ('lying', 0)), ('<=>', ('telling-truth', 5), ('lying', 4)), ('->', ('telling-truth', 5), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('lying', 4)))", "index": 457}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Evelyn, Zoey, Chloe, Logan, and Michael. As Olivia put it, \"Logan is a knave\". \"Olivia is a knave and Logan is a knight,\" Evelyn mentioned. Zoey said that If Logan is a knave then Olivia is a knave. In a statement by Chloe: \"If Evelyn is a knave then Logan is a knight\". In a statement by Logan: \"If Chloe is a knave then Zoey is a knave\". Michael stated, \"Chloe is a knave if and only if Zoey is a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Evelyn", "Zoey", "Chloe", "Logan", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Olivia is a knave, Evelyn is a knight, Zoey is a knight, Chloe is a knight, Logan is a knight, and Michael is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) Evelyn is a knight\n(3) Zoey is a knight\n(4) Chloe is a knight\n(5) Logan is a knight\n(6) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Olivia that Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that If Chloe is a knave then Zoey is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Logan that If Chloe is a knave then Zoey is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that If Evelyn is a knave then Logan is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Logan is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Olivia is a knave and Logan is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that If Logan is a knave then Olivia is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of Logan that If Chloe is a knave then Zoey is a knave.", "We have exhausted all possibilities for Zoey, Evelyn, Chloe, and Logan, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that If Chloe is a knave then Zoey is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Evelyn is a knave then Logan is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Olivia is a knave and Logan is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Logan is a knave then Olivia is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('and', ('lying', 0), ('telling-truth', 4)), ('->', ('lying', 4), ('lying', 0)), ('->', ('lying', 1), ('telling-truth', 4)), ('->', ('lying', 3), ('lying', 2)), ('<=>', ('lying', 3), ('lying', 2)))", "index": 458}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Victoria, Olivia, Lily, Scarlett, and Daniel. Evelyn was heard saying, \"Lily is a knave and Olivia is a knave\". Victoria was heard saying, \"Lily is a knight and Evelyn is a knight\". Olivia said, \"Evelyn is a knight or Scarlett is a knight.\" Lily remarked, \"If Daniel is a knight then Scarlett is a knight\". As Scarlett put it, \"Victoria is a knight if and only if Daniel is a knight\". Daniel said, \"If Evelyn is a knave then Scarlett is a knave.\" So who is a knight and who is a knave?", "names": ["Evelyn", "Victoria", "Olivia", "Lily", "Scarlett", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Evelyn is a knave, Victoria is a knave, Olivia is a knight, Lily is a knight, Scarlett is a knight, and Daniel is a knave.", "solution_text_format": "(1) Evelyn is a knave\n(2) Victoria is a knave\n(3) Olivia is a knight\n(4) Lily is a knight\n(5) Scarlett is a knight\n(6) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Lily is a knave and Olivia is a knave.", "Lily cannot be a knight, because this would contradict the claim of Evelyn that Lily is a knave and Olivia is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that If Daniel is a knight then Scarlett is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Evelyn is a knave then Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Lily that If Daniel is a knight then Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Daniel is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Evelyn is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Lily is a knight and Evelyn is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Evelyn that Lily is a knave and Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Evelyn is a knight or Scarlett is a knight.", "We have exhausted all possibilities for Olivia, Victoria, and Scarlett, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of Lily that If Daniel is a knight then Scarlett is a knight.", "We have exhausted all possibilities for Daniel and Lily, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Lily is a knave and Olivia is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Daniel is a knight then Scarlett is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Evelyn is a knave then Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Daniel that If Evelyn is a knave then Scarlett is a knave.", "Scarlett cannot be a knave, because this would contradict the claim of Lily that If Daniel is a knight then Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Evelyn is a knave then Scarlett is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Daniel is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Evelyn is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Lily is a knight and Evelyn is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Evelyn is a knight or Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 2)), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 4)), ('->', ('telling-truth', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('telling-truth', 5)), ('->', ('lying', 0), ('lying', 4)))", "index": 459}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Samuel, Logan, Owen, Mason, and Riley. William stated, \"Owen is a knave and Mason is a knight\". \"William is not a knight\" - Samuel. Logan said, \"Mason is a knave or Riley is a knight.\" Owen expressed that Logan is not a knave. Mason stated, \"If Logan is a knave then William is a knave\". \"Riley is a knight,\" Riley claimed. So who is a knight and who is a knave?", "names": ["William", "Samuel", "Logan", "Owen", "Mason", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "William is a knave, Samuel is a knight, Logan is a knight, Owen is a knight, Mason is a knight, and Riley is a knight.", "solution_text_format": "(1) William is a knave\n(2) Samuel is a knight\n(3) Logan is a knight\n(4) Owen is a knight\n(5) Mason is a knight\n(6) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Owen is a knave and Mason is a knight.", "Owen cannot be a knight, because this would contradict the claim of William that Owen is a knave and Mason is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Logan is not a knave.", "Logan cannot be a knight, because this would contradict the false claim of Owen that Logan is not a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Mason is a knave or Riley is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that If Logan is a knave then William is a knave.", "Mason cannot be a knave, because this would contradict the claim of William that Owen is a knave and Mason is a knight.", "We have exhausted all possibilities for Mason, Logan, and Owen, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Owen is a knave and Mason is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Logan is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Mason is a knave or Riley is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Logan is a knave then William is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that William is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 4)), ('not', ('telling-truth', 0)), ('or', ('lying', 4), ('telling-truth', 5)), ('not', ('lying', 2)), ('->', ('lying', 2), ('lying', 0)), ('telling-truth', 5))", "index": 460}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Aiden, Sofia, Ethan, Harper, and Logan. Owen noted, \"Harper is a knave if and only if Ethan is a knight\". As Aiden put it, \"If Ethan is a knave then Logan is a knave\". Sofia told you that Harper is a knave if and only if Ethan is a knight. \"Logan is a knight or Sofia is a knight,\" Ethan claimed. Harper commented, \"Ethan is a knave if and only if Harper is a knight\". Logan commented, \"Ethan is a knight if and only if Aiden is a knight\". So who is a knight and who is a knave?", "names": ["Owen", "Aiden", "Sofia", "Ethan", "Harper", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false], "solution_text": "Owen is a knave, Aiden is a knight, Sofia is a knave, Ethan is a knave, Harper is a knave, and Logan is a knave.", "solution_text_format": "(1) Owen is a knave\n(2) Aiden is a knight\n(3) Sofia is a knave\n(4) Ethan is a knave\n(5) Harper is a knave\n(6) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Harper is a knave if and only if Ethan is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Harper is a knight.", "Ethan cannot be a knight, because this would contradict the claim of Owen that Harper is a knave if and only if Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Logan is a knight or Sofia is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Ethan that Logan is a knight or Sofia is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Ethan is a knave then Logan is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Ethan that Logan is a knight or Sofia is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Harper is a knave if and only if Ethan is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that If Ethan is a knave then Logan is a knave.", "We have exhausted all possibilities for Aiden, Logan, and Ethan, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Harper is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Harper that Ethan is a knave if and only if Harper is a knight.", "Ethan cannot be a knave, because this would contradict the claim of Owen that Harper is a knave if and only if Ethan is a knight.", "We have exhausted all possibilities for Ethan and Harper, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Ethan is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Harper is a knight.", "Ethan cannot be a knight, because this would contradict the claim of Harper that Ethan is a knave if and only if Harper is a knight.", "Ethan cannot be a knave, because this would contradict the false claim of Owen that Harper is a knave if and only if Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Harper is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Owen that Harper is a knave if and only if Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Logan is a knight or Sofia is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Ethan that Logan is a knight or Sofia is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Ethan is a knave then Logan is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Harper is a knave if and only if Ethan is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('telling-truth', 3)), ('->', ('lying', 3), ('lying', 5)), ('<=>', ('lying', 4), ('telling-truth', 3)), ('or', ('telling-truth', 5), ('telling-truth', 2)), ('<=>', ('lying', 3), ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('telling-truth', 1)))", "index": 461}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, James, Alexander, Aiden, Joseph, and Jack. Aria was heard saying, \"James is a knight or Joseph is a knight\". \"Aria is not a knight,\" James claimed. Alexander said that James is a knight and James is a knave. \"Aria is a knave if and only if James is a knave,\" Aiden claimed. \"Aria is a knight,\" Joseph mentioned. In Jack's words: \"Aria is a knight if and only if Alexander is a knave\". So who is a knight and who is a knave?", "names": ["Aria", "James", "Alexander", "Aiden", "Joseph", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true], "solution_text": "Aria is a knight, James is a knave, Alexander is a knave, Aiden is a knave, Joseph is a knight, and Jack is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) James is a knave\n(3) Alexander is a knave\n(4) Aiden is a knave\n(5) Joseph is a knight\n(6) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that James is a knight or Joseph is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Aria is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Aria is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that James is a knight and James is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that James is a knight and James is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Aria is a knave if and only if James is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aria is a knave if and only if James is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Aria is a knight if and only if Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 4)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 1), ('lying', 1)), ('<=>', ('lying', 0), ('lying', 1)), ('telling-truth', 0), ('<=>', ('telling-truth', 0), ('lying', 2)))", "index": 462}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Owen, Chloe, Scarlett, Henry, and Aiden. \"Scarlett is a knave or Henry is a knave,\" Mason mentioned. Owen asserted: \"Chloe is a knight and Mason is a knight\". In a statement by Chloe: \"Henry is a knight and Owen is a knight\". Scarlett asserted: \"Owen is a knight or Mason is a knight\". Henry said, \"Aiden is a knight.\" In a statement by Aiden: \"If Owen is a knave then Scarlett is a knave\". So who is a knight and who is a knave?", "names": ["Mason", "Owen", "Chloe", "Scarlett", "Henry", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false], "solution_text": "Mason is a knight, Owen is a knave, Chloe is a knave, Scarlett is a knight, Henry is a knave, and Aiden is a knave.", "solution_text_format": "(1) Mason is a knight\n(2) Owen is a knave\n(3) Chloe is a knave\n(4) Scarlett is a knight\n(5) Henry is a knave\n(6) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Scarlett is a knave or Henry is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Owen is a knight or Mason is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Chloe is a knight and Mason is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Henry is a knight and Owen is a knight.", "Henry cannot be a knight, because this would contradict the claim of Mason that Scarlett is a knave or Henry is a knave.", "Henry cannot be a knave, because this would contradict the claim of Chloe that Henry is a knight and Owen is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Owen that Chloe is a knight and Mason is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Chloe is a knight and Mason is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Owen that Chloe is a knight and Mason is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Henry is a knight and Owen is a knight.", "Henry cannot be a knight, because this would contradict the claim of Mason that Scarlett is a knave or Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Henry that Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Owen is a knave then Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 4)), ('and', ('telling-truth', 2), ('telling-truth', 0)), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('telling-truth', 5), ('->', ('lying', 1), ('lying', 3)))", "index": 463}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Mia, Matthew, Victoria, Sebastian, and Noah. As James put it, \"James is a knight if and only if Victoria is a knight\". Mia asserted: \"If James is a knight then Sebastian is a knave\". Matthew asserted: \"If Matthew is a knight then James is a knave\". In a statement by Victoria: \"James is a knave if and only if Sebastian is a knave\". Sebastian stated, \"James is a knight\". As Noah put it, \"Victoria is a knight\". So who is a knight and who is a knave?", "names": ["James", "Mia", "Matthew", "Victoria", "Sebastian", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "James is a knave, Mia is a knight, Matthew is a knight, Victoria is a knight, Sebastian is a knave, and Noah is a knight.", "solution_text_format": "(1) James is a knave\n(2) Mia is a knight\n(3) Matthew is a knight\n(4) Victoria is a knight\n(5) Sebastian is a knave\n(6) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that James is a knight if and only if Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that James is a knave if and only if Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that James is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that If James is a knight then Sebastian is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that If James is a knight then Sebastian is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that If Matthew is a knight then James is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knight then James is a knave.", "We have exhausted all possibilities for Matthew and Mia, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Victoria that James is a knave if and only if Sebastian is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the claim of James that James is a knight if and only if Victoria is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that James is a knight if and only if Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that James is a knave if and only if Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Victoria that James is a knave if and only if Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that James is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If James is a knight then Sebastian is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Matthew is a knight then James is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('->', ('telling-truth', 0), ('lying', 4)), ('->', ('telling-truth', 2), ('lying', 0)), ('<=>', ('lying', 0), ('lying', 4)), ('telling-truth', 0), ('telling-truth', 3))", "index": 464}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Lucas, Logan, William, Mason, and Matthew. As Mia put it, \"William is a knave and Mia is a knight\". \"Mia is a knave\" - Lucas. Logan asserted: \"Lucas is not a knight\". William was heard saying, \"Matthew is a knight and Lucas is a knave\". Mason commented, \"Logan is a knave\". Matthew remarked, \"Logan is a knave if and only if Lucas is a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Lucas", "Logan", "William", "Mason", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true], "solution_text": "Mia is a knave, Lucas is a knight, Logan is a knave, William is a knave, Mason is a knight, and Matthew is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Lucas is a knight\n(3) Logan is a knave\n(4) William is a knave\n(5) Mason is a knight\n(6) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that William is a knave and Mia is a knight.", "William cannot be a knight, because this would contradict the claim of Mia that William is a knave and Mia is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Matthew is a knight and Lucas is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Logan is a knave if and only if Lucas is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Lucas is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Mia is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of William that Matthew is a knight and Lucas is a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Mia is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of Logan that Lucas is not a knight.", "We have exhausted all possibilities for Lucas and Logan, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Lucas is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Lucas is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Mia is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of Matthew that Logan is a knave if and only if Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Mia is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of Logan that Lucas is not a knight.", "We have exhausted all possibilities for Lucas, Logan, Matthew, and William, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that William is a knave and Mia is a knight.", "Assume William is a knight. No contradiction is found in their claim that Matthew is a knight and Lucas is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Logan is a knave if and only if Lucas is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Lucas is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of Logan that Lucas is not a knight.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Mia is a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of William that Matthew is a knight and Lucas is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Mia is a knave.", "We have exhausted all possibilities for Lucas and Logan, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of William that Matthew is a knight and Lucas is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Matthew is a knight and Lucas is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Logan is a knave if and only if Lucas is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Lucas is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of Logan that Lucas is not a knight.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Mia is a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Mia is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 0)), ('lying', 0), ('not', ('telling-truth', 1)), ('and', ('telling-truth', 5), ('lying', 1)), ('lying', 2), ('<=>', ('lying', 2), ('telling-truth', 1)))", "index": 465}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Aiden, Emma, Matthew, Logan, and Ava. In a statement by Emily: \"Matthew is a knave if and only if Ava is a knave\". Aiden asserted: \"Logan is a knave if and only if Ava is a knight\". Emma told you that Emily is a knight and Logan is a knight. As Matthew put it, \"Ava is a knave if and only if Matthew is a knight\". Logan asserted: \"Logan is a knight and Matthew is a knave\". \"Logan is a knave or Emma is a knave,\" Ava declared. So who is a knight and who is a knave?", "names": ["Emily", "Aiden", "Emma", "Matthew", "Logan", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Emily is a knight, Aiden is a knight, Emma is a knight, Matthew is a knave, Logan is a knight, and Ava is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Aiden is a knight\n(3) Emma is a knight\n(4) Matthew is a knave\n(5) Logan is a knight\n(6) Ava is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Ava is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Ava is a knave if and only if Matthew is a knight.", "Ava cannot be a knight, because this would contradict the claim of Matthew that Ava is a knave if and only if Matthew is a knight.", "Ava cannot be a knave, because this would contradict the claim of Emily that Matthew is a knave if and only if Ava is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Matthew is a knight.", "Ava cannot be a knight, because this would contradict the claim of Emily that Matthew is a knave if and only if Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Logan is a knave or Emma is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight and Matthew is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Emily is a knight and Logan is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Logan is a knave if and only if Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 5)), ('<=>', ('lying', 4), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('telling-truth', 4)), ('<=>', ('lying', 5), ('telling-truth', 3)), ('and', ('telling-truth', 4), ('lying', 3)), ('or', ('lying', 4), ('lying', 2)))", "index": 466}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Riley, Grace, Evelyn, Matthew, and Ava. Amelia told you that Matthew is not a knave. According to Riley, \"If Matthew is a knight then Ava is a knave\". Grace remarked, \"If Ava is a knight then Riley is a knave\". Evelyn said that Matthew is a knight or Riley is a knight. Matthew told you that Grace is not a knave. \"Amelia is not a knave\" - Ava. So who is a knight and who is a knave?", "names": ["Amelia", "Riley", "Grace", "Evelyn", "Matthew", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Amelia is a knight, Riley is a knave, Grace is a knight, Evelyn is a knight, Matthew is a knight, and Ava is a knight.", "solution_text_format": "(1) Amelia is a knight\n(2) Riley is a knave\n(3) Grace is a knight\n(4) Evelyn is a knight\n(5) Matthew is a knight\n(6) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Grace is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Ava is a knight then Riley is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that If Matthew is a knight then Ava is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that If Matthew is a knight then Ava is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Matthew is a knight or Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('->', ('telling-truth', 4), ('lying', 5)), ('->', ('telling-truth', 5), ('lying', 1)), ('or', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('lying', 2)), ('not', ('lying', 0)))", "index": 467}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Olivia, Joseph, William, Benjamin, and Sebastian. According to Ethan, \"William is a knight and Olivia is a knave\". \"Joseph is a knave or William is a knave,\" Olivia declared. According to Joseph, \"Ethan is a knight\". William expressed that Joseph is a knight if and only if Sebastian is a knight. Benjamin commented, \"Joseph is a knight\". Sebastian commented, \"Benjamin is not a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Olivia", "Joseph", "William", "Benjamin", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true], "solution_text": "Ethan is a knave, Olivia is a knight, Joseph is a knave, William is a knave, Benjamin is a knave, and Sebastian is a knight.", "solution_text_format": "(1) Ethan is a knave\n(2) Olivia is a knight\n(3) Joseph is a knave\n(4) William is a knave\n(5) Benjamin is a knave\n(6) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that William is a knight and Olivia is a knave.", "Assume William is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Sebastian is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Sebastian that Benjamin is not a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of William that Joseph is a knight if and only if Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Ethan that William is a knight and Olivia is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that William is a knight and Olivia is a knave.", "Assume William is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Sebastian is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Ethan is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of William that Joseph is a knight if and only if Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Joseph is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of Sebastian that Benjamin is not a knight.", "We have exhausted all possibilities for Benjamin, Sebastian, and Joseph, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Sebastian is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Ethan is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Joseph is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Joseph is a knave or William is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 1)), ('or', ('lying', 2), ('lying', 3)), ('telling-truth', 0), ('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('telling-truth', 2), ('not', ('telling-truth', 4)))", "index": 468}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Zoey, Lily, Evelyn, Aria, and Aiden. Avery commented, \"Zoey is a knight if and only if Aiden is a knave\". Zoey commented, \"Aria is not a knave\". As Lily put it, \"Zoey is a knight and Aiden is a knight\". Evelyn said that Aria is a knave or Lily is a knight. Aria asserted: \"Evelyn is a knight or Avery is a knave\". \"Avery is a knave,\" Aiden declared. So who is a knight and who is a knave?", "names": ["Avery", "Zoey", "Lily", "Evelyn", "Aria", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Avery is a knave, Zoey is a knight, Lily is a knight, Evelyn is a knight, Aria is a knight, and Aiden is a knight.", "solution_text_format": "(1) Avery is a knave\n(2) Zoey is a knight\n(3) Lily is a knight\n(4) Evelyn is a knight\n(5) Aria is a knight\n(6) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Aiden is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Evelyn is a knight or Avery is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Aria is a knave or Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Zoey is a knight and Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Avery that Zoey is a knight if and only if Aiden is a knave.", "Aiden cannot be a knave, because this would contradict the claim of Lily that Zoey is a knight and Aiden is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Evelyn that Aria is a knave or Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Aria that Evelyn is a knight or Avery is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Zoey that Aria is not a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the false claim of Zoey that Aria is not a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Evelyn is a knight or Avery is a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of Aria that Evelyn is a knight or Avery is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Aria is a knave or Lily is a knight.", "We have exhausted all possibilities for Evelyn, Aria, and Zoey, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Aiden is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Evelyn is a knight or Avery is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Aria is a knave or Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Zoey is a knight and Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 5)), ('not', ('lying', 4)), ('and', ('telling-truth', 1), ('telling-truth', 5)), ('or', ('lying', 4), ('telling-truth', 2)), ('or', ('telling-truth', 3), ('lying', 0)), ('lying', 0))", "index": 469}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, Emily, David, Elizabeth, Emma, and Aria. \"If Penelope is a knight then Emma is a knight,\" Penelope declared. \"Emma is a knave if and only if Aria is a knave,\" Emily declared. In David's words: \"Emma is a knight and Penelope is a knight\". Elizabeth was heard saying, \"Aria is a knave if and only if David is a knight\". \"Elizabeth is a knight and David is a knight,\" Emma declared. \"David is not a knight\" - Aria. So who is a knight and who is a knave?", "names": ["Penelope", "Emily", "David", "Elizabeth", "Emma", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Penelope is a knight, Emily is a knave, David is a knight, Elizabeth is a knight, Emma is a knight, and Aria is a knave.", "solution_text_format": "(1) Penelope is a knight\n(2) Emily is a knave\n(3) David is a knight\n(4) Elizabeth is a knight\n(5) Emma is a knight\n(6) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that If Penelope is a knight then Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Elizabeth is a knight and David is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Aria is a knave if and only if David is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that David is not a knight.", "David cannot be a knight, because this would contradict the claim of Elizabeth that Aria is a knave if and only if David is a knight.", "David cannot be a knave, because this would contradict the false claim of their own that Emma is a knight and Penelope is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that David is not a knight.", "Assume David is a knight. No contradiction is found in their claim that Emma is a knight and Penelope is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Emma is a knave if and only if Aria is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Aria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 4)), ('<=>', ('lying', 4), ('lying', 5)), ('and', ('telling-truth', 4), ('telling-truth', 0)), ('<=>', ('lying', 5), ('telling-truth', 2)), ('and', ('telling-truth', 3), ('telling-truth', 2)), ('not', ('telling-truth', 2)))", "index": 470}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Zoey, Aria, Isabella, Matthew, and Alexander. Jacob was heard saying, \"Isabella is not a knave\". In Zoey's words: \"Isabella is a knave if and only if Jacob is a knave\". Aria said, \"Matthew is a knight or Isabella is a knave.\" In Isabella's words: \"Alexander is a knave and Zoey is a knave\". Matthew was heard saying, \"Zoey is a knight and Jacob is a knight\". Alexander was heard saying, \"Isabella is a knight and Aria is a knight\". So who is a knight and who is a knave?", "names": ["Jacob", "Zoey", "Aria", "Isabella", "Matthew", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Jacob is a knave, Zoey is a knight, Aria is a knight, Isabella is a knave, Matthew is a knave, and Alexander is a knave.", "solution_text_format": "(1) Jacob is a knave\n(2) Zoey is a knight\n(3) Aria is a knight\n(4) Isabella is a knave\n(5) Matthew is a knave\n(6) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Alexander is a knave and Zoey is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Isabella that Alexander is a knave and Zoey is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Isabella is a knight and Aria is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Alexander that Isabella is a knight and Aria is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Matthew is a knight or Isabella is a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Aria that Matthew is a knight or Isabella is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Zoey is a knight and Jacob is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Isabella that Alexander is a knave and Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Isabella is a knave if and only if Jacob is a knave.", "We have exhausted all possibilities for Zoey, Matthew, Aria, and Alexander, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Jacob that Isabella is not a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Isabella is not a knave.", "Isabella cannot be a knight, because this would contradict the false claim of Jacob that Isabella is not a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Alexander is a knave and Zoey is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Isabella is a knight and Aria is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Isabella is a knight and Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Matthew is a knight or Isabella is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Zoey is a knight and Jacob is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Zoey is a knight and Jacob is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('<=>', ('lying', 3), ('lying', 0)), ('or', ('telling-truth', 4), ('lying', 3)), ('and', ('lying', 5), ('lying', 1)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('telling-truth', 3), ('telling-truth', 2)))", "index": 471}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Charlotte, Luke, Riley, Scarlett, and Emma. Evelyn said that If Scarlett is a knight then Emma is a knight. Charlotte remarked, \"Luke is a knave and Riley is a knight\". As Luke put it, \"Luke is a knight or Evelyn is a knight\". In a statement by Riley: \"Scarlett is a knave if and only if Emma is a knight\". Scarlett told you that Scarlett is a knight if and only if Charlotte is a knight. Emma noted, \"Scarlett is a knight and Charlotte is a knave\". So who is a knight and who is a knave?", "names": ["Evelyn", "Charlotte", "Luke", "Riley", "Scarlett", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Evelyn is a knave, Charlotte is a knight, Luke is a knave, Riley is a knight, Scarlett is a knight, and Emma is a knave.", "solution_text_format": "(1) Evelyn is a knave\n(2) Charlotte is a knight\n(3) Luke is a knave\n(4) Riley is a knight\n(5) Scarlett is a knight\n(6) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that If Scarlett is a knight then Emma is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Luke is a knave and Riley is a knight.", "Luke cannot be a knight, because this would contradict the claim of Charlotte that Luke is a knave and Riley is a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that Luke is a knight or Evelyn is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the claim of Scarlett that Scarlett is a knight if and only if Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Luke is a knave and Riley is a knight.", "Luke cannot be a knight, because this would contradict the claim of Charlotte that Luke is a knave and Riley is a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that Luke is a knight or Evelyn is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Charlotte.", "Charlotte cannot be a knave, because this would contradict the false claim of Scarlett that Scarlett is a knight if and only if Charlotte is a knight.", "We have exhausted all possibilities for Charlotte and Scarlett, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Scarlett is a knight then Emma is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Luke is a knave and Riley is a knight.", "Luke cannot be a knight, because this would contradict the claim of Charlotte that Luke is a knave and Riley is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Luke is a knight or Evelyn is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Evelyn that If Scarlett is a knight then Emma is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Scarlett is a knight and Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('telling-truth', 5)), ('and', ('lying', 2), ('telling-truth', 3)), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('<=>', ('lying', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('and', ('telling-truth', 4), ('lying', 1)))", "index": 472}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Emily, Ella, Isabella, Lily, and Riley. Evelyn asserted: \"Lily is a knave\". Emily asserted: \"Isabella is a knight or Riley is a knave\". \"If Evelyn is a knight then Lily is a knave,\" Ella mentioned. Isabella was heard saying, \"Lily is a knave\". \"If Isabella is a knight then Riley is a knave\" - Lily. Riley commented, \"Emily is a knave or Isabella is a knave\". So who is a knight and who is a knave?", "names": ["Evelyn", "Emily", "Ella", "Isabella", "Lily", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true], "solution_text": "Evelyn is a knave, Emily is a knave, Ella is a knight, Isabella is a knave, Lily is a knight, and Riley is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Emily is a knave\n(3) Ella is a knight\n(4) Isabella is a knave\n(5) Lily is a knight\n(6) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Evelyn that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that If Isabella is a knight then Riley is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Lily is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Emily is a knave or Isabella is a knave.", "Emily cannot be a knight, because this would contradict the claim of Riley that Emily is a knave or Isabella is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that Isabella is a knight or Riley is a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of Lily that If Isabella is a knight then Riley is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Lily is a knave.", "We have exhausted all possibilities for Isabella and Lily, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Isabella is a knight then Riley is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Lily is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Lily is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Emily is a knave or Isabella is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Isabella is a knight or Riley is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Isabella is a knight or Riley is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Evelyn is a knight then Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('or', ('telling-truth', 3), ('lying', 5)), ('->', ('telling-truth', 0), ('lying', 4)), ('lying', 4), ('->', ('telling-truth', 3), ('lying', 5)), ('or', ('lying', 1), ('lying', 3)))", "index": 473}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Noah, Oliver, Isabella, Henry, and James. In Aiden's words: \"Oliver is not a knave\". Noah said that James is not a knave. Oliver said that Henry is not a knight. Isabella said, \"Noah is a knave if and only if Oliver is a knight.\" Henry told you that James is not a knave. James stated, \"Henry is a knave and Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Noah", "Oliver", "Isabella", "Henry", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false], "solution_text": "Aiden is a knight, Noah is a knave, Oliver is a knight, Isabella is a knight, Henry is a knave, and James is a knave.", "solution_text_format": "(1) Aiden is a knight\n(2) Noah is a knave\n(3) Oliver is a knight\n(4) Isabella is a knight\n(5) Henry is a knave\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of Oliver that Henry is not a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that James is not a knave.", "James cannot be a knight, because this would contradict the false claim of Henry that James is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Henry is a knave and Aiden is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that James is not a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that James is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Noah is a knave if and only if Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('not', ('lying', 5)), ('not', ('telling-truth', 4)), ('<=>', ('lying', 1), ('telling-truth', 2)), ('not', ('lying', 5)), ('and', ('lying', 4), ('lying', 0)))", "index": 474}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Olivia, Ella, Matthew, Ethan, and Noah. Luke was heard saying, \"Olivia is a knight and Ethan is a knight\". According to Olivia, \"If Matthew is a knave then Luke is a knave\". Ella said that If Luke is a knave then Ethan is a knight. \"Luke is a knight if and only if Ella is a knave,\" Matthew claimed. Ethan noted, \"Ella is a knave and Luke is a knight\". \"Ella is a knight if and only if Luke is a knave\" - Noah. So who is a knight and who is a knave?", "names": ["Luke", "Olivia", "Ella", "Matthew", "Ethan", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false], "solution_text": "Luke is a knave, Olivia is a knight, Ella is a knave, Matthew is a knave, Ethan is a knave, and Noah is a knave.", "solution_text_format": "(1) Luke is a knave\n(2) Olivia is a knight\n(3) Ella is a knave\n(4) Matthew is a knave\n(5) Ethan is a knave\n(6) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Olivia is a knight and Ethan is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Matthew is a knave then Luke is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Luke is a knight if and only if Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Matthew that Luke is a knight if and only if Ella is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Luke is a knave then Ethan is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Olivia that If Matthew is a knave then Luke is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the claim of Luke that Olivia is a knight and Ethan is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Olivia is a knight and Ethan is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Matthew is a knave then Luke is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Luke is a knight if and only if Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Luke is a knave then Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Luke that Olivia is a knight and Ethan is a knight.", "Ethan cannot be a knave, because this would contradict the claim of Ella that If Luke is a knave then Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Matthew that Luke is a knight if and only if Ella is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Ella is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Matthew that Luke is a knight if and only if Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that If Luke is a knave then Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Luke that Olivia is a knight and Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Ella is a knave and Luke is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Ella is a knight if and only if Luke is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 4)), ('->', ('lying', 3), ('lying', 0)), ('->', ('lying', 0), ('telling-truth', 4)), ('<=>', ('telling-truth', 0), ('lying', 2)), ('and', ('lying', 2), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('lying', 0)))", "index": 475}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Luke, Charlotte, Ella, Aiden, and Mason. Jackson expressed that If Mason is a knave then Aiden is a knight. \"If Aiden is a knave then Charlotte is a knave\" - Luke. Charlotte remarked, \"If Ella is a knave then Jackson is a knight\". \"Luke is a knight and Charlotte is a knave,\" Ella claimed. Aiden expressed that Aiden is a knight. \"Aiden is a knave if and only if Charlotte is a knave,\" Mason declared. So who is a knight and who is a knave?", "names": ["Jackson", "Luke", "Charlotte", "Ella", "Aiden", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Jackson is a knight, Luke is a knight, Charlotte is a knight, Ella is a knave, Aiden is a knight, and Mason is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Luke is a knight\n(3) Charlotte is a knight\n(4) Ella is a knave\n(5) Aiden is a knight\n(6) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that If Mason is a knave then Aiden is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Charlotte is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Ella is a knave then Jackson is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Luke is a knight and Charlotte is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Luke is a knight and Charlotte is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Aiden is a knave then Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 4)), ('->', ('lying', 4), ('lying', 2)), ('->', ('lying', 3), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('lying', 2)), ('telling-truth', 4), ('<=>', ('lying', 4), ('lying', 2)))", "index": 476}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Riley, Liam, Evelyn, Mia, and Aria. In a statement by Owen: \"Mia is not a knave\". \"If Aria is a knave then Evelyn is a knight\" - Riley. Liam asserted: \"Aria is a knight and Mia is a knave\". \"Owen is a knight or Aria is a knight,\" Evelyn claimed. Mia noted, \"Liam is a knave or Riley is a knight\". Aria told you that Evelyn is a knight and Evelyn is a knave. So who is a knight and who is a knave?", "names": ["Owen", "Riley", "Liam", "Evelyn", "Mia", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "Owen is a knight, Riley is a knight, Liam is a knave, Evelyn is a knight, Mia is a knight, and Aria is a knave.", "solution_text_format": "(1) Owen is a knight\n(2) Riley is a knight\n(3) Liam is a knave\n(4) Evelyn is a knight\n(5) Mia is a knight\n(6) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Mia is not a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Liam is a knave or Riley is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Mia is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Aria is a knight and Mia is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight and Evelyn is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Evelyn is a knight and Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Owen is a knight or Aria is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Aria is a knave then Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('->', ('lying', 5), ('telling-truth', 3)), ('and', ('telling-truth', 5), ('lying', 4)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('or', ('lying', 2), ('telling-truth', 1)), ('and', ('telling-truth', 3), ('lying', 3)))", "index": 477}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Matthew, Evelyn, Zoey, Abigail, and Aria. Emily stated, \"Zoey is a knight and Abigail is a knave\". Matthew asserted: \"If Evelyn is a knave then Matthew is a knight\". Evelyn was heard saying, \"If Emily is a knight then Abigail is a knave\". Zoey asserted: \"Aria is a knight or Emily is a knave\". As Abigail put it, \"Evelyn is not a knight\". In Aria's words: \"Matthew is not a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Matthew", "Evelyn", "Zoey", "Abigail", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Emily is a knight, Matthew is a knight, Evelyn is a knight, Zoey is a knight, Abigail is a knave, and Aria is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Matthew is a knight\n(3) Evelyn is a knight\n(4) Zoey is a knight\n(5) Abigail is a knave\n(6) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Zoey is a knight and Abigail is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Aria is a knight or Emily is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Evelyn is a knave then Matthew is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Emily is a knight then Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Emily that Zoey is a knight and Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Evelyn is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 4)), ('->', ('lying', 2), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('lying', 4)), ('or', ('telling-truth', 5), ('lying', 0)), ('not', ('telling-truth', 2)), ('not', ('lying', 1)))", "index": 478}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Samuel, William, Alexander, Mason, and Jacob. \"Mason is not a knight,\" Benjamin mentioned. Samuel was heard saying, \"Jacob is a knave\". \"Benjamin is a knight if and only if Samuel is a knight,\" William declared. Alexander was heard saying, \"Alexander is a knight or Benjamin is a knight\". Mason said that Benjamin is a knight if and only if William is a knave. According to Jacob, \"Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Samuel", "William", "Alexander", "Mason", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Benjamin is a knave, Samuel is a knave, William is a knight, Alexander is a knight, Mason is a knight, and Jacob is a knight.", "solution_text_format": "(1) Benjamin is a knave\n(2) Samuel is a knave\n(3) William is a knight\n(4) Alexander is a knight\n(5) Mason is a knight\n(6) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Mason is not a knight.", "Mason cannot be a knight, because this would contradict the claim of Benjamin that Mason is not a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if William is a knave.", "Assume William is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Samuel that Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Jacob that Alexander is a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight or Benjamin is a knight.", "We have exhausted all possibilities for Alexander and Jacob, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the claim of William that Benjamin is a knight if and only if Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Mason that Benjamin is a knight if and only if William is a knave.", "We have exhausted all possibilities for William and Mason, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Mason is not a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if William is a knave.", "Assume William is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Samuel is a knight.", "Samuel cannot be a knight, because this would contradict the claim of William that Benjamin is a knight if and only if Samuel is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Alexander is a knight or Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('lying', 5), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('<=>', ('telling-truth', 0), ('lying', 2)), ('telling-truth', 3))", "index": 479}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Ava, Jack, Olivia, Lily, and Ethan. Lucas stated, \"Ethan is a knight if and only if Ava is a knave\". As Ava put it, \"Ava is a knight and Lucas is a knave\". Jack expressed that Olivia is a knave. \"Ava is a knave if and only if Lily is a knave,\" Olivia declared. In Lily's words: \"Lucas is a knave if and only if Ethan is a knave\". Ethan remarked, \"Lily is a knight or Ava is a knave\". So who is a knight and who is a knave?", "names": ["Lucas", "Ava", "Jack", "Olivia", "Lily", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Lucas is a knight, Ava is a knave, Jack is a knight, Olivia is a knave, Lily is a knight, and Ethan is a knight.", "solution_text_format": "(1) Lucas is a knight\n(2) Ava is a knave\n(3) Jack is a knight\n(4) Olivia is a knave\n(5) Lily is a knight\n(6) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Ava is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Lily is a knight or Ava is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Ethan is a knave.", "Ava cannot be a knight, because this would contradict the claim of Lucas that Ethan is a knight if and only if Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Ava is a knight and Lucas is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Jack that Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 1)), ('and', ('telling-truth', 1), ('lying', 0)), ('lying', 3), ('<=>', ('lying', 1), ('lying', 4)), ('<=>', ('lying', 0), ('lying', 5)), ('or', ('telling-truth', 4), ('lying', 1)))", "index": 480}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Scarlett, Chloe, Michael, Luke, and Ethan. According to Oliver, \"Scarlett is a knight or Ethan is a knave\". \"Luke is not a knave,\" Scarlett mentioned. In Chloe's words: \"Oliver is a knave or Scarlett is a knave\". In Michael's words: \"Luke is a knave if and only if Luke is a knight\". Luke was heard saying, \"Oliver is not a knave\". \"Scarlett is a knave if and only if Ethan is a knight,\" Ethan declared. So who is a knight and who is a knave?", "names": ["Oliver", "Scarlett", "Chloe", "Michael", "Luke", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true], "solution_text": "Oliver is a knave, Scarlett is a knave, Chloe is a knight, Michael is a knave, Luke is a knave, and Ethan is a knight.", "solution_text_format": "(1) Oliver is a knave\n(2) Scarlett is a knave\n(3) Chloe is a knight\n(4) Michael is a knave\n(5) Luke is a knave\n(6) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Scarlett is a knight or Ethan is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Luke is not a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave if and only if Ethan is a knight.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knave if and only if Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Scarlett that Luke is not a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the false claim of Scarlett that Luke is not a knave.", "Luke cannot be a knave, because this would contradict the false claim of their own that Oliver is not a knave.", "We have exhausted all possibilities for Luke and Scarlett, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Scarlett is a knight or Ethan is a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of Oliver that Scarlett is a knight or Ethan is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the false claim of Scarlett that Luke is not a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Oliver is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Ethan is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Oliver is a knave or Scarlett is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Luke is a knave if and only if Luke is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 5)), ('not', ('lying', 4)), ('or', ('lying', 0), ('lying', 1)), ('<=>', ('lying', 4), ('telling-truth', 4)), ('not', ('lying', 0)), ('<=>', ('lying', 1), ('telling-truth', 5)))", "index": 481}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Michael, Noah, Henry, Oliver, and David. As Grace put it, \"Oliver is not a knave\". Michael remarked, \"Grace is a knave or Oliver is a knight\". In a statement by Noah: \"David is a knave or Grace is a knave\". \"Grace is a knave if and only if Michael is a knave\" - Henry. Oliver noted, \"Noah is a knave or Michael is a knight\". David stated, \"Grace is a knave and Noah is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Michael", "Noah", "Henry", "Oliver", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Grace is a knight, Michael is a knight, Noah is a knight, Henry is a knight, Oliver is a knight, and David is a knave.", "solution_text_format": "(1) Grace is a knight\n(2) Michael is a knight\n(3) Noah is a knight\n(4) Henry is a knight\n(5) Oliver is a knight\n(6) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Noah is a knave or Michael is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that David is a knave or Grace is a knave.", "David cannot be a knight, because this would contradict the claim of Noah that David is a knave or Grace is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Grace is a knave and Noah is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Grace is a knave or Oliver is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Grace is a knave if and only if Michael is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('or', ('lying', 0), ('telling-truth', 4)), ('or', ('lying', 5), ('lying', 0)), ('<=>', ('lying', 0), ('lying', 1)), ('or', ('lying', 2), ('telling-truth', 1)), ('and', ('lying', 0), ('lying', 2)))", "index": 482}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, David, Mason, Evelyn, Liam, and Sophia. \"Liam is a knave if and only if Mason is a knight,\" Grace claimed. David remarked, \"Evelyn is not a knight\". Mason said that Sophia is a knave. Evelyn expressed that Liam is a knight if and only if Mason is a knight. Liam stated, \"Evelyn is a knight or Sophia is a knight\". In Sophia's words: \"Grace is a knight and Mason is a knight\". So who is a knight and who is a knave?", "names": ["Grace", "David", "Mason", "Evelyn", "Liam", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Grace is a knave, David is a knave, Mason is a knight, Evelyn is a knight, Liam is a knight, and Sophia is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) David is a knave\n(3) Mason is a knight\n(4) Evelyn is a knight\n(5) Liam is a knight\n(6) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Liam is a knave if and only if Mason is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Evelyn is a knight or Sophia is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Liam is a knight if and only if Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of Grace that Liam is a knave if and only if Mason is a knight.", "Mason cannot be a knave, because this would contradict the claim of Evelyn that Liam is a knight if and only if Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of Grace that Liam is a knave if and only if Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Mason is a knight.", "Sophia cannot be a knave, because this would contradict the false claim of Mason that Sophia is a knave.", "We have exhausted all possibilities for Sophia, Mason, and Evelyn, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Evelyn is a knight or Sophia is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Liam that Evelyn is a knight or Sophia is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Mason that Sophia is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Grace is a knight and Mason is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Grace that Liam is a knave if and only if Mason is a knight.", "We have exhausted all possibilities for Mason, Evelyn, and Liam, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Mason is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Evelyn is a knight or Sophia is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Liam is a knight if and only if Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Mason that Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Grace is a knight and Mason is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Evelyn is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that Evelyn is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('telling-truth', 2)), ('not', ('telling-truth', 3)), ('lying', 5), ('<=>', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('telling-truth', 3), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('telling-truth', 2)))", "index": 483}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Oliver, Jacob, David, Isabella, and Sebastian. Scarlett stated, \"Sebastian is a knight if and only if Sebastian is a knave\". According to Oliver, \"If Scarlett is a knight then Isabella is a knight\". \"Isabella is a knave,\" Jacob declared. David remarked, \"Isabella is a knight or Jacob is a knave\". Isabella said, \"Scarlett is not a knight.\" Sebastian said, \"David is a knight.\" So who is a knight and who is a knave?", "names": ["Scarlett", "Oliver", "Jacob", "David", "Isabella", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Scarlett is a knave, Oliver is a knight, Jacob is a knave, David is a knight, Isabella is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Scarlett is a knave\n(2) Oliver is a knight\n(3) Jacob is a knave\n(4) David is a knight\n(5) Isabella is a knight\n(6) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Scarlett cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight if and only if Sebastian is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Isabella is a knight or Jacob is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Scarlett is not a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Isabella is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Scarlett is a knight then Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 5)), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('lying', 4), ('or', ('telling-truth', 4), ('lying', 2)), ('not', ('telling-truth', 0)), ('telling-truth', 3))", "index": 484}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Avery, Joseph, Zoey, David, and Amelia. Ella told you that Avery is not a knight. Avery asserted: \"If Zoey is a knave then David is a knight\". Joseph commented, \"Zoey is a knave if and only if Ella is a knave\". In a statement by Zoey: \"Ella is a knight\". David noted, \"Amelia is not a knight\". In Amelia's words: \"David is a knave\". So who is a knight and who is a knave?", "names": ["Ella", "Avery", "Joseph", "Zoey", "David", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false], "solution_text": "Ella is a knave, Avery is a knight, Joseph is a knight, Zoey is a knave, David is a knight, and Amelia is a knave.", "solution_text_format": "(1) Ella is a knave\n(2) Avery is a knight\n(3) Joseph is a knight\n(4) Zoey is a knave\n(5) David is a knight\n(6) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Ella that Avery is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that If Zoey is a knave then David is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Avery that If Zoey is a knave then David is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Ella is a knight.", "We have exhausted all possibilities for Zoey and Avery, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Zoey is a knave then David is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Ella is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ella is a knight.", "Assume David is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of David that Amelia is not a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that David is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('->', ('lying', 3), ('telling-truth', 4)), ('<=>', ('lying', 3), ('lying', 0)), ('telling-truth', 0), ('not', ('telling-truth', 5)), ('lying', 4))", "index": 485}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Daniel, Ava, Liam, Olivia, and Charlotte. As Oliver put it, \"If Charlotte is a knight then Ava is a knight\". Daniel remarked, \"Liam is a knight or Olivia is a knave\". In Ava's words: \"Olivia is a knight if and only if Oliver is a knave\". Liam commented, \"If Daniel is a knave then Oliver is a knave\". Olivia expressed that Oliver is a knight or Ava is a knave. In Charlotte's words: \"Liam is a knight or Daniel is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Daniel", "Ava", "Liam", "Olivia", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false], "solution_text": "Oliver is a knight, Daniel is a knave, Ava is a knave, Liam is a knave, Olivia is a knight, and Charlotte is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) Daniel is a knave\n(3) Ava is a knave\n(4) Liam is a knave\n(5) Olivia is a knight\n(6) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that If Charlotte is a knight then Ava is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Liam is a knight or Daniel is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Daniel is a knave then Oliver is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Liam is a knight or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Oliver is a knight or Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Olivia is a knight if and only if Oliver is a knave.", "Ava cannot be a knave, because this would contradict the claim of Oliver that If Charlotte is a knight then Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Oliver is a knight or Ava is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Liam is a knight or Olivia is a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that If Daniel is a knave then Oliver is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Liam that If Daniel is a knave then Oliver is a knave.", "Daniel cannot be a knave, because this would contradict the claim of Charlotte that Liam is a knight or Daniel is a knight.", "We have exhausted all possibilities for Daniel and Liam, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Liam is a knight or Daniel is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Charlotte that Liam is a knight or Daniel is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that If Daniel is a knave then Oliver is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Liam that If Daniel is a knave then Oliver is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Liam is a knight or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Oliver is a knight or Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Olivia is a knight if and only if Oliver is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('telling-truth', 3), ('lying', 4)), ('<=>', ('telling-truth', 4), ('lying', 0)), ('->', ('lying', 1), ('lying', 0)), ('or', ('telling-truth', 0), ('lying', 2)), ('or', ('telling-truth', 3), ('telling-truth', 1)))", "index": 486}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Avery, James, Luke, Henry, and Lily. Owen said that Lily is a knight or Owen is a knight. Avery commented, \"Owen is not a knight\". James expressed that Henry is a knight. \"James is a knave or James is a knight\" - Luke. Henry expressed that Lily is not a knave. Lily told you that Avery is a knight if and only if Luke is a knight. So who is a knight and who is a knave?", "names": ["Owen", "Avery", "James", "Luke", "Henry", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false], "solution_text": "Owen is a knight, Avery is a knave, James is a knave, Luke is a knight, Henry is a knave, and Lily is a knave.", "solution_text_format": "(1) Owen is a knight\n(2) Avery is a knave\n(3) James is a knave\n(4) Luke is a knight\n(5) Henry is a knave\n(6) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Lily is a knight or Owen is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Avery is a knight if and only if Luke is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Owen is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Lily that Avery is a knight if and only if Luke is a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that James is a knave or James is a knight.", "We have exhausted all possibilities for Luke and Avery, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Luke is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Owen is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that James is a knave or James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Lily is not a knave.", "Henry cannot be a knave, because this would contradict the claim of James that Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Henry is a knight.", "Henry cannot be a knight, because this would contradict the false claim of James that Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Lily is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('telling-truth', 4), ('or', ('lying', 2), ('telling-truth', 2)), ('not', ('lying', 5)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)))", "index": 487}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Amelia, Olivia, Penelope, Joseph, and Mia. In Benjamin's words: \"Mia is a knight or Penelope is a knight\". Amelia stated, \"Joseph is a knight if and only if Olivia is a knave\". As Olivia put it, \"Mia is not a knave\". Penelope expressed that Benjamin is a knave or Olivia is a knave. Joseph commented, \"Penelope is a knight\". Mia commented, \"Penelope is a knight or Amelia is a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Amelia", "Olivia", "Penelope", "Joseph", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Benjamin is a knight, Amelia is a knight, Olivia is a knight, Penelope is a knave, Joseph is a knave, and Mia is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Amelia is a knight\n(3) Olivia is a knight\n(4) Penelope is a knave\n(5) Joseph is a knave\n(6) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Mia is a knight or Penelope is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Penelope is a knight or Amelia is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Benjamin is a knave or Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Penelope that Benjamin is a knave or Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Mia is not a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Benjamin is a knave or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Mia is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Olivia is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Amelia that Joseph is a knight if and only if Olivia is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 4), ('lying', 2)), ('not', ('lying', 5)), ('or', ('lying', 0), ('lying', 2)), ('telling-truth', 3), ('or', ('telling-truth', 3), ('telling-truth', 1)))", "index": 488}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Logan, Grace, Henry, Mason, and Lucas. Abigail stated, \"Mason is a knave and Grace is a knight\". In a statement by Logan: \"Abigail is a knight if and only if Abigail is a knave\". Grace stated, \"Abigail is a knave\". According to Henry, \"Henry is a knight and Mason is a knave\". Mason stated, \"Abigail is a knave\". In a statement by Lucas: \"If Abigail is a knave then Henry is a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Logan", "Grace", "Henry", "Mason", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "Abigail is a knave, Logan is a knave, Grace is a knight, Henry is a knave, Mason is a knight, and Lucas is a knave.", "solution_text_format": "(1) Abigail is a knave\n(2) Logan is a knave\n(3) Grace is a knight\n(4) Henry is a knave\n(5) Mason is a knight\n(6) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Mason is a knave and Grace is a knight.", "Mason cannot be a knight, because this would contradict the claim of Abigail that Mason is a knave and Grace is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Grace cannot be a knave, because this would contradict the claim of Abigail that Mason is a knave and Grace is a knight.", "We have exhausted all possibilities for Grace and Mason, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Mason is a knave and Grace is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Abigail is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Abigail is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Abigail is a knight if and only if Abigail is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Abigail is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Mason is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Henry is a knight and Mason is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that If Abigail is a knave then Henry is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Abigail is a knave then Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 2)), ('<=>', ('telling-truth', 0), ('lying', 0)), ('lying', 0), ('and', ('telling-truth', 3), ('lying', 4)), ('lying', 0), ('->', ('lying', 0), ('telling-truth', 3)))", "index": 489}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Aiden, Liam, Logan, Zoey, and Victoria. Emily expressed that Aiden is a knave and Liam is a knight. In Aiden's words: \"Liam is not a knave\". In a statement by Liam: \"Aiden is a knight or Victoria is a knave\". Logan noted, \"Logan is a knight or Zoey is a knight\". \"Logan is not a knight,\" Zoey mentioned. Victoria said, \"Liam is a knight and Liam is a knave.\" So who is a knight and who is a knave?", "names": ["Emily", "Aiden", "Liam", "Logan", "Zoey", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Emily is a knave, Aiden is a knight, Liam is a knight, Logan is a knight, Zoey is a knave, and Victoria is a knave.", "solution_text_format": "(1) Emily is a knave\n(2) Aiden is a knight\n(3) Liam is a knight\n(4) Logan is a knight\n(5) Zoey is a knave\n(6) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Aiden is a knave and Liam is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Emily that Aiden is a knave and Liam is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Liam is not a knave.", "Liam cannot be a knight, because this would contradict the false claim of Aiden that Liam is not a knave.", "Liam cannot be a knave, because this would contradict the claim of Emily that Aiden is a knave and Liam is a knight.", "We have exhausted all possibilities for Liam and Aiden, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Aiden is a knave and Liam is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Aiden is a knight or Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Liam is a knight and Liam is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Liam is a knight and Liam is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight or Zoey is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Logan is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Logan is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 2)), ('not', ('lying', 2)), ('or', ('telling-truth', 1), ('lying', 5)), ('or', ('telling-truth', 3), ('telling-truth', 4)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 2), ('lying', 2)))", "index": 490}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Benjamin, Olivia, Mason, Zoey, and Grace. Michael commented, \"Benjamin is a knave if and only if Grace is a knave\". \"Mason is a knight or Olivia is a knave,\" Benjamin mentioned. Olivia said, \"Benjamin is a knave.\" \"Olivia is a knight or Michael is a knave,\" Mason declared. Zoey commented, \"Benjamin is not a knight\". According to Grace, \"If Olivia is a knave then Zoey is a knave\". So who is a knight and who is a knave?", "names": ["Michael", "Benjamin", "Olivia", "Mason", "Zoey", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true], "solution_text": "Michael is a knight, Benjamin is a knight, Olivia is a knave, Mason is a knave, Zoey is a knave, and Grace is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Benjamin is a knight\n(3) Olivia is a knave\n(4) Mason is a knave\n(5) Zoey is a knave\n(6) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Grace is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Mason is a knight or Olivia is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Olivia is a knight or Michael is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave.", "Olivia cannot be a knave, because this would contradict the claim of Mason that Olivia is a knight or Michael is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Olivia is a knight or Michael is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Benjamin that Mason is a knight or Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Olivia is a knave then Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Benjamin is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 5)), ('or', ('telling-truth', 3), ('lying', 2)), ('lying', 1), ('or', ('telling-truth', 2), ('lying', 0)), ('not', ('telling-truth', 1)), ('->', ('lying', 2), ('lying', 4)))", "index": 491}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Henry, Owen, Abigail, Emily, and Ava. Benjamin remarked, \"Benjamin is a knight and Owen is a knave\". Henry said that Owen is a knight and Abigail is a knave. Owen remarked, \"Ava is a knave\". Abigail expressed that If Benjamin is a knave then Owen is a knight. In Emily's words: \"Benjamin is a knight if and only if Emily is a knight\". Ava commented, \"Emily is a knave if and only if Owen is a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Henry", "Owen", "Abigail", "Emily", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true], "solution_text": "Benjamin is a knight, Henry is a knave, Owen is a knave, Abigail is a knight, Emily is a knight, and Ava is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Henry is a knave\n(3) Owen is a knave\n(4) Abigail is a knight\n(5) Emily is a knight\n(6) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Benjamin is a knight and Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Benjamin that Benjamin is a knight and Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Emily is a knave if and only if Owen is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Emily is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Abigail is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Owen is a knight and Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Benjamin is a knave then Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('lying', 2)), ('and', ('telling-truth', 2), ('lying', 3)), ('lying', 5), ('->', ('lying', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('<=>', ('lying', 4), ('telling-truth', 2)))", "index": 492}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Emma, Olivia, Abigail, Mia, and Aurora. In a statement by Elizabeth: \"Olivia is a knight and Abigail is a knight\". Emma was heard saying, \"Aurora is not a knave\". As Olivia put it, \"Aurora is a knight if and only if Aurora is a knave\". \"If Emma is a knave then Aurora is a knave,\" Abigail declared. Mia remarked, \"Aurora is a knight\". \"Emma is a knave if and only if Emma is a knight\" - Aurora. So who is a knight and who is a knave?", "names": ["Elizabeth", "Emma", "Olivia", "Abigail", "Mia", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false], "solution_text": "Elizabeth is a knave, Emma is a knave, Olivia is a knave, Abigail is a knight, Mia is a knave, and Aurora is a knave.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Emma is a knave\n(3) Olivia is a knave\n(4) Abigail is a knight\n(5) Mia is a knave\n(6) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Olivia is a knight and Abigail is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Aurora is a knight if and only if Aurora is a knave.", "Olivia cannot be a knave, because this would contradict the claim of Elizabeth that Olivia is a knight and Abigail is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Olivia is a knight and Abigail is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Aurora is a knight if and only if Aurora is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Emma is a knave if and only if Emma is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Emma is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Aurora is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Aurora is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Emma is a knave then Aurora is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Aurora is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('lying', 5)), ('<=>', ('telling-truth', 5), ('lying', 5)), ('->', ('lying', 1), ('lying', 5)), ('telling-truth', 5), ('<=>', ('lying', 1), ('telling-truth', 1)))", "index": 493}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Logan, Amelia, Chloe, Grace, and Aurora. Sophia remarked, \"Grace is not a knave\". Logan said that Logan is a knight. \"Logan is a knight and Grace is a knave\" - Amelia. Chloe stated, \"Logan is not a knave\". Grace told you that Aurora is a knave or Sophia is a knave. Aurora remarked, \"Chloe is not a knight\". So who is a knight and who is a knave?", "names": ["Sophia", "Logan", "Amelia", "Chloe", "Grace", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "Sophia is a knight, Logan is a knight, Amelia is a knave, Chloe is a knight, Grace is a knight, and Aurora is a knave.", "solution_text_format": "(1) Sophia is a knight\n(2) Logan is a knight\n(3) Amelia is a knave\n(4) Chloe is a knight\n(5) Grace is a knight\n(6) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Grace is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Aurora is a knave or Sophia is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Grace that Aurora is a knave or Sophia is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Logan is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Grace is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Logan is a knight and Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('telling-truth', 1), ('and', ('telling-truth', 1), ('lying', 4)), ('not', ('lying', 1)), ('or', ('lying', 5), ('lying', 0)), ('not', ('telling-truth', 3)))", "index": 494}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Amelia, Isabella, Oliver, Henry, and Aiden. \"Isabella is a knight and Oliver is a knight,\" Liam claimed. Amelia said that Aiden is a knave if and only if Oliver is a knave. Isabella was heard saying, \"Aiden is a knight if and only if Liam is a knight\". \"Isabella is a knave\" - Oliver. Henry said, \"Oliver is a knight and Isabella is a knight.\" Aiden said, \"Aiden is a knight if and only if Isabella is a knight.\" So who is a knight and who is a knave?", "names": ["Liam", "Amelia", "Isabella", "Oliver", "Henry", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Liam is a knave, Amelia is a knight, Isabella is a knight, Oliver is a knave, Henry is a knave, and Aiden is a knave.", "solution_text_format": "(1) Liam is a knave\n(2) Amelia is a knight\n(3) Isabella is a knight\n(4) Oliver is a knave\n(5) Henry is a knave\n(6) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Isabella is a knight and Oliver is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Liam is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Isabella is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Isabella is a knave.", "Oliver cannot be a knave, because this would contradict the claim of Liam that Isabella is a knight and Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Isabella that Aiden is a knight if and only if Liam is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the claim of Liam that Isabella is a knight and Oliver is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Isabella is a knight and Oliver is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Liam is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Isabella that Aiden is a knight if and only if Liam is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Isabella is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Liam that Isabella is a knight and Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Oliver is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Oliver is a knight and Isabella is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Oliver is a knight and Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('lying', 5), ('lying', 3)), ('<=>', ('telling-truth', 5), ('telling-truth', 0)), ('lying', 2), ('and', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('telling-truth', 2)))", "index": 495}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Sebastian, Aiden, Henry, Emma, and David. In a statement by Michael: \"Sebastian is a knight if and only if Aiden is a knave\". Sebastian noted, \"Emma is a knight if and only if Henry is a knight\". \"Emma is a knight if and only if David is a knave,\" Aiden claimed. Henry expressed that Aiden is a knave. In Emma's words: \"Sebastian is a knave and Aiden is a knight\". \"Emma is a knight,\" David declared. So who is a knight and who is a knave?", "names": ["Michael", "Sebastian", "Aiden", "Henry", "Emma", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false], "solution_text": "Michael is a knave, Sebastian is a knave, Aiden is a knave, Henry is a knight, Emma is a knave, and David is a knave.", "solution_text_format": "(1) Michael is a knave\n(2) Sebastian is a knave\n(3) Aiden is a knave\n(4) Henry is a knight\n(5) Emma is a knave\n(6) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Aiden is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Emma is a knight if and only if Henry is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Aiden is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Sebastian is a knave and Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Michael that Sebastian is a knight if and only if Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Emma is a knight if and only if David is a knave.", "David cannot be a knight, because this would contradict the false claim of Aiden that Emma is a knight if and only if David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Emma is a knight.", "Henry cannot be a knight, because this would contradict the claim of Sebastian that Emma is a knight if and only if Henry is a knight.", "Henry cannot be a knave, because this would contradict the false claim of their own that Aiden is a knave.", "We have exhausted all possibilities for Henry, David, Aiden, and Emma, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Emma is a knight if and only if Henry is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Sebastian is a knave and Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Emma is a knight if and only if David is a knave.", "David cannot be a knight, because this would contradict the claim of Aiden that Emma is a knight if and only if David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that Emma is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Michael that Sebastian is a knight if and only if Aiden is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Sebastian is a knave and Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Emma that Sebastian is a knave and Aiden is a knight.", "Aiden cannot be a knave, because this would contradict the claim of Michael that Sebastian is a knight if and only if Aiden is a knave.", "We have exhausted all possibilities for Aiden, Emma, and Sebastian, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Aiden is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Emma is a knight if and only if Henry is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Aiden is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Sebastian is a knave and Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Emma is a knight if and only if David is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Emma is a knight.", "David cannot be a knave, because this would contradict the claim of Aiden that Emma is a knight if and only if David is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of Michael that Sebastian is a knight if and only if Aiden is a knave.", "We have exhausted all possibilities for Aiden and Emma, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Emma is a knight if and only if Henry is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Sebastian is a knave and Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Michael that Sebastian is a knight if and only if Aiden is a knave.", "Aiden cannot be a knave, because this would contradict the claim of Emma that Sebastian is a knave and Aiden is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Sebastian is a knave and Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Michael that Sebastian is a knight if and only if Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Emma is a knight if and only if David is a knave.", "David cannot be a knight, because this would contradict the false claim of Aiden that Emma is a knight if and only if David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Emma is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 3)), ('<=>', ('telling-truth', 4), ('lying', 5)), ('lying', 2), ('and', ('lying', 1), ('telling-truth', 2)), ('telling-truth', 4))", "index": 496}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Alexander, Jacob, Aurora, Harper, and Luke. As James put it, \"Alexander is not a knight\". In a statement by Alexander: \"James is a knave if and only if Harper is a knave\". Jacob commented, \"Alexander is a knave\". In Aurora's words: \"James is a knave if and only if Harper is a knave\". Harper told you that Aurora is a knight. According to Luke, \"James is a knave or Harper is a knave\". So who is a knight and who is a knave?", "names": ["James", "Alexander", "Jacob", "Aurora", "Harper", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "James is a knight, Alexander is a knave, Jacob is a knight, Aurora is a knave, Harper is a knave, and Luke is a knight.", "solution_text_format": "(1) James is a knight\n(2) Alexander is a knave\n(3) Jacob is a knight\n(4) Aurora is a knave\n(5) Harper is a knave\n(6) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of James that Alexander is not a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that James is a knave if and only if Harper is a knave.", "Harper cannot be a knight, because this would contradict the false claim of Alexander that James is a knave if and only if Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that James is a knave if and only if Harper is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that James is a knave if and only if Harper is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Alexander is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that James is a knave or Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('<=>', ('lying', 0), ('lying', 4)), ('lying', 1), ('<=>', ('lying', 0), ('lying', 4)), ('telling-truth', 3), ('or', ('lying', 0), ('lying', 4)))", "index": 497}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Matthew, Scarlett, Noah, Lucas, and Liam. \"If Scarlett is a knave then Liam is a knave,\" Sebastian declared. Matthew told you that Lucas is a knave and Scarlett is a knight. \"If Liam is a knave then Matthew is a knight\" - Scarlett. Noah was heard saying, \"Sebastian is a knight or Noah is a knight\". \"Noah is a knight,\" Lucas declared. \"Liam is a knight if and only if Scarlett is a knave\" - Liam. So who is a knight and who is a knave?", "names": ["Sebastian", "Matthew", "Scarlett", "Noah", "Lucas", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false], "solution_text": "Sebastian is a knight, Matthew is a knave, Scarlett is a knave, Noah is a knight, Lucas is a knight, and Liam is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Matthew is a knave\n(3) Scarlett is a knave\n(4) Noah is a knight\n(5) Lucas is a knight\n(6) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that If Scarlett is a knave then Liam is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Liam is a knave then Matthew is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Liam is a knight if and only if Scarlett is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that Liam is a knight if and only if Scarlett is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that If Liam is a knave then Matthew is a knight.", "Liam cannot be a knight, because this would contradict the claim of Sebastian that If Scarlett is a knave then Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Scarlett is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Scarlett is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Lucas is a knave and Scarlett is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Sebastian is a knight or Noah is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 5)), ('and', ('lying', 4), ('telling-truth', 2)), ('->', ('lying', 5), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('telling-truth', 3), ('<=>', ('telling-truth', 5), ('lying', 2)))", "index": 498}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Sophia, William, Aurora, Charlotte, and Mason. Michael stated, \"Sophia is a knave\". As Sophia put it, \"Charlotte is a knight and William is a knight\". In William's words: \"Michael is a knight or Mason is a knight\". According to Aurora, \"Michael is a knave and Michael is a knight\". Charlotte asserted: \"If Aurora is a knave then William is a knave\". Mason said, \"Aurora is a knave.\" So who is a knight and who is a knave?", "names": ["Michael", "Sophia", "William", "Aurora", "Charlotte", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Michael is a knight, Sophia is a knave, William is a knight, Aurora is a knave, Charlotte is a knave, and Mason is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Sophia is a knave\n(3) William is a knight\n(4) Aurora is a knave\n(5) Charlotte is a knave\n(6) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Michael that Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Charlotte is a knight and William is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Aurora is a knave then William is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Michael is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Michael is a knave and Michael is a knight.", "William cannot be a knight, because this would contradict the false claim of Sophia that Charlotte is a knight and William is a knight.", "William cannot be a knave, because this would contradict the false claim of their own that Michael is a knight or Mason is a knight.", "We have exhausted all possibilities for William and Aurora, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Aurora is a knave then William is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Michael is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Michael is a knave and Michael is a knight.", "Assume William is a knight. No contradiction is found in their claim that Michael is a knight or Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('and', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('lying', 0), ('telling-truth', 0)), ('->', ('lying', 3), ('lying', 2)), ('lying', 3))", "index": 499}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Daniel, Harper, Oliver, Grace, and Sophia. William was heard saying, \"Grace is a knave and Oliver is a knave\". \"Sophia is a knave and Sophia is a knight,\" Daniel mentioned. Harper said that Sophia is a knight and Harper is a knight. Oliver commented, \"Grace is a knave\". As Grace put it, \"Oliver is a knight or Harper is a knave\". Sophia stated, \"Daniel is a knight\". So who is a knight and who is a knave?", "names": ["William", "Daniel", "Harper", "Oliver", "Grace", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false], "solution_text": "William is a knave, Daniel is a knave, Harper is a knave, Oliver is a knave, Grace is a knight, and Sophia is a knave.", "solution_text_format": "(1) William is a knave\n(2) Daniel is a knave\n(3) Harper is a knave\n(4) Oliver is a knave\n(5) Grace is a knight\n(6) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Grace is a knave and Oliver is a knave.", "Grace cannot be a knight, because this would contradict the claim of William that Grace is a knave and Oliver is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Oliver is a knight or Harper is a knave.", "Oliver cannot be a knight, because this would contradict the claim of William that Grace is a knave and Oliver is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that Grace is a knave.", "We have exhausted all possibilities for Oliver and Grace, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Grace is a knave and Oliver is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Oliver is a knight or Harper is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Grace is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Grace is a knave.", "Harper cannot be a knight, because this would contradict the claim of Grace that Oliver is a knight or Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Sophia is a knight and Harper is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Sophia is a knight.", "Daniel cannot be a knave, because this would contradict the claim of Sophia that Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Sophia is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Sophia is a knave and Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 3)), ('and', ('lying', 5), ('telling-truth', 5)), ('and', ('telling-truth', 5), ('telling-truth', 2)), ('lying', 4), ('or', ('telling-truth', 3), ('lying', 2)), ('telling-truth', 1))", "index": 500}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Sophia, Chloe, Michael, Jackson, and Grace. As Aurora put it, \"If Jackson is a knave then Chloe is a knight\". Sophia expressed that Chloe is a knave. Chloe noted, \"Michael is a knave if and only if Jackson is a knight\". \"Aurora is a knight,\" Michael mentioned. \"Chloe is a knight or Sophia is a knave,\" Jackson declared. Grace commented, \"Chloe is not a knave\". So who is a knight and who is a knave?", "names": ["Aurora", "Sophia", "Chloe", "Michael", "Jackson", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false], "solution_text": "Aurora is a knave, Sophia is a knight, Chloe is a knave, Michael is a knave, Jackson is a knave, and Grace is a knave.", "solution_text_format": "(1) Aurora is a knave\n(2) Sophia is a knight\n(3) Chloe is a knave\n(4) Michael is a knave\n(5) Jackson is a knave\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that If Jackson is a knave then Chloe is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Chloe is a knight or Sophia is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Michael is a knave if and only if Jackson is a knight.", "Michael cannot be a knight, because this would contradict the claim of Chloe that Michael is a knave if and only if Jackson is a knight.", "Michael cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Jackson is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Aurora is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Jackson that Chloe is a knight or Sophia is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the false claim of Chloe that Michael is a knave if and only if Jackson is a knight.", "We have exhausted all possibilities for Michael and Chloe, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Chloe is a knight or Sophia is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Jackson that Chloe is a knight or Sophia is a knave.", "Chloe cannot be a knave, because this would contradict the claim of Aurora that If Jackson is a knave then Chloe is a knight.", "We have exhausted all possibilities for Chloe and Jackson, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that If Jackson is a knave then Chloe is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Aurora that If Jackson is a knave then Chloe is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Chloe is a knight or Sophia is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Aurora that If Jackson is a knave then Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Jackson is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Chloe that Michael is a knave if and only if Jackson is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Aurora is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Chloe is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Chloe is not a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Chloe is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('telling-truth', 2)), ('lying', 2), ('<=>', ('lying', 3), ('telling-truth', 4)), ('telling-truth', 0), ('or', ('telling-truth', 2), ('lying', 1)), ('not', ('lying', 2)))", "index": 501}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Henry, Lucas, Daniel, Ethan, and Logan. Oliver was heard saying, \"Ethan is a knight if and only if Oliver is a knight\". In Henry's words: \"Lucas is a knave and Oliver is a knave\". \"Henry is a knight or Logan is a knight,\" Lucas claimed. Daniel told you that Logan is a knave if and only if Henry is a knight. Ethan remarked, \"Daniel is not a knave\". Logan asserted: \"Oliver is a knight or Lucas is a knave\". So who is a knight and who is a knave?", "names": ["Oliver", "Henry", "Lucas", "Daniel", "Ethan", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Oliver is a knight, Henry is a knave, Lucas is a knight, Daniel is a knight, Ethan is a knight, and Logan is a knight.", "solution_text_format": "(1) Oliver is a knight\n(2) Henry is a knave\n(3) Lucas is a knight\n(4) Daniel is a knight\n(5) Ethan is a knight\n(6) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Oliver is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Logan is a knave if and only if Henry is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Oliver is a knight or Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Henry is a knight or Logan is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Oliver is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Lucas is a knave and Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('lying', 2), ('lying', 0)), ('or', ('telling-truth', 1), ('telling-truth', 5)), ('<=>', ('lying', 5), ('telling-truth', 1)), ('not', ('lying', 3)), ('or', ('telling-truth', 0), ('lying', 2)))", "index": 502}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, William, Scarlett, Aurora, Luke, and Oliver. According to Henry, \"If Aurora is a knight then Luke is a knave\". William asserted: \"Henry is a knight and Aurora is a knight\". Scarlett was heard saying, \"Henry is a knight\". According to Aurora, \"Henry is a knight and Henry is a knave\". In Luke's words: \"Henry is a knight or William is a knave\". Oliver remarked, \"William is a knight and Luke is a knave\". So who is a knight and who is a knave?", "names": ["Henry", "William", "Scarlett", "Aurora", "Luke", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false], "solution_text": "Henry is a knight, William is a knave, Scarlett is a knight, Aurora is a knave, Luke is a knight, and Oliver is a knave.", "solution_text_format": "(1) Henry is a knight\n(2) William is a knave\n(3) Scarlett is a knight\n(4) Aurora is a knave\n(5) Luke is a knight\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that If Aurora is a knight then Luke is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Henry is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Henry is a knight and Henry is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Henry is a knight or William is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Henry is a knight and Aurora is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Henry is a knight and Aurora is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Henry is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that William is a knight and Luke is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that William is a knight and Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 4)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('telling-truth', 0), ('and', ('telling-truth', 0), ('lying', 0)), ('or', ('telling-truth', 0), ('lying', 1)), ('and', ('telling-truth', 1), ('lying', 4)))", "index": 503}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Joseph, Olivia, Luke, Riley, and Victoria. According to Samuel, \"If Joseph is a knight then Samuel is a knight\". Joseph commented, \"Luke is a knight if and only if Riley is a knight\". Olivia expressed that If Luke is a knight then Victoria is a knave. In a statement by Luke: \"Olivia is a knight and Joseph is a knave\". Riley was heard saying, \"Victoria is not a knave\". \"Riley is a knight if and only if Joseph is a knave,\" Victoria mentioned. So who is a knight and who is a knave?", "names": ["Samuel", "Joseph", "Olivia", "Luke", "Riley", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false], "solution_text": "Samuel is a knight, Joseph is a knave, Olivia is a knight, Luke is a knight, Riley is a knave, and Victoria is a knave.", "solution_text_format": "(1) Samuel is a knight\n(2) Joseph is a knave\n(3) Olivia is a knight\n(4) Luke is a knight\n(5) Riley is a knave\n(6) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that If Joseph is a knight then Samuel is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Luke is a knight if and only if Riley is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Olivia is a knight and Joseph is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Olivia is a knight and Joseph is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Luke is a knight then Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Riley is a knight if and only if Joseph is a knave.", "Riley cannot be a knight, because this would contradict the claim of Joseph that Luke is a knight if and only if Riley is a knight.", "Riley cannot be a knave, because this would contradict the false claim of their own that Victoria is not a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Joseph is a knave.", "Riley cannot be a knight, because this would contradict the claim of Joseph that Luke is a knight if and only if Riley is a knight.", "Riley cannot be a knave, because this would contradict the false claim of Victoria that Riley is a knight if and only if Joseph is a knave.", "We have exhausted all possibilities for Riley and Victoria, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the false claim of their own that If Luke is a knight then Victoria is a knave.", "We have exhausted all possibilities for Olivia and Luke, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Riley is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Olivia is a knight and Joseph is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Luke is a knight then Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Olivia that If Luke is a knight then Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Joseph is a knave.", "Riley cannot be a knight, because this would contradict the false claim of Joseph that Luke is a knight if and only if Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Victoria is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('lying', 5)), ('and', ('telling-truth', 2), ('lying', 1)), ('not', ('lying', 5)), ('<=>', ('telling-truth', 4), ('lying', 1)))", "index": 504}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Riley, Avery, Michael, Evelyn, and Logan. Ava asserted: \"If Ava is a knight then Riley is a knight\". Riley asserted: \"Evelyn is a knave and Logan is a knight\". Avery stated, \"Riley is not a knight\". Michael asserted: \"Evelyn is a knight\". Evelyn asserted: \"Michael is a knight or Logan is a knave\". \"If Michael is a knight then Evelyn is a knight,\" Logan claimed. So who is a knight and who is a knave?", "names": ["Ava", "Riley", "Avery", "Michael", "Evelyn", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true], "solution_text": "Ava is a knight, Riley is a knight, Avery is a knave, Michael is a knave, Evelyn is a knave, and Logan is a knight.", "solution_text_format": "(1) Ava is a knight\n(2) Riley is a knight\n(3) Avery is a knave\n(4) Michael is a knave\n(5) Evelyn is a knave\n(6) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that If Ava is a knight then Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Evelyn is a knave and Logan is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Riley that Evelyn is a knave and Logan is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Michael is a knight or Logan is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Evelyn is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Michael is a knight then Evelyn is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Riley is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Riley is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('and', ('lying', 4), ('telling-truth', 5)), ('not', ('telling-truth', 1)), ('telling-truth', 4), ('or', ('telling-truth', 3), ('lying', 5)), ('->', ('telling-truth', 3), ('telling-truth', 4)))", "index": 505}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Sophia, Victoria, Henry, Riley, and Mason. Alexander noted, \"Victoria is a knave or Henry is a knight\". \"Henry is a knave or Riley is a knight,\" Sophia claimed. Victoria said that Sophia is a knave or Mason is a knight. Henry said that Alexander is a knight. \"If Henry is a knave then Mason is a knave,\" Riley mentioned. \"Henry is a knight\" - Mason. So who is a knight and who is a knave?", "names": ["Alexander", "Sophia", "Victoria", "Henry", "Riley", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Alexander is a knight, Sophia is a knight, Victoria is a knight, Henry is a knight, Riley is a knight, and Mason is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Sophia is a knight\n(3) Victoria is a knight\n(4) Henry is a knight\n(5) Riley is a knight\n(6) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Victoria is a knave or Henry is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Sophia is a knave or Mason is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Henry is a knave or Riley is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Henry is a knave then Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 3)), ('or', ('lying', 3), ('telling-truth', 4)), ('or', ('lying', 1), ('telling-truth', 5)), ('telling-truth', 0), ('->', ('lying', 3), ('lying', 5)), ('telling-truth', 3))", "index": 506}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Aurora, Lucas, Liam, Sofia, and Aiden. Harper was heard saying, \"Aiden is a knave if and only if Lucas is a knave\". Aurora expressed that If Sofia is a knave then Aurora is a knight. \"Sofia is a knave,\" Lucas mentioned. \"Lucas is a knave or Sofia is a knave,\" Liam claimed. Sofia told you that Harper is a knight. Aiden stated, \"Sofia is not a knight\". So who is a knight and who is a knave?", "names": ["Harper", "Aurora", "Lucas", "Liam", "Sofia", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "Harper is a knight, Aurora is a knight, Lucas is a knave, Liam is a knight, Sofia is a knight, and Aiden is a knave.", "solution_text_format": "(1) Harper is a knight\n(2) Aurora is a knight\n(3) Lucas is a knave\n(4) Liam is a knight\n(5) Sofia is a knight\n(6) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Lucas is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of Aiden that Sofia is not a knight.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Harper is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Sofia is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Harper is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Harper that Aiden is a knave if and only if Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Sofia is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Sofia is a knave then Aurora is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Lucas is a knave or Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 2)), ('->', ('lying', 4), ('telling-truth', 1)), ('lying', 4), ('or', ('lying', 2), ('lying', 4)), ('telling-truth', 0), ('not', ('telling-truth', 4)))", "index": 507}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Jacob, Matthew, Sofia, David, and Chloe. \"If Sofia is a knight then Chloe is a knave,\" Jackson claimed. In a statement by Jacob: \"Chloe is a knave and Matthew is a knight\". Matthew told you that Chloe is a knave or Jackson is a knave. Sofia commented, \"Chloe is a knave and Jackson is a knight\". David said, \"Chloe is not a knight.\" According to Chloe, \"If Matthew is a knight then Sofia is a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Jacob", "Matthew", "Sofia", "David", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true], "solution_text": "Jackson is a knight, Jacob is a knave, Matthew is a knave, Sofia is a knave, David is a knave, and Chloe is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Jacob is a knave\n(3) Matthew is a knave\n(4) Sofia is a knave\n(5) David is a knave\n(6) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that If Sofia is a knight then Chloe is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Chloe is a knave and Jackson is a knight.", "Chloe cannot be a knight, because this would contradict the claim of Jackson that If Sofia is a knight then Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knight then Sofia is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Chloe is a knave and Jackson is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Matthew is a knight then Sofia is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Chloe is a knave or Jackson is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Chloe is a knave or Jackson is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Matthew is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Chloe is a knave and Matthew is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Chloe is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that Chloe is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 5)), ('and', ('lying', 5), ('telling-truth', 2)), ('or', ('lying', 5), ('lying', 0)), ('and', ('lying', 5), ('telling-truth', 0)), ('not', ('telling-truth', 5)), ('->', ('telling-truth', 2), ('telling-truth', 3)))", "index": 508}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Benjamin, Henry, Aiden, Alexander, and Logan. Abigail said, \"If Abigail is a knight then Logan is a knave.\" Benjamin told you that If Henry is a knight then Alexander is a knave. Henry was heard saying, \"Logan is not a knight\". In a statement by Aiden: \"If Benjamin is a knave then Alexander is a knave\". Alexander was heard saying, \"Henry is not a knight\". Logan told you that If Alexander is a knave then Benjamin is a knave. So who is a knight and who is a knave?", "names": ["Abigail", "Benjamin", "Henry", "Aiden", "Alexander", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Abigail is a knight, Benjamin is a knight, Henry is a knight, Aiden is a knight, Alexander is a knave, and Logan is a knave.", "solution_text_format": "(1) Abigail is a knight\n(2) Benjamin is a knight\n(3) Henry is a knight\n(4) Aiden is a knight\n(5) Alexander is a knave\n(6) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that If Abigail is a knight then Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Abigail that If Abigail is a knight then Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that If Alexander is a knave then Benjamin is a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Logan that If Alexander is a knave then Benjamin is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Logan is not a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Henry is a knight then Alexander is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Benjamin is a knave then Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('lying', 5)), ('->', ('telling-truth', 2), ('lying', 4)), ('not', ('telling-truth', 5)), ('->', ('lying', 1), ('lying', 4)), ('not', ('telling-truth', 2)), ('->', ('lying', 4), ('lying', 1)))", "index": 509}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Joseph, Amelia, William, Lily, and Ethan. In a statement by Abigail: \"If Ethan is a knave then Joseph is a knave\". \"Amelia is a knave if and only if William is a knight\" - Joseph. Amelia remarked, \"Lily is not a knight\". As William put it, \"Amelia is a knave or Amelia is a knight\". Lily commented, \"Abigail is a knight if and only if Lily is a knight\". Ethan asserted: \"Joseph is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Joseph", "Amelia", "William", "Lily", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "Abigail is a knight, Joseph is a knave, Amelia is a knight, William is a knight, Lily is a knave, and Ethan is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) Joseph is a knave\n(3) Amelia is a knight\n(4) William is a knight\n(5) Lily is a knave\n(6) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that If Ethan is a knave then Joseph is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Ethan that Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if William is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Amelia that Lily is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Lily is a knight.", "Assume William is a knight. No contradiction is found in their claim that Amelia is a knave or Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 1)), ('<=>', ('lying', 2), ('telling-truth', 3)), ('not', ('telling-truth', 4)), ('or', ('lying', 2), ('telling-truth', 2)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('lying', 1))", "index": 510}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Aria, Scarlett, Penelope, David, and Noah. Sebastian said that David is a knave. \"If Noah is a knight then Sebastian is a knave,\" Aria claimed. \"Sebastian is a knave and Noah is a knave\" - Scarlett. As Penelope put it, \"David is a knave\". David said that Noah is a knave if and only if Aria is a knave. Noah said that If Noah is a knight then Sebastian is a knight. So who is a knight and who is a knave?", "names": ["Sebastian", "Aria", "Scarlett", "Penelope", "David", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true], "solution_text": "Sebastian is a knight, Aria is a knave, Scarlett is a knave, Penelope is a knight, David is a knave, and Noah is a knight.", "solution_text_format": "(1) Sebastian is a knight\n(2) Aria is a knave\n(3) Scarlett is a knave\n(4) Penelope is a knight\n(5) David is a knave\n(6) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Sebastian that David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Aria is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Noah is a knight then Sebastian is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that If Noah is a knight then Sebastian is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that If Noah is a knight then Sebastian is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Noah is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Sebastian is a knave and Noah is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('->', ('telling-truth', 5), ('lying', 0)), ('and', ('lying', 0), ('lying', 5)), ('lying', 4), ('<=>', ('lying', 5), ('lying', 1)), ('->', ('telling-truth', 5), ('telling-truth', 0)))", "index": 511}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Joseph, Lucas, Emma, Grace, and Chloe. Mason commented, \"Joseph is a knight if and only if Mason is a knight\". According to Joseph, \"Emma is a knight and Joseph is a knight\". Lucas stated, \"Joseph is not a knave\". In a statement by Emma: \"Grace is not a knight\". Grace expressed that Chloe is a knight. \"Mason is a knight,\" Chloe claimed. So who is a knight and who is a knave?", "names": ["Mason", "Joseph", "Lucas", "Emma", "Grace", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Mason is a knave, Joseph is a knight, Lucas is a knight, Emma is a knight, Grace is a knave, and Chloe is a knave.", "solution_text_format": "(1) Mason is a knave\n(2) Joseph is a knight\n(3) Lucas is a knight\n(4) Emma is a knight\n(5) Grace is a knave\n(6) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Mason is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Emma is a knight and Joseph is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Grace is not a knight.", "Grace cannot be a knight, because this would contradict the claim of Emma that Grace is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Grace that Chloe is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Mason is a knight.", "We have exhausted all possibilities for Chloe and Grace, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the claim of Joseph that Emma is a knight and Joseph is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Mason that Joseph is a knight if and only if Mason is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Mason is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Emma is a knight and Joseph is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Grace is not a knight.", "Grace cannot be a knight, because this would contradict the claim of Emma that Grace is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Grace that Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Mason is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Joseph is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('telling-truth', 3), ('telling-truth', 1)), ('not', ('lying', 1)), ('not', ('telling-truth', 4)), ('telling-truth', 5), ('telling-truth', 0))", "index": 512}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Matthew, Noah, Scarlett, Jackson, and Evelyn. David noted, \"Scarlett is not a knave\". Matthew said that Noah is a knave or David is a knave. Noah told you that Jackson is a knave or Matthew is a knight. \"David is a knave if and only if David is a knight,\" Scarlett mentioned. As Jackson put it, \"Matthew is a knave\". Evelyn expressed that Evelyn is a knight and Jackson is a knight. So who is a knight and who is a knave?", "names": ["David", "Matthew", "Noah", "Scarlett", "Jackson", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "David is a knave, Matthew is a knight, Noah is a knight, Scarlett is a knave, Jackson is a knave, and Evelyn is a knave.", "solution_text_format": "(1) David is a knave\n(2) Matthew is a knight\n(3) Noah is a knight\n(4) Scarlett is a knave\n(5) Jackson is a knave\n(6) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that David is a knave if and only if David is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of David that Scarlett is not a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Scarlett cannot be a knight, because this would contradict the false claim of David that Scarlett is not a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that David is a knave if and only if David is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Noah is a knave or David is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Jackson is a knave or Matthew is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Matthew is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Matthew is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight and Jackson is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Evelyn is a knight and Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('or', ('lying', 2), ('lying', 0)), ('or', ('lying', 4), ('telling-truth', 1)), ('<=>', ('lying', 0), ('telling-truth', 0)), ('lying', 1), ('and', ('telling-truth', 5), ('telling-truth', 4)))", "index": 513}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Jack, Ella, Scarlett, Noah, and Amelia. In James's words: \"Ella is a knave\". Jack said that Scarlett is a knave or Ella is a knight. Ella asserted: \"Scarlett is a knave if and only if Jack is a knight\". Scarlett expressed that Noah is a knight if and only if Amelia is a knight. Noah expressed that James is a knight and Ella is a knave. Amelia commented, \"Ella is not a knave\". So who is a knight and who is a knave?", "names": ["James", "Jack", "Ella", "Scarlett", "Noah", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "James is a knave, Jack is a knight, Ella is a knight, Scarlett is a knave, Noah is a knave, and Amelia is a knight.", "solution_text_format": "(1) James is a knave\n(2) Jack is a knight\n(3) Ella is a knight\n(4) Scarlett is a knave\n(5) Noah is a knave\n(6) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of James that Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Jack is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Noah is a knight if and only if Amelia is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that James is a knight and Ella is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.", "Amelia cannot be a knave, because this would contradict the claim of Scarlett that Noah is a knight if and only if Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of their own that James is a knight and Ella is a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Amelia is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that James is a knight and Ella is a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Scarlett that Noah is a knight if and only if Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Jack cannot be a knight, because this would contradict the false claim of Ella that Scarlett is a knave if and only if Jack is a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knave or Ella is a knight.", "We have exhausted all possibilities for Jack and Amelia, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the false claim of their own that James is a knight and Ella is a knave.", "We have exhausted all possibilities for Noah, Scarlett, and Ella, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Jack is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Noah is a knight if and only if Amelia is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that James is a knight and Ella is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that James is a knight and Ella is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Scarlett that Noah is a knight if and only if Amelia is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Ella is not a knave.", "We have exhausted all possibilities for Amelia and Noah, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Amelia is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that James is a knight and Ella is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that James is a knight and Ella is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Scarlett is a knave or Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('or', ('lying', 3), ('telling-truth', 2)), ('<=>', ('lying', 3), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('lying', 2)), ('not', ('lying', 2)))", "index": 514}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Lucas, Victoria, Michael, Sophia, and Amelia. William stated, \"Victoria is a knave and Michael is a knight\". \"Victoria is a knave and Michael is a knave,\" Lucas claimed. Victoria remarked, \"Lucas is a knight and William is a knave\". Michael told you that If Lucas is a knight then Victoria is a knave. Sophia said that William is a knight if and only if Lucas is a knave. \"Lucas is a knight if and only if William is a knight,\" Amelia declared. So who is a knight and who is a knave?", "names": ["William", "Lucas", "Victoria", "Michael", "Sophia", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false], "solution_text": "William is a knight, Lucas is a knave, Victoria is a knave, Michael is a knight, Sophia is a knight, and Amelia is a knave.", "solution_text_format": "(1) William is a knight\n(2) Lucas is a knave\n(3) Victoria is a knave\n(4) Michael is a knight\n(5) Sophia is a knight\n(6) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Victoria is a knave and Michael is a knight.", "Victoria cannot be a knight, because this would contradict the claim of William that Victoria is a knave and Michael is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Lucas is a knight and William is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Victoria is a knave and Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Lucas that Victoria is a knave and Michael is a knave.", "Michael cannot be a knave, because this would contradict the claim of William that Victoria is a knave and Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Victoria is a knave and Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Lucas is a knight then Victoria is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that William is a knight if and only if Lucas is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Lucas is a knight if and only if William is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('telling-truth', 3)), ('and', ('lying', 2), ('lying', 3)), ('and', ('telling-truth', 1), ('lying', 0)), ('->', ('telling-truth', 1), ('lying', 2)), ('<=>', ('telling-truth', 0), ('lying', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)))", "index": 515}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Emily, Aria, Harper, Samuel, and Sophia. Sebastian told you that Emily is a knave. Emily expressed that Sophia is a knave. Aria told you that If Harper is a knight then Samuel is a knight. Harper noted, \"Samuel is a knight\". Samuel was heard saying, \"Sebastian is a knight or Aria is a knave\". Sophia noted, \"If Harper is a knight then Sophia is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "Emily", "Aria", "Harper", "Samuel", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Sebastian is a knight, Emily is a knave, Aria is a knight, Harper is a knight, Samuel is a knight, and Sophia is a knight.", "solution_text_format": "(1) Sebastian is a knight\n(2) Emily is a knave\n(3) Aria is a knight\n(4) Harper is a knight\n(5) Samuel is a knight\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Sebastian that Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Harper is a knight then Sophia is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Sebastian is a knight or Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Harper is a knight then Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('lying', 5), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('telling-truth', 4), ('or', ('telling-truth', 0), ('lying', 2)), ('->', ('telling-truth', 3), ('telling-truth', 5)))", "index": 516}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Aria, Samuel, Sofia, Zoey, and Emma. According to Emily, \"Aria is a knight and Samuel is a knave\". \"Samuel is a knave if and only if Emma is a knave\" - Aria. Samuel noted, \"If Sofia is a knave then Aria is a knave\". \"If Aria is a knave then Emily is a knave,\" Sofia declared. \"If Aria is a knight then Sofia is a knave,\" Zoey claimed. \"Sofia is not a knave,\" Emma declared. So who is a knight and who is a knave?", "names": ["Emily", "Aria", "Samuel", "Sofia", "Zoey", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Emily is a knave, Aria is a knight, Samuel is a knight, Sofia is a knight, Zoey is a knave, and Emma is a knight.", "solution_text_format": "(1) Emily is a knave\n(2) Aria is a knight\n(3) Samuel is a knight\n(4) Sofia is a knight\n(5) Zoey is a knave\n(6) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Aria is a knight and Samuel is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Emma is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Emily that Aria is a knight and Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that If Sofia is a knave then Aria is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Samuel that If Sofia is a knave then Aria is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Aria is a knave then Emily is a knave.", "We have exhausted all possibilities for Sofia and Samuel, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Emily that Aria is a knight and Samuel is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Aria is a knight and Samuel is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Emma is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Sofia is a knave then Aria is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Aria is a knave then Emily is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that If Aria is a knight then Sofia is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Aria is a knight then Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 2)), ('<=>', ('lying', 2), ('lying', 5)), ('->', ('lying', 3), ('lying', 1)), ('->', ('lying', 1), ('lying', 0)), ('->', ('telling-truth', 1), ('lying', 3)), ('not', ('lying', 3)))", "index": 517}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, William, Jack, Chloe, Scarlett, and Henry. As Jackson put it, \"If William is a knave then Henry is a knight\". William stated, \"Jack is a knave and Chloe is a knight\". In Jack's words: \"Scarlett is a knight or Scarlett is a knave\". Chloe commented, \"William is a knave and Scarlett is a knave\". In a statement by Scarlett: \"Jack is a knave\". In a statement by Henry: \"If Jack is a knight then Chloe is a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "William", "Jack", "Chloe", "Scarlett", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "Jackson is a knight, William is a knave, Jack is a knight, Chloe is a knight, Scarlett is a knave, and Henry is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) William is a knave\n(3) Jack is a knight\n(4) Chloe is a knight\n(5) Scarlett is a knave\n(6) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that If William is a knave then Henry is a knight.", "Assume William is a knight. No contradiction is found in their claim that Jack is a knave and Chloe is a knight.", "Jack cannot be a knight, because this would contradict the claim of William that Jack is a knave and Chloe is a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knight or Scarlett is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Jack is a knave and Chloe is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Scarlett is a knight or Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Jack is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Jack is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that William is a knave and Scarlett is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Jack is a knight then Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 5)), ('and', ('lying', 2), ('telling-truth', 3)), ('or', ('telling-truth', 4), ('lying', 4)), ('and', ('lying', 1), ('lying', 4)), ('lying', 2), ('->', ('telling-truth', 2), ('telling-truth', 3)))", "index": 518}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, William, Chloe, Logan, Scarlett, and Sebastian. Amelia noted, \"Chloe is a knight and William is a knight\". William commented, \"William is a knight or Logan is a knight\". Chloe said, \"Logan is a knight and Scarlett is a knight.\" \"Sebastian is a knave,\" Logan declared. \"Chloe is a knave or Chloe is a knight,\" Scarlett declared. Sebastian remarked, \"William is not a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "William", "Chloe", "Logan", "Scarlett", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true], "solution_text": "Amelia is a knave, William is a knight, Chloe is a knave, Logan is a knave, Scarlett is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Amelia is a knave\n(2) William is a knight\n(3) Chloe is a knave\n(4) Logan is a knave\n(5) Scarlett is a knight\n(6) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Chloe is a knight and William is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Logan is a knight and Scarlett is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Logan that Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that William is not a knave.", "William cannot be a knight, because this would contradict the false claim of Sebastian that William is not a knave.", "William cannot be a knave, because this would contradict the claim of Amelia that Chloe is a knight and William is a knight.", "We have exhausted all possibilities for William and Sebastian, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Chloe that Logan is a knight and Scarlett is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Amelia that Chloe is a knight and William is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Chloe is a knight and William is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Logan is a knight and Scarlett is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Logan that Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that William is not a knave.", "William cannot be a knight, because this would contradict the false claim of Amelia that Chloe is a knight and William is a knight.", "William cannot be a knave, because this would contradict the false claim of their own that William is a knight or Logan is a knight.", "We have exhausted all possibilities for William and Sebastian, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Chloe that Logan is a knight and Scarlett is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Logan is a knight and Scarlett is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Logan that Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that William is not a knave.", "William cannot be a knight, because this would contradict the false claim of Sebastian that William is not a knave.", "William cannot be a knave, because this would contradict the false claim of their own that William is a knight or Logan is a knight.", "We have exhausted all possibilities for William and Sebastian, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that William is not a knave.", "Assume William is a knight. No contradiction is found in their claim that William is a knight or Logan is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Chloe is a knave or Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('and', ('telling-truth', 3), ('telling-truth', 4)), ('lying', 5), ('or', ('lying', 2), ('telling-truth', 2)), ('not', ('lying', 1)))", "index": 519}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Avery, Benjamin, Oliver, Isabella, and Aiden. Riley stated, \"Benjamin is a knave\". Avery told you that Aiden is a knight or Benjamin is a knave. Benjamin commented, \"Aiden is a knight or Oliver is a knave\". Oliver told you that Isabella is a knight if and only if Aiden is a knight. \"Riley is not a knight,\" Isabella declared. Aiden said, \"Oliver is a knave.\" So who is a knight and who is a knave?", "names": ["Riley", "Avery", "Benjamin", "Oliver", "Isabella", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Riley is a knight, Avery is a knight, Benjamin is a knave, Oliver is a knight, Isabella is a knave, and Aiden is a knave.", "solution_text_format": "(1) Riley is a knight\n(2) Avery is a knight\n(3) Benjamin is a knave\n(4) Oliver is a knight\n(5) Isabella is a knave\n(6) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Riley that Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Aiden is a knight or Oliver is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Benjamin that Aiden is a knight or Oliver is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Aiden is a knight.", "Isabella cannot be a knight, because this would contradict the claim of Oliver that Isabella is a knight if and only if Aiden is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Aiden is a knight or Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('or', ('telling-truth', 5), ('lying', 2)), ('or', ('telling-truth', 5), ('lying', 3)), ('<=>', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('telling-truth', 0)), ('lying', 3))", "index": 520}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Logan, Aria, Owen, Alexander, and William. \"William is not a knave\" - Evelyn. Logan noted, \"If Evelyn is a knight then Aria is a knave\". \"Logan is a knight and William is a knave\" - Aria. In Owen's words: \"William is a knave if and only if Evelyn is a knight\". Alexander told you that Owen is not a knave. \"If Logan is a knight then Alexander is a knight,\" William mentioned. So who is a knight and who is a knave?", "names": ["Evelyn", "Logan", "Aria", "Owen", "Alexander", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Evelyn is a knave, Logan is a knight, Aria is a knight, Owen is a knave, Alexander is a knave, and William is a knave.", "solution_text_format": "(1) Evelyn is a knave\n(2) Logan is a knight\n(3) Aria is a knight\n(4) Owen is a knave\n(5) Alexander is a knave\n(6) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that William is not a knave.", "Assume William is a knight. No contradiction is found in their claim that If Logan is a knight then Alexander is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Evelyn is a knight then Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Logan that If Evelyn is a knight then Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Logan is a knight and William is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Owen is not a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that William is a knave if and only if Evelyn is a knight.", "Owen cannot be a knave, because this would contradict the claim of Alexander that Owen is not a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of William that If Logan is a knight then Alexander is a knight.", "We have exhausted all possibilities for Alexander and Aria, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Logan is a knight and William is a knave.", "Aria cannot be a knave, because this would contradict the false claim of Logan that If Evelyn is a knight then Aria is a knave.", "We have exhausted all possibilities for Aria and Logan, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Evelyn that William is not a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that William is not a knave.", "William cannot be a knight, because this would contradict the false claim of Evelyn that William is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that If Logan is a knight then Alexander is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Evelyn is a knight then Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Logan is a knight and William is a knave.", "Alexander cannot be a knight, because this would contradict the false claim of William that If Logan is a knight then Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Owen is not a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that William is a knave if and only if Evelyn is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that William is a knave if and only if Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('->', ('telling-truth', 0), ('lying', 2)), ('and', ('telling-truth', 1), ('lying', 5)), ('<=>', ('lying', 5), ('telling-truth', 0)), ('not', ('lying', 3)), ('->', ('telling-truth', 1), ('telling-truth', 4)))", "index": 521}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Ella, Scarlett, Ethan, Riley, and Victoria. Avery stated, \"Avery is a knight and Ella is a knight\". In a statement by Ella: \"Scarlett is not a knight\". In Scarlett's words: \"Victoria is a knight if and only if Riley is a knave\". Ethan remarked, \"Avery is not a knave\". \"Ethan is a knave\" - Riley. In a statement by Victoria: \"Riley is a knave and Ella is a knight\". So who is a knight and who is a knave?", "names": ["Avery", "Ella", "Scarlett", "Ethan", "Riley", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "Avery is a knave, Ella is a knave, Scarlett is a knight, Ethan is a knave, Riley is a knight, and Victoria is a knave.", "solution_text_format": "(1) Avery is a knave\n(2) Ella is a knave\n(3) Scarlett is a knight\n(4) Ethan is a knave\n(5) Riley is a knight\n(6) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Avery is a knight and Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Scarlett is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Ella that Scarlett is not a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Riley is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Riley is a knave and Ella is a knight.", "Riley cannot be a knight, because this would contradict the claim of Victoria that Riley is a knave and Ella is a knight.", "Riley cannot be a knave, because this would contradict the false claim of Scarlett that Victoria is a knight if and only if Riley is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Riley is a knave and Ella is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Scarlett that Victoria is a knight if and only if Riley is a knave.", "Riley cannot be a knave, because this would contradict the false claim of Victoria that Riley is a knave and Ella is a knight.", "We have exhausted all possibilities for Riley, Victoria, and Scarlett, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Avery that Avery is a knight and Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Avery is a knight and Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Scarlett is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Ella that Scarlett is not a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Riley is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Riley is a knave and Ella is a knight.", "Riley cannot be a knight, because this would contradict the claim of Victoria that Riley is a knave and Ella is a knight.", "Riley cannot be a knave, because this would contradict the false claim of Scarlett that Victoria is a knight if and only if Riley is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Riley is a knave and Ella is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Scarlett that Victoria is a knight if and only if Riley is a knave.", "Riley cannot be a knave, because this would contradict the false claim of Victoria that Riley is a knave and Ella is a knight.", "We have exhausted all possibilities for Riley, Victoria, and Scarlett, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Scarlett is not a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Riley is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Ella is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Riley is a knave and Ella is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Avery is not a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Avery is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('lying', 4)), ('not', ('lying', 0)), ('lying', 3), ('and', ('lying', 4), ('telling-truth', 1)))", "index": 522}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Jacob, Sebastian, Emily, Alexander, and David. Olivia said, \"Alexander is a knight.\" In a statement by Jacob: \"If Emily is a knight then David is a knave\". Sebastian expressed that Olivia is a knave. According to Emily, \"Jacob is a knight\". Alexander expressed that Jacob is a knave. According to David, \"Jacob is a knight if and only if Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Olivia", "Jacob", "Sebastian", "Emily", "Alexander", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Olivia is a knave, Jacob is a knight, Sebastian is a knight, Emily is a knight, Alexander is a knave, and David is a knave.", "solution_text_format": "(1) Olivia is a knave\n(2) Jacob is a knight\n(3) Sebastian is a knight\n(4) Emily is a knight\n(5) Alexander is a knave\n(6) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Alexander that Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Emily is a knight then David is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Jacob is a knight.", "Emily cannot be a knave, because this would contradict the false claim of Jacob that If Emily is a knight then David is a knave.", "We have exhausted all possibilities for Emily and Jacob, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Olivia that Alexander is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Olivia that Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Emily is a knight then David is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Jacob is a knight.", "David cannot be a knight, because this would contradict the claim of Jacob that If Emily is a knight then David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Alexander is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('->', ('telling-truth', 3), ('lying', 5)), ('lying', 0), ('telling-truth', 1), ('lying', 1), ('<=>', ('telling-truth', 1), ('telling-truth', 4)))", "index": 523}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, James, William, Grace, Chloe, and David. Olivia said, \"Chloe is a knave or William is a knave.\" James commented, \"David is not a knave\". As William put it, \"David is not a knight\". Grace remarked, \"James is a knight if and only if Chloe is a knave\". Chloe said that William is a knight and Olivia is a knave. According to David, \"James is a knave or Grace is a knight\". So who is a knight and who is a knave?", "names": ["Olivia", "James", "William", "Grace", "Chloe", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Olivia is a knight, James is a knight, William is a knave, Grace is a knight, Chloe is a knave, and David is a knight.", "solution_text_format": "(1) Olivia is a knight\n(2) James is a knight\n(3) William is a knave\n(4) Grace is a knight\n(5) Chloe is a knave\n(6) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Chloe is a knave or William is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that William is a knight and Olivia is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that William is a knight and Olivia is a knave.", "Assume William is a knight. No contradiction is found in their claim that David is not a knight.", "David cannot be a knight, because this would contradict the claim of William that David is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that James is a knave or Grace is a knight.", "James cannot be a knight, because this would contradict the claim of their own that David is not a knave.", "James cannot be a knave, because this would contradict the false claim of David that James is a knave or Grace is a knight.", "We have exhausted all possibilities for James and David, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that David is not a knight.", "Assume David is a knight. No contradiction is found in their claim that James is a knave or Grace is a knight.", "Assume James is a knight. No contradiction is found in their claim that David is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that James is a knight if and only if Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('lying', 2)), ('not', ('lying', 5)), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 1), ('lying', 4)), ('and', ('telling-truth', 2), ('lying', 0)), ('or', ('lying', 1), ('telling-truth', 3)))", "index": 524}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Elizabeth, Charlotte, Oliver, Daniel, and Michael. Luke said that Charlotte is a knave and Elizabeth is a knave. Elizabeth asserted: \"Charlotte is a knave or Oliver is a knave\". \"If Elizabeth is a knight then Luke is a knave,\" Charlotte claimed. \"Oliver is a knight or Michael is a knight,\" Oliver mentioned. As Daniel put it, \"Michael is not a knave\". Michael remarked, \"Oliver is a knight and Daniel is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Elizabeth", "Charlotte", "Oliver", "Daniel", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Luke is a knave, Elizabeth is a knight, Charlotte is a knight, Oliver is a knave, Daniel is a knave, and Michael is a knave.", "solution_text_format": "(1) Luke is a knave\n(2) Elizabeth is a knight\n(3) Charlotte is a knight\n(4) Oliver is a knave\n(5) Daniel is a knave\n(6) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Charlotte is a knave and Elizabeth is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Luke that Charlotte is a knave and Elizabeth is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Elizabeth is a knight then Luke is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Luke that Charlotte is a knave and Elizabeth is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Charlotte is a knave or Oliver is a knave.", "We have exhausted all possibilities for Elizabeth and Charlotte, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Charlotte is a knave and Elizabeth is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Luke is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Charlotte is a knave or Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Elizabeth that Charlotte is a knave or Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Oliver is a knight or Michael is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Oliver that Oliver is a knight or Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Oliver is a knight and Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Michael is not a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Michael is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 1)), ('or', ('lying', 2), ('lying', 3)), ('->', ('telling-truth', 1), ('lying', 0)), ('or', ('telling-truth', 3), ('telling-truth', 5)), ('not', ('lying', 5)), ('and', ('telling-truth', 3), ('lying', 4)))", "index": 525}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Chloe, Alexander, Scarlett, Evelyn, and Charlotte. Sophia expressed that Chloe is not a knight. \"Evelyn is not a knave,\" Chloe claimed. Alexander noted, \"Evelyn is a knight or Alexander is a knight\". In a statement by Scarlett: \"Charlotte is a knight or Chloe is a knight\". \"If Alexander is a knave then Alexander is a knight,\" Evelyn mentioned. As Charlotte put it, \"If Charlotte is a knight then Evelyn is a knight\". So who is a knight and who is a knave?", "names": ["Sophia", "Chloe", "Alexander", "Scarlett", "Evelyn", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Sophia is a knave, Chloe is a knight, Alexander is a knight, Scarlett is a knight, Evelyn is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Sophia is a knave\n(2) Chloe is a knight\n(3) Alexander is a knight\n(4) Scarlett is a knight\n(5) Evelyn is a knight\n(6) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of Sophia that Chloe is not a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Evelyn is not a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of Chloe that Evelyn is not a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Alexander is a knave then Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Evelyn that If Alexander is a knave then Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Evelyn is a knight or Alexander is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Charlotte is a knight or Chloe is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that If Charlotte is a knight then Evelyn is a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Scarlett that Charlotte is a knight or Chloe is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Charlotte is a knight or Chloe is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Scarlett that Charlotte is a knight or Chloe is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Charlotte is a knight then Evelyn is a knight.", "We have exhausted all possibilities for Charlotte, Scarlett, Alexander, Evelyn, and Chloe, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Evelyn is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Alexander is a knave then Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Evelyn is a knight or Alexander is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Charlotte is a knight or Chloe is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Charlotte is a knight then Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('not', ('lying', 4)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('telling-truth', 5), ('telling-truth', 1)), ('->', ('lying', 2), ('telling-truth', 2)), ('->', ('telling-truth', 5), ('telling-truth', 4)))", "index": 526}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Emma, Olivia, William, Lily, and Ella. Owen asserted: \"Ella is a knight\". Emma stated, \"Lily is a knight and William is a knight\". In Olivia's words: \"William is not a knight\". William expressed that Owen is a knave if and only if Olivia is a knight. Lily asserted: \"Olivia is a knave\". As Ella put it, \"Lily is a knave and Ella is a knight\". So who is a knight and who is a knave?", "names": ["Owen", "Emma", "Olivia", "William", "Lily", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Owen is a knight, Emma is a knave, Olivia is a knight, William is a knave, Lily is a knave, and Ella is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Emma is a knave\n(3) Olivia is a knight\n(4) William is a knave\n(5) Lily is a knave\n(6) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Lily is a knave and Ella is a knight.", "Lily cannot be a knight, because this would contradict the claim of Ella that Lily is a knave and Ella is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that William is not a knight.", "William cannot be a knight, because this would contradict the claim of Olivia that William is not a knight.", "Assume William is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Olivia is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Lily is a knight and William is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Lily is a knight and William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('and', ('telling-truth', 4), ('telling-truth', 3)), ('not', ('telling-truth', 3)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('lying', 2), ('and', ('lying', 4), ('telling-truth', 5)))", "index": 527}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Lucas, Logan, Elizabeth, Ethan, and Noah. Michael said, \"Logan is a knave if and only if Ethan is a knave.\" \"Noah is a knave,\" Lucas mentioned. Logan noted, \"Ethan is not a knight\". Elizabeth said, \"Logan is a knave and Noah is a knave.\" Ethan said that Lucas is a knave if and only if Noah is a knave. Noah remarked, \"Elizabeth is not a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Lucas", "Logan", "Elizabeth", "Ethan", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true], "solution_text": "Michael is a knave, Lucas is a knave, Logan is a knight, Elizabeth is a knave, Ethan is a knave, and Noah is a knight.", "solution_text_format": "(1) Michael is a knave\n(2) Lucas is a knave\n(3) Logan is a knight\n(4) Elizabeth is a knave\n(5) Ethan is a knave\n(6) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Logan is a knave if and only if Ethan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of Logan that Ethan is not a knight.", "Ethan cannot be a knave, because this would contradict the claim of Michael that Logan is a knave if and only if Ethan is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of Michael that Logan is a knave if and only if Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of Logan that Ethan is not a knight.", "We have exhausted all possibilities for Ethan and Logan, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Ethan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Michael that Logan is a knave if and only if Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Noah is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Lucas that Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Noah is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of Noah that Elizabeth is not a knight.", "We have exhausted all possibilities for Elizabeth and Noah, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Noah is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Logan is a knave and Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 4)), ('lying', 5), ('not', ('telling-truth', 4)), ('and', ('lying', 2), ('lying', 5)), ('<=>', ('lying', 1), ('lying', 5)), ('not', ('telling-truth', 3)))", "index": 528}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Ella, Elizabeth, Aiden, Zoey, and Mason. \"If Elizabeth is a knave then Aiden is a knave\" - Ethan. \"Aiden is a knight or Elizabeth is a knight,\" Ella claimed. Elizabeth noted, \"Mason is a knight or Ella is a knight\". Aiden told you that If Zoey is a knight then Mason is a knight. \"Ella is a knight if and only if Aiden is a knave,\" Zoey mentioned. \"If Ella is a knight then Zoey is a knight,\" Mason mentioned. So who is a knight and who is a knave?", "names": ["Ethan", "Ella", "Elizabeth", "Aiden", "Zoey", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Ethan is a knight, Ella is a knight, Elizabeth is a knight, Aiden is a knight, Zoey is a knave, and Mason is a knave.", "solution_text_format": "(1) Ethan is a knight\n(2) Ella is a knight\n(3) Elizabeth is a knight\n(4) Aiden is a knight\n(5) Zoey is a knave\n(6) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Aiden is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Mason is a knight or Ella is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Ella is a knight then Zoey is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Aiden is a knight or Elizabeth is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Zoey is a knight then Mason is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Ella is a knight if and only if Aiden is a knave.", "Zoey cannot be a knave, because this would contradict the claim of Mason that If Ella is a knight then Zoey is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that If Zoey is a knight then Mason is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that Aiden is a knight or Elizabeth is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that If Ella is a knight then Zoey is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Aiden is a knight or Elizabeth is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Zoey is a knight then Mason is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Aiden that If Zoey is a knight then Mason is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 3)), ('or', ('telling-truth', 3), ('telling-truth', 2)), ('or', ('telling-truth', 5), ('telling-truth', 1)), ('->', ('telling-truth', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 1), ('lying', 3)), ('->', ('telling-truth', 1), ('telling-truth', 4)))", "index": 529}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Benjamin, Ava, Jacob, Charlotte, and Chloe. Harper noted, \"Ava is a knight if and only if Charlotte is a knight\". \"Ava is a knight and Charlotte is a knight,\" Benjamin declared. \"Charlotte is a knave and Jacob is a knight,\" Ava mentioned. Jacob stated, \"If Chloe is a knight then Ava is a knight\". As Charlotte put it, \"If Chloe is a knave then Benjamin is a knave\". In Chloe's words: \"Ava is not a knave\". So who is a knight and who is a knave?", "names": ["Harper", "Benjamin", "Ava", "Jacob", "Charlotte", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false], "solution_text": "Harper is a knave, Benjamin is a knave, Ava is a knave, Jacob is a knight, Charlotte is a knight, and Chloe is a knave.", "solution_text_format": "(1) Harper is a knave\n(2) Benjamin is a knave\n(3) Ava is a knave\n(4) Jacob is a knight\n(5) Charlotte is a knight\n(6) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Ava is a knight if and only if Charlotte is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Charlotte is a knave and Jacob is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Ava that Charlotte is a knave and Jacob is a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Harper that Ava is a knight if and only if Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Charlotte is a knave and Jacob is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Harper that Ava is a knight if and only if Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Chloe is a knave then Benjamin is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Charlotte that If Chloe is a knave then Benjamin is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Ava is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Ava is a knight and Charlotte is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of Charlotte that If Chloe is a knave then Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, Chloe, Charlotte, and Ava, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Charlotte is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Charlotte is a knave and Jacob is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Harper that Ava is a knight if and only if Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Chloe is a knave then Benjamin is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Charlotte that If Chloe is a knave then Benjamin is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Ava is not a knave.", "We have exhausted all possibilities for Chloe and Charlotte, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Charlotte is a knave and Jacob is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Chloe is a knave then Benjamin is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Ava is not a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Ava is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Ava is a knight and Charlotte is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ava is a knight and Charlotte is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Chloe is a knight then Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('and', ('telling-truth', 2), ('telling-truth', 4)), ('and', ('lying', 4), ('telling-truth', 3)), ('->', ('telling-truth', 5), ('telling-truth', 2)), ('->', ('lying', 5), ('lying', 1)), ('not', ('lying', 2)))", "index": 530}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Sofia, Logan, Ella, Emma, and Victoria. As Charlotte put it, \"Victoria is a knave\". In Sofia's words: \"If Emma is a knight then Charlotte is a knave\". Logan was heard saying, \"Sofia is a knight and Charlotte is a knight\". According to Ella, \"Logan is not a knave\". As Emma put it, \"Charlotte is not a knave\". Victoria noted, \"Emma is a knave or Sofia is a knave\". So who is a knight and who is a knave?", "names": ["Charlotte", "Sofia", "Logan", "Ella", "Emma", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true], "solution_text": "Charlotte is a knave, Sofia is a knight, Logan is a knave, Ella is a knave, Emma is a knave, and Victoria is a knight.", "solution_text_format": "(1) Charlotte is a knave\n(2) Sofia is a knight\n(3) Logan is a knave\n(4) Ella is a knave\n(5) Emma is a knave\n(6) Victoria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Charlotte that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Emma is a knave or Sofia is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that If Emma is a knight then Charlotte is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of Victoria that Emma is a knave or Sofia is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the false claim of their own that Charlotte is not a knave.", "We have exhausted all possibilities for Emma and Victoria, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Emma is a knave or Sofia is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Charlotte is not a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Emma is a knight then Charlotte is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Charlotte is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Sofia is a knight and Charlotte is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Logan is not a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Logan is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('->', ('telling-truth', 4), ('lying', 0)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('lying', 2)), ('not', ('lying', 0)), ('or', ('lying', 4), ('lying', 1)))", "index": 531}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Isabella, Benjamin, Ella, Zoey, and Aiden. Oliver commented, \"Benjamin is not a knave\". Isabella said, \"Zoey is a knave.\" \"If Benjamin is a knight then Ella is a knight,\" Benjamin declared. Ella said, \"Zoey is a knight.\" Zoey said that If Oliver is a knave then Ella is a knight. According to Aiden, \"Isabella is a knave if and only if Oliver is a knave\". So who is a knight and who is a knave?", "names": ["Oliver", "Isabella", "Benjamin", "Ella", "Zoey", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Oliver is a knight, Isabella is a knave, Benjamin is a knight, Ella is a knight, Zoey is a knight, and Aiden is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) Isabella is a knave\n(3) Benjamin is a knight\n(4) Ella is a knight\n(5) Zoey is a knight\n(6) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Benjamin is a knight then Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Oliver is a knave then Ella is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Isabella is a knave if and only if Oliver is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('lying', 4), ('->', ('telling-truth', 2), ('telling-truth', 3)), ('telling-truth', 4), ('->', ('lying', 0), ('telling-truth', 3)), ('<=>', ('lying', 1), ('lying', 0)))", "index": 532}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Charlotte, Jack, Penelope, Luke, and Elizabeth. Scarlett stated, \"Luke is a knight or Charlotte is a knave\". Charlotte expressed that Scarlett is a knight and Elizabeth is a knight. Jack asserted: \"Charlotte is a knight\". Penelope commented, \"If Luke is a knave then Jack is a knight\". In a statement by Luke: \"Charlotte is a knight and Scarlett is a knight\". Elizabeth expressed that If Scarlett is a knave then Scarlett is a knight. So who is a knight and who is a knave?", "names": ["Scarlett", "Charlotte", "Jack", "Penelope", "Luke", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Scarlett is a knight, Charlotte is a knight, Jack is a knight, Penelope is a knight, Luke is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Scarlett is a knight\n(2) Charlotte is a knight\n(3) Jack is a knight\n(4) Penelope is a knight\n(5) Luke is a knight\n(6) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Luke is a knight or Charlotte is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Charlotte is a knight and Scarlett is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Scarlett is a knight and Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Scarlett is a knave then Scarlett is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Luke is a knave then Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('lying', 1)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('telling-truth', 1), ('->', ('lying', 4), ('telling-truth', 2)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('lying', 0), ('telling-truth', 0)))", "index": 533}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Jackson, Chloe, Scarlett, Noah, and Samuel. \"Samuel is a knave or Samuel is a knight,\" Benjamin claimed. Jackson expressed that Samuel is not a knight. Chloe stated, \"If Samuel is a knave then Noah is a knight\". Scarlett asserted: \"Scarlett is a knight or Chloe is a knave\". Noah expressed that Jackson is a knight and Benjamin is a knave. Samuel told you that Scarlett is not a knave. So who is a knight and who is a knave?", "names": ["Benjamin", "Jackson", "Chloe", "Scarlett", "Noah", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "Benjamin is a knight, Jackson is a knave, Chloe is a knight, Scarlett is a knight, Noah is a knave, and Samuel is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Jackson is a knave\n(3) Chloe is a knight\n(4) Scarlett is a knight\n(5) Noah is a knave\n(6) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Samuel is a knave or Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Scarlett is a knight or Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Samuel is a knave then Noah is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Jackson is a knight and Benjamin is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Jackson is a knight and Benjamin is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Samuel is not a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Samuel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 5)), ('not', ('telling-truth', 5)), ('->', ('lying', 5), ('telling-truth', 4)), ('or', ('telling-truth', 3), ('lying', 2)), ('and', ('telling-truth', 1), ('lying', 0)), ('not', ('lying', 3)))", "index": 534}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Sebastian, Amelia, Logan, Aurora, and Ethan. Luke remarked, \"Luke is a knight and Amelia is a knave\". \"Ethan is not a knave\" - Sebastian. Amelia stated, \"Luke is a knight if and only if Sebastian is a knave\". In a statement by Logan: \"Ethan is not a knight\". Aurora commented, \"Amelia is not a knave\". According to Ethan, \"Luke is a knave or Amelia is a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Sebastian", "Amelia", "Logan", "Aurora", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Luke is a knave, Sebastian is a knight, Amelia is a knight, Logan is a knave, Aurora is a knight, and Ethan is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Sebastian is a knight\n(3) Amelia is a knight\n(4) Logan is a knave\n(5) Aurora is a knight\n(6) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Luke is a knight and Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Luke that Luke is a knight and Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Luke is a knave or Amelia is a knight.", "Ethan cannot be a knave, because this would contradict the claim of Sebastian that Ethan is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of Amelia that Luke is a knight if and only if Sebastian is a knave.", "We have exhausted all possibilities for Sebastian and Amelia, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Luke is a knight and Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Luke is a knight if and only if Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Luke is a knave or Amelia is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Ethan is not a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Amelia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('lying', 2)), ('not', ('lying', 5)), ('<=>', ('telling-truth', 0), ('lying', 1)), ('not', ('telling-truth', 5)), ('not', ('lying', 2)), ('or', ('lying', 0), ('telling-truth', 2)))", "index": 535}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Elizabeth, Alexander, Jacob, Grace, and Joseph. \"Alexander is a knave if and only if Joseph is a knave,\" Harper mentioned. In a statement by Elizabeth: \"Elizabeth is a knight\". \"If Joseph is a knight then Jacob is a knight,\" Alexander declared. Jacob said, \"Joseph is a knave if and only if Elizabeth is a knight.\" Grace told you that Alexander is not a knight. Joseph was heard saying, \"Elizabeth is a knave and Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Harper", "Elizabeth", "Alexander", "Jacob", "Grace", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Harper is a knave, Elizabeth is a knight, Alexander is a knight, Jacob is a knight, Grace is a knave, and Joseph is a knave.", "solution_text_format": "(1) Harper is a knave\n(2) Elizabeth is a knight\n(3) Alexander is a knight\n(4) Jacob is a knight\n(5) Grace is a knave\n(6) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Joseph is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Joseph is a knight then Jacob is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Elizabeth is a knave and Jacob is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Joseph that Elizabeth is a knave and Jacob is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Joseph that Elizabeth is a knave and Jacob is a knave.", "Jacob cannot be a knave, because this would contradict the claim of Alexander that If Joseph is a knight then Jacob is a knight.", "We have exhausted all possibilities for Jacob and Elizabeth, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Harper that Alexander is a knave if and only if Joseph is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Joseph is a knight then Jacob is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Harper that Alexander is a knave if and only if Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of Alexander that If Joseph is a knight then Jacob is a knight.", "We have exhausted all possibilities for Joseph and Alexander, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Alexander is a knave if and only if Joseph is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Joseph is a knight then Jacob is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Harper that Alexander is a knave if and only if Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Jacob is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Elizabeth is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Alexander is not a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Alexander is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 5)), ('telling-truth', 1), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('<=>', ('lying', 5), ('telling-truth', 1)), ('not', ('telling-truth', 2)), ('and', ('lying', 1), ('lying', 3)))", "index": 536}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Abigail, Aria, Liam, Sebastian, and Scarlett. \"Abigail is a knave or Scarlett is a knight,\" Chloe claimed. Abigail noted, \"Liam is a knight\". \"Abigail is not a knave,\" Aria declared. Liam stated, \"Sebastian is a knight or Chloe is a knight\". Sebastian was heard saying, \"Aria is a knave if and only if Scarlett is a knight\". Scarlett expressed that Liam is not a knave. So who is a knight and who is a knave?", "names": ["Chloe", "Abigail", "Aria", "Liam", "Sebastian", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Chloe is a knight, Abigail is a knight, Aria is a knight, Liam is a knight, Sebastian is a knave, and Scarlett is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Abigail is a knight\n(3) Aria is a knight\n(4) Liam is a knight\n(5) Sebastian is a knave\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Abigail is a knave or Scarlett is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Sebastian is a knight or Chloe is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Aria is a knave if and only if Scarlett is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Sebastian that Aria is a knave if and only if Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Chloe that Abigail is a knave or Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the false claim of their own that Abigail is not a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Scarlett is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Liam is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 5)), ('telling-truth', 3), ('not', ('lying', 1)), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('<=>', ('lying', 2), ('telling-truth', 5)), ('not', ('lying', 3)))", "index": 537}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Mason, Elizabeth, Avery, Oliver, and Sofia. In a statement by Abigail: \"Abigail is a knight and Sofia is a knave\". Mason remarked, \"If Abigail is a knight then Sofia is a knight\". Elizabeth told you that Oliver is a knight and Avery is a knave. Avery commented, \"If Oliver is a knave then Mason is a knave\". Oliver was heard saying, \"Abigail is not a knave\". Sofia noted, \"If Elizabeth is a knight then Elizabeth is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Mason", "Elizabeth", "Avery", "Oliver", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true], "solution_text": "Abigail is a knave, Mason is a knight, Elizabeth is a knave, Avery is a knave, Oliver is a knave, and Sofia is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Mason is a knight\n(3) Elizabeth is a knave\n(4) Avery is a knave\n(5) Oliver is a knave\n(6) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Abigail is a knight and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Abigail that Abigail is a knight and Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Elizabeth is a knight then Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Oliver is a knight and Avery is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Avery cannot be a knight, because this would contradict the claim of Elizabeth that Oliver is a knight and Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that If Oliver is a knave then Mason is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Elizabeth that Oliver is a knight and Avery is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the false claim of Sofia that If Elizabeth is a knight then Elizabeth is a knave.", "We have exhausted all possibilities for Elizabeth and Sofia, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Abigail is a knight and Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Sofia that If Elizabeth is a knight then Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Oliver is a knight and Avery is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Abigail is not a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Abigail is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Oliver is a knave then Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Avery that If Oliver is a knave then Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that If Abigail is a knight then Sofia is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Oliver is a knave then Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Abigail is a knight then Sofia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('lying', 5)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('telling-truth', 4), ('lying', 3)), ('->', ('lying', 4), ('lying', 1)), ('not', ('lying', 0)), ('->', ('telling-truth', 2), ('lying', 2)))", "index": 538}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Ava, Amelia, William, Abigail, and Mason. Chloe expressed that Amelia is a knave if and only if Mason is a knave. \"William is a knight if and only if Mason is a knight,\" Ava declared. Amelia commented, \"Abigail is a knave and Ava is a knave\". \"Abigail is a knave\" - William. Abigail was heard saying, \"Chloe is a knight or Amelia is a knight\". Mason was heard saying, \"William is a knave if and only if Abigail is a knight\". So who is a knight and who is a knave?", "names": ["Chloe", "Ava", "Amelia", "William", "Abigail", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true], "solution_text": "Chloe is a knave, Ava is a knight, Amelia is a knave, William is a knight, Abigail is a knave, and Mason is a knight.", "solution_text_format": "(1) Chloe is a knave\n(2) Ava is a knight\n(3) Amelia is a knave\n(4) William is a knight\n(5) Abigail is a knave\n(6) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Mason is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Abigail is a knave and Ava is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Amelia that Abigail is a knave and Ava is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight or Amelia is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Abigail is a knave and Ava is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Chloe is a knight or Amelia is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that William is a knight if and only if Mason is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Mason cannot be a knight, because this would contradict the claim of Chloe that Amelia is a knave if and only if Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that William is a knave if and only if Abigail is a knight.", "We have exhausted all possibilities for Mason and William, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that William is a knight if and only if Mason is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Mason cannot be a knight, because this would contradict the claim of Chloe that Amelia is a knave if and only if Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of Ava that William is a knight if and only if Mason is a knight.", "We have exhausted all possibilities for Mason, William, and Ava, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight or Amelia is a knight.", "We have exhausted all possibilities for Abigail and Amelia, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Mason is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Abigail is a knave and Ava is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Amelia that Abigail is a knave and Ava is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight or Amelia is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Abigail is a knave and Ava is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Chloe is a knight or Amelia is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Chloe is a knight or Amelia is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that William is a knight if and only if Mason is a knight.", "Assume William is a knight. No contradiction is found in their claim that Abigail is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that William is a knave if and only if Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 5)), ('<=>', ('telling-truth', 3), ('telling-truth', 5)), ('and', ('lying', 4), ('lying', 1)), ('lying', 4), ('or', ('telling-truth', 0), ('telling-truth', 2)), ('<=>', ('lying', 3), ('telling-truth', 4)))", "index": 539}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Luke, Avery, Daniel, David, and Jack. According to Michael, \"If David is a knight then Luke is a knight\". As Luke put it, \"Jack is a knight or Michael is a knight\". \"Avery is a knight,\" Avery claimed. \"Michael is a knave or Avery is a knave,\" Daniel mentioned. \"If David is a knight then Jack is a knight,\" David mentioned. Jack expressed that Avery is a knave. So who is a knight and who is a knave?", "names": ["Michael", "Luke", "Avery", "Daniel", "David", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Michael is a knight, Luke is a knight, Avery is a knave, Daniel is a knight, David is a knight, and Jack is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Luke is a knight\n(3) Avery is a knave\n(4) Daniel is a knight\n(5) David is a knight\n(6) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that If David is a knight then Luke is a knight.", "Assume David is a knight. No contradiction is found in their claim that If David is a knight then Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Jack that Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Avery is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Jack is a knight or Michael is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Michael is a knave or Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('telling-truth', 1)), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('telling-truth', 2), ('or', ('lying', 0), ('lying', 2)), ('->', ('telling-truth', 4), ('telling-truth', 5)), ('lying', 2))", "index": 540}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Chloe, Harper, Emily, Avery, and Olivia. \"Avery is a knave or Olivia is a knave,\" Benjamin claimed. Chloe remarked, \"Harper is a knight if and only if Harper is a knave\". In a statement by Harper: \"If Olivia is a knave then Chloe is a knight\". Emily commented, \"If Avery is a knave then Olivia is a knight\". Avery asserted: \"Chloe is a knave and Emily is a knight\". Olivia noted, \"Emily is a knave and Benjamin is a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Chloe", "Harper", "Emily", "Avery", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false], "solution_text": "Benjamin is a knight, Chloe is a knave, Harper is a knave, Emily is a knight, Avery is a knight, and Olivia is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Chloe is a knave\n(3) Harper is a knave\n(4) Emily is a knight\n(5) Avery is a knight\n(6) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Avery is a knave or Olivia is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Chloe is a knave and Emily is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Harper is a knight if and only if Harper is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Olivia is a knave then Chloe is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Benjamin that Avery is a knave or Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the claim of Harper that If Olivia is a knave then Chloe is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that If Olivia is a knave then Chloe is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Benjamin that Avery is a knave or Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Emily is a knave and Benjamin is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Avery is a knave then Olivia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('lying', 5)), ('<=>', ('telling-truth', 2), ('lying', 2)), ('->', ('lying', 5), ('telling-truth', 1)), ('->', ('lying', 4), ('telling-truth', 5)), ('and', ('lying', 1), ('telling-truth', 3)), ('and', ('lying', 3), ('telling-truth', 0)))", "index": 541}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, David, Ethan, Scarlett, Olivia, and William. Jacob told you that Scarlett is a knight. \"Ethan is a knave or Scarlett is a knight,\" David declared. In Ethan's words: \"Scarlett is a knave\". As Scarlett put it, \"David is a knave and David is a knight\". Olivia asserted: \"David is not a knight\". \"Jacob is a knight and Scarlett is a knight\" - William. So who is a knight and who is a knave?", "names": ["Jacob", "David", "Ethan", "Scarlett", "Olivia", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "Jacob is a knave, David is a knave, Ethan is a knight, Scarlett is a knave, Olivia is a knight, and William is a knave.", "solution_text_format": "(1) Jacob is a knave\n(2) David is a knave\n(3) Ethan is a knight\n(4) Scarlett is a knave\n(5) Olivia is a knight\n(6) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that David is a knave and David is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Jacob that Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Jacob that Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that David is a knave and David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Ethan is a knave or Scarlett is a knight.", "Ethan cannot be a knight, because this would contradict the claim of David that Ethan is a knave or Scarlett is a knight.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Ethan is a knave or Scarlett is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that David is not a knight.", "William cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Scarlett is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Jacob is a knight and Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('or', ('lying', 2), ('telling-truth', 3)), ('lying', 3), ('and', ('lying', 1), ('telling-truth', 1)), ('not', ('telling-truth', 1)), ('and', ('telling-truth', 0), ('telling-truth', 3)))", "index": 542}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Michael, Riley, Elizabeth, Scarlett, and Sebastian. Isabella said, \"Riley is a knight if and only if Sebastian is a knight.\" Michael commented, \"Elizabeth is a knave if and only if Michael is a knight\". \"If Sebastian is a knight then Michael is a knight\" - Riley. In a statement by Elizabeth: \"Isabella is a knight and Michael is a knight\". Scarlett told you that Sebastian is not a knight. \"Isabella is not a knight\" - Sebastian. So who is a knight and who is a knave?", "names": ["Isabella", "Michael", "Riley", "Elizabeth", "Scarlett", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true], "solution_text": "Isabella is a knave, Michael is a knave, Riley is a knave, Elizabeth is a knave, Scarlett is a knave, and Sebastian is a knight.", "solution_text_format": "(1) Isabella is a knave\n(2) Michael is a knave\n(3) Riley is a knave\n(4) Elizabeth is a knave\n(5) Scarlett is a knave\n(6) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Riley is a knight if and only if Sebastian is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Sebastian is a knight then Michael is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Isabella is not a knight.", "Sebastian cannot be a knave, because this would contradict the claim of Isabella that Riley is a knight if and only if Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Michael is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Isabella that Riley is a knight if and only if Sebastian is a knight.", "Sebastian cannot be a knave, because this would contradict the false claim of Riley that If Sebastian is a knight then Michael is a knight.", "We have exhausted all possibilities for Sebastian and Riley, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Sebastian is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Sebastian is a knight then Michael is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Isabella that Riley is a knight if and only if Sebastian is a knight.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that Isabella is not a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Michael is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Michael cannot be a knight, because this would contradict the false claim of Riley that If Sebastian is a knight then Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Michael is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Michael that Elizabeth is a knave if and only if Michael is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Isabella is a knight and Michael is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Sebastian is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('<=>', ('lying', 3), ('telling-truth', 1)), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('telling-truth', 5)), ('not', ('telling-truth', 0)))", "index": 543}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Victoria, Abigail, Michael, Owen, and James. Joseph remarked, \"Abigail is a knave if and only if Michael is a knave\". Victoria said that Owen is not a knave. Abigail said, \"Joseph is not a knave.\" \"James is a knave or Victoria is a knave\" - Michael. Owen was heard saying, \"Abigail is a knight or Michael is a knight\". James was heard saying, \"Michael is a knight and Abigail is a knight\". So who is a knight and who is a knave?", "names": ["Joseph", "Victoria", "Abigail", "Michael", "Owen", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Joseph is a knave, Victoria is a knight, Abigail is a knave, Michael is a knight, Owen is a knight, and James is a knave.", "solution_text_format": "(1) Joseph is a knave\n(2) Victoria is a knight\n(3) Abigail is a knave\n(4) Michael is a knight\n(5) Owen is a knight\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Michael is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that James is a knave or Victoria is a knave.", "Assume James is a knight. No contradiction is found in their claim that Michael is a knight and Abigail is a knight.", "Victoria cannot be a knight, because this would contradict the claim of Michael that James is a knave or Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Owen is not a knave.", "Owen cannot be a knight, because this would contradict the false claim of Victoria that Owen is not a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that Abigail is a knight or Michael is a knight.", "We have exhausted all possibilities for Owen and Victoria, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the false claim of their own that Michael is a knight and Abigail is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Joseph that Abigail is a knave if and only if Michael is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Joseph is not a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Michael is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Joseph is not a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Joseph is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that James is a knave or Victoria is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Abigail is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Michael is a knight and Abigail is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Owen is not a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Abigail is a knight or Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 3)), ('not', ('lying', 4)), ('not', ('lying', 0)), ('or', ('lying', 5), ('lying', 1)), ('or', ('telling-truth', 2), ('telling-truth', 3)), ('and', ('telling-truth', 3), ('telling-truth', 2)))", "index": 544}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Scarlett, Ethan, Lily, Penelope, and Aria. Ella told you that Scarlett is a knave. As Scarlett put it, \"Ethan is a knight if and only if Ethan is a knave\". Ethan noted, \"Ella is a knight\". Lily stated, \"If Ella is a knave then Ethan is a knave\". Penelope said, \"Ella is a knave or Scarlett is a knight.\" Aria said that If Ethan is a knave then Scarlett is a knave. So who is a knight and who is a knave?", "names": ["Ella", "Scarlett", "Ethan", "Lily", "Penelope", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "Ella is a knight, Scarlett is a knave, Ethan is a knight, Lily is a knight, Penelope is a knave, and Aria is a knight.", "solution_text_format": "(1) Ella is a knight\n(2) Scarlett is a knave\n(3) Ethan is a knight\n(4) Lily is a knight\n(5) Penelope is a knave\n(6) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Ella that Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Ella is a knave then Ethan is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Ella is a knave or Scarlett is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Ella is a knave or Scarlett is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Ethan is a knave then Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('<=>', ('telling-truth', 2), ('lying', 2)), ('telling-truth', 0), ('->', ('lying', 0), ('lying', 2)), ('or', ('lying', 0), ('telling-truth', 1)), ('->', ('lying', 2), ('lying', 1)))", "index": 545}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Sophia, Benjamin, Victoria, Elizabeth, and Ethan. Sofia remarked, \"Sofia is a knight and Ethan is a knave\". Sophia was heard saying, \"Elizabeth is not a knight\". \"Elizabeth is a knave or Sophia is a knight,\" Benjamin declared. According to Victoria, \"Ethan is a knight or Benjamin is a knave\". In a statement by Elizabeth: \"Sofia is not a knave\". Ethan noted, \"Sophia is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Sophia", "Benjamin", "Victoria", "Elizabeth", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Sofia is a knave, Sophia is a knight, Benjamin is a knight, Victoria is a knave, Elizabeth is a knave, and Ethan is a knave.", "solution_text_format": "(1) Sofia is a knave\n(2) Sophia is a knight\n(3) Benjamin is a knight\n(4) Victoria is a knave\n(5) Elizabeth is a knave\n(6) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Sofia is a knight and Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Sofia that Sofia is a knight and Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Sophia that Elizabeth is not a knight.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Sofia is not a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the false claim of Ethan that Sophia is a knave.", "We have exhausted all possibilities for Sophia and Ethan, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Sofia is a knight and Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Sophia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of Ethan that Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Sofia is not a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of Sophia that Elizabeth is not a knight.", "We have exhausted all possibilities for Elizabeth and Sophia, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Sophia that Elizabeth is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sofia is not a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Elizabeth is a knave or Sophia is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Ethan is a knight or Benjamin is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Ethan is a knight or Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('lying', 5)), ('not', ('telling-truth', 4)), ('or', ('lying', 4), ('telling-truth', 1)), ('or', ('telling-truth', 5), ('lying', 2)), ('not', ('lying', 0)), ('lying', 1))", "index": 546}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Amelia, Joseph, Aurora, Benjamin, and Lily. \"If Joseph is a knight then Amelia is a knight,\" Victoria claimed. Amelia commented, \"Benjamin is not a knight\". Joseph was heard saying, \"Aurora is a knave\". Aurora expressed that Joseph is a knave or Joseph is a knight. Benjamin expressed that Joseph is a knight. Lily told you that Amelia is a knave or Aurora is a knight. So who is a knight and who is a knave?", "names": ["Victoria", "Amelia", "Joseph", "Aurora", "Benjamin", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Victoria is a knight, Amelia is a knight, Joseph is a knave, Aurora is a knight, Benjamin is a knave, and Lily is a knight.", "solution_text_format": "(1) Victoria is a knight\n(2) Amelia is a knight\n(3) Joseph is a knave\n(4) Aurora is a knight\n(5) Benjamin is a knave\n(6) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that If Joseph is a knight then Amelia is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Joseph that Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Joseph is a knave or Joseph is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Aurora is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Joseph is a knave or Joseph is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Amelia that Benjamin is not a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Amelia is a knave or Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 1)), ('not', ('telling-truth', 4)), ('lying', 3), ('or', ('lying', 2), ('telling-truth', 2)), ('telling-truth', 2), ('or', ('lying', 1), ('telling-truth', 3)))", "index": 547}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Matthew, Jack, Daniel, Benjamin, and Oliver. \"If Oliver is a knight then Jack is a knight,\" Samuel mentioned. Matthew said that Benjamin is not a knight. Jack said that Matthew is a knave if and only if Benjamin is a knave. Daniel noted, \"If Oliver is a knight then Oliver is a knave\". As Benjamin put it, \"Samuel is a knight or Daniel is a knave\". Oliver said that If Matthew is a knight then Oliver is a knight. So who is a knight and who is a knave?", "names": ["Samuel", "Matthew", "Jack", "Daniel", "Benjamin", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Samuel is a knave, Matthew is a knave, Jack is a knave, Daniel is a knave, Benjamin is a knight, and Oliver is a knight.", "solution_text_format": "(1) Samuel is a knave\n(2) Matthew is a knave\n(3) Jack is a knave\n(4) Daniel is a knave\n(5) Benjamin is a knight\n(6) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that If Oliver is a knight then Jack is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Matthew is a knight then Oliver is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Matthew that Benjamin is not a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight or Daniel is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Samuel is a knight or Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that If Oliver is a knight then Oliver is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Oliver is a knight then Oliver is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Matthew is a knave if and only if Benjamin is a knave.", "Jack cannot be a knave, because this would contradict the claim of Samuel that If Oliver is a knight then Jack is a knight.", "We have exhausted all possibilities for Jack and Daniel, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of Matthew that Benjamin is not a knight.", "We have exhausted all possibilities for Benjamin and Matthew, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Matthew is a knight then Oliver is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Matthew that Benjamin is not a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight or Daniel is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of Oliver that If Matthew is a knight then Oliver is a knight.", "We have exhausted all possibilities for Matthew and Oliver, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that If Oliver is a knight then Jack is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Matthew is a knight then Oliver is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Matthew that Benjamin is not a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Samuel is a knight or Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that If Oliver is a knight then Oliver is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of Benjamin that Samuel is a knight or Daniel is a knave.", "We have exhausted all possibilities for Daniel and Benjamin, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Samuel is a knight or Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that If Oliver is a knight then Oliver is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Oliver is a knight then Oliver is a knave.", "Jack cannot be a knight, because this would contradict the false claim of Samuel that If Oliver is a knight then Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('telling-truth', 2)), ('not', ('telling-truth', 4)), ('<=>', ('lying', 1), ('lying', 4)), ('->', ('telling-truth', 5), ('lying', 5)), ('or', ('telling-truth', 0), ('lying', 3)), ('->', ('telling-truth', 1), ('telling-truth', 5)))", "index": 548}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Jackson, David, Sofia, Owen, and Elizabeth. \"Jackson is a knight or David is a knave,\" Isabella mentioned. In Jackson's words: \"If Elizabeth is a knave then David is a knave\". \"Jackson is a knight or Isabella is a knave,\" David mentioned. \"Jackson is a knave and Isabella is a knave,\" Sofia claimed. Owen stated, \"Owen is a knight if and only if Jackson is a knight\". \"Owen is a knave,\" Elizabeth mentioned. So who is a knight and who is a knave?", "names": ["Isabella", "Jackson", "David", "Sofia", "Owen", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Isabella is a knight, Jackson is a knight, David is a knight, Sofia is a knave, Owen is a knave, and Elizabeth is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Jackson is a knight\n(3) David is a knight\n(4) Sofia is a knave\n(5) Owen is a knave\n(6) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Jackson is a knight or David is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Elizabeth is a knave then David is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Elizabeth that Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Jackson is a knight.", "Assume David is a knight. No contradiction is found in their claim that Jackson is a knight or Isabella is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Jackson is a knave and Isabella is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Jackson is a knave and Isabella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 2)), ('->', ('lying', 5), ('lying', 2)), ('or', ('telling-truth', 1), ('lying', 0)), ('and', ('lying', 1), ('lying', 0)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('lying', 4))", "index": 549}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Matthew, Amelia, Abigail, Ava, and Aiden. Chloe noted, \"Matthew is a knave or Ava is a knave\". Matthew was heard saying, \"Abigail is a knight\". In a statement by Amelia: \"Abigail is a knight if and only if Aiden is a knight\". In a statement by Abigail: \"Ava is a knave and Abigail is a knight\". In Ava's words: \"Matthew is a knight or Chloe is a knight\". Aiden was heard saying, \"Chloe is a knight if and only if Ava is a knight\". So who is a knight and who is a knave?", "names": ["Chloe", "Matthew", "Amelia", "Abigail", "Ava", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true], "solution_text": "Chloe is a knight, Matthew is a knave, Amelia is a knave, Abigail is a knave, Ava is a knight, and Aiden is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Matthew is a knave\n(3) Amelia is a knave\n(4) Abigail is a knave\n(5) Ava is a knight\n(6) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Matthew is a knave or Ava is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Ava is a knave and Abigail is a knight.", "Ava cannot be a knight, because this would contradict the claim of Chloe that Matthew is a knave or Ava is a knave.", "Ava cannot be a knave, because this would contradict the false claim of their own that Matthew is a knight or Chloe is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Matthew that Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Matthew that Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Ava is a knave and Abigail is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Matthew is a knight or Chloe is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Amelia that Abigail is a knight if and only if Aiden is a knight.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight if and only if Ava is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('lying', 4)), ('telling-truth', 3), ('<=>', ('telling-truth', 3), ('telling-truth', 5)), ('and', ('lying', 4), ('telling-truth', 3)), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)))", "index": 550}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Liam, Olivia, Henry, Jackson, and Owen. Ethan was heard saying, \"Owen is a knight and Henry is a knight\". \"Liam is a knight\" - Liam. \"Ethan is a knave or Liam is a knight,\" Olivia claimed. \"Olivia is not a knave\" - Henry. According to Jackson, \"Owen is a knight or Henry is a knave\". Owen noted, \"Olivia is not a knave\". So who is a knight and who is a knave?", "names": ["Ethan", "Liam", "Olivia", "Henry", "Jackson", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Ethan is a knight, Liam is a knight, Olivia is a knight, Henry is a knight, Jackson is a knight, and Owen is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Liam is a knight\n(3) Olivia is a knight\n(4) Henry is a knight\n(5) Jackson is a knight\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Owen is a knight and Henry is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Ethan is a knave or Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Owen is a knight or Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 3)), ('telling-truth', 1), ('or', ('lying', 0), ('telling-truth', 1)), ('not', ('lying', 2)), ('or', ('telling-truth', 5), ('lying', 3)), ('not', ('lying', 2)))", "index": 551}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Jack, Zoey, William, Harper, and David. Victoria noted, \"If Victoria is a knight then Jack is a knight\". Jack stated, \"If William is a knight then William is a knave\". Zoey was heard saying, \"David is a knave\". William asserted: \"Jack is a knave\". Harper noted, \"Victoria is a knight and Jack is a knave\". David said that William is a knave. So who is a knight and who is a knave?", "names": ["Victoria", "Jack", "Zoey", "William", "Harper", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true], "solution_text": "Victoria is a knight, Jack is a knight, Zoey is a knave, William is a knave, Harper is a knave, and David is a knight.", "solution_text_format": "(1) Victoria is a knight\n(2) Jack is a knight\n(3) Zoey is a knave\n(4) William is a knave\n(5) Harper is a knave\n(6) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that If Victoria is a knight then Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If William is a knight then William is a knave.", "William cannot be a knight, because this would contradict the claim of Jack that If William is a knight then William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Jack is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Zoey that David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that William is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that David is a knave.", "Assume David is a knight. No contradiction is found in their claim that William is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Jack is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Victoria is a knight and Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 3), ('lying', 3)), ('lying', 5), ('lying', 1), ('and', ('telling-truth', 0), ('lying', 1)), ('lying', 3))", "index": 552}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Evelyn, Aria, Mason, Logan, and Mia. Grace commented, \"Mason is a knave\". Evelyn stated, \"Aria is a knight\". Aria said, \"Grace is a knight or Mason is a knight.\" \"Logan is a knight or Evelyn is a knight,\" Mason mentioned. Logan told you that If Grace is a knight then Logan is a knight. Mia noted, \"Grace is a knight and Evelyn is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Evelyn", "Aria", "Mason", "Logan", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Grace is a knave, Evelyn is a knight, Aria is a knight, Mason is a knight, Logan is a knight, and Mia is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) Evelyn is a knight\n(3) Aria is a knight\n(4) Mason is a knight\n(5) Logan is a knight\n(6) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Grace that Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Logan is a knight or Evelyn is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Mason that Logan is a knight or Evelyn is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that If Grace is a knight then Logan is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Mason that Logan is a knight or Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Aria is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Evelyn that Aria is a knight.", "Aria cannot be a knave, because this would contradict the false claim of their own that Grace is a knight or Mason is a knight.", "We have exhausted all possibilities for Aria, Evelyn, Logan, and Mason, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Logan is a knight or Evelyn is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Grace is a knight then Logan is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Grace is a knight or Mason is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Evelyn is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Grace is a knight and Evelyn is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('telling-truth', 2), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('telling-truth', 4), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('and', ('telling-truth', 0), ('lying', 1)))", "index": 553}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Charlotte, Penelope, Harper, Noah, and Daniel. According to Jack, \"Harper is a knave\". \"If Jack is a knave then Daniel is a knight,\" Charlotte claimed. \"If Daniel is a knight then Daniel is a knave\" - Penelope. Harper was heard saying, \"If Charlotte is a knave then Penelope is a knight\". In a statement by Noah: \"Jack is not a knight\". Daniel asserted: \"Noah is not a knight\". So who is a knight and who is a knave?", "names": ["Jack", "Charlotte", "Penelope", "Harper", "Noah", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Jack is a knave, Charlotte is a knave, Penelope is a knight, Harper is a knight, Noah is a knight, and Daniel is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Charlotte is a knave\n(3) Penelope is a knight\n(4) Harper is a knight\n(5) Noah is a knight\n(6) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of Jack that Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that If Charlotte is a knave then Penelope is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Harper that If Charlotte is a knave then Penelope is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Jack is a knave then Daniel is a knight.", "We have exhausted all possibilities for Charlotte and Harper, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Charlotte is a knave then Penelope is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Jack is a knave then Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Noah is not a knight.", "Noah cannot be a knight, because this would contradict the claim of Daniel that Noah is not a knight.", "Noah cannot be a knave, because this would contradict the false claim of their own that Jack is not a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Charlotte that If Jack is a knave then Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Jack is a knave then Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Charlotte that If Jack is a knave then Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Jack is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Daniel is a knight then Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('->', ('lying', 0), ('telling-truth', 5)), ('->', ('telling-truth', 5), ('lying', 5)), ('->', ('lying', 1), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 4)))", "index": 554}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Matthew, Scarlett, Daniel, Sebastian, and Abigail. Riley told you that If Daniel is a knight then Daniel is a knave. Matthew commented, \"Riley is a knight or Sebastian is a knight\". Scarlett commented, \"Sebastian is a knight or Riley is a knave\". As Daniel put it, \"Scarlett is a knight\". Sebastian said that Riley is a knight or Scarlett is a knight. Abigail told you that Daniel is not a knight. So who is a knight and who is a knave?", "names": ["Riley", "Matthew", "Scarlett", "Daniel", "Sebastian", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Riley is a knave, Matthew is a knight, Scarlett is a knight, Daniel is a knight, Sebastian is a knight, and Abigail is a knave.", "solution_text_format": "(1) Riley is a knave\n(2) Matthew is a knight\n(3) Scarlett is a knight\n(4) Daniel is a knight\n(5) Sebastian is a knight\n(6) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that If Daniel is a knight then Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Riley that If Daniel is a knight then Daniel is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Daniel that Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Sebastian is a knight or Riley is a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Scarlett that Sebastian is a knight or Riley is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that Riley is a knight or Scarlett is a knight.", "We have exhausted all possibilities for Sebastian, Scarlett, and Daniel, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that If Daniel is a knight then Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Sebastian is a knight or Riley is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Riley is a knight or Scarlett is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Riley is a knight or Sebastian is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Daniel is not a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Daniel is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 3)), ('or', ('telling-truth', 0), ('telling-truth', 4)), ('or', ('telling-truth', 4), ('lying', 0)), ('telling-truth', 2), ('or', ('telling-truth', 0), ('telling-truth', 2)), ('not', ('telling-truth', 3)))", "index": 555}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Ella, Evelyn, Amelia, Chloe, and Jack. Owen said that Ella is a knave or Jack is a knight. Ella said, \"Amelia is a knight.\" \"Ella is a knave\" - Evelyn. Amelia noted, \"Jack is a knave\". Chloe expressed that Owen is a knave if and only if Jack is a knave. Jack said that Chloe is a knight. So who is a knight and who is a knave?", "names": ["Owen", "Ella", "Evelyn", "Amelia", "Chloe", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Owen is a knight, Ella is a knave, Evelyn is a knight, Amelia is a knave, Chloe is a knight, and Jack is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Ella is a knave\n(3) Evelyn is a knight\n(4) Amelia is a knave\n(5) Chloe is a knight\n(6) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Ella is a knave or Jack is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Amelia that Jack is a knave.", "Jack cannot be a knave, because this would contradict the claim of Owen that Ella is a knave or Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Ella that Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Ella that Amelia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Owen is a knave if and only if Jack is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 5)), ('telling-truth', 3), ('lying', 1), ('lying', 5), ('<=>', ('lying', 0), ('lying', 5)), ('telling-truth', 4))", "index": 556}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Joseph, Olivia, Alexander, Ethan, and David. Amelia was heard saying, \"If Alexander is a knave then Joseph is a knave\". Joseph was heard saying, \"Ethan is a knight\". In Olivia's words: \"Alexander is a knight or David is a knave\". Alexander noted, \"Joseph is a knave or Ethan is a knight\". Ethan commented, \"David is a knight if and only if Amelia is a knave\". \"Amelia is a knave or Olivia is a knave,\" David declared. So who is a knight and who is a knave?", "names": ["Amelia", "Joseph", "Olivia", "Alexander", "Ethan", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Amelia is a knight, Joseph is a knight, Olivia is a knight, Alexander is a knight, Ethan is a knight, and David is a knave.", "solution_text_format": "(1) Amelia is a knight\n(2) Joseph is a knight\n(3) Olivia is a knight\n(4) Alexander is a knight\n(5) Ethan is a knight\n(6) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that If Alexander is a knave then Joseph is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Joseph is a knave or Ethan is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that David is a knight if and only if Amelia is a knave.", "David cannot be a knight, because this would contradict the claim of Ethan that David is a knight if and only if Amelia is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Amelia is a knave or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Alexander is a knight or David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 1)), ('telling-truth', 4), ('or', ('telling-truth', 3), ('lying', 5)), ('or', ('lying', 1), ('telling-truth', 4)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('or', ('lying', 0), ('lying', 2)))", "index": 557}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Emma, Daniel, Grace, Lucas, and Isabella. Jack was heard saying, \"If Lucas is a knight then Isabella is a knave\". \"If Jack is a knave then Daniel is a knight\" - Emma. Daniel told you that Lucas is a knight. Grace was heard saying, \"Daniel is not a knave\". In a statement by Lucas: \"Emma is a knight\". \"Daniel is a knave\" - Isabella. So who is a knight and who is a knave?", "names": ["Jack", "Emma", "Daniel", "Grace", "Lucas", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Jack is a knight, Emma is a knight, Daniel is a knight, Grace is a knight, Lucas is a knight, and Isabella is a knave.", "solution_text_format": "(1) Jack is a knight\n(2) Emma is a knight\n(3) Daniel is a knight\n(4) Grace is a knight\n(5) Lucas is a knight\n(6) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that If Lucas is a knight then Isabella is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Jack is a knave then Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Lucas is a knight.", "Isabella cannot be a knight, because this would contradict the claim of Jack that If Lucas is a knight then Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Daniel is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Daniel is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 5)), ('->', ('lying', 0), ('telling-truth', 2)), ('telling-truth', 4), ('not', ('lying', 2)), ('telling-truth', 1), ('lying', 2))", "index": 558}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Aiden, Elizabeth, Sofia, Amelia, and Sebastian. David noted, \"Sebastian is a knave if and only if Sebastian is a knight\". Aiden stated, \"Elizabeth is not a knight\". \"Amelia is not a knight,\" Elizabeth claimed. \"If David is a knave then Aiden is a knave,\" Sofia claimed. Amelia said, \"If Elizabeth is a knight then Sofia is a knight.\" Sebastian expressed that Sebastian is a knight and Aiden is a knave. So who is a knight and who is a knave?", "names": ["David", "Aiden", "Elizabeth", "Sofia", "Amelia", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "David is a knave, Aiden is a knight, Elizabeth is a knave, Sofia is a knave, Amelia is a knight, and Sebastian is a knave.", "solution_text_format": "(1) David is a knave\n(2) Aiden is a knight\n(3) Elizabeth is a knave\n(4) Sofia is a knave\n(5) Amelia is a knight\n(6) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["David cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave if and only if Sebastian is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sebastian is a knight and Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Sebastian that Sebastian is a knight and Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Elizabeth is not a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of Elizabeth that Amelia is not a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Elizabeth is a knight then Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Amelia that If Elizabeth is a knight then Sofia is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If David is a knave then Aiden is a knave.", "We have exhausted all possibilities for Sofia and Amelia, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the false claim of Aiden that Elizabeth is not a knight.", "We have exhausted all possibilities for Elizabeth and Aiden, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Sebastian is a knight and Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Aiden that Elizabeth is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Amelia is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that If David is a knave then Aiden is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that If David is a knave then Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('telling-truth', 5)), ('not', ('telling-truth', 2)), ('not', ('telling-truth', 4)), ('->', ('lying', 0), ('lying', 1)), ('->', ('telling-truth', 2), ('telling-truth', 3)), ('and', ('telling-truth', 5), ('lying', 1)))", "index": 559}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Olivia, Samuel, Scarlett, Benjamin, and James. Matthew expressed that Benjamin is a knight. \"James is not a knight\" - Olivia. \"Matthew is a knight,\" Samuel declared. Scarlett asserted: \"Matthew is not a knave\". Benjamin expressed that If Olivia is a knight then Matthew is a knave. According to James, \"Olivia is a knave\". So who is a knight and who is a knave?", "names": ["Matthew", "Olivia", "Samuel", "Scarlett", "Benjamin", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Matthew is a knight, Olivia is a knave, Samuel is a knight, Scarlett is a knight, Benjamin is a knight, and James is a knight.", "solution_text_format": "(1) Matthew is a knight\n(2) Olivia is a knave\n(3) Samuel is a knight\n(4) Scarlett is a knight\n(5) Benjamin is a knight\n(6) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Olivia is a knight then Matthew is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Benjamin that If Olivia is a knight then Matthew is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that James is not a knight.", "Assume James is a knight. No contradiction is found in their claim that Olivia is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Matthew is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('not', ('telling-truth', 5)), ('telling-truth', 0), ('not', ('lying', 0)), ('->', ('telling-truth', 1), ('lying', 0)), ('lying', 1))", "index": 560}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, William, Michael, Harper, Mia, and Aria. In Scarlett's words: \"Mia is not a knave\". William stated, \"Scarlett is a knave and Scarlett is a knight\". \"Harper is a knight or Aria is a knave,\" Michael mentioned. In Harper's words: \"Aria is not a knave\". \"Scarlett is a knave and Scarlett is a knight\" - Mia. Aria stated, \"If Michael is a knave then Harper is a knave\". So who is a knight and who is a knave?", "names": ["Scarlett", "William", "Michael", "Harper", "Mia", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Scarlett is a knave, William is a knave, Michael is a knight, Harper is a knight, Mia is a knave, and Aria is a knight.", "solution_text_format": "(1) Scarlett is a knave\n(2) William is a knave\n(3) Michael is a knight\n(4) Harper is a knight\n(5) Mia is a knave\n(6) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave and Scarlett is a knight.", "Mia cannot be a knave, because this would contradict the claim of Scarlett that Mia is not a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the false claim of Scarlett that Mia is not a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Scarlett is a knave and Scarlett is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave and Scarlett is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Scarlett is a knave and Scarlett is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Harper is a knight or Aria is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Michael is a knave then Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('and', ('lying', 0), ('telling-truth', 0)), ('or', ('telling-truth', 3), ('lying', 5)), ('not', ('lying', 5)), ('and', ('lying', 0), ('telling-truth', 0)), ('->', ('lying', 2), ('lying', 3)))", "index": 561}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Elizabeth, Henry, Liam, Grace, and Penelope. Scarlett stated, \"If Grace is a knave then Elizabeth is a knave\". Elizabeth said, \"Henry is not a knight.\" \"Grace is a knave or Scarlett is a knight,\" Henry declared. Liam was heard saying, \"If Elizabeth is a knave then Elizabeth is a knight\". In a statement by Grace: \"Liam is a knave or Scarlett is a knave\". Penelope told you that Liam is a knave if and only if Liam is a knight. So who is a knight and who is a knave?", "names": ["Scarlett", "Elizabeth", "Henry", "Liam", "Grace", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false], "solution_text": "Scarlett is a knight, Elizabeth is a knave, Henry is a knight, Liam is a knave, Grace is a knight, and Penelope is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Elizabeth is a knave\n(3) Henry is a knight\n(4) Liam is a knave\n(5) Grace is a knight\n(6) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that If Grace is a knave then Elizabeth is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Liam is a knave or Scarlett is a knave.", "Liam cannot be a knight, because this would contradict the claim of Grace that Liam is a knave or Scarlett is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Liam that If Elizabeth is a knave then Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Grace is a knave or Scarlett is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Liam is a knave if and only if Liam is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('lying', 1)), ('not', ('telling-truth', 2)), ('or', ('lying', 4), ('telling-truth', 0)), ('->', ('lying', 1), ('telling-truth', 1)), ('or', ('lying', 3), ('lying', 0)), ('<=>', ('lying', 3), ('telling-truth', 3)))", "index": 562}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Aria, Jack, Matthew, Abigail, and Chloe. Emily commented, \"Abigail is a knight and Chloe is a knight\". Aria asserted: \"Abigail is a knave\". \"Abigail is not a knave\" - Jack. \"Chloe is a knave and Aria is a knight,\" Matthew mentioned. In Abigail's words: \"If Chloe is a knave then Jack is a knave\". Chloe said that Abigail is a knight and Emily is a knight. So who is a knight and who is a knave?", "names": ["Emily", "Aria", "Jack", "Matthew", "Abigail", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Emily is a knight, Aria is a knave, Jack is a knight, Matthew is a knave, Abigail is a knight, and Chloe is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Aria is a knave\n(3) Jack is a knight\n(4) Matthew is a knave\n(5) Abigail is a knight\n(6) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Abigail is a knight and Chloe is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Chloe is a knave then Jack is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Abigail is a knight and Emily is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Aria is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Chloe is a knave and Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('telling-truth', 5)), ('lying', 4), ('not', ('lying', 4)), ('and', ('lying', 5), ('telling-truth', 1)), ('->', ('lying', 5), ('lying', 2)), ('and', ('telling-truth', 4), ('telling-truth', 0)))", "index": 563}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Avery, Abigail, Aria, Owen, and Sofia. Daniel remarked, \"If Abigail is a knight then Avery is a knave\". Avery commented, \"Sofia is a knave and Owen is a knight\". \"Sofia is a knight and Daniel is a knave,\" Abigail declared. Aria remarked, \"Daniel is a knave and Owen is a knave\". As Owen put it, \"Owen is a knight or Sofia is a knight\". In a statement by Sofia: \"Abigail is a knight or Daniel is a knight\". So who is a knight and who is a knave?", "names": ["Daniel", "Avery", "Abigail", "Aria", "Owen", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true], "solution_text": "Daniel is a knight, Avery is a knave, Abigail is a knave, Aria is a knave, Owen is a knight, and Sofia is a knight.", "solution_text_format": "(1) Daniel is a knight\n(2) Avery is a knave\n(3) Abigail is a knave\n(4) Aria is a knave\n(5) Owen is a knight\n(6) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that If Abigail is a knight then Avery is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Daniel is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Sofia is a knight and Daniel is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Abigail is a knight or Daniel is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Owen is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Sofia is a knave and Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Owen is a knight or Sofia is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Owen is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Daniel is a knave and Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 1)), ('and', ('lying', 5), ('telling-truth', 4)), ('and', ('telling-truth', 5), ('lying', 0)), ('and', ('lying', 0), ('lying', 4)), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('or', ('telling-truth', 2), ('telling-truth', 0)))", "index": 564}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Aurora, Emily, Aiden, Jackson, and Sofia. \"If Emily is a knave then Sofia is a knight\" - Daniel. Aurora said that Sofia is a knight if and only if Jackson is a knight. In a statement by Emily: \"If Aurora is a knight then Emily is a knight\". \"If Jackson is a knave then Emily is a knave,\" Aiden mentioned. Jackson told you that Aiden is a knight or Aiden is a knave. Sofia was heard saying, \"Emily is a knight\". So who is a knight and who is a knave?", "names": ["Daniel", "Aurora", "Emily", "Aiden", "Jackson", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Daniel is a knight, Aurora is a knight, Emily is a knight, Aiden is a knight, Jackson is a knight, and Sofia is a knight.", "solution_text_format": "(1) Daniel is a knight\n(2) Aurora is a knight\n(3) Emily is a knight\n(4) Aiden is a knight\n(5) Jackson is a knight\n(6) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that If Emily is a knave then Sofia is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Aurora is a knight then Emily is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Jackson is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Aiden is a knight or Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Jackson is a knave then Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 5)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('lying', 4), ('lying', 2)), ('or', ('telling-truth', 3), ('lying', 3)), ('telling-truth', 2))", "index": 565}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Sofia, Zoey, Riley, Aiden, and Oliver. In a statement by Elizabeth: \"Riley is a knave\". Sofia said that Riley is a knave if and only if Zoey is a knight. Zoey said that Zoey is a knight and Oliver is a knave. According to Riley, \"Elizabeth is a knight and Oliver is a knight\". In Aiden's words: \"Sofia is not a knight\". \"Sofia is a knight,\" Oliver claimed. So who is a knight and who is a knave?", "names": ["Elizabeth", "Sofia", "Zoey", "Riley", "Aiden", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false], "solution_text": "Elizabeth is a knight, Sofia is a knave, Zoey is a knave, Riley is a knave, Aiden is a knight, and Oliver is a knave.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Sofia is a knave\n(3) Zoey is a knave\n(4) Riley is a knave\n(5) Aiden is a knight\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of Elizabeth that Riley is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Riley that Elizabeth is a knight and Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Oliver that Sofia is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Zoey is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Sofia that Riley is a knave if and only if Zoey is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Zoey is a knight and Oliver is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Sofia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('<=>', ('lying', 3), ('telling-truth', 2)), ('and', ('telling-truth', 2), ('lying', 5)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('not', ('telling-truth', 1)), ('telling-truth', 1))", "index": 566}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Ella, Sofia, Noah, Victoria, and Emily. Mason told you that Sofia is a knight and Emily is a knight. Ella asserted: \"Mason is a knight and Emily is a knave\". In Sofia's words: \"Victoria is a knave if and only if Emily is a knave\". In a statement by Noah: \"Noah is a knight or Ella is a knave\". According to Victoria, \"Emily is a knave and Mason is a knight\". In Emily's words: \"Noah is a knave or Noah is a knight\". So who is a knight and who is a knave?", "names": ["Mason", "Ella", "Sofia", "Noah", "Victoria", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "Mason is a knave, Ella is a knave, Sofia is a knave, Noah is a knight, Victoria is a knave, and Emily is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Ella is a knave\n(3) Sofia is a knave\n(4) Noah is a knight\n(5) Victoria is a knave\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Sofia is a knight and Emily is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Emily is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Emily is a knave and Mason is a knight.", "Emily cannot be a knight, because this would contradict the claim of Victoria that Emily is a knave and Mason is a knight.", "Emily cannot be a knave, because this would contradict the claim of Mason that Sofia is a knight and Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Emily is a knave and Mason is a knight.", "Emily cannot be a knight, because this would contradict the claim of Sofia that Victoria is a knave if and only if Emily is a knave.", "Emily cannot be a knave, because this would contradict the claim of Mason that Sofia is a knight and Emily is a knight.", "We have exhausted all possibilities for Emily and Victoria, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of Mason that Sofia is a knight and Emily is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Sofia is a knight and Emily is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Emily is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Emily is a knave and Mason is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Emily is a knave and Mason is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Mason that Sofia is a knight and Emily is a knight.", "Emily cannot be a knave, because this would contradict the false claim of their own that Noah is a knave or Noah is a knight.", "We have exhausted all possibilities for Emily and Victoria, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Emily is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Emily is a knave and Mason is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Emily is a knave and Mason is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Noah is a knave or Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Noah is a knight or Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Emily is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Mason is a knight and Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('lying', 5)), ('<=>', ('lying', 4), ('lying', 5)), ('or', ('telling-truth', 3), ('lying', 1)), ('and', ('lying', 5), ('telling-truth', 0)), ('or', ('lying', 3), ('telling-truth', 3)))", "index": 567}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Lily, Avery, Grace, Victoria, and Mia. Emily remarked, \"If Emily is a knight then Avery is a knight\". Lily stated, \"Victoria is a knight and Avery is a knave\". Avery stated, \"Victoria is a knight\". Grace noted, \"Avery is not a knave\". \"Avery is a knight\" - Victoria. Mia asserted: \"Emily is a knight and Emily is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Lily", "Avery", "Grace", "Victoria", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Emily is a knight, Lily is a knave, Avery is a knight, Grace is a knight, Victoria is a knight, and Mia is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Lily is a knave\n(3) Avery is a knight\n(4) Grace is a knight\n(5) Victoria is a knight\n(6) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that If Emily is a knight then Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Avery is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Avery is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Victoria is a knight and Avery is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Avery is not a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Emily is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Emily is a knight and Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 2)), ('and', ('telling-truth', 4), ('lying', 2)), ('telling-truth', 4), ('not', ('lying', 2)), ('telling-truth', 2), ('and', ('telling-truth', 0), ('lying', 0)))", "index": 568}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Sebastian, Owen, Lily, Alexander, and Emily. As Ava put it, \"Owen is a knight or Ava is a knight\". Sebastian said that Emily is a knight or Emily is a knave. Owen remarked, \"If Lily is a knight then Ava is a knight\". Lily commented, \"Owen is a knight\". Alexander noted, \"Lily is a knight or Sebastian is a knave\". \"Lily is not a knight\" - Emily. So who is a knight and who is a knave?", "names": ["Ava", "Sebastian", "Owen", "Lily", "Alexander", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Ava is a knight, Sebastian is a knight, Owen is a knight, Lily is a knight, Alexander is a knight, and Emily is a knave.", "solution_text_format": "(1) Ava is a knight\n(2) Sebastian is a knight\n(3) Owen is a knight\n(4) Lily is a knight\n(5) Alexander is a knight\n(6) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Owen is a knight or Ava is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Lily is a knight then Ava is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Owen is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Emily is a knight or Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Lily is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Lily is a knight or Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('telling-truth', 5), ('lying', 5)), ('->', ('telling-truth', 3), ('telling-truth', 0)), ('telling-truth', 2), ('or', ('telling-truth', 3), ('lying', 1)), ('not', ('telling-truth', 3)))", "index": 569}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Matthew, Ethan, Oliver, Emily, and James. \"Joseph is a knight or Oliver is a knight\" - Joseph. Matthew expressed that Oliver is a knave. In a statement by Ethan: \"If Oliver is a knave then Emily is a knave\". Oliver remarked, \"Matthew is a knight or Oliver is a knight\". Emily was heard saying, \"If Matthew is a knave then Ethan is a knight\". James told you that Ethan is a knight or Emily is a knave. So who is a knight and who is a knave?", "names": ["Joseph", "Matthew", "Ethan", "Oliver", "Emily", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Joseph is a knight, Matthew is a knave, Ethan is a knight, Oliver is a knight, Emily is a knight, and James is a knight.", "solution_text_format": "(1) Joseph is a knight\n(2) Matthew is a knave\n(3) Ethan is a knight\n(4) Oliver is a knight\n(5) Emily is a knight\n(6) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Joseph is a knight or Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Matthew is a knight or Oliver is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Oliver is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Oliver is a knave then Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Matthew is a knave then Ethan is a knight.", "Assume James is a knight. No contradiction is found in their claim that Ethan is a knight or Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 3)), ('lying', 3), ('->', ('lying', 3), ('lying', 4)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('->', ('lying', 1), ('telling-truth', 2)), ('or', ('telling-truth', 2), ('lying', 4)))", "index": 570}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Joseph, Matthew, Olivia, Jacob, and Harper. \"Joseph is not a knave,\" Owen mentioned. Joseph commented, \"Harper is a knight or Jacob is a knave\". Matthew remarked, \"Harper is a knight and Olivia is a knave\". In Olivia's words: \"Harper is a knight\". Jacob said, \"Joseph is a knave and Joseph is a knight.\" Harper remarked, \"Owen is a knave\". So who is a knight and who is a knave?", "names": ["Owen", "Joseph", "Matthew", "Olivia", "Jacob", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Owen is a knight, Joseph is a knight, Matthew is a knave, Olivia is a knave, Jacob is a knave, and Harper is a knave.", "solution_text_format": "(1) Owen is a knight\n(2) Joseph is a knight\n(3) Matthew is a knave\n(4) Olivia is a knave\n(5) Jacob is a knave\n(6) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Harper is a knight or Jacob is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Owen is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Owen is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Joseph that Harper is a knight or Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Joseph is a knave and Joseph is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Olivia is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Harper is a knight and Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Harper is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('or', ('telling-truth', 5), ('lying', 4)), ('and', ('telling-truth', 5), ('lying', 3)), ('telling-truth', 5), ('and', ('lying', 1), ('telling-truth', 1)), ('lying', 0))", "index": 571}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Logan, Michael, Evelyn, Luke, and Mia. Liam commented, \"Michael is a knight if and only if Michael is a knave\". Logan was heard saying, \"Luke is a knight if and only if Michael is a knight\". Michael stated, \"Evelyn is a knave\". \"If Liam is a knight then Luke is a knave,\" Evelyn declared. Luke noted, \"Liam is a knave\". Mia was heard saying, \"Liam is a knight\". So who is a knight and who is a knave?", "names": ["Liam", "Logan", "Michael", "Evelyn", "Luke", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false], "solution_text": "Liam is a knave, Logan is a knave, Michael is a knave, Evelyn is a knight, Luke is a knight, and Mia is a knave.", "solution_text_format": "(1) Liam is a knave\n(2) Logan is a knave\n(3) Michael is a knave\n(4) Evelyn is a knight\n(5) Luke is a knight\n(6) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Liam cannot be a knight, because this would contradict the claim of their own that Michael is a knight if and only if Michael is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Michael that Evelyn is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that If Liam is a knight then Luke is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Liam is a knight then Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Liam is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Luke is a knight if and only if Michael is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Michael is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Liam is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 2)), ('lying', 3), ('->', ('telling-truth', 0), ('lying', 4)), ('lying', 0), ('telling-truth', 0))", "index": 572}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Mia, Henry, Alexander, Emma, and Lucas. \"Mia is a knight or Emma is a knave\" - Elizabeth. \"Lucas is a knight,\" Mia claimed. Henry told you that Alexander is a knave and Mia is a knight. \"Mia is a knight if and only if Elizabeth is a knight\" - Alexander. Emma commented, \"Henry is not a knight\". According to Lucas, \"Alexander is a knave and Mia is a knight\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Mia", "Henry", "Alexander", "Emma", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false], "solution_text": "Elizabeth is a knave, Mia is a knave, Henry is a knave, Alexander is a knight, Emma is a knight, and Lucas is a knave.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Mia is a knave\n(3) Henry is a knave\n(4) Alexander is a knight\n(5) Emma is a knight\n(6) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Mia is a knight or Emma is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Alexander is a knave and Mia is a knight.", "Alexander cannot be a knight, because this would contradict the claim of Lucas that Alexander is a knave and Mia is a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Mia is a knight if and only if Elizabeth is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Mia that Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Mia that Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Alexander is a knave and Mia is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Mia is a knight if and only if Elizabeth is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Elizabeth is a knight.", "Emma cannot be a knight, because this would contradict the claim of Elizabeth that Mia is a knight or Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Alexander is a knave and Mia is a knight.", "Henry cannot be a knave, because this would contradict the false claim of Emma that Henry is not a knight.", "We have exhausted all possibilities for Henry, Emma, Alexander, Lucas, and Mia, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Mia is a knight or Emma is a knave.", "Mia cannot be a knight, because this would contradict the false claim of Elizabeth that Mia is a knight or Emma is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Mia that Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Alexander is a knave and Mia is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Mia is a knight if and only if Elizabeth is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Alexander is a knave and Mia is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Alexander is a knave and Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 4)), ('telling-truth', 5), ('and', ('lying', 3), ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('telling-truth', 2)), ('and', ('lying', 3), ('telling-truth', 1)))", "index": 573}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Daniel, Chloe, Aurora, Jacob, and James. Jack expressed that Aurora is a knave or Chloe is a knave. Daniel said, \"Jack is not a knave.\" Chloe noted, \"Jacob is a knight and Aurora is a knight\". Aurora noted, \"If James is a knave then Daniel is a knight\". Jacob expressed that James is a knave or Daniel is a knave. James noted, \"Jack is a knight or Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Jack", "Daniel", "Chloe", "Aurora", "Jacob", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Jack is a knight, Daniel is a knight, Chloe is a knave, Aurora is a knight, Jacob is a knave, and James is a knight.", "solution_text_format": "(1) Jack is a knight\n(2) Daniel is a knight\n(3) Chloe is a knave\n(4) Aurora is a knight\n(5) Jacob is a knave\n(6) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Aurora is a knave or Chloe is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If James is a knave then Daniel is a knight.", "Assume James is a knight. No contradiction is found in their claim that Jack is a knight or Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that James is a knave or Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Jacob that James is a knave or Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Jack is not a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that James is a knave or Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Jack is not a knave.", "Chloe cannot be a knight, because this would contradict the claim of Jack that Aurora is a knave or Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jacob is a knight and Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 2)), ('not', ('lying', 0)), ('and', ('telling-truth', 4), ('telling-truth', 3)), ('->', ('lying', 5), ('telling-truth', 1)), ('or', ('lying', 5), ('lying', 1)), ('or', ('telling-truth', 0), ('lying', 4)))", "index": 574}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Mia, Grace, James, Victoria, and Joseph. Luke said, \"If Mia is a knight then Grace is a knave.\" Mia asserted: \"Grace is a knight or Luke is a knave\". According to Grace, \"Victoria is a knight or Mia is a knave\". \"If Mia is a knave then Grace is a knight,\" James declared. In a statement by Victoria: \"Joseph is not a knave\". Joseph noted, \"Luke is not a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Mia", "Grace", "James", "Victoria", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Luke is a knave, Mia is a knight, Grace is a knight, James is a knight, Victoria is a knight, and Joseph is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Mia is a knight\n(3) Grace is a knight\n(4) James is a knight\n(5) Victoria is a knight\n(6) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that If Mia is a knight then Grace is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Grace is a knight or Luke is a knave.", "Grace cannot be a knight, because this would contradict the claim of Luke that If Mia is a knight then Grace is a knave.", "Grace cannot be a knave, because this would contradict the claim of Mia that Grace is a knight or Luke is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Grace is a knight or Luke is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Mia that Grace is a knight or Luke is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Victoria is a knight or Mia is a knave.", "We have exhausted all possibilities for Grace and Mia, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that If Mia is a knight then Grace is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Grace is a knight or Luke is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Victoria is a knight or Mia is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Luke is not a knight.", "Assume James is a knight. No contradiction is found in their claim that If Mia is a knave then Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('lying', 2)), ('or', ('telling-truth', 2), ('lying', 0)), ('or', ('telling-truth', 4), ('lying', 1)), ('->', ('lying', 1), ('telling-truth', 2)), ('not', ('lying', 5)), ('not', ('telling-truth', 0)))", "index": 575}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Abigail, Aurora, Emily, Luke, and Aria. Evelyn commented, \"Abigail is a knight if and only if Luke is a knave\". Abigail told you that Evelyn is a knight and Emily is a knight. Aurora commented, \"Luke is a knave\". Emily remarked, \"Aria is a knight if and only if Aria is a knave\". Luke said, \"If Aria is a knight then Evelyn is a knight.\" Aria noted, \"Aurora is a knight if and only if Emily is a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "Abigail", "Aurora", "Emily", "Luke", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true], "solution_text": "Evelyn is a knight, Abigail is a knave, Aurora is a knave, Emily is a knave, Luke is a knight, and Aria is a knight.", "solution_text_format": "(1) Evelyn is a knight\n(2) Abigail is a knave\n(3) Aurora is a knave\n(4) Emily is a knave\n(5) Luke is a knight\n(6) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Luke is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Evelyn is a knight and Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Aria is a knight if and only if Aria is a knave.", "Emily cannot be a knave, because this would contradict the claim of Abigail that Evelyn is a knight and Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Evelyn is a knight and Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Abigail that Evelyn is a knight and Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Emily is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Aria that Aurora is a knight if and only if Emily is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Aria is a knight then Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 4)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('lying', 4), ('<=>', ('telling-truth', 5), ('lying', 5)), ('->', ('telling-truth', 5), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 3)))", "index": 576}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Aria, Chloe, Harper, Sebastian, and Amelia. \"If Chloe is a knight then Amelia is a knight,\" Riley declared. Aria commented, \"Amelia is not a knight\". \"Aria is a knave if and only if Aria is a knight,\" Chloe declared. Harper noted, \"Amelia is a knave\". Sebastian said, \"Riley is a knave and Riley is a knight.\" Amelia commented, \"If Chloe is a knight then Chloe is a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Aria", "Chloe", "Harper", "Sebastian", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true], "solution_text": "Riley is a knight, Aria is a knave, Chloe is a knave, Harper is a knave, Sebastian is a knave, and Amelia is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Aria is a knave\n(3) Chloe is a knave\n(4) Harper is a knave\n(5) Sebastian is a knave\n(6) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that If Chloe is a knight then Amelia is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Aria is a knave if and only if Aria is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of Aria that Amelia is not a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that If Chloe is a knight then Chloe is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Amelia is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Chloe is a knight then Chloe is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Amelia is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Riley is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Riley is a knave and Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('telling-truth', 5)), ('<=>', ('lying', 1), ('telling-truth', 1)), ('lying', 5), ('and', ('lying', 0), ('telling-truth', 0)), ('->', ('telling-truth', 2), ('lying', 2)))", "index": 577}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Ella, Henry, Samuel, Logan, and Penelope. Sofia asserted: \"Samuel is a knave if and only if Ella is a knave\". As Ella put it, \"Henry is a knight\". In a statement by Henry: \"If Samuel is a knight then Sofia is a knave\". As Samuel put it, \"Ella is a knave\". Logan said that Penelope is a knight and Samuel is a knave. As Penelope put it, \"Henry is not a knight\". So who is a knight and who is a knave?", "names": ["Sofia", "Ella", "Henry", "Samuel", "Logan", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Sofia is a knave, Ella is a knight, Henry is a knight, Samuel is a knave, Logan is a knave, and Penelope is a knave.", "solution_text_format": "(1) Sofia is a knave\n(2) Ella is a knight\n(3) Henry is a knight\n(4) Samuel is a knave\n(5) Logan is a knave\n(6) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Ella is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Samuel that Ella is a knave.", "Ella cannot be a knave, because this would contradict the claim of Sofia that Samuel is a knave if and only if Ella is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Sofia that Samuel is a knave if and only if Ella is a knave.", "Ella cannot be a knave, because this would contradict the false claim of Samuel that Ella is a knave.", "We have exhausted all possibilities for Ella and Samuel, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Ella is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the false claim of Sofia that Samuel is a knave if and only if Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Henry is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Ella that Henry is a knight.", "Henry cannot be a knave, because this would contradict the false claim of their own that If Samuel is a knight then Sofia is a knave.", "We have exhausted all possibilities for Henry and Ella, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Samuel is a knight then Sofia is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Penelope is a knight and Samuel is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Henry is not a knight.", "Penelope cannot be a knave, because this would contradict the claim of Logan that Penelope is a knight and Samuel is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Penelope is a knight and Samuel is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Logan that Penelope is a knight and Samuel is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Henry is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 1)), ('telling-truth', 2), ('->', ('telling-truth', 3), ('lying', 0)), ('lying', 1), ('and', ('telling-truth', 5), ('lying', 3)), ('not', ('telling-truth', 2)))", "index": 578}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Owen, Isabella, Amelia, James, and Abigail. Henry expressed that If Owen is a knight then Henry is a knight. \"Amelia is a knight,\" Owen claimed. In a statement by Isabella: \"Henry is a knave and James is a knave\". According to Amelia, \"If Henry is a knave then Amelia is a knight\". James commented, \"Owen is a knave or Isabella is a knight\". Abigail stated, \"Amelia is a knave and Amelia is a knight\". So who is a knight and who is a knave?", "names": ["Henry", "Owen", "Isabella", "Amelia", "James", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Henry is a knight, Owen is a knight, Isabella is a knave, Amelia is a knight, James is a knave, and Abigail is a knave.", "solution_text_format": "(1) Henry is a knight\n(2) Owen is a knight\n(3) Isabella is a knave\n(4) Amelia is a knight\n(5) James is a knave\n(6) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that If Owen is a knight then Henry is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Henry is a knave then Amelia is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Henry is a knave and James is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Henry is a knave and James is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Owen is a knave or Isabella is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Owen is a knave or Isabella is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Amelia is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Amelia is a knave and Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('telling-truth', 0)), ('telling-truth', 3), ('and', ('lying', 0), ('lying', 4)), ('->', ('lying', 0), ('telling-truth', 3)), ('or', ('lying', 1), ('telling-truth', 2)), ('and', ('lying', 3), ('telling-truth', 3)))", "index": 579}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Jacob, Aiden, Harper, Henry, and Scarlett. As Chloe put it, \"Harper is a knave if and only if Jacob is a knight\". Jacob said that Henry is a knight or Chloe is a knight. \"Jacob is a knight or Chloe is a knight\" - Aiden. According to Harper, \"Henry is a knave and Jacob is a knight\". Henry said, \"Harper is a knight and Aiden is a knave.\" \"Henry is a knight or Harper is a knave,\" Scarlett claimed. So who is a knight and who is a knave?", "names": ["Chloe", "Jacob", "Aiden", "Harper", "Henry", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true], "solution_text": "Chloe is a knave, Jacob is a knave, Aiden is a knave, Harper is a knave, Henry is a knave, and Scarlett is a knight.", "solution_text_format": "(1) Chloe is a knave\n(2) Jacob is a knave\n(3) Aiden is a knave\n(4) Harper is a knave\n(5) Henry is a knave\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Harper is a knave if and only if Jacob is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Henry is a knave and Jacob is a knight.", "Henry cannot be a knight, because this would contradict the claim of Harper that Henry is a knave and Jacob is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Harper is a knight and Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Jacob is a knight or Chloe is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Chloe that Harper is a knave if and only if Jacob is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of their own that Henry is a knight or Chloe is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Jacob is a knight or Chloe is a knight.", "We have exhausted all possibilities for Aiden and Henry, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Henry is a knave and Jacob is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Aiden is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Harper is a knight and Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Jacob is a knight or Chloe is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Harper that Henry is a knave and Jacob is a knight.", "Jacob cannot be a knave, because this would contradict the claim of Chloe that Harper is a knave if and only if Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Jacob is a knight or Chloe is a knight.", "We have exhausted all possibilities for Aiden, Henry, and Harper, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Jacob is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Henry is a knave and Jacob is a knight.", "Henry cannot be a knight, because this would contradict the claim of Harper that Henry is a knave and Jacob is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Harper is a knight and Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Jacob is a knight or Chloe is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Henry is a knight or Chloe is a knight.", "Jacob cannot be a knave, because this would contradict the false claim of Chloe that Harper is a knave if and only if Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of Henry that Harper is a knight and Aiden is a knave.", "We have exhausted all possibilities for Aiden and Henry, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Henry is a knave and Jacob is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Aiden is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Harper is a knight and Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Jacob is a knight or Chloe is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Chloe that Harper is a knave if and only if Jacob is a knight.", "Jacob cannot be a knave, because this would contradict the claim of Aiden that Jacob is a knight or Chloe is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Jacob is a knight or Chloe is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Chloe that Harper is a knave if and only if Jacob is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Henry is a knight or Chloe is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Henry is a knight or Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 1)), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('lying', 4), ('telling-truth', 1)), ('and', ('telling-truth', 3), ('lying', 2)), ('or', ('telling-truth', 4), ('lying', 3)))", "index": 580}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Aurora, Jackson, Noah, James, and Mason. As Ella put it, \"If Mason is a knight then James is a knave\". Aurora commented, \"James is a knave\". Jackson remarked, \"Noah is a knight or Mason is a knight\". Noah commented, \"Mason is a knight\". James said, \"Ella is a knave.\" Mason expressed that Aurora is not a knave. So who is a knight and who is a knave?", "names": ["Ella", "Aurora", "Jackson", "Noah", "James", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Ella is a knight, Aurora is a knight, Jackson is a knight, Noah is a knight, James is a knave, and Mason is a knight.", "solution_text_format": "(1) Ella is a knight\n(2) Aurora is a knight\n(3) Jackson is a knight\n(4) Noah is a knight\n(5) James is a knave\n(6) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that If Mason is a knight then James is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Ella that If Mason is a knight then James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Noah is a knight or Mason is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 4)), ('lying', 4), ('or', ('telling-truth', 3), ('telling-truth', 5)), ('telling-truth', 5), ('lying', 0), ('not', ('lying', 1)))", "index": 581}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Avery, Lily, Riley, Olivia, and Sebastian. Michael remarked, \"Olivia is a knight\". Avery said that Sebastian is a knight and Michael is a knight. Lily asserted: \"Riley is a knight if and only if Michael is a knave\". \"Michael is not a knight,\" Riley claimed. Olivia said that Avery is not a knight. Sebastian told you that Lily is a knave. So who is a knight and who is a knave?", "names": ["Michael", "Avery", "Lily", "Riley", "Olivia", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false], "solution_text": "Michael is a knight, Avery is a knave, Lily is a knight, Riley is a knave, Olivia is a knight, and Sebastian is a knave.", "solution_text_format": "(1) Michael is a knight\n(2) Avery is a knave\n(3) Lily is a knight\n(4) Riley is a knave\n(5) Olivia is a knight\n(6) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Olivia that Avery is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Sebastian is a knight and Michael is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Avery that Sebastian is a knight and Michael is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Riley is a knight if and only if Michael is a knave.", "Riley cannot be a knight, because this would contradict the claim of Lily that Riley is a knight if and only if Michael is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Michael is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('and', ('telling-truth', 5), ('telling-truth', 0)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 1)), ('lying', 2))", "index": 582}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Oliver, Michael, Chloe, Ethan, and David. \"Ethan is a knave if and only if Michael is a knight,\" Ella declared. \"Ethan is not a knight,\" Oliver mentioned. \"David is a knave\" - Michael. Chloe remarked, \"If Michael is a knight then Oliver is a knave\". Ethan told you that Ella is not a knave. David expressed that If Michael is a knave then Ella is a knave. So who is a knight and who is a knave?", "names": ["Ella", "Oliver", "Michael", "Chloe", "Ethan", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true], "solution_text": "Ella is a knave, Oliver is a knight, Michael is a knave, Chloe is a knight, Ethan is a knave, and David is a knight.", "solution_text_format": "(1) Ella is a knave\n(2) Oliver is a knight\n(3) Michael is a knave\n(4) Chloe is a knight\n(5) Ethan is a knave\n(6) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Michael is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Ella is not a knave.", "Michael cannot be a knight, because this would contradict the claim of Ella that Ethan is a knave if and only if Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of their own that If Michael is a knave then Ella is a knave.", "David cannot be a knave, because this would contradict the false claim of Michael that David is a knave.", "We have exhausted all possibilities for David and Michael, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Ella is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Michael is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Michael cannot be a knight, because this would contradict the false claim of Ella that Ethan is a knave if and only if Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that David is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Michael is a knave then Ella is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Michael is a knight then Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('telling-truth', 2)), ('not', ('telling-truth', 4)), ('lying', 5), ('->', ('telling-truth', 2), ('lying', 1)), ('not', ('lying', 0)), ('->', ('lying', 2), ('lying', 0)))", "index": 583}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Olivia, Avery, Penelope, Owen, and Riley. William expressed that If Olivia is a knave then Owen is a knight. \"Riley is a knight,\" Olivia claimed. \"William is a knave and Riley is a knave,\" Avery mentioned. \"Riley is not a knight,\" Penelope claimed. Owen stated, \"Avery is a knight\". According to Riley, \"Owen is a knave or Olivia is a knave\". So who is a knight and who is a knave?", "names": ["William", "Olivia", "Avery", "Penelope", "Owen", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true], "solution_text": "William is a knight, Olivia is a knight, Avery is a knave, Penelope is a knave, Owen is a knave, and Riley is a knight.", "solution_text_format": "(1) William is a knight\n(2) Olivia is a knight\n(3) Avery is a knave\n(4) Penelope is a knave\n(5) Owen is a knave\n(6) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that If Olivia is a knave then Owen is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Owen is a knave or Olivia is a knave.", "Owen cannot be a knight, because this would contradict the claim of Riley that Owen is a knave or Olivia is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Avery is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that William is a knave and Riley is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that William is a knave and Riley is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Riley is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Riley is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 4)), ('telling-truth', 5), ('and', ('lying', 0), ('lying', 5)), ('not', ('telling-truth', 5)), ('telling-truth', 2), ('or', ('lying', 4), ('lying', 1)))", "index": 584}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Elizabeth, Aurora, Aria, Olivia, and David. James said that Aria is a knight. Elizabeth stated, \"James is a knave or Olivia is a knight\". Aurora said, \"If Aria is a knight then Elizabeth is a knight.\" Aria commented, \"If Elizabeth is a knave then Aurora is a knight\". \"David is a knight\" - Olivia. \"Elizabeth is a knight or David is a knight,\" David declared. So who is a knight and who is a knave?", "names": ["James", "Elizabeth", "Aurora", "Aria", "Olivia", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "James is a knight, Elizabeth is a knight, Aurora is a knight, Aria is a knight, Olivia is a knight, and David is a knight.", "solution_text_format": "(1) James is a knight\n(2) Elizabeth is a knight\n(3) Aurora is a knight\n(4) Aria is a knight\n(5) Olivia is a knight\n(6) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Aurora is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that James is a knave or Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Elizabeth is a knight or David is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Aria is a knight then Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('or', ('lying', 0), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('->', ('lying', 1), ('telling-truth', 2)), ('telling-truth', 5), ('or', ('telling-truth', 1), ('telling-truth', 5)))", "index": 585}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Aiden, Ava, Jackson, Matthew, and Penelope. Michael said, \"Aiden is a knight or Ava is a knave.\" According to Aiden, \"Penelope is not a knave\". \"Matthew is a knight or Matthew is a knave,\" Ava mentioned. \"Ava is not a knave,\" Jackson declared. \"Michael is a knight if and only if Jackson is a knave,\" Matthew mentioned. Penelope said that Michael is a knave or Penelope is a knight. So who is a knight and who is a knave?", "names": ["Michael", "Aiden", "Ava", "Jackson", "Matthew", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Michael is a knight, Aiden is a knight, Ava is a knight, Jackson is a knight, Matthew is a knave, and Penelope is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Aiden is a knight\n(3) Ava is a knight\n(4) Jackson is a knight\n(5) Matthew is a knave\n(6) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Aiden is a knight or Ava is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Michael is a knave or Penelope is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Matthew is a knight or Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Michael is a knight if and only if Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Matthew that Michael is a knight if and only if Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Ava is not a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Michael is a knight if and only if Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Ava is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 2)), ('not', ('lying', 5)), ('or', ('telling-truth', 4), ('lying', 4)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 0), ('lying', 3)), ('or', ('lying', 0), ('telling-truth', 5)))", "index": 586}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Amelia, Alexander, Evelyn, Riley, and Isabella. According to Sofia, \"Isabella is not a knight\". In a statement by Amelia: \"If Amelia is a knight then Riley is a knight\". Alexander was heard saying, \"Amelia is a knight or Amelia is a knave\". Evelyn said, \"Alexander is not a knight.\" Riley remarked, \"Isabella is a knight if and only if Sofia is a knave\". Isabella remarked, \"Evelyn is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Amelia", "Alexander", "Evelyn", "Riley", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Sofia is a knave, Amelia is a knight, Alexander is a knight, Evelyn is a knave, Riley is a knight, and Isabella is a knight.", "solution_text_format": "(1) Sofia is a knave\n(2) Amelia is a knight\n(3) Alexander is a knight\n(4) Evelyn is a knave\n(5) Riley is a knight\n(6) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Sofia that Isabella is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Evelyn that Alexander is not a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight or Amelia is a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of Isabella that Evelyn is a knave.", "We have exhausted all possibilities for Evelyn and Isabella, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Isabella that Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Amelia is a knight or Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Amelia is a knight then Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('or', ('telling-truth', 1), ('lying', 1)), ('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('lying', 3))", "index": 587}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Amelia, Charlotte, Jack, Penelope, and Oliver. Ella commented, \"Penelope is not a knight\". \"Ella is a knight or Jack is a knave,\" Amelia claimed. Charlotte said, \"Penelope is a knave and Penelope is a knight.\" Jack commented, \"Oliver is a knight if and only if Charlotte is a knave\". Penelope expressed that If Jack is a knight then Amelia is a knight. Oliver told you that Amelia is a knave. So who is a knight and who is a knave?", "names": ["Ella", "Amelia", "Charlotte", "Jack", "Penelope", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "Ella is a knave, Amelia is a knight, Charlotte is a knave, Jack is a knave, Penelope is a knight, and Oliver is a knave.", "solution_text_format": "(1) Ella is a knave\n(2) Amelia is a knight\n(3) Charlotte is a knave\n(4) Jack is a knave\n(5) Penelope is a knight\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Ella that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Jack is a knight then Amelia is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Charlotte is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Penelope that If Jack is a knight then Amelia is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Jack is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the false claim of Penelope that If Jack is a knight then Amelia is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Jack is a knave.", "We have exhausted all possibilities for Amelia and Oliver, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of Penelope that If Jack is a knight then Amelia is a knight.", "We have exhausted all possibilities for Jack and Penelope, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Jack is a knight then Amelia is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Charlotte is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Ella is a knight or Jack is a knave.", "Amelia cannot be a knave, because this would contradict the claim of Penelope that If Jack is a knight then Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Ella is a knight or Jack is a knave.", "Amelia cannot be a knave, because this would contradict the claim of Penelope that If Jack is a knight then Amelia is a knight.", "We have exhausted all possibilities for Amelia and Oliver, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Charlotte is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Oliver that Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Jack is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Ella is a knight or Jack is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Penelope is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Penelope is a knave and Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('or', ('telling-truth', 0), ('lying', 3)), ('and', ('lying', 4), ('telling-truth', 4)), ('<=>', ('telling-truth', 5), ('lying', 2)), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('lying', 1))", "index": 588}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Henry, Abigail, Ethan, Charlotte, and Zoey. James expressed that Zoey is a knight if and only if Henry is a knight. Henry noted, \"Abigail is a knave or Zoey is a knight\". In a statement by Abigail: \"Ethan is a knave and Abigail is a knight\". Ethan stated, \"Abigail is a knave if and only if Charlotte is a knight\". \"Ethan is not a knight,\" Charlotte declared. \"If Abigail is a knight then Abigail is a knave,\" Zoey claimed. So who is a knight and who is a knave?", "names": ["James", "Henry", "Abigail", "Ethan", "Charlotte", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false], "solution_text": "James is a knight, Henry is a knave, Abigail is a knight, Ethan is a knave, Charlotte is a knight, and Zoey is a knave.", "solution_text_format": "(1) James is a knight\n(2) Henry is a knave\n(3) Abigail is a knight\n(4) Ethan is a knave\n(5) Charlotte is a knight\n(6) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Henry is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Abigail is a knight then Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Zoey that If Abigail is a knight then Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Ethan is a knave and Abigail is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Ethan is not a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Ethan that Abigail is a knave if and only if Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Ethan that Abigail is a knave if and only if Charlotte is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Ethan is not a knight.", "We have exhausted all possibilities for Charlotte, Ethan, and Abigail, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Abigail is a knight then Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Ethan is a knave and Abigail is a knight.", "Ethan cannot be a knight, because this would contradict the claim of Abigail that Ethan is a knave and Abigail is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Henry cannot be a knight, because this would contradict the claim of James that Zoey is a knight if and only if Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Abigail is a knave or Zoey is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('or', ('lying', 2), ('telling-truth', 5)), ('and', ('lying', 3), ('telling-truth', 2)), ('<=>', ('lying', 2), ('telling-truth', 4)), ('not', ('telling-truth', 3)), ('->', ('telling-truth', 2), ('lying', 2)))", "index": 589}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Owen, William, David, Noah, and Daniel. Sebastian was heard saying, \"William is a knave or Noah is a knight\". Owen was heard saying, \"Sebastian is not a knight\". William told you that Owen is a knave and Owen is a knight. In a statement by David: \"Noah is a knight\". In a statement by Noah: \"William is a knave\". Daniel commented, \"David is a knight and William is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "Owen", "William", "David", "Noah", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false], "solution_text": "Sebastian is a knight, Owen is a knave, William is a knave, David is a knight, Noah is a knight, and Daniel is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Owen is a knave\n(3) William is a knave\n(4) David is a knight\n(5) Noah is a knight\n(6) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that William is a knave or Noah is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Owen is a knave and Owen is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Owen is a knave and Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that William is a knave.", "Assume David is a knight. No contradiction is found in their claim that Noah is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that David is a knight and William is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that David is a knight and William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 4)), ('not', ('telling-truth', 0)), ('and', ('lying', 1), ('telling-truth', 1)), ('telling-truth', 4), ('lying', 2), ('and', ('telling-truth', 3), ('telling-truth', 2)))", "index": 590}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Elizabeth, Lucas, Lily, Jack, and Luke. Victoria was heard saying, \"Elizabeth is a knave if and only if Jack is a knave\". Elizabeth commented, \"If Lily is a knave then Jack is a knave\". Lucas said that If Lily is a knight then Victoria is a knight. According to Lily, \"Lucas is a knight and Elizabeth is a knave\". Jack expressed that Lily is a knight or Victoria is a knight. Luke noted, \"Victoria is a knight and Jack is a knave\". So who is a knight and who is a knave?", "names": ["Victoria", "Elizabeth", "Lucas", "Lily", "Jack", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Victoria is a knave, Elizabeth is a knight, Lucas is a knight, Lily is a knave, Jack is a knave, and Luke is a knave.", "solution_text_format": "(1) Victoria is a knave\n(2) Elizabeth is a knight\n(3) Lucas is a knight\n(4) Lily is a knave\n(5) Jack is a knave\n(6) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if Jack is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Lily is a knave then Jack is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Lucas is a knight and Elizabeth is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Lucas is a knight and Elizabeth is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Lily is a knight then Victoria is a knight.", "Jack cannot be a knight, because this would contradict the claim of Elizabeth that If Lily is a knave then Jack is a knave.", "Jack cannot be a knave, because this would contradict the claim of Victoria that Elizabeth is a knave if and only if Jack is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of their own that If Lily is a knight then Victoria is a knight.", "We have exhausted all possibilities for Lucas and Lily, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that If Lily is a knave then Jack is a knave.", "Lily cannot be a knight, because this would contradict the false claim of Elizabeth that If Lily is a knave then Jack is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Lucas is a knight and Elizabeth is a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Lily that Lucas is a knight and Elizabeth is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of their own that If Lily is a knight then Victoria is a knight.", "We have exhausted all possibilities for Lucas, Lily, and Elizabeth, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Jack is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Lily is a knave then Jack is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Lucas is a knight and Elizabeth is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Lucas is a knight and Elizabeth is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Lily is a knight then Victoria is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Victoria that Elizabeth is a knave if and only if Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Lily is a knight or Victoria is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Jack is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Victoria is a knight and Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 4)), ('->', ('lying', 3), ('lying', 4)), ('->', ('telling-truth', 3), ('telling-truth', 0)), ('and', ('telling-truth', 2), ('lying', 1)), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('lying', 4)))", "index": 591}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Liam, Lily, Isabella, Samuel, and Avery. Joseph noted, \"Lily is not a knave\". Liam commented, \"Samuel is a knight if and only if Isabella is a knight\". Lily was heard saying, \"Liam is a knave if and only if Joseph is a knave\". Isabella said, \"Joseph is a knave or Avery is a knight.\" Samuel was heard saying, \"Avery is a knave and Avery is a knight\". According to Avery, \"Isabella is not a knave\". So who is a knight and who is a knave?", "names": ["Joseph", "Liam", "Lily", "Isabella", "Samuel", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Joseph is a knight, Liam is a knight, Lily is a knight, Isabella is a knave, Samuel is a knave, and Avery is a knave.", "solution_text_format": "(1) Joseph is a knight\n(2) Liam is a knight\n(3) Lily is a knight\n(4) Isabella is a knave\n(5) Samuel is a knave\n(6) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Lily is not a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Liam is a knave if and only if Joseph is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Isabella is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Avery is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Avery is a knave and Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Isabella cannot be a knight, because this would contradict the claim of Liam that Samuel is a knight if and only if Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Joseph is a knave or Avery is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Isabella is not a knave.", "Isabella cannot be a knight, because this would contradict the claim of Liam that Samuel is a knight if and only if Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Joseph is a knave or Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 3)), ('<=>', ('lying', 1), ('lying', 0)), ('or', ('lying', 0), ('telling-truth', 5)), ('and', ('lying', 5), ('telling-truth', 5)), ('not', ('lying', 3)))", "index": 592}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Emma, Liam, Mason, Mia, and Luke. Aurora remarked, \"Liam is not a knave\". Emma commented, \"Luke is a knave if and only if Luke is a knight\". Liam told you that Luke is a knight and Emma is a knave. In a statement by Mason: \"Luke is a knave if and only if Mia is a knight\". \"Emma is not a knight,\" Mia mentioned. \"Aurora is a knave or Mason is a knave,\" Luke claimed. So who is a knight and who is a knave?", "names": ["Aurora", "Emma", "Liam", "Mason", "Mia", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Aurora is a knight, Emma is a knave, Liam is a knight, Mason is a knave, Mia is a knight, and Luke is a knight.", "solution_text_format": "(1) Aurora is a knight\n(2) Emma is a knave\n(3) Liam is a knight\n(4) Mason is a knave\n(5) Mia is a knight\n(6) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Luke is a knight and Emma is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Aurora is a knave or Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Luke that Aurora is a knave or Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Emma is not a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Luke is a knave if and only if Luke is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('<=>', ('lying', 5), ('telling-truth', 5)), ('and', ('telling-truth', 5), ('lying', 1)), ('<=>', ('lying', 5), ('telling-truth', 4)), ('not', ('telling-truth', 1)), ('or', ('lying', 0), ('lying', 3)))", "index": 593}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Samuel, Jack, Elizabeth, Oliver, and Grace. Sofia remarked, \"Jack is not a knave\". Samuel asserted: \"Elizabeth is a knave if and only if Sofia is a knave\". Jack expressed that Elizabeth is a knight. \"Grace is a knave if and only if Elizabeth is a knight,\" Elizabeth mentioned. \"Elizabeth is not a knight,\" Oliver mentioned. \"Elizabeth is not a knight,\" Grace declared. So who is a knight and who is a knave?", "names": ["Sofia", "Samuel", "Jack", "Elizabeth", "Oliver", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Sofia is a knight, Samuel is a knight, Jack is a knight, Elizabeth is a knight, Oliver is a knave, and Grace is a knave.", "solution_text_format": "(1) Sofia is a knight\n(2) Samuel is a knight\n(3) Jack is a knight\n(4) Elizabeth is a knight\n(5) Oliver is a knave\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Grace is a knave if and only if Elizabeth is a knight.", "Grace cannot be a knight, because this would contradict the claim of Elizabeth that Grace is a knave if and only if Elizabeth is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Elizabeth is not a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if Sofia is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that Elizabeth is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Elizabeth is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('<=>', ('lying', 3), ('lying', 0)), ('telling-truth', 3), ('<=>', ('lying', 5), ('telling-truth', 3)), ('not', ('telling-truth', 3)), ('not', ('telling-truth', 3)))", "index": 594}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Riley, Victoria, Avery, Sofia, and William. In Henry's words: \"William is a knight if and only if Avery is a knight\". Riley asserted: \"Victoria is not a knave\". \"Sofia is a knave or Henry is a knight,\" Victoria mentioned. Avery told you that Victoria is a knight and Henry is a knight. \"Riley is a knight or William is a knave,\" Sofia declared. In William's words: \"Avery is a knave or Avery is a knight\". So who is a knight and who is a knave?", "names": ["Henry", "Riley", "Victoria", "Avery", "Sofia", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Henry is a knight, Riley is a knight, Victoria is a knight, Avery is a knight, Sofia is a knight, and William is a knight.", "solution_text_format": "(1) Henry is a knight\n(2) Riley is a knight\n(3) Victoria is a knight\n(4) Avery is a knight\n(5) Sofia is a knight\n(6) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that William is a knight if and only if Avery is a knight.", "Assume William is a knight. No contradiction is found in their claim that Avery is a knave or Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Victoria is a knight and Henry is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Sofia is a knave or Henry is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Riley is a knight or William is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Victoria is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('telling-truth', 3)), ('not', ('lying', 2)), ('or', ('lying', 4), ('telling-truth', 0)), ('and', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('telling-truth', 1), ('lying', 5)), ('or', ('lying', 3), ('telling-truth', 3)))", "index": 595}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Penelope, Mia, Noah, Matthew, and Lily. \"Noah is a knave\" - Grace. Penelope asserted: \"Mia is a knight\". In a statement by Mia: \"Grace is a knave\". Noah said, \"Mia is a knight if and only if Matthew is a knight.\" Matthew said that Noah is not a knave. \"Mia is not a knight\" - Lily. So who is a knight and who is a knave?", "names": ["Grace", "Penelope", "Mia", "Noah", "Matthew", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Grace is a knave, Penelope is a knight, Mia is a knight, Noah is a knight, Matthew is a knight, and Lily is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) Penelope is a knight\n(3) Mia is a knight\n(4) Noah is a knight\n(5) Matthew is a knight\n(6) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Grace that Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Matthew is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Grace is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Grace is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Noah is not a knave.", "Matthew cannot be a knave, because this would contradict the false claim of Noah that Mia is a knight if and only if Matthew is a knight.", "We have exhausted all possibilities for Matthew, Mia, and Noah, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Mia is a knight if and only if Matthew is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Grace is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Noah is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Mia is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Mia is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Mia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('telling-truth', 2), ('lying', 0), ('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('not', ('lying', 3)), ('not', ('telling-truth', 2)))", "index": 596}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Aiden, William, Elizabeth, Logan, and Jack. Joseph told you that Elizabeth is a knave or Aiden is a knave. Aiden noted, \"Elizabeth is a knave\". William told you that If Jack is a knight then Aiden is a knight. Elizabeth remarked, \"If William is a knight then Jack is a knight\". According to Logan, \"Elizabeth is a knight if and only if William is a knave\". As Jack put it, \"Logan is not a knave\". So who is a knight and who is a knave?", "names": ["Joseph", "Aiden", "William", "Elizabeth", "Logan", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true], "solution_text": "Joseph is a knight, Aiden is a knave, William is a knave, Elizabeth is a knight, Logan is a knight, and Jack is a knight.", "solution_text_format": "(1) Joseph is a knight\n(2) Aiden is a knave\n(3) William is a knave\n(4) Elizabeth is a knight\n(5) Logan is a knight\n(6) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Elizabeth is a knave or Aiden is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If William is a knight then Jack is a knight.", "Assume William is a knight. No contradiction is found in their claim that If Jack is a knight then Aiden is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Logan is not a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight if and only if William is a knave.", "Logan cannot be a knave, because this would contradict the claim of Jack that Logan is not a knave.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Elizabeth that If William is a knight then Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that If Jack is a knight then Aiden is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Logan is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if William is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Joseph that Elizabeth is a knave or Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 1)), ('lying', 3), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('->', ('telling-truth', 2), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('not', ('lying', 4)))", "index": 597}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, James, Avery, Samuel, Elizabeth, and Michael. William remarked, \"William is a knight\". James told you that William is a knight if and only if Elizabeth is a knight. \"William is a knight and Michael is a knight,\" Avery mentioned. Samuel told you that Elizabeth is a knight if and only if William is a knight. Elizabeth noted, \"If William is a knight then James is a knave\". Michael was heard saying, \"Samuel is a knight if and only if James is a knave\". So who is a knight and who is a knave?", "names": ["William", "James", "Avery", "Samuel", "Elizabeth", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false], "solution_text": "William is a knave, James is a knave, Avery is a knave, Samuel is a knave, Elizabeth is a knight, and Michael is a knave.", "solution_text_format": "(1) William is a knave\n(2) James is a knave\n(3) Avery is a knave\n(4) Samuel is a knave\n(5) Elizabeth is a knight\n(6) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that William is a knight.", "Assume James is a knight. No contradiction is found in their claim that William is a knight if and only if Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that If William is a knight then James is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of James that William is a knight if and only if Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that William is a knight if and only if Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of James that William is a knight if and only if Elizabeth is a knight.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that If William is a knight then James is a knave.", "We have exhausted all possibilities for Elizabeth and James, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that William is a knight.", "Assume James is a knight. No contradiction is found in their claim that William is a knight if and only if Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of James that William is a knight if and only if Elizabeth is a knight.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that If William is a knight then James is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that William is a knight if and only if Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If William is a knight then James is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that William is a knight and Michael is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that William is a knight and Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Samuel is a knight if and only if James is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight if and only if William is a knight.", "Samuel cannot be a knave, because this would contradict the claim of Michael that Samuel is a knight if and only if James is a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if James is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight if and only if William is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 0), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('lying', 1)), ('<=>', ('telling-truth', 3), ('lying', 1)))", "index": 598}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Henry, Ella, Evelyn, Charlotte, and Daniel. Ethan was heard saying, \"Charlotte is a knight\". According to Henry, \"Charlotte is a knight if and only if Evelyn is a knight\". According to Ella, \"Charlotte is a knight if and only if Ethan is a knight\". In a statement by Evelyn: \"Daniel is not a knave\". Charlotte told you that Ethan is a knight if and only if Evelyn is a knight. \"Charlotte is a knight if and only if Ella is a knight,\" Daniel claimed. So who is a knight and who is a knave?", "names": ["Ethan", "Henry", "Ella", "Evelyn", "Charlotte", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Ethan is a knight, Henry is a knight, Ella is a knight, Evelyn is a knight, Charlotte is a knight, and Daniel is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Henry is a knight\n(3) Ella is a knight\n(4) Evelyn is a knight\n(5) Charlotte is a knight\n(6) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Ethan is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('<=>', ('telling-truth', 4), ('telling-truth', 3)), ('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('not', ('lying', 5)), ('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('<=>', ('telling-truth', 4), ('telling-truth', 2)))", "index": 599}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Michael, Joseph, Grace, Harper, and Benjamin. Jack remarked, \"Harper is a knight if and only if Harper is a knave\". \"Harper is a knight if and only if Harper is a knave,\" Michael mentioned. \"If Benjamin is a knight then Jack is a knave,\" Joseph claimed. Grace said, \"If Joseph is a knight then Michael is a knave.\" Harper expressed that Michael is not a knave. Benjamin stated, \"Jack is not a knave\". So who is a knight and who is a knave?", "names": ["Jack", "Michael", "Joseph", "Grace", "Harper", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Jack is a knave, Michael is a knave, Joseph is a knight, Grace is a knight, Harper is a knave, and Benjamin is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Michael is a knave\n(3) Joseph is a knight\n(4) Grace is a knight\n(5) Harper is a knave\n(6) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Jack cannot be a knight, because this would contradict the claim of their own that Harper is a knight if and only if Harper is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Michael is not a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Harper is a knight if and only if Harper is a knave.", "Michael cannot be a knave, because this would contradict the claim of Harper that Michael is not a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Michael is not a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Harper is a knight if and only if Harper is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Harper is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that If Benjamin is a knight then Jack is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Jack is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Jack is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Joseph is a knight then Michael is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('lying', 4)), ('<=>', ('telling-truth', 4), ('lying', 4)), ('->', ('telling-truth', 5), ('lying', 0)), ('->', ('telling-truth', 2), ('lying', 1)), ('not', ('lying', 1)), ('not', ('lying', 0)))", "index": 600}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Emma, Evelyn, Mia, William, and Daniel. \"Evelyn is a knight,\" Abigail mentioned. In Emma's words: \"If Emma is a knight then Daniel is a knave\". Evelyn remarked, \"Abigail is a knight or William is a knight\". As Mia put it, \"Evelyn is a knight\". William said, \"Daniel is a knight.\" Daniel said, \"Mia is a knight or Evelyn is a knight.\" So who is a knight and who is a knave?", "names": ["Abigail", "Emma", "Evelyn", "Mia", "William", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false], "solution_text": "Abigail is a knave, Emma is a knight, Evelyn is a knave, Mia is a knave, William is a knave, and Daniel is a knave.", "solution_text_format": "(1) Abigail is a knave\n(2) Emma is a knight\n(3) Evelyn is a knave\n(4) Mia is a knave\n(5) William is a knave\n(6) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Abigail is a knight or William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Mia is a knight or Evelyn is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that If Emma is a knight then Daniel is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Daniel is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of their own that Evelyn is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of William that Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of William that Daniel is a knight.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Mia is a knight or Evelyn is a knight.", "We have exhausted all possibilities for Daniel and William, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Abigail that Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Abigail that Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Abigail is a knight or William is a knight.", "William cannot be a knight, because this would contradict the false claim of Evelyn that Abigail is a knight or William is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of William that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Mia is a knight or Evelyn is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Evelyn is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Emma is a knight then Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('->', ('telling-truth', 1), ('lying', 5)), ('or', ('telling-truth', 0), ('telling-truth', 4)), ('telling-truth', 2), ('telling-truth', 5), ('or', ('telling-truth', 3), ('telling-truth', 2)))", "index": 601}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Daniel, Penelope, Matthew, Owen, and James. Sebastian remarked, \"James is a knave or Owen is a knight\". Daniel told you that Sebastian is a knight or Penelope is a knight. Penelope asserted: \"James is a knave if and only if Penelope is a knight\". Matthew commented, \"Owen is a knave\". Owen commented, \"Sebastian is a knight\". James told you that Owen is a knave if and only if Penelope is a knight. So who is a knight and who is a knave?", "names": ["Sebastian", "Daniel", "Penelope", "Matthew", "Owen", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Sebastian is a knight, Daniel is a knight, Penelope is a knight, Matthew is a knave, Owen is a knight, and James is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Daniel is a knight\n(3) Penelope is a knight\n(4) Matthew is a knave\n(5) Owen is a knight\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that James is a knave or Owen is a knight.", "Assume James is a knight. No contradiction is found in their claim that Owen is a knave if and only if Penelope is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that James is a knave if and only if Penelope is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that James is a knave if and only if Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Sebastian that James is a knave or Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Penelope is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that James is a knave if and only if Penelope is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Sebastian is a knight or Penelope is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Owen is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 4)), ('or', ('telling-truth', 0), ('telling-truth', 2)), ('<=>', ('lying', 5), ('telling-truth', 2)), ('lying', 4), ('telling-truth', 0), ('<=>', ('lying', 4), ('telling-truth', 2)))", "index": 602}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Mia, Charlotte, Matthew, Luke, and Zoey. Lily remarked, \"Mia is not a knight\". Mia told you that Matthew is a knave. Charlotte was heard saying, \"Lily is a knight\". In a statement by Matthew: \"Luke is a knave and Charlotte is a knight\". Luke expressed that If Mia is a knight then Zoey is a knave. \"Matthew is not a knave,\" Zoey declared. So who is a knight and who is a knave?", "names": ["Lily", "Mia", "Charlotte", "Matthew", "Luke", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "Lily is a knave, Mia is a knight, Charlotte is a knave, Matthew is a knave, Luke is a knight, and Zoey is a knave.", "solution_text_format": "(1) Lily is a knave\n(2) Mia is a knight\n(3) Charlotte is a knave\n(4) Matthew is a knave\n(5) Luke is a knight\n(6) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Mia is not a knight.", "Mia cannot be a knight, because this would contradict the claim of Lily that Mia is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Luke is a knave and Charlotte is a knight.", "Luke cannot be a knight, because this would contradict the claim of Matthew that Luke is a knave and Charlotte is a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that If Mia is a knight then Zoey is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of Mia that Matthew is a knave.", "We have exhausted all possibilities for Matthew and Mia, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Mia is not a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Mia that Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Luke is a knave and Charlotte is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Mia is a knight then Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Luke that If Mia is a knight then Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Matthew is not a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Lily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('lying', 3), ('telling-truth', 0), ('and', ('lying', 4), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('lying', 5)), ('not', ('lying', 3)))", "index": 603}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Lily, Aria, Penelope, Lucas, and Ava. Mason asserted: \"If Lily is a knight then Lily is a knave\". Lily noted, \"Ava is a knave if and only if Lily is a knight\". \"Lily is not a knave,\" Aria declared. Penelope expressed that Lily is a knight or Aria is a knight. Lucas noted, \"Lily is a knave and Penelope is a knight\". Ava said, \"Mason is not a knight.\" So who is a knight and who is a knave?", "names": ["Mason", "Lily", "Aria", "Penelope", "Lucas", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false], "solution_text": "Mason is a knight, Lily is a knave, Aria is a knave, Penelope is a knave, Lucas is a knave, and Ava is a knave.", "solution_text_format": "(1) Mason is a knight\n(2) Lily is a knave\n(3) Aria is a knave\n(4) Penelope is a knave\n(5) Lucas is a knave\n(6) Ava is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that If Lily is a knight then Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Mason that If Lily is a knight then Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Lily is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Lily that Ava is a knave if and only if Lily is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Mason is not a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Lily is not a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Lily is not a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Lily is a knight or Aria is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Lily is a knight or Aria is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Penelope is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Lily is a knave and Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('lying', 1)), ('<=>', ('lying', 5), ('telling-truth', 1)), ('not', ('lying', 1)), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('lying', 1), ('telling-truth', 3)), ('not', ('telling-truth', 0)))", "index": 604}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, David, Michael, Luke, Jackson, and Evelyn. \"Michael is a knave\" - Charlotte. \"If Evelyn is a knight then Charlotte is a knight,\" David declared. Michael expressed that If Jackson is a knave then Charlotte is a knight. Luke remarked, \"Jackson is a knight\". Jackson stated, \"Luke is a knight and Evelyn is a knave\". Evelyn noted, \"Jackson is a knave\". So who is a knight and who is a knave?", "names": ["Charlotte", "David", "Michael", "Luke", "Jackson", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Charlotte is a knave, David is a knight, Michael is a knight, Luke is a knight, Jackson is a knight, and Evelyn is a knave.", "solution_text_format": "(1) Charlotte is a knave\n(2) David is a knight\n(3) Michael is a knight\n(4) Luke is a knight\n(5) Jackson is a knight\n(6) Evelyn is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Charlotte that Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knave then Charlotte is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Jackson is a knave then Charlotte is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Luke is a knight and Evelyn is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Jackson is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Jackson that Luke is a knight and Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jackson is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Evelyn is a knight then Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('->', ('telling-truth', 5), ('telling-truth', 0)), ('->', ('lying', 4), ('telling-truth', 0)), ('telling-truth', 4), ('and', ('telling-truth', 3), ('lying', 5)), ('lying', 4))", "index": 605}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Elizabeth, Harper, Aria, Michael, and Alexander. \"Alexander is a knave if and only if Harper is a knave,\" Emily declared. Elizabeth commented, \"Michael is a knight or Aria is a knave\". In a statement by Harper: \"Emily is a knave or Elizabeth is a knight\". Aria remarked, \"Emily is a knight if and only if Michael is a knight\". Michael told you that If Emily is a knave then Aria is a knave. Alexander asserted: \"Harper is a knight and Michael is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Elizabeth", "Harper", "Aria", "Michael", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false], "solution_text": "Emily is a knave, Elizabeth is a knight, Harper is a knight, Aria is a knave, Michael is a knight, and Alexander is a knave.", "solution_text_format": "(1) Emily is a knave\n(2) Elizabeth is a knight\n(3) Harper is a knight\n(4) Aria is a knave\n(5) Michael is a knight\n(6) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Harper is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Harper is a knight and Michael is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Emily is a knave or Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Michael is a knight or Aria is a knave.", "Michael cannot be a knight, because this would contradict the claim of Alexander that Harper is a knight and Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that If Emily is a knave then Aria is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Harper that Emily is a knave or Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Emily that Alexander is a knave if and only if Harper is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Harper is a knight and Michael is a knave.", "Harper cannot be a knight, because this would contradict the claim of Emily that Alexander is a knave if and only if Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Emily is a knave or Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Harper that Emily is a knave or Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Michael is a knight or Aria is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Elizabeth that Michael is a knight or Aria is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that If Emily is a knave then Aria is a knave.", "We have exhausted all possibilities for Michael, Elizabeth, Harper, and Alexander, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Alexander is a knave if and only if Harper is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Harper is a knight and Michael is a knave.", "Harper cannot be a knight, because this would contradict the false claim of Emily that Alexander is a knave if and only if Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of their own that Emily is a knave or Elizabeth is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Harper is a knight and Michael is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Emily is a knave or Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Michael is a knight or Aria is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Emily is a knave then Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Emily is a knight if and only if Michael is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 2)), ('or', ('telling-truth', 4), ('lying', 3)), ('or', ('lying', 0), ('telling-truth', 1)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('->', ('lying', 0), ('lying', 3)), ('and', ('telling-truth', 2), ('lying', 4)))", "index": 606}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Harper, Owen, Elizabeth, Emma, and Abigail. Olivia noted, \"Emma is a knight or Emma is a knave\". Harper noted, \"Abigail is a knave and Emma is a knave\". According to Owen, \"If Olivia is a knave then Elizabeth is a knight\". \"If Abigail is a knave then Olivia is a knight,\" Elizabeth mentioned. Emma stated, \"If Emma is a knight then Elizabeth is a knight\". Abigail was heard saying, \"Emma is not a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Harper", "Owen", "Elizabeth", "Emma", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Olivia is a knight, Harper is a knave, Owen is a knight, Elizabeth is a knight, Emma is a knight, and Abigail is a knight.", "solution_text_format": "(1) Olivia is a knight\n(2) Harper is a knave\n(3) Owen is a knight\n(4) Elizabeth is a knight\n(5) Emma is a knight\n(6) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Emma is a knight or Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If Emma is a knight then Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Abigail is a knave then Olivia is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Emma is not a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Emma is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Abigail is a knave and Emma is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Olivia is a knave then Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('lying', 4)), ('and', ('lying', 5), ('lying', 4)), ('->', ('lying', 0), ('telling-truth', 3)), ('->', ('lying', 5), ('telling-truth', 0)), ('->', ('telling-truth', 4), ('telling-truth', 3)), ('not', ('lying', 4)))", "index": 607}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Amelia, Liam, Joseph, Daniel, and Chloe. Jackson expressed that Jackson is a knight if and only if Chloe is a knave. Amelia told you that If Jackson is a knave then Amelia is a knight. Liam said, \"Chloe is a knave.\" Joseph said that Liam is a knight if and only if Daniel is a knave. \"Jackson is a knight if and only if Daniel is a knight,\" Daniel claimed. Chloe expressed that Joseph is a knight and Liam is a knight. So who is a knight and who is a knave?", "names": ["Jackson", "Amelia", "Liam", "Joseph", "Daniel", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Jackson is a knight, Amelia is a knight, Liam is a knight, Joseph is a knave, Daniel is a knight, and Chloe is a knave.", "solution_text_format": "(1) Jackson is a knight\n(2) Amelia is a knight\n(3) Liam is a knight\n(4) Joseph is a knave\n(5) Daniel is a knight\n(6) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Jackson that Jackson is a knight if and only if Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Joseph is a knight and Liam is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Liam is a knight if and only if Daniel is a knave.", "Liam cannot be a knight, because this would contradict the false claim of Chloe that Joseph is a knight and Liam is a knight.", "Liam cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Daniel is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Chloe is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Daniel is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Jackson is a knave then Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 5)), ('->', ('lying', 0), ('telling-truth', 1)), ('lying', 5), ('<=>', ('telling-truth', 2), ('lying', 4)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('and', ('telling-truth', 3), ('telling-truth', 2)))", "index": 608}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Aiden, Sebastian, Grace, Abigail, and Benjamin. In Elizabeth's words: \"Grace is a knave if and only if Abigail is a knave\". Aiden told you that Sebastian is a knave or Benjamin is a knight. Sebastian remarked, \"Benjamin is a knight or Abigail is a knight\". Grace said, \"Abigail is not a knight.\" \"If Elizabeth is a knight then Abigail is a knight\" - Abigail. In Benjamin's words: \"Grace is a knave if and only if Abigail is a knight\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Aiden", "Sebastian", "Grace", "Abigail", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Elizabeth is a knave, Aiden is a knight, Sebastian is a knight, Grace is a knave, Abigail is a knight, and Benjamin is a knight.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Aiden is a knight\n(3) Sebastian is a knight\n(4) Grace is a knave\n(5) Abigail is a knight\n(6) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Grace is a knave if and only if Abigail is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of Grace that Abigail is not a knight.", "Abigail cannot be a knave, because this would contradict the claim of Elizabeth that Grace is a knave if and only if Abigail is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of Elizabeth that Grace is a knave if and only if Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of Grace that Abigail is not a knight.", "We have exhausted all possibilities for Abigail and Grace, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Abigail is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Elizabeth that Grace is a knave if and only if Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that If Elizabeth is a knight then Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Abigail is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Sebastian is a knave or Benjamin is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Benjamin is a knight or Abigail is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Grace is a knave if and only if Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 4)), ('or', ('lying', 2), ('telling-truth', 5)), ('or', ('telling-truth', 5), ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('<=>', ('lying', 3), ('telling-truth', 4)))", "index": 609}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Zoey, Oliver, Lily, Daniel, Luke, and Joseph. According to Zoey, \"Joseph is a knave\". Oliver noted, \"Daniel is not a knave\". \"Daniel is a knave and Luke is a knight\" - Lily. According to Daniel, \"If Luke is a knight then Zoey is a knave\". \"If Joseph is a knave then Zoey is a knave,\" Luke mentioned. In a statement by Joseph: \"Oliver is a knight if and only if Lily is a knight\". So who is a knight and who is a knave?", "names": ["Zoey", "Oliver", "Lily", "Daniel", "Luke", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Zoey is a knight, Oliver is a knight, Lily is a knave, Daniel is a knight, Luke is a knave, and Joseph is a knave.", "solution_text_format": "(1) Zoey is a knight\n(2) Oliver is a knight\n(3) Lily is a knave\n(4) Daniel is a knight\n(5) Luke is a knave\n(6) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Zoey that Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Lily is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Luke is a knight then Zoey is a knave.", "Luke cannot be a knight, because this would contradict the claim of Daniel that If Luke is a knight then Zoey is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that If Joseph is a knave then Zoey is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Luke is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Daniel is a knave and Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('not', ('lying', 3)), ('and', ('lying', 3), ('telling-truth', 4)), ('->', ('telling-truth', 4), ('lying', 0)), ('->', ('lying', 5), ('lying', 0)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)))", "index": 610}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Daniel, Mia, William, Aurora, and Liam. Jack told you that Daniel is not a knave. \"William is a knave,\" Daniel mentioned. \"If Daniel is a knight then William is a knight\" - Mia. William was heard saying, \"Liam is a knave\". Aurora was heard saying, \"Jack is a knave or William is a knight\". \"Mia is a knight and Mia is a knave,\" Liam declared. So who is a knight and who is a knave?", "names": ["Jack", "Daniel", "Mia", "William", "Aurora", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Jack is a knave, Daniel is a knave, Mia is a knight, William is a knight, Aurora is a knight, and Liam is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Daniel is a knave\n(3) Mia is a knight\n(4) William is a knight\n(5) Aurora is a knight\n(6) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Daniel that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Mia is a knave.", "Liam cannot be a knave, because this would contradict the false claim of William that Liam is a knave.", "We have exhausted all possibilities for Liam and William, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Jack that Daniel is not a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Daniel is not a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Jack that Daniel is not a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that William is a knave.", "Assume William is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of William that Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Mia is a knight and Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Daniel is a knight then William is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Jack is a knave or William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('lying', 3), ('->', ('telling-truth', 1), ('telling-truth', 3)), ('lying', 5), ('or', ('lying', 0), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('lying', 2)))", "index": 611}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Logan, Owen, Matthew, Zoey, and Ava. Jackson commented, \"Logan is a knight or Ava is a knave\". In Logan's words: \"Ava is not a knight\". \"If Ava is a knave then Logan is a knight,\" Owen mentioned. Matthew noted, \"Owen is a knave if and only if Logan is a knight\". \"Matthew is a knave or Ava is a knave,\" Zoey mentioned. In a statement by Ava: \"Matthew is a knave or Owen is a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Logan", "Owen", "Matthew", "Zoey", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Jackson is a knave, Logan is a knave, Owen is a knight, Matthew is a knight, Zoey is a knave, and Ava is a knight.", "solution_text_format": "(1) Jackson is a knave\n(2) Logan is a knave\n(3) Owen is a knight\n(4) Matthew is a knight\n(5) Zoey is a knave\n(6) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Logan is a knight or Ava is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Logan that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Matthew is a knave or Owen is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Owen is a knave if and only if Logan is a knight.", "Owen cannot be a knight, because this would contradict the claim of Matthew that Owen is a knave if and only if Logan is a knight.", "Owen cannot be a knave, because this would contradict the false claim of their own that If Ava is a knave then Logan is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of Ava that Matthew is a knave or Owen is a knight.", "We have exhausted all possibilities for Matthew and Ava, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Jackson that Logan is a knight or Ava is a knave.", "Ava cannot be a knave, because this would contradict the false claim of Logan that Ava is not a knight.", "We have exhausted all possibilities for Ava and Logan, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Logan is a knight or Ava is a knave.", "Logan cannot be a knight, because this would contradict the false claim of Jackson that Logan is a knight or Ava is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Matthew is a knave or Owen is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Owen is a knave if and only if Logan is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Ava is a knave then Logan is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Matthew is a knave or Ava is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Matthew is a knave or Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 5)), ('not', ('telling-truth', 5)), ('->', ('lying', 5), ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 1)), ('or', ('lying', 3), ('lying', 5)), ('or', ('lying', 3), ('telling-truth', 2)))", "index": 612}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Zoey, Riley, Mia, Ella, Lily, and Harper. Zoey remarked, \"Riley is not a knave\". According to Riley, \"Harper is a knight or Mia is a knight\". Mia commented, \"If Lily is a knave then Zoey is a knave\". As Ella put it, \"Riley is a knight\". Lily stated, \"Lily is a knight\". In a statement by Harper: \"Zoey is not a knight\". So who is a knight and who is a knave?", "names": ["Zoey", "Riley", "Mia", "Ella", "Lily", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Zoey is a knight, Riley is a knight, Mia is a knight, Ella is a knight, Lily is a knight, and Harper is a knave.", "solution_text_format": "(1) Zoey is a knight\n(2) Riley is a knight\n(3) Mia is a knight\n(4) Ella is a knight\n(5) Lily is a knight\n(6) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Riley is not a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Harper is a knight or Mia is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Zoey is not a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Lily is a knave then Zoey is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('or', ('telling-truth', 5), ('telling-truth', 2)), ('->', ('lying', 4), ('lying', 0)), ('telling-truth', 1), ('telling-truth', 4), ('not', ('telling-truth', 0)))", "index": 613}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Lucas, Victoria, Alexander, Matthew, and Lily. \"Olivia is a knight if and only if Lucas is a knave,\" Olivia declared. \"Olivia is a knave if and only if Lucas is a knight\" - Lucas. In Victoria's words: \"Matthew is not a knave\". Alexander expressed that Victoria is a knave or Olivia is a knave. In Matthew's words: \"Olivia is a knight\". Lily expressed that If Lucas is a knight then Matthew is a knave. So who is a knight and who is a knave?", "names": ["Olivia", "Lucas", "Victoria", "Alexander", "Matthew", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "Olivia is a knave, Lucas is a knave, Victoria is a knave, Alexander is a knight, Matthew is a knave, and Lily is a knight.", "solution_text_format": "(1) Olivia is a knave\n(2) Lucas is a knave\n(3) Victoria is a knave\n(4) Alexander is a knight\n(5) Matthew is a knave\n(6) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Olivia that Olivia is a knight if and only if Lucas is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave if and only if Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Olivia that Olivia is a knight if and only if Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Lucas is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Olivia is a knight.", "Matthew cannot be a knave, because this would contradict the claim of Victoria that Matthew is not a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Matthew is not a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Victoria that Matthew is not a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Olivia is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Victoria is a knave or Olivia is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Lucas is a knight then Matthew is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('not', ('lying', 4)), ('or', ('lying', 2), ('lying', 0)), ('telling-truth', 0), ('->', ('telling-truth', 1), ('lying', 4)))", "index": 614}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, William, Elizabeth, Riley, Matthew, and David. Luke expressed that Riley is a knight if and only if William is a knave. \"Riley is a knight,\" William claimed. Elizabeth commented, \"Riley is not a knave\". As Riley put it, \"Matthew is a knave or Matthew is a knight\". Matthew said, \"William is a knight and Riley is a knave.\" \"Elizabeth is a knight or Riley is a knight,\" David declared. So who is a knight and who is a knave?", "names": ["Luke", "William", "Elizabeth", "Riley", "Matthew", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Luke is a knave, William is a knight, Elizabeth is a knight, Riley is a knight, Matthew is a knave, and David is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) William is a knight\n(3) Elizabeth is a knight\n(4) Riley is a knight\n(5) Matthew is a knave\n(6) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Riley is a knight if and only if William is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Matthew is a knave or Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that William is a knight and Riley is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that William is a knight and Riley is a knave.", "William cannot be a knight, because this would contradict the claim of Luke that Riley is a knight if and only if William is a knave.", "William cannot be a knave, because this would contradict the false claim of their own that Riley is a knight.", "We have exhausted all possibilities for William and Matthew, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave or Matthew is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Riley is a knight if and only if William is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Matthew is a knave or Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that William is a knight and Riley is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that William is a knight and Riley is a knave.", "Assume William is a knight. No contradiction is found in their claim that Riley is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Riley is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Elizabeth is a knight or Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 1)), ('telling-truth', 3), ('not', ('lying', 3)), ('or', ('lying', 4), ('telling-truth', 4)), ('and', ('telling-truth', 1), ('lying', 3)), ('or', ('telling-truth', 2), ('telling-truth', 3)))", "index": 615}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Isabella, Riley, Emily, Aria, and Oliver. In a statement by Owen: \"If Aria is a knave then Oliver is a knight\". Isabella told you that Owen is not a knight. Riley told you that If Riley is a knight then Aria is a knight. \"Oliver is a knave if and only if Oliver is a knight,\" Emily claimed. Aria noted, \"Owen is a knight or Emily is a knave\". Oliver said that Aria is a knave. So who is a knight and who is a knave?", "names": ["Owen", "Isabella", "Riley", "Emily", "Aria", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false], "solution_text": "Owen is a knight, Isabella is a knave, Riley is a knight, Emily is a knave, Aria is a knight, and Oliver is a knave.", "solution_text_format": "(1) Owen is a knight\n(2) Isabella is a knave\n(3) Riley is a knight\n(4) Emily is a knave\n(5) Aria is a knight\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that If Aria is a knave then Oliver is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Owen is a knight or Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Oliver is a knave if and only if Oliver is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Oliver is a knave if and only if Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Aria is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Aria is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Owen is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Riley is a knight then Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('telling-truth', 5)), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('lying', 5), ('telling-truth', 5)), ('or', ('telling-truth', 0), ('lying', 3)), ('lying', 4))", "index": 616}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Isabella, Owen, Luke, Matthew, and Avery. Emma stated, \"Luke is a knight\". Isabella stated, \"Emma is a knight and Isabella is a knight\". In a statement by Owen: \"Luke is a knave and Luke is a knight\". Luke said that Matthew is a knight or Isabella is a knave. Matthew told you that Isabella is a knight if and only if Emma is a knave. Avery expressed that Matthew is a knave or Owen is a knave. So who is a knight and who is a knave?", "names": ["Emma", "Isabella", "Owen", "Luke", "Matthew", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true], "solution_text": "Emma is a knight, Isabella is a knave, Owen is a knave, Luke is a knight, Matthew is a knight, and Avery is a knight.", "solution_text_format": "(1) Emma is a knight\n(2) Isabella is a knave\n(3) Owen is a knave\n(4) Luke is a knight\n(5) Matthew is a knight\n(6) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Matthew is a knight or Isabella is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Emma is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Matthew that Isabella is a knight if and only if Emma is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Emma is a knight and Isabella is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Luke is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Luke is a knave and Luke is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Matthew is a knave or Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('and', ('lying', 3), ('telling-truth', 3)), ('or', ('telling-truth', 4), ('lying', 1)), ('<=>', ('telling-truth', 1), ('lying', 0)), ('or', ('lying', 4), ('lying', 2)))", "index": 617}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Isabella, Lucas, Charlotte, Matthew, and Liam. \"Liam is a knave or Liam is a knight,\" Henry claimed. According to Isabella, \"Charlotte is a knight if and only if Henry is a knave\". \"Matthew is a knave and Lucas is a knight\" - Lucas. \"Lucas is a knave and Matthew is a knight,\" Charlotte mentioned. According to Matthew, \"If Henry is a knave then Lucas is a knight\". In a statement by Liam: \"Henry is not a knight\". So who is a knight and who is a knave?", "names": ["Henry", "Isabella", "Lucas", "Charlotte", "Matthew", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false], "solution_text": "Henry is a knight, Isabella is a knave, Lucas is a knave, Charlotte is a knight, Matthew is a knight, and Liam is a knave.", "solution_text_format": "(1) Henry is a knight\n(2) Isabella is a knave\n(3) Lucas is a knave\n(4) Charlotte is a knight\n(5) Matthew is a knight\n(6) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Liam is a knave or Liam is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Henry is not a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Henry is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Isabella that Charlotte is a knight if and only if Henry is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Lucas is a knave and Matthew is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Matthew is a knave and Lucas is a knight.", "Matthew cannot be a knight, because this would contradict the claim of Lucas that Matthew is a knave and Lucas is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that If Henry is a knave then Lucas is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Matthew is a knave and Lucas is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Charlotte that Lucas is a knave and Matthew is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that If Henry is a knave then Lucas is a knight.", "We have exhausted all possibilities for Matthew, Lucas, and Charlotte, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Henry is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Lucas is a knave and Matthew is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Charlotte that Lucas is a knave and Matthew is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Matthew is a knave and Lucas is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Henry is a knave then Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('and', ('lying', 4), ('telling-truth', 2)), ('and', ('lying', 2), ('telling-truth', 4)), ('->', ('lying', 0), ('telling-truth', 2)), ('not', ('telling-truth', 0)))", "index": 618}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Noah, Alexander, Riley, Sofia, Ethan, and Charlotte. \"If Riley is a knave then Sofia is a knight\" - Noah. In Alexander's words: \"If Charlotte is a knight then Sofia is a knave\". In Riley's words: \"Alexander is a knave or Alexander is a knight\". In Sofia's words: \"Noah is a knave if and only if Charlotte is a knight\". Ethan was heard saying, \"Sofia is a knight if and only if Riley is a knight\". Charlotte commented, \"Alexander is not a knight\". So who is a knight and who is a knave?", "names": ["Noah", "Alexander", "Riley", "Sofia", "Ethan", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Noah is a knight, Alexander is a knight, Riley is a knight, Sofia is a knight, Ethan is a knight, and Charlotte is a knave.", "solution_text_format": "(1) Noah is a knight\n(2) Alexander is a knight\n(3) Riley is a knight\n(4) Sofia is a knight\n(5) Ethan is a knight\n(6) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that If Riley is a knave then Sofia is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Alexander is a knave or Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Charlotte is a knight then Sofia is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Alexander is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Noah is a knave if and only if Charlotte is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 3)), ('->', ('telling-truth', 5), ('lying', 3)), ('or', ('lying', 1), ('telling-truth', 1)), ('<=>', ('lying', 0), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('telling-truth', 2)), ('not', ('telling-truth', 1)))", "index": 619}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Joseph, Oliver, Avery, Zoey, and Owen. Michael was heard saying, \"Joseph is a knave and Oliver is a knave\". Joseph commented, \"Zoey is not a knave\". Oliver commented, \"Owen is a knight and Owen is a knave\". As Avery put it, \"Owen is a knight or Zoey is a knave\". \"Owen is a knave and Oliver is a knight,\" Zoey declared. Owen noted, \"Joseph is not a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Joseph", "Oliver", "Avery", "Zoey", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true], "solution_text": "Michael is a knight, Joseph is a knave, Oliver is a knave, Avery is a knight, Zoey is a knave, and Owen is a knight.", "solution_text_format": "(1) Michael is a knight\n(2) Joseph is a knave\n(3) Oliver is a knave\n(4) Avery is a knight\n(5) Zoey is a knave\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Joseph is a knave and Oliver is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Michael that Joseph is a knave and Oliver is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Joseph that Zoey is not a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Owen is a knave and Oliver is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Oliver cannot be a knight, because this would contradict the claim of Michael that Joseph is a knave and Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Owen is a knight and Owen is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Owen is a knight or Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('lying', 2)), ('not', ('lying', 4)), ('and', ('telling-truth', 5), ('lying', 5)), ('or', ('telling-truth', 5), ('lying', 4)), ('and', ('lying', 5), ('telling-truth', 2)), ('not', ('telling-truth', 1)))", "index": 620}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Michael, Oliver, Jackson, Lily, and Alexander. Chloe commented, \"Alexander is not a knight\". Michael told you that Chloe is a knight. Oliver remarked, \"Lily is a knight and Chloe is a knave\". As Jackson put it, \"Lily is a knave and Alexander is a knave\". Lily stated, \"Oliver is a knight\". In a statement by Alexander: \"If Chloe is a knave then Lily is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Michael", "Oliver", "Jackson", "Lily", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true], "solution_text": "Chloe is a knave, Michael is a knave, Oliver is a knave, Jackson is a knave, Lily is a knave, and Alexander is a knight.", "solution_text_format": "(1) Chloe is a knave\n(2) Michael is a knave\n(3) Oliver is a knave\n(4) Jackson is a knave\n(5) Lily is a knave\n(6) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Chloe that Alexander is not a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that If Chloe is a knave then Lily is a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Chloe is a knave then Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Alexander that If Chloe is a knave then Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Chloe is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Lily is a knight and Chloe is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Chloe is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Alexander is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Lily is a knave and Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('telling-truth', 0), ('and', ('telling-truth', 4), ('lying', 0)), ('and', ('lying', 4), ('lying', 5)), ('telling-truth', 2), ('->', ('lying', 0), ('lying', 4)))", "index": 621}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Ethan, Logan, Penelope, Henry, and Lily. Victoria said, \"Penelope is a knave or Henry is a knight.\" \"Henry is a knight if and only if Henry is a knave,\" Ethan mentioned. Logan expressed that Penelope is a knight or Lily is a knight. In Penelope's words: \"Ethan is a knight\". As Henry put it, \"Ethan is a knight if and only if Logan is a knight\". Lily asserted: \"Henry is a knight or Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Victoria", "Ethan", "Logan", "Penelope", "Henry", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Victoria is a knight, Ethan is a knave, Logan is a knight, Penelope is a knave, Henry is a knave, and Lily is a knight.", "solution_text_format": "(1) Victoria is a knight\n(2) Ethan is a knave\n(3) Logan is a knight\n(4) Penelope is a knave\n(5) Henry is a knave\n(6) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Penelope is a knave or Henry is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Henry is a knight if and only if Henry is a knave.", "Ethan cannot be a knave, because this would contradict the claim of Penelope that Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Henry is a knight if and only if Henry is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Logan is a knight.", "Logan cannot be a knight, because this would contradict the claim of Henry that Ethan is a knight if and only if Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Penelope is a knight or Lily is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Logan that Penelope is a knight or Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Henry is a knight or Penelope is a knave.", "We have exhausted all possibilities for Lily and Logan, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Penelope is a knight or Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Henry is a knight or Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('lying', 4)), ('or', ('telling-truth', 3), ('telling-truth', 5)), ('telling-truth', 1), ('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('lying', 3)))", "index": 622}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Benjamin, Jack, Jacob, Logan, and Oliver. In Evelyn's words: \"Jacob is a knave or Logan is a knight\". Benjamin remarked, \"Jack is a knight if and only if Jacob is a knave\". Jack expressed that Logan is a knave if and only if Evelyn is a knave. Jacob was heard saying, \"Jack is a knight if and only if Evelyn is a knight\". According to Logan, \"If Jack is a knave then Benjamin is a knave\". As Oliver put it, \"Jacob is a knight or Logan is a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "Benjamin", "Jack", "Jacob", "Logan", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Evelyn is a knight, Benjamin is a knave, Jack is a knight, Jacob is a knight, Logan is a knight, and Oliver is a knight.", "solution_text_format": "(1) Evelyn is a knight\n(2) Benjamin is a knave\n(3) Jack is a knight\n(4) Jacob is a knight\n(5) Logan is a knight\n(6) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Jacob is a knave or Logan is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Jack is a knight if and only if Evelyn is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Logan is a knave if and only if Evelyn is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that If Jack is a knave then Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Jack is a knight if and only if Jacob is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Jack is a knight if and only if Jacob is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Jacob is a knight or Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 4)), ('<=>', ('telling-truth', 2), ('lying', 3)), ('<=>', ('lying', 4), ('lying', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('lying', 2), ('lying', 1)), ('or', ('telling-truth', 3), ('telling-truth', 4)))", "index": 623}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Abigail, Matthew, Benjamin, Lily, and Amelia. \"Amelia is a knave and Abigail is a knight,\" Samuel mentioned. Abigail commented, \"Benjamin is a knight\". Matthew told you that Amelia is not a knight. Benjamin asserted: \"Lily is a knave or Abigail is a knight\". Lily told you that Matthew is a knave. Amelia told you that If Amelia is a knight then Abigail is a knave. So who is a knight and who is a knave?", "names": ["Samuel", "Abigail", "Matthew", "Benjamin", "Lily", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Samuel is a knave, Abigail is a knave, Matthew is a knave, Benjamin is a knave, Lily is a knight, and Amelia is a knight.", "solution_text_format": "(1) Samuel is a knave\n(2) Abigail is a knave\n(3) Matthew is a knave\n(4) Benjamin is a knave\n(5) Lily is a knight\n(6) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Amelia is a knave and Abigail is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Samuel that Amelia is a knave and Abigail is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that If Amelia is a knight then Abigail is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Amelia is a knave and Abigail is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Amelia is a knight then Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Amelia that If Amelia is a knight then Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Abigail that Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Lily is a knave or Abigail is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Amelia is not a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Amelia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 1)), ('telling-truth', 3), ('not', ('telling-truth', 5)), ('or', ('lying', 4), ('telling-truth', 1)), ('lying', 2), ('->', ('telling-truth', 5), ('lying', 1)))", "index": 624}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Aria, Isabella, Emily, Aiden, and Michael. Jacob asserted: \"Michael is not a knight\". Aria said that Emily is a knight and Emily is a knave. Isabella commented, \"Jacob is a knight and Aria is a knight\". Emily noted, \"Aiden is not a knave\". \"If Aiden is a knight then Jacob is a knight\" - Aiden. Michael commented, \"Emily is a knave and Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Jacob", "Aria", "Isabella", "Emily", "Aiden", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false], "solution_text": "Jacob is a knight, Aria is a knave, Isabella is a knave, Emily is a knight, Aiden is a knight, and Michael is a knave.", "solution_text_format": "(1) Jacob is a knight\n(2) Aria is a knave\n(3) Isabella is a knave\n(4) Emily is a knight\n(5) Aiden is a knight\n(6) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Jacob that Michael is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Emily is a knave and Aiden is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Aiden is a knight then Jacob is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Emily is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Emily is a knight and Emily is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Aria is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Jacob is a knight and Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('and', ('telling-truth', 3), ('lying', 3)), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('lying', 4)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('lying', 3), ('lying', 4)))", "index": 625}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Penelope, Elizabeth, Riley, Chloe, and James. Mason said that Chloe is a knight. As Penelope put it, \"Elizabeth is a knight if and only if Riley is a knave\". \"Elizabeth is a knight and Penelope is a knight,\" Elizabeth mentioned. \"Penelope is a knight and James is a knave,\" Riley claimed. In a statement by Chloe: \"Penelope is a knave\". James expressed that Chloe is a knight or Elizabeth is a knave. So who is a knight and who is a knave?", "names": ["Mason", "Penelope", "Elizabeth", "Riley", "Chloe", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true], "solution_text": "Mason is a knight, Penelope is a knave, Elizabeth is a knave, Riley is a knave, Chloe is a knight, and James is a knight.", "solution_text_format": "(1) Mason is a knight\n(2) Penelope is a knave\n(3) Elizabeth is a knave\n(4) Riley is a knave\n(5) Chloe is a knight\n(6) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Chloe that Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if Riley is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Penelope is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Penelope is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Penelope that Elizabeth is a knight if and only if Riley is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Penelope is a knight and James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Chloe is a knight or Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('<=>', ('telling-truth', 2), ('lying', 3)), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('and', ('telling-truth', 1), ('lying', 5)), ('lying', 1), ('or', ('telling-truth', 4), ('lying', 2)))", "index": 626}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Jack, Harper, Elizabeth, Jacob, and Mason. Scarlett expressed that Elizabeth is a knight or Harper is a knave. Jack expressed that Mason is a knave. Harper expressed that If Jack is a knave then Mason is a knave. Elizabeth commented, \"Scarlett is a knight or Scarlett is a knave\". Jacob noted, \"Harper is a knave\". \"If Jack is a knight then Elizabeth is a knight\" - Mason. So who is a knight and who is a knave?", "names": ["Scarlett", "Jack", "Harper", "Elizabeth", "Jacob", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true], "solution_text": "Scarlett is a knight, Jack is a knave, Harper is a knave, Elizabeth is a knight, Jacob is a knight, and Mason is a knight.", "solution_text_format": "(1) Scarlett is a knight\n(2) Jack is a knave\n(3) Harper is a knave\n(4) Elizabeth is a knight\n(5) Jacob is a knight\n(6) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Elizabeth is a knight or Harper is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Scarlett is a knight or Scarlett is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Jack is a knave then Mason is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Jack that Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that If Jack is a knight then Elizabeth is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Harper that If Jack is a knave then Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of Jack that Mason is a knave.", "We have exhausted all possibilities for Mason and Jack, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that If Jack is a knave then Mason is a knave.", "Jack cannot be a knight, because this would contradict the false claim of Harper that If Jack is a knave then Mason is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Jack is a knight then Elizabeth is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('lying', 2)), ('lying', 5), ('->', ('lying', 1), ('lying', 5)), ('or', ('telling-truth', 0), ('lying', 0)), ('lying', 2), ('->', ('telling-truth', 1), ('telling-truth', 3)))", "index": 627}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Zoey, William, Olivia, Avery, and Ethan. According to Benjamin, \"Olivia is a knave if and only if Olivia is a knight\". \"If Olivia is a knight then William is a knight,\" Zoey claimed. William said that Zoey is a knight if and only if Avery is a knight. Olivia was heard saying, \"Ethan is a knight\". Avery noted, \"Ethan is a knave if and only if Zoey is a knight\". \"Ethan is a knight or Benjamin is a knave,\" Ethan declared. So who is a knight and who is a knave?", "names": ["Benjamin", "Zoey", "William", "Olivia", "Avery", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Benjamin is a knave, Zoey is a knave, William is a knave, Olivia is a knight, Avery is a knight, and Ethan is a knight.", "solution_text_format": "(1) Benjamin is a knave\n(2) Zoey is a knave\n(3) William is a knave\n(4) Olivia is a knight\n(5) Avery is a knight\n(6) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Benjamin cannot be a knight, because this would contradict the claim of their own that Olivia is a knave if and only if Olivia is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Ethan is a knight or Benjamin is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Olivia is a knight then William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Avery is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Ethan is a knave if and only if Zoey is a knight.", "Avery cannot be a knave, because this would contradict the claim of William that Zoey is a knight if and only if Avery is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Zoey that If Olivia is a knight then William is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Olivia is a knight then William is a knight.", "William cannot be a knight, because this would contradict the false claim of Zoey that If Olivia is a knight then William is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Zoey is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 4)), ('telling-truth', 5), ('<=>', ('lying', 5), ('telling-truth', 1)), ('or', ('telling-truth', 5), ('lying', 0)))", "index": 628}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Alexander, Aria, David, Zoey, and Penelope. Ava stated, \"David is a knave or Aria is a knave\". \"Zoey is a knight or Penelope is a knave,\" Alexander declared. Aria said that Aria is a knight or Zoey is a knave. David asserted: \"Penelope is not a knave\". Zoey stated, \"Ava is a knave if and only if David is a knave\". \"Aria is a knave and Aria is a knight,\" Penelope mentioned. So who is a knight and who is a knave?", "names": ["Ava", "Alexander", "Aria", "David", "Zoey", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Ava is a knight, Alexander is a knight, Aria is a knight, David is a knave, Zoey is a knave, and Penelope is a knave.", "solution_text_format": "(1) Ava is a knight\n(2) Alexander is a knight\n(3) Aria is a knight\n(4) David is a knave\n(5) Zoey is a knave\n(6) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that David is a knave or Aria is a knave.", "Assume David is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Aria is a knave and Aria is a knight.", "Penelope cannot be a knave, because this would contradict the claim of David that Penelope is not a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Penelope cannot be a knight, because this would contradict the false claim of David that Penelope is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Aria is a knave and Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Aria is a knight or Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if David is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ava is a knave if and only if David is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Zoey is a knight or Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 2)), ('or', ('telling-truth', 4), ('lying', 5)), ('or', ('telling-truth', 2), ('lying', 4)), ('not', ('lying', 5)), ('<=>', ('lying', 0), ('lying', 3)), ('and', ('lying', 2), ('telling-truth', 2)))", "index": 629}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Ella, Ethan, Lily, Joseph, and Scarlett. Sophia told you that Ethan is a knave or Joseph is a knave. \"Sophia is not a knight,\" Ella declared. \"Ella is not a knave,\" Ethan declared. Lily asserted: \"Scarlett is a knave or Joseph is a knight\". Joseph remarked, \"Scarlett is a knave and Ethan is a knight\". Scarlett asserted: \"If Ethan is a knight then Lily is a knight\". So who is a knight and who is a knave?", "names": ["Sophia", "Ella", "Ethan", "Lily", "Joseph", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true], "solution_text": "Sophia is a knight, Ella is a knave, Ethan is a knave, Lily is a knave, Joseph is a knave, and Scarlett is a knight.", "solution_text_format": "(1) Sophia is a knight\n(2) Ella is a knave\n(3) Ethan is a knave\n(4) Lily is a knave\n(5) Joseph is a knave\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Ethan is a knave or Joseph is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Sophia is not a knight.", "Ella cannot be a knave, because this would contradict the claim of Ethan that Ella is not a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Sophia is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave and Ethan is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Scarlett is a knave and Ethan is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Ethan is a knight then Lily is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave or Joseph is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Scarlett is a knave or Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('lying', 4)), ('not', ('telling-truth', 0)), ('not', ('lying', 1)), ('or', ('lying', 5), ('telling-truth', 4)), ('and', ('lying', 5), ('telling-truth', 2)), ('->', ('telling-truth', 2), ('telling-truth', 3)))", "index": 630}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Luke, Zoey, James, Lily, and Amelia. In a statement by Riley: \"Lily is a knight\". Luke said that If Zoey is a knight then James is a knight. Zoey noted, \"Zoey is a knight\". James said that Riley is not a knight. \"Luke is a knight,\" Lily declared. Amelia told you that Luke is a knave. So who is a knight and who is a knave?", "names": ["Riley", "Luke", "Zoey", "James", "Lily", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false], "solution_text": "Riley is a knight, Luke is a knight, Zoey is a knave, James is a knave, Lily is a knight, and Amelia is a knave.", "solution_text_format": "(1) Riley is a knight\n(2) Luke is a knight\n(3) Zoey is a knave\n(4) James is a knave\n(5) Lily is a knight\n(6) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Zoey is a knight then James is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Zoey is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Riley is not a knight.", "James cannot be a knave, because this would contradict the claim of Luke that If Zoey is a knight then James is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Zoey is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Riley is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Luke is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('->', ('telling-truth', 2), ('telling-truth', 3)), ('telling-truth', 2), ('not', ('telling-truth', 0)), ('telling-truth', 1), ('lying', 1))", "index": 631}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Owen, Sofia, Evelyn, James, and Victoria. Jackson stated, \"Sofia is a knave or James is a knight\". Owen said, \"Evelyn is a knave.\" According to Sofia, \"James is a knight if and only if Evelyn is a knave\". Evelyn was heard saying, \"Owen is a knight and Evelyn is a knight\". James remarked, \"Owen is a knight or Owen is a knave\". According to Victoria, \"If Evelyn is a knave then Evelyn is a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Owen", "Sofia", "Evelyn", "James", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Jackson is a knight, Owen is a knight, Sofia is a knight, Evelyn is a knave, James is a knight, and Victoria is a knave.", "solution_text_format": "(1) Jackson is a knight\n(2) Owen is a knight\n(3) Sofia is a knight\n(4) Evelyn is a knave\n(5) James is a knight\n(6) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Sofia is a knave or James is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that James is a knight if and only if Evelyn is a knave.", "Assume James is a knight. No contradiction is found in their claim that Owen is a knight or Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Owen that Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Owen is a knight and Evelyn is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that If Evelyn is a knave then Evelyn is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Evelyn is a knave then Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 4)), ('lying', 3), ('<=>', ('telling-truth', 4), ('lying', 3)), ('and', ('telling-truth', 1), ('telling-truth', 3)), ('or', ('telling-truth', 1), ('lying', 1)), ('->', ('lying', 3), ('telling-truth', 3)))", "index": 632}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Jack, Henry, Liam, Penelope, and Sebastian. Lily stated, \"Jack is a knave or Penelope is a knave\". Jack stated, \"Lily is a knave or Sebastian is a knight\". \"Sebastian is a knight and Liam is a knave,\" Henry claimed. In Liam's words: \"Penelope is not a knight\". Penelope expressed that Sebastian is not a knight. Sebastian was heard saying, \"Penelope is a knight or Liam is a knight\". So who is a knight and who is a knave?", "names": ["Lily", "Jack", "Henry", "Liam", "Penelope", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Lily is a knight, Jack is a knight, Henry is a knave, Liam is a knight, Penelope is a knave, and Sebastian is a knight.", "solution_text_format": "(1) Lily is a knight\n(2) Jack is a knight\n(3) Henry is a knave\n(4) Liam is a knight\n(5) Penelope is a knave\n(6) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Jack is a knave or Penelope is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Lily is a knave or Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Penelope is a knight or Liam is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Lily that Jack is a knave or Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Liam is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Sebastian is a knight and Liam is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('lying', 4)), ('or', ('lying', 0), ('telling-truth', 5)), ('and', ('telling-truth', 5), ('lying', 3)), ('not', ('telling-truth', 4)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 4), ('telling-truth', 3)))", "index": 633}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, David, Daniel, Emma, Noah, and Aiden. \"If Noah is a knight then Emma is a knave,\" Oliver declared. \"Emma is a knave and Emma is a knight,\" David claimed. Daniel said, \"Aiden is a knight.\" \"David is a knight and Aiden is a knight\" - Emma. Noah stated, \"Oliver is a knave or Daniel is a knight\". \"Emma is a knave if and only if Oliver is a knave,\" Aiden claimed. So who is a knight and who is a knave?", "names": ["Oliver", "David", "Daniel", "Emma", "Noah", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false], "solution_text": "Oliver is a knight, David is a knave, Daniel is a knave, Emma is a knave, Noah is a knave, and Aiden is a knave.", "solution_text_format": "(1) Oliver is a knight\n(2) David is a knave\n(3) Daniel is a knave\n(4) Emma is a knave\n(5) Noah is a knave\n(6) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that If Noah is a knight then Emma is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Oliver is a knave or Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Emma is a knave if and only if Oliver is a knave.", "Emma cannot be a knight, because this would contradict the claim of Oliver that If Noah is a knight then Emma is a knave.", "Emma cannot be a knave, because this would contradict the claim of Aiden that Emma is a knave if and only if Oliver is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Daniel that Aiden is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Noah that Oliver is a knave or Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Oliver is a knave or Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Noah that Oliver is a knave or Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Daniel that Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Oliver is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that David is a knight and Aiden is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that David is a knight and Aiden is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Emma is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Emma is a knave and Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 3)), ('and', ('lying', 3), ('telling-truth', 3)), ('telling-truth', 5), ('and', ('telling-truth', 1), ('telling-truth', 5)), ('or', ('lying', 0), ('telling-truth', 2)), ('<=>', ('lying', 3), ('lying', 0)))", "index": 634}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Ella, Mason, Aurora, Aria, and Matthew. Ethan said, \"If Aurora is a knight then Aurora is a knave.\" \"If Aria is a knight then Matthew is a knave,\" Ella declared. According to Mason, \"Ella is a knave if and only if Matthew is a knave\". As Aurora put it, \"If Aurora is a knight then Matthew is a knave\". Aria commented, \"Mason is a knight or Ella is a knave\". \"Aria is a knave and Mason is a knight,\" Matthew mentioned. So who is a knight and who is a knave?", "names": ["Ethan", "Ella", "Mason", "Aurora", "Aria", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false], "solution_text": "Ethan is a knave, Ella is a knight, Mason is a knave, Aurora is a knight, Aria is a knave, and Matthew is a knave.", "solution_text_format": "(1) Ethan is a knave\n(2) Ella is a knight\n(3) Mason is a knave\n(4) Aurora is a knight\n(5) Aria is a knave\n(6) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that If Aurora is a knight then Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Ethan that If Aurora is a knight then Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knight then Matthew is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Aurora is a knight then Aurora is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Aurora is a knight then Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Aurora that If Aurora is a knight then Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Aria is a knave and Mason is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Mason is a knight or Ella is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Ella is a knave if and only if Matthew is a knave.", "Ella cannot be a knight, because this would contradict the claim of Mason that Ella is a knave if and only if Matthew is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Aria is a knight then Matthew is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Matthew is a knave.", "Ella cannot be a knight, because this would contradict the claim of Aria that Mason is a knight or Ella is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Aria is a knight then Matthew is a knave.", "We have exhausted all possibilities for Ella and Mason, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Mason is a knight or Ella is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Aria that Mason is a knight or Ella is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Matthew is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Aria is a knight then Matthew is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 3)), ('->', ('telling-truth', 4), ('lying', 5)), ('<=>', ('lying', 1), ('lying', 5)), ('->', ('telling-truth', 3), ('lying', 5)), ('or', ('telling-truth', 2), ('lying', 1)), ('and', ('lying', 4), ('telling-truth', 2)))", "index": 635}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Olivia, William, Owen, Logan, and Charlotte. \"Olivia is a knave if and only if Charlotte is a knave,\" Evelyn declared. Olivia asserted: \"If Logan is a knight then Owen is a knave\". William expressed that Olivia is a knave if and only if Evelyn is a knight. Owen asserted: \"Charlotte is a knight or William is a knight\". In a statement by Logan: \"Owen is a knight or William is a knave\". Charlotte told you that Olivia is a knight if and only if Owen is a knave. So who is a knight and who is a knave?", "names": ["Evelyn", "Olivia", "William", "Owen", "Logan", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Evelyn is a knave, Olivia is a knave, William is a knave, Owen is a knight, Logan is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Olivia is a knave\n(3) William is a knave\n(4) Owen is a knight\n(5) Logan is a knight\n(6) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Charlotte is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Logan is a knight then Owen is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Owen is a knight or William is a knave.", "Owen cannot be a knight, because this would contradict the claim of Olivia that If Logan is a knight then Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Charlotte is a knight or William is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Owen that Charlotte is a knight or William is a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Evelyn that Olivia is a knave if and only if Charlotte is a knave.", "We have exhausted all possibilities for Charlotte and Owen, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Owen is a knight or William is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Logan that Owen is a knight or William is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Charlotte is a knight or William is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Owen that Charlotte is a knight or William is a knight.", "Charlotte cannot be a knave, because this would contradict the claim of Evelyn that Olivia is a knave if and only if Charlotte is a knave.", "We have exhausted all possibilities for Charlotte, Owen, and Logan, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that If Logan is a knight then Owen is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Owen is a knight or William is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Charlotte is a knight or William is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of Evelyn that Olivia is a knave if and only if Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Olivia is a knight if and only if Owen is a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Olivia that If Logan is a knight then Owen is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of Olivia that If Logan is a knight then Owen is a knave.", "We have exhausted all possibilities for Logan and Olivia, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Charlotte is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Logan is a knight then Owen is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Owen is a knight or William is a knave.", "Owen cannot be a knight, because this would contradict the claim of Olivia that If Logan is a knight then Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Charlotte is a knight or William is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Evelyn that Olivia is a knave if and only if Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Olivia is a knight if and only if Owen is a knave.", "We have exhausted all possibilities for Charlotte and Owen, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Owen is a knight or William is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Logan that Owen is a knight or William is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Charlotte is a knight or William is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Evelyn that Olivia is a knave if and only if Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Olivia is a knight if and only if Owen is a knave.", "We have exhausted all possibilities for Charlotte, Owen, and Logan, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that If Logan is a knight then Owen is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Owen is a knight or William is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Charlotte is a knight or William is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Owen is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Olivia is a knave if and only if Evelyn is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 5)), ('->', ('telling-truth', 4), ('lying', 3)), ('<=>', ('lying', 1), ('telling-truth', 0)), ('or', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('telling-truth', 3), ('lying', 2)), ('<=>', ('telling-truth', 1), ('lying', 3)))", "index": 636}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Charlotte, Alexander, Sophia, Jack, and Avery. David was heard saying, \"If Sophia is a knight then Alexander is a knave\". Charlotte said that David is a knight. \"Charlotte is a knave or Avery is a knave,\" Alexander mentioned. In Sophia's words: \"If Sophia is a knight then Avery is a knave\". As Jack put it, \"David is a knave if and only if David is a knight\". Avery expressed that Charlotte is a knight. So who is a knight and who is a knave?", "names": ["David", "Charlotte", "Alexander", "Sophia", "Jack", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "David is a knave, Charlotte is a knave, Alexander is a knight, Sophia is a knight, Jack is a knave, and Avery is a knave.", "solution_text_format": "(1) David is a knave\n(2) Charlotte is a knave\n(3) Alexander is a knight\n(4) Sophia is a knight\n(5) Jack is a knave\n(6) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that If Sophia is a knight then Alexander is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Sophia is a knight then Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Sophia that If Sophia is a knight then Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Avery that Charlotte is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that David is a knight.", "We have exhausted all possibilities for Charlotte and Avery, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knight then Avery is a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that If Sophia is a knight then Alexander is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Sophia is a knight then Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Sophia that If Sophia is a knight then Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that David is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that David is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Charlotte is a knave or Avery is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that David is a knave if and only if David is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that David is a knave if and only if David is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 2)), ('telling-truth', 0), ('or', ('lying', 1), ('lying', 5)), ('->', ('telling-truth', 3), ('lying', 5)), ('<=>', ('lying', 0), ('telling-truth', 0)), ('telling-truth', 1))", "index": 637}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Samuel, Matthew, Emily, Liam, and Jackson. Amelia said, \"If Samuel is a knight then Matthew is a knave.\" \"Amelia is a knave\" - Samuel. As Matthew put it, \"Samuel is not a knight\". Emily said that If Samuel is a knave then Samuel is a knight. Liam asserted: \"Emily is not a knave\". Jackson said that Matthew is a knave if and only if Emily is a knave. So who is a knight and who is a knave?", "names": ["Amelia", "Samuel", "Matthew", "Emily", "Liam", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Amelia is a knight, Samuel is a knave, Matthew is a knight, Emily is a knave, Liam is a knave, and Jackson is a knave.", "solution_text_format": "(1) Amelia is a knight\n(2) Samuel is a knave\n(3) Matthew is a knight\n(4) Emily is a knave\n(5) Liam is a knave\n(6) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that If Samuel is a knight then Matthew is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Amelia is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that If Samuel is a knave then Samuel is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that If Samuel is a knave then Samuel is a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Emily is not a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Matthew is a knave if and only if Emily is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('lying', 2)), ('lying', 0), ('not', ('telling-truth', 1)), ('->', ('lying', 1), ('telling-truth', 1)), ('not', ('lying', 3)), ('<=>', ('lying', 2), ('lying', 3)))", "index": 638}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Riley, William, Ella, Sophia, and Elizabeth. Luke commented, \"Sophia is a knave and William is a knight\". Riley said, \"Sophia is a knight.\" \"Luke is a knave if and only if Sophia is a knave,\" William declared. Ella noted, \"Luke is a knight or William is a knave\". Sophia said that Luke is a knight or William is a knave. In a statement by Elizabeth: \"Sophia is a knight if and only if Sophia is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Riley", "William", "Ella", "Sophia", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Luke is a knave, Riley is a knight, William is a knave, Ella is a knight, Sophia is a knight, and Elizabeth is a knave.", "solution_text_format": "(1) Luke is a knave\n(2) Riley is a knight\n(3) William is a knave\n(4) Ella is a knight\n(5) Sophia is a knight\n(6) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Sophia is a knave and William is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Luke that Sophia is a knave and William is a knight.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Luke is a knight or William is a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Sophia is a knave and William is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Luke is a knight or William is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Luke is a knave if and only if Sophia is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Sophia is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Sophia is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Luke is a knight or William is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Sophia is a knight if and only if Sophia is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 2)), ('telling-truth', 4), ('<=>', ('lying', 0), ('lying', 4)), ('or', ('telling-truth', 0), ('lying', 2)), ('or', ('telling-truth', 0), ('lying', 2)), ('<=>', ('telling-truth', 4), ('lying', 4)))", "index": 639}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Sebastian, Alexander, Jackson, Michael, and Emily. Aria told you that Sebastian is a knight and Alexander is a knave. \"Jackson is a knight if and only if Emily is a knave,\" Sebastian claimed. \"Michael is a knave or Emily is a knight\" - Alexander. \"Aria is a knight,\" Jackson mentioned. In a statement by Michael: \"Aria is a knight and Jackson is a knave\". \"Aria is a knave,\" Emily mentioned. So who is a knight and who is a knave?", "names": ["Aria", "Sebastian", "Alexander", "Jackson", "Michael", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Aria is a knave, Sebastian is a knight, Alexander is a knight, Jackson is a knave, Michael is a knave, and Emily is a knight.", "solution_text_format": "(1) Aria is a knave\n(2) Sebastian is a knight\n(3) Alexander is a knight\n(4) Jackson is a knave\n(5) Michael is a knave\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Sebastian is a knight and Alexander is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Emily is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Aria is a knight.", "Emily cannot be a knight, because this would contradict the claim of Sebastian that Jackson is a knight if and only if Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Aria is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Aria that Sebastian is a knight and Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Michael is a knave or Emily is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Jackson is a knave.", "Michael cannot be a knave, because this would contradict the false claim of Alexander that Michael is a knave or Emily is a knight.", "We have exhausted all possibilities for Michael, Alexander, and Emily, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Aria is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Aria that Sebastian is a knight and Alexander is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Sebastian is a knight and Alexander is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Emily is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Aria is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Aria is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Aria is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Michael is a knave or Emily is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Jackson is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Aria is a knight and Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 2)), ('<=>', ('telling-truth', 3), ('lying', 5)), ('or', ('lying', 4), ('telling-truth', 5)), ('telling-truth', 0), ('and', ('telling-truth', 0), ('lying', 3)), ('lying', 0))", "index": 640}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Jacob, Penelope, James, Liam, and Sofia. \"Jacob is a knave if and only if James is a knight,\" Samuel declared. Jacob asserted: \"Penelope is a knave\". In Penelope's words: \"James is a knight\". \"Samuel is a knight or Jacob is a knave\" - James. Liam said that If Penelope is a knave then Samuel is a knight. Sofia said, \"Liam is a knave or James is a knave.\" So who is a knight and who is a knave?", "names": ["Samuel", "Jacob", "Penelope", "James", "Liam", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Samuel is a knight, Jacob is a knave, Penelope is a knight, James is a knight, Liam is a knight, and Sofia is a knave.", "solution_text_format": "(1) Samuel is a knight\n(2) Jacob is a knave\n(3) Penelope is a knight\n(4) James is a knight\n(5) Liam is a knight\n(6) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Jacob is a knave if and only if James is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of Jacob that Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that James is a knight.", "James cannot be a knight, because this would contradict the claim of Samuel that Jacob is a knave if and only if James is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight or Jacob is a knave.", "We have exhausted all possibilities for James and Penelope, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Samuel is a knight or Jacob is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Penelope is a knave then Samuel is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Liam is a knave or James is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Liam is a knave or James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 3)), ('lying', 2), ('telling-truth', 3), ('or', ('telling-truth', 0), ('lying', 1)), ('->', ('lying', 2), ('telling-truth', 0)), ('or', ('lying', 4), ('lying', 3)))", "index": 641}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Jackson, Mia, Owen, William, and Ethan. Ella said, \"William is a knave.\" Jackson said that Ethan is a knight if and only if Jackson is a knight. Mia asserted: \"Ethan is a knave if and only if Owen is a knight\". \"If Jackson is a knight then Ethan is a knave,\" Owen claimed. William stated, \"If Ethan is a knave then Ella is a knave\". Ethan commented, \"Owen is not a knight\". So who is a knight and who is a knave?", "names": ["Ella", "Jackson", "Mia", "Owen", "William", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Ella is a knave, Jackson is a knight, Mia is a knight, Owen is a knave, William is a knight, and Ethan is a knight.", "solution_text_format": "(1) Ella is a knave\n(2) Jackson is a knight\n(3) Mia is a knight\n(4) Owen is a knave\n(5) William is a knight\n(6) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that William is a knave.", "William cannot be a knight, because this would contradict the claim of Ella that William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that If Ethan is a knave then Ella is a knave.", "Ethan cannot be a knight, because this would contradict the false claim of William that If Ethan is a knave then Ella is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Jackson is a knight then Ethan is a knave.", "Jackson cannot be a knight, because this would contradict the claim of their own that Ethan is a knight if and only if Jackson is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight if and only if Jackson is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knight then Ethan is a knave.", "We have exhausted all possibilities for Owen, Ethan, and William, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that William is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Ethan is a knave then Ella is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of Ethan that Owen is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that If Jackson is a knight then Ethan is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Jackson is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('<=>', ('lying', 5), ('telling-truth', 3)), ('->', ('telling-truth', 1), ('lying', 5)), ('->', ('lying', 5), ('lying', 0)), ('not', ('telling-truth', 3)))", "index": 642}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Mason, Amelia, Zoey, Elizabeth, and Ethan. According to Michael, \"Mason is a knight if and only if Amelia is a knight\". According to Mason, \"Ethan is a knave and Zoey is a knave\". Amelia commented, \"If Michael is a knave then Elizabeth is a knight\". Zoey noted, \"If Ethan is a knight then Amelia is a knight\". Elizabeth noted, \"If Zoey is a knave then Michael is a knight\". Ethan said that Mason is a knight and Ethan is a knight. So who is a knight and who is a knave?", "names": ["Michael", "Mason", "Amelia", "Zoey", "Elizabeth", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Michael is a knave, Mason is a knave, Amelia is a knight, Zoey is a knight, Elizabeth is a knight, and Ethan is a knave.", "solution_text_format": "(1) Michael is a knave\n(2) Mason is a knave\n(3) Amelia is a knight\n(4) Zoey is a knight\n(5) Elizabeth is a knight\n(6) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Mason is a knight if and only if Amelia is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Ethan is a knave and Zoey is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Mason that Ethan is a knave and Zoey is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Mason is a knight and Ethan is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Mason that Ethan is a knave and Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that If Ethan is a knight then Amelia is a knight.", "We have exhausted all possibilities for Zoey and Ethan, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Ethan is a knave and Zoey is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Mason is a knight and Ethan is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Ethan is a knight then Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Michael that Mason is a knight if and only if Amelia is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that If Michael is a knave then Elizabeth is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the false claim of Mason that Ethan is a knave and Zoey is a knave.", "We have exhausted all possibilities for Zoey, Ethan, and Mason, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Amelia is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Ethan is a knave and Zoey is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Mason that Ethan is a knave and Zoey is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Mason is a knight and Ethan is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Mason that Ethan is a knave and Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that If Ethan is a knight then Amelia is a knight.", "We have exhausted all possibilities for Zoey and Ethan, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Ethan is a knave and Zoey is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Mason is a knight and Ethan is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Ethan is a knight then Amelia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Michael is a knave then Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Zoey is a knave then Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('lying', 5), ('lying', 3)), ('->', ('lying', 0), ('telling-truth', 4)), ('->', ('telling-truth', 5), ('telling-truth', 2)), ('->', ('lying', 3), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('telling-truth', 5)))", "index": 643}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Logan, Aria, Scarlett, Joseph, and Sebastian. Luke noted, \"Logan is a knave or Joseph is a knight\". Logan asserted: \"Luke is a knave or Luke is a knight\". \"Luke is a knight or Logan is a knight,\" Aria mentioned. Scarlett asserted: \"Aria is a knave\". In a statement by Joseph: \"Sebastian is a knave\". In Sebastian's words: \"Aria is not a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Logan", "Aria", "Scarlett", "Joseph", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Luke is a knave, Logan is a knight, Aria is a knight, Scarlett is a knave, Joseph is a knave, and Sebastian is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Logan is a knight\n(3) Aria is a knight\n(4) Scarlett is a knave\n(5) Joseph is a knave\n(6) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Logan is a knave or Joseph is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Luke is a knave or Luke is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Joseph that Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Aria cannot be a knight, because this would contradict the false claim of Sebastian that Aria is not a knave.", "Aria cannot be a knave, because this would contradict the false claim of their own that Luke is a knight or Logan is a knight.", "We have exhausted all possibilities for Aria and Sebastian, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Luke that Logan is a knave or Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of their own that Luke is a knave or Luke is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Logan is a knave or Joseph is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Luke is a knave or Luke is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Luke that Logan is a knave or Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Luke is a knight or Logan is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Aria is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Aria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 4)), ('or', ('lying', 0), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('lying', 2), ('lying', 5), ('not', ('lying', 2)))", "index": 644}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Benjamin, Emily, Emma, Daniel, and Alexander. Scarlett expressed that Benjamin is a knave. Benjamin told you that Daniel is a knave or Daniel is a knight. Emily asserted: \"Emma is a knight and Alexander is a knight\". In Emma's words: \"Scarlett is a knave if and only if Alexander is a knave\". \"Emma is a knave and Scarlett is a knight,\" Daniel declared. As Alexander put it, \"Scarlett is a knave and Emily is a knave\". So who is a knight and who is a knave?", "names": ["Scarlett", "Benjamin", "Emily", "Emma", "Daniel", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true], "solution_text": "Scarlett is a knave, Benjamin is a knight, Emily is a knave, Emma is a knave, Daniel is a knave, and Alexander is a knight.", "solution_text_format": "(1) Scarlett is a knave\n(2) Benjamin is a knight\n(3) Emily is a knave\n(4) Emma is a knave\n(5) Daniel is a knave\n(6) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Scarlett that Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Daniel is a knave or Daniel is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Daniel is a knave or Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Scarlett is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Emma is a knave and Scarlett is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Emma that Scarlett is a knave if and only if Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Scarlett is a knave and Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Alexander is a knight.", "Emily cannot be a knave, because this would contradict the false claim of Alexander that Scarlett is a knave and Emily is a knave.", "We have exhausted all possibilities for Emily and Alexander, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Scarlett is a knave and Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Alexander is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Emma is a knight and Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('or', ('lying', 4), ('telling-truth', 4)), ('and', ('telling-truth', 3), ('telling-truth', 5)), ('<=>', ('lying', 0), ('lying', 5)), ('and', ('lying', 3), ('telling-truth', 0)), ('and', ('lying', 0), ('lying', 2)))", "index": 645}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Harper, Ava, Luke, Sophia, and Jack. In David's words: \"Sophia is a knave and Sophia is a knight\". Harper stated, \"Luke is not a knave\". In Ava's words: \"David is a knave or Sophia is a knight\". In a statement by Luke: \"Ava is a knight if and only if David is a knave\". Sophia expressed that David is a knave if and only if David is a knight. Jack said that Sophia is a knight if and only if Sophia is a knave. So who is a knight and who is a knave?", "names": ["David", "Harper", "Ava", "Luke", "Sophia", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "David is a knave, Harper is a knight, Ava is a knight, Luke is a knight, Sophia is a knave, and Jack is a knave.", "solution_text_format": "(1) David is a knave\n(2) Harper is a knight\n(3) Ava is a knight\n(4) Luke is a knight\n(5) Sophia is a knave\n(6) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["David cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Sophia is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Sophia is a knave and Sophia is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that David is a knave if and only if David is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that David is a knave if and only if David is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Luke is not a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Ava is a knight if and only if David is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that David is a knave or Sophia is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Sophia is a knight if and only if Sophia is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 4)), ('not', ('lying', 3)), ('or', ('lying', 0), ('telling-truth', 4)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('<=>', ('lying', 0), ('telling-truth', 0)), ('<=>', ('telling-truth', 4), ('lying', 4)))", "index": 646}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Benjamin, Matthew, Oliver, Emma, and Joseph. Grace told you that Matthew is a knave if and only if Joseph is a knight. Benjamin remarked, \"Joseph is a knave or Grace is a knave\". Matthew commented, \"Benjamin is a knight or Oliver is a knight\". Oliver told you that Benjamin is not a knight. According to Emma, \"Joseph is a knight or Grace is a knave\". Joseph stated, \"Matthew is a knight\". So who is a knight and who is a knave?", "names": ["Grace", "Benjamin", "Matthew", "Oliver", "Emma", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Grace is a knave, Benjamin is a knight, Matthew is a knight, Oliver is a knave, Emma is a knight, and Joseph is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Benjamin is a knight\n(3) Matthew is a knight\n(4) Oliver is a knave\n(5) Emma is a knight\n(6) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Joseph is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Benjamin is a knight or Oliver is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Joseph is a knave or Grace is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Grace that Matthew is a knave if and only if Joseph is a knight.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Matthew is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Joseph is a knave or Grace is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Grace that Matthew is a knave if and only if Joseph is a knight.", "Joseph cannot be a knave, because this would contradict the false claim of Benjamin that Joseph is a knave or Grace is a knave.", "We have exhausted all possibilities for Joseph and Benjamin, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Benjamin is a knight or Oliver is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Matthew that Benjamin is a knight or Oliver is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Joseph is a knave or Grace is a knave.", "Joseph cannot be a knight, because this would contradict the claim of their own that Matthew is a knight.", "Joseph cannot be a knave, because this would contradict the claim of Grace that Matthew is a knave if and only if Joseph is a knight.", "We have exhausted all possibilities for Joseph, Benjamin, and Matthew, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Joseph is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Benjamin is a knight or Oliver is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Joseph is a knave or Grace is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Matthew is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Joseph is a knight or Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 5)), ('or', ('lying', 5), ('lying', 0)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('not', ('telling-truth', 1)), ('or', ('telling-truth', 5), ('lying', 0)), ('telling-truth', 2))", "index": 647}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, James, Daniel, Henry, Owen, and Chloe. \"Chloe is a knave or Jack is a knight,\" Jack claimed. \"Owen is a knave and Jack is a knave,\" James claimed. Daniel noted, \"Henry is a knave\". \"Owen is a knight if and only if Jack is a knight\" - Henry. Owen told you that If Jack is a knight then Jack is a knave. Chloe asserted: \"Owen is a knave or James is a knight\". So who is a knight and who is a knave?", "names": ["Jack", "James", "Daniel", "Henry", "Owen", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Jack is a knight, James is a knave, Daniel is a knight, Henry is a knave, Owen is a knave, and Chloe is a knight.", "solution_text_format": "(1) Jack is a knight\n(2) James is a knave\n(3) Daniel is a knight\n(4) Henry is a knave\n(5) Owen is a knave\n(6) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Chloe is a knave or Jack is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Owen is a knave or James is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that If Jack is a knight then Jack is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that If Jack is a knight then Jack is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Owen is a knave and Jack is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Owen is a knave and Jack is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Daniel that Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 0)), ('and', ('lying', 4), ('lying', 0)), ('lying', 3), ('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('->', ('telling-truth', 0), ('lying', 0)), ('or', ('lying', 4), ('telling-truth', 1)))", "index": 648}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Evelyn, Alexander, Luke, Joseph, and Penelope. In Mason's words: \"Penelope is not a knave\". Evelyn told you that Penelope is a knave and Luke is a knight. According to Alexander, \"If Evelyn is a knave then Mason is a knave\". Luke commented, \"Luke is a knight or Evelyn is a knight\". In Joseph's words: \"Luke is a knight or Alexander is a knave\". In Penelope's words: \"Alexander is a knight and Evelyn is a knight\". So who is a knight and who is a knave?", "names": ["Mason", "Evelyn", "Alexander", "Luke", "Joseph", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false], "solution_text": "Mason is a knave, Evelyn is a knave, Alexander is a knight, Luke is a knave, Joseph is a knave, and Penelope is a knave.", "solution_text_format": "(1) Mason is a knave\n(2) Evelyn is a knave\n(3) Alexander is a knight\n(4) Luke is a knave\n(5) Joseph is a knave\n(6) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Alexander is a knight and Evelyn is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Evelyn is a knave then Mason is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Penelope is a knave and Luke is a knight.", "Evelyn cannot be a knave, because this would contradict the claim of Alexander that If Evelyn is a knave then Mason is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Penelope that Alexander is a knight and Evelyn is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Mason that Penelope is not a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Mason that Penelope is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Alexander is a knight and Evelyn is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Evelyn is a knave then Mason is a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of Penelope that Alexander is a knight and Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Penelope is a knave and Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Evelyn that Penelope is a knave and Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Luke is a knight or Evelyn is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Luke is a knight or Alexander is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Luke is a knight or Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('and', ('lying', 5), ('telling-truth', 3)), ('->', ('lying', 1), ('lying', 0)), ('or', ('telling-truth', 3), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('lying', 2)), ('and', ('telling-truth', 2), ('telling-truth', 1)))", "index": 649}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Isabella, Amelia, Victoria, Noah, and Mason. Joseph told you that Amelia is a knight if and only if Isabella is a knave. Isabella said that Noah is a knave and Isabella is a knight. Amelia expressed that Noah is a knave if and only if Isabella is a knight. \"Amelia is a knave,\" Victoria mentioned. \"If Mason is a knight then Victoria is a knave\" - Noah. Mason asserted: \"If Mason is a knight then Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Joseph", "Isabella", "Amelia", "Victoria", "Noah", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Joseph is a knight, Isabella is a knave, Amelia is a knight, Victoria is a knave, Noah is a knight, and Mason is a knight.", "solution_text_format": "(1) Joseph is a knight\n(2) Isabella is a knave\n(3) Amelia is a knight\n(4) Victoria is a knave\n(5) Noah is a knight\n(6) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Isabella is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Noah is a knave if and only if Isabella is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Mason is a knight then Victoria is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Mason is a knight then Joseph is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Amelia is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Joseph that Amelia is a knight if and only if Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Noah is a knave and Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 1)), ('and', ('lying', 4), ('telling-truth', 1)), ('<=>', ('lying', 4), ('telling-truth', 1)), ('lying', 2), ('->', ('telling-truth', 5), ('lying', 3)), ('->', ('telling-truth', 5), ('telling-truth', 0)))", "index": 650}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Daniel, Sebastian, Victoria, Sofia, and William. \"Daniel is a knight or William is a knave,\" David mentioned. Daniel stated, \"Victoria is a knight if and only if David is a knight\". Sebastian said, \"William is a knave or Victoria is a knave.\" \"William is not a knave,\" Victoria mentioned. \"If David is a knave then Sebastian is a knave\" - Sofia. William stated, \"David is a knight if and only if Sofia is a knight\". So who is a knight and who is a knave?", "names": ["David", "Daniel", "Sebastian", "Victoria", "Sofia", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "David is a knight, Daniel is a knight, Sebastian is a knave, Victoria is a knight, Sofia is a knight, and William is a knight.", "solution_text_format": "(1) David is a knight\n(2) Daniel is a knight\n(3) Sebastian is a knave\n(4) Victoria is a knight\n(5) Sofia is a knight\n(6) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Daniel is a knight or William is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Victoria is a knight if and only if David is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that William is not a knave.", "Assume William is a knight. No contradiction is found in their claim that David is a knight if and only if Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If David is a knave then Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that William is a knave or Victoria is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that William is a knave or Victoria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 5)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('lying', 5), ('lying', 3)), ('not', ('lying', 5)), ('->', ('lying', 0), ('lying', 2)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)))", "index": 651}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Sophia, Daniel, Olivia, Jackson, and Lucas. Oliver noted, \"If Daniel is a knight then Daniel is a knave\". \"Daniel is a knight,\" Sophia claimed. Daniel was heard saying, \"Jackson is a knave if and only if Daniel is a knight\". Olivia said that Oliver is a knight and Lucas is a knave. Jackson told you that Daniel is not a knight. \"Oliver is a knight or Daniel is a knight,\" Lucas mentioned. So who is a knight and who is a knave?", "names": ["Oliver", "Sophia", "Daniel", "Olivia", "Jackson", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Oliver is a knave, Sophia is a knight, Daniel is a knight, Olivia is a knave, Jackson is a knave, and Lucas is a knight.", "solution_text_format": "(1) Oliver is a knave\n(2) Sophia is a knight\n(3) Daniel is a knight\n(4) Olivia is a knave\n(5) Jackson is a knave\n(6) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that If Daniel is a knight then Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Oliver that If Daniel is a knight then Daniel is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Daniel is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Daniel that Jackson is a knave if and only if Daniel is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Daniel is not a knight.", "We have exhausted all possibilities for Jackson and Daniel, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Daniel is a knight then Daniel is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Daniel is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Daniel that Jackson is a knave if and only if Daniel is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Daniel is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Oliver is a knight and Lucas is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Oliver is a knight and Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Oliver is a knight or Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 2)), ('telling-truth', 2), ('<=>', ('lying', 4), ('telling-truth', 2)), ('and', ('telling-truth', 0), ('lying', 5)), ('not', ('telling-truth', 2)), ('or', ('telling-truth', 0), ('telling-truth', 2)))", "index": 652}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Zoey, Mia, Michael, Sebastian, Jack, and Aiden. \"Mia is a knight or Aiden is a knave\" - Zoey. Mia asserted: \"Michael is not a knight\". \"Jack is a knave or Aiden is a knight\" - Michael. In a statement by Sebastian: \"Zoey is a knave or Aiden is a knight\". Jack stated, \"Jack is a knight or Aiden is a knight\". Aiden expressed that Michael is a knave. So who is a knight and who is a knave?", "names": ["Zoey", "Mia", "Michael", "Sebastian", "Jack", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Zoey is a knight, Mia is a knave, Michael is a knight, Sebastian is a knave, Jack is a knave, and Aiden is a knave.", "solution_text_format": "(1) Zoey is a knight\n(2) Mia is a knave\n(3) Michael is a knight\n(4) Sebastian is a knave\n(5) Jack is a knave\n(6) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Mia is a knight or Aiden is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Mia that Michael is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Jack is a knave or Aiden is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Jack is a knight or Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Michael that Jack is a knave or Aiden is a knight.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Michael is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of Michael that Jack is a knave or Aiden is a knight.", "We have exhausted all possibilities for Jack and Michael, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Jack is a knave or Aiden is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Jack is a knight or Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Zoey that Mia is a knight or Aiden is a knave.", "Aiden cannot be a knave, because this would contradict the claim of Michael that Jack is a knave or Aiden is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Jack is a knight or Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Zoey that Mia is a knight or Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Michael is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Zoey is a knave or Aiden is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Zoey is a knave or Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 5)), ('not', ('telling-truth', 2)), ('or', ('lying', 4), ('telling-truth', 5)), ('or', ('lying', 0), ('telling-truth', 5)), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('lying', 2))", "index": 653}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Victoria, Isabella, Jack, Daniel, and Emma. Lucas expressed that Emma is not a knight. Victoria commented, \"Isabella is not a knave\". Isabella stated, \"Isabella is a knight or Emma is a knave\". \"Jack is a knight and Emma is a knave\" - Jack. In a statement by Daniel: \"Lucas is not a knave\". Emma commented, \"Jack is a knight\". So who is a knight and who is a knave?", "names": ["Lucas", "Victoria", "Isabella", "Jack", "Daniel", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Lucas is a knight, Victoria is a knight, Isabella is a knight, Jack is a knave, Daniel is a knight, and Emma is a knave.", "solution_text_format": "(1) Lucas is a knight\n(2) Victoria is a knight\n(3) Isabella is a knight\n(4) Jack is a knave\n(5) Daniel is a knight\n(6) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Emma is not a knight.", "Emma cannot be a knight, because this would contradict the claim of Lucas that Emma is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Emma that Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Jack is a knight and Emma is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Isabella is a knight or Emma is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Lucas is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('not', ('lying', 2)), ('or', ('telling-truth', 2), ('lying', 5)), ('and', ('telling-truth', 3), ('lying', 5)), ('not', ('lying', 0)), ('telling-truth', 3))", "index": 654}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Jack, Samuel, Scarlett, Abigail, and James. Riley was heard saying, \"Scarlett is a knave and Jack is a knave\". \"Abigail is a knave,\" Jack mentioned. \"If Abigail is a knight then Jack is a knight,\" Samuel claimed. \"James is a knave or Abigail is a knight,\" Scarlett mentioned. \"If Scarlett is a knight then Samuel is a knave,\" Abigail mentioned. \"Abigail is a knave,\" James declared. So who is a knight and who is a knave?", "names": ["Riley", "Jack", "Samuel", "Scarlett", "Abigail", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false], "solution_text": "Riley is a knave, Jack is a knave, Samuel is a knave, Scarlett is a knight, Abigail is a knight, and James is a knave.", "solution_text_format": "(1) Riley is a knave\n(2) Jack is a knave\n(3) Samuel is a knave\n(4) Scarlett is a knight\n(5) Abigail is a knight\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Scarlett is a knave and Jack is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Riley that Scarlett is a knave and Jack is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that James is a knave or Abigail is a knight.", "Assume James is a knight. No contradiction is found in their claim that Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Scarlett that James is a knave or Abigail is a knight.", "Abigail cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knight then Samuel is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the false claim of Scarlett that James is a knave or Abigail is a knight.", "We have exhausted all possibilities for James and Scarlett, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Scarlett is a knave and Jack is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that James is a knave or Abigail is a knight.", "Assume James is a knight. No contradiction is found in their claim that Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of James that Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the claim of Scarlett that James is a knave or Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Scarlett is a knight then Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Abigail that If Scarlett is a knight then Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that If Abigail is a knight then Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Abigail is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 1)), ('lying', 4), ('->', ('telling-truth', 4), ('telling-truth', 1)), ('or', ('lying', 5), ('telling-truth', 4)), ('->', ('telling-truth', 3), ('lying', 2)), ('lying', 4))", "index": 655}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Isabella, William, Ella, Lily, and Emma. Joseph asserted: \"If Ella is a knave then Emma is a knight\". \"If William is a knave then Isabella is a knight\" - Isabella. William told you that William is a knight or Joseph is a knight. \"Isabella is a knave or William is a knight,\" Ella mentioned. Lily expressed that Ella is a knight if and only if Joseph is a knave. Emma told you that Joseph is a knave and William is a knave. So who is a knight and who is a knave?", "names": ["Joseph", "Isabella", "William", "Ella", "Lily", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Joseph is a knight, Isabella is a knight, William is a knight, Ella is a knight, Lily is a knave, and Emma is a knave.", "solution_text_format": "(1) Joseph is a knight\n(2) Isabella is a knight\n(3) William is a knight\n(4) Ella is a knight\n(5) Lily is a knave\n(6) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that If Ella is a knave then Emma is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Isabella is a knave or William is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If William is a knave then Isabella is a knight.", "Assume William is a knight. No contradiction is found in their claim that William is a knight or Joseph is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Joseph is a knave and William is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Joseph is a knave and William is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Ella is a knight if and only if Joseph is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 5)), ('->', ('lying', 2), ('telling-truth', 1)), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('lying', 1), ('telling-truth', 2)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('and', ('lying', 0), ('lying', 2)))", "index": 656}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Aurora, Victoria, Noah, Lucas, and Jackson. Olivia remarked, \"If Lucas is a knave then Aurora is a knave\". Aurora commented, \"If Jackson is a knight then Lucas is a knight\". In a statement by Victoria: \"If Aurora is a knave then Noah is a knave\". Noah commented, \"If Lucas is a knight then Jackson is a knight\". In a statement by Lucas: \"If Aurora is a knave then Olivia is a knave\". Jackson remarked, \"Aurora is a knight if and only if Victoria is a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Aurora", "Victoria", "Noah", "Lucas", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Olivia is a knight, Aurora is a knight, Victoria is a knight, Noah is a knave, Lucas is a knight, and Jackson is a knave.", "solution_text_format": "(1) Olivia is a knight\n(2) Aurora is a knight\n(3) Victoria is a knight\n(4) Noah is a knave\n(5) Lucas is a knight\n(6) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that If Lucas is a knave then Aurora is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Aurora is a knave then Olivia is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Jackson is a knight then Lucas is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Jackson that Aurora is a knight if and only if Victoria is a knave.", "Victoria cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knave then Noah is a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Aurora is a knave then Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that If Lucas is a knight then Jackson is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that If Lucas is a knight then Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('lying', 1)), ('->', ('telling-truth', 5), ('telling-truth', 4)), ('->', ('lying', 1), ('lying', 3)), ('->', ('telling-truth', 4), ('telling-truth', 5)), ('->', ('lying', 1), ('lying', 0)), ('<=>', ('telling-truth', 1), ('lying', 2)))", "index": 657}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Alexander, Charlotte, Harper, Elizabeth, and Zoey. In Jacob's words: \"Alexander is a knight\". \"If Alexander is a knight then Jacob is a knight\" - Alexander. According to Charlotte, \"Elizabeth is not a knave\". Harper said that Charlotte is a knight. Elizabeth was heard saying, \"Alexander is a knave and Charlotte is a knave\". According to Zoey, \"Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Jacob", "Alexander", "Charlotte", "Harper", "Elizabeth", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Jacob is a knight, Alexander is a knight, Charlotte is a knave, Harper is a knave, Elizabeth is a knave, and Zoey is a knave.", "solution_text_format": "(1) Jacob is a knight\n(2) Alexander is a knight\n(3) Charlotte is a knave\n(4) Harper is a knave\n(5) Elizabeth is a knave\n(6) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Alexander is a knight then Jacob is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Elizabeth is not a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Alexander is a knave and Charlotte is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Charlotte that Elizabeth is not a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Elizabeth is not a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Charlotte that Elizabeth is not a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Alexander is a knave and Charlotte is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Jacob is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('->', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('lying', 4)), ('telling-truth', 2), ('and', ('lying', 1), ('lying', 2)), ('lying', 0))", "index": 658}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Aiden, Grace, Emma, Michael, and Avery. In a statement by Sofia: \"Aiden is a knight if and only if Avery is a knight\". In a statement by Aiden: \"Emma is not a knight\". Grace was heard saying, \"Sofia is a knight\". In Emma's words: \"Avery is a knight if and only if Michael is a knave\". Michael expressed that Michael is a knight and Grace is a knight. Avery expressed that Grace is a knave and Aiden is a knight. So who is a knight and who is a knave?", "names": ["Sofia", "Aiden", "Grace", "Emma", "Michael", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Sofia is a knight, Aiden is a knave, Grace is a knight, Emma is a knight, Michael is a knight, and Avery is a knave.", "solution_text_format": "(1) Sofia is a knight\n(2) Aiden is a knave\n(3) Grace is a knight\n(4) Emma is a knight\n(5) Michael is a knight\n(6) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Avery is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Emma is not a knight.", "Emma cannot be a knight, because this would contradict the claim of Aiden that Emma is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Michael is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Grace is a knave and Aiden is a knight.", "Grace cannot be a knight, because this would contradict the claim of Avery that Grace is a knave and Aiden is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Sofia that Aiden is a knight if and only if Avery is a knight.", "We have exhausted all possibilities for Avery and Emma, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Avery is a knight if and only if Michael is a knave.", "Avery cannot be a knight, because this would contradict the claim of Sofia that Aiden is a knight if and only if Avery is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Grace is a knave and Aiden is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Sofia is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Michael is a knight and Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 5)), ('not', ('telling-truth', 3)), ('telling-truth', 0), ('<=>', ('telling-truth', 5), ('lying', 4)), ('and', ('telling-truth', 4), ('telling-truth', 2)), ('and', ('lying', 2), ('telling-truth', 1)))", "index": 659}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Henry, Jack, Grace, Daniel, and Elizabeth. Ava commented, \"Grace is a knave or Ava is a knight\". As Henry put it, \"Elizabeth is a knight or Jack is a knave\". Jack told you that Daniel is a knight. Grace said that Jack is a knight or Ava is a knave. As Daniel put it, \"Ava is a knave and Elizabeth is a knight\". Elizabeth stated, \"If Elizabeth is a knight then Jack is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Henry", "Jack", "Grace", "Daniel", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Ava is a knave, Henry is a knight, Jack is a knight, Grace is a knight, Daniel is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Ava is a knave\n(2) Henry is a knight\n(3) Jack is a knight\n(4) Grace is a knight\n(5) Daniel is a knight\n(6) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Grace is a knave or Ava is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Jack is a knight or Ava is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Ava is a knave and Elizabeth is a knight.", "Daniel cannot be a knave, because this would contradict the claim of Jack that Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Grace that Jack is a knight or Ava is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Jack is a knight or Ava is a knave.", "Jack cannot be a knight, because this would contradict the false claim of Grace that Jack is a knight or Ava is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Jack that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ava is a knave and Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that If Elizabeth is a knight then Jack is a knight.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that If Elizabeth is a knight then Jack is a knight.", "We have exhausted all possibilities for Elizabeth, Daniel, Jack, and Grace, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Grace is a knave or Ava is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Jack is a knight or Ava is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Ava is a knave and Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Jack is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Elizabeth is a knight or Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 0)), ('or', ('telling-truth', 5), ('lying', 2)), ('telling-truth', 4), ('or', ('telling-truth', 2), ('lying', 0)), ('and', ('lying', 0), ('telling-truth', 5)), ('->', ('telling-truth', 5), ('telling-truth', 2)))", "index": 660}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Luke, Owen, Jacob, Scarlett, and Lucas. Amelia stated, \"Jacob is a knight or Luke is a knight\". Luke said, \"Lucas is a knight and Scarlett is a knave.\" In Owen's words: \"Jacob is a knave or Amelia is a knight\". Jacob expressed that Luke is a knight or Scarlett is a knave. Scarlett commented, \"Amelia is a knight or Luke is a knave\". In a statement by Lucas: \"Jacob is a knave or Luke is a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "Luke", "Owen", "Jacob", "Scarlett", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true], "solution_text": "Amelia is a knave, Luke is a knave, Owen is a knight, Jacob is a knave, Scarlett is a knight, and Lucas is a knight.", "solution_text_format": "(1) Amelia is a knave\n(2) Luke is a knave\n(3) Owen is a knight\n(4) Jacob is a knave\n(5) Scarlett is a knight\n(6) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Jacob is a knight or Luke is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Luke is a knight or Scarlett is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Lucas is a knight and Scarlett is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Jacob is a knave or Luke is a knave.", "Lucas cannot be a knave, because this would contradict the claim of Luke that Lucas is a knight and Scarlett is a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Lucas is a knight and Scarlett is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Jacob is a knave or Luke is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Jacob that Luke is a knight or Scarlett is a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of Luke that Lucas is a knight and Scarlett is a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Jacob is a knave or Luke is a knave.", "We have exhausted all possibilities for Lucas and Luke, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Luke is a knight or Scarlett is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Jacob that Luke is a knight or Scarlett is a knave.", "Luke cannot be a knave, because this would contradict the claim of Amelia that Jacob is a knight or Luke is a knight.", "We have exhausted all possibilities for Luke and Jacob, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Jacob is a knight or Luke is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Amelia that Jacob is a knight or Luke is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Luke is a knight or Scarlett is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Amelia that Jacob is a knight or Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Lucas is a knight and Scarlett is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Jacob is a knave or Luke is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Amelia is a knight or Luke is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Jacob is a knave or Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 1)), ('and', ('telling-truth', 5), ('lying', 4)), ('or', ('lying', 3), ('telling-truth', 0)), ('or', ('telling-truth', 1), ('lying', 4)), ('or', ('telling-truth', 0), ('lying', 1)), ('or', ('lying', 3), ('lying', 1)))", "index": 661}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Logan, Alexander, Ethan, Jack, and James. Matthew remarked, \"If Logan is a knave then Jack is a knave\". Logan asserted: \"Matthew is a knight or James is a knight\". \"Jack is a knight,\" Alexander declared. Ethan asserted: \"Alexander is not a knight\". Jack said, \"James is a knight.\" James said, \"Alexander is a knave and James is a knight.\" So who is a knight and who is a knave?", "names": ["Matthew", "Logan", "Alexander", "Ethan", "Jack", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Matthew is a knight, Logan is a knight, Alexander is a knave, Ethan is a knight, Jack is a knave, and James is a knave.", "solution_text_format": "(1) Matthew is a knight\n(2) Logan is a knight\n(3) Alexander is a knave\n(4) Ethan is a knight\n(5) Jack is a knave\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that If Logan is a knave then Jack is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Matthew is a knight or James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Alexander is a knave and James is a knight.", "Alexander cannot be a knight, because this would contradict the claim of James that Alexander is a knave and James is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Alexander that Jack is a knight.", "Jack cannot be a knave, because this would contradict the false claim of their own that James is a knight.", "We have exhausted all possibilities for Jack and Alexander, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Alexander is a knave and James is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that James is a knight.", "Jack cannot be a knave, because this would contradict the claim of Alexander that Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Alexander that Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that James is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Alexander is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('lying', 4)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('telling-truth', 4), ('not', ('telling-truth', 2)), ('telling-truth', 5), ('and', ('lying', 2), ('telling-truth', 5)))", "index": 662}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Aria, Ella, Ava, Abigail, and Ethan. Elizabeth expressed that Ava is a knight if and only if Ella is a knight. Aria expressed that Ella is a knave and Ava is a knight. Ella said, \"Ava is a knight and Abigail is a knight.\" Ava told you that Ava is a knight or Aria is a knave. According to Abigail, \"Ethan is not a knave\". Ethan was heard saying, \"Ava is a knight or Elizabeth is a knave\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Aria", "Ella", "Ava", "Abigail", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Elizabeth is a knight, Aria is a knave, Ella is a knight, Ava is a knight, Abigail is a knight, and Ethan is a knight.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Aria is a knave\n(3) Ella is a knight\n(4) Ava is a knight\n(5) Abigail is a knight\n(6) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Ava is a knight if and only if Ella is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Ava is a knight or Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Ella is a knave and Ava is a knight.", "Ella cannot be a knight, because this would contradict the claim of Aria that Ella is a knave and Ava is a knight.", "Ella cannot be a knave, because this would contradict the claim of Elizabeth that Ava is a knight if and only if Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Ella is a knave and Ava is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Ava is a knight and Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Ava is a knight or Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('telling-truth', 2)), ('and', ('lying', 2), ('telling-truth', 3)), ('and', ('telling-truth', 3), ('telling-truth', 4)), ('or', ('telling-truth', 3), ('lying', 1)), ('not', ('lying', 5)), ('or', ('telling-truth', 3), ('lying', 0)))", "index": 663}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Sebastian, Benjamin, Luke, Mason, and Owen. \"Benjamin is a knight if and only if Owen is a knight,\" Joseph claimed. Sebastian remarked, \"Joseph is not a knave\". In Benjamin's words: \"Luke is not a knight\". According to Luke, \"Owen is a knave\". According to Mason, \"Owen is not a knight\". Owen told you that Mason is a knave if and only if Benjamin is a knave. So who is a knight and who is a knave?", "names": ["Joseph", "Sebastian", "Benjamin", "Luke", "Mason", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "Joseph is a knight, Sebastian is a knight, Benjamin is a knave, Luke is a knight, Mason is a knight, and Owen is a knave.", "solution_text_format": "(1) Joseph is a knight\n(2) Sebastian is a knight\n(3) Benjamin is a knave\n(4) Luke is a knight\n(5) Mason is a knight\n(6) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Owen is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Benjamin that Luke is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Mason is a knave if and only if Benjamin is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Owen is not a knight.", "Mason cannot be a knave, because this would contradict the claim of Owen that Mason is a knave if and only if Benjamin is a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Joseph that Benjamin is a knight if and only if Owen is a knight.", "We have exhausted all possibilities for Owen and Luke, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Luke is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Joseph that Benjamin is a knight if and only if Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Benjamin is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Owen is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Joseph is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('lying', 0)), ('not', ('telling-truth', 3)), ('lying', 5), ('not', ('telling-truth', 5)), ('<=>', ('lying', 4), ('lying', 2)))", "index": 664}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Daniel, Joseph, Henry, David, and Amelia. In Sophia's words: \"Joseph is a knight if and only if Joseph is a knave\". Daniel said that Amelia is a knight if and only if Sophia is a knight. \"Sophia is a knave or Henry is a knight\" - Joseph. \"Daniel is not a knight,\" Henry claimed. David commented, \"Amelia is not a knight\". Amelia asserted: \"Henry is a knight if and only if Daniel is a knave\". So who is a knight and who is a knave?", "names": ["Sophia", "Daniel", "Joseph", "Henry", "David", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Sophia is a knave, Daniel is a knave, Joseph is a knight, Henry is a knight, David is a knave, and Amelia is a knight.", "solution_text_format": "(1) Sophia is a knave\n(2) Daniel is a knave\n(3) Joseph is a knight\n(4) Henry is a knight\n(5) David is a knave\n(6) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Sophia cannot be a knight, because this would contradict the claim of their own that Joseph is a knight if and only if Joseph is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Sophia is a knave or Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of Henry that Daniel is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Sophia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Henry is a knight if and only if Daniel is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Amelia is not a knight.", "Assume David is a knave. No contradiction is found in their false claim that Amelia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 2)), ('<=>', ('telling-truth', 5), ('telling-truth', 0)), ('or', ('lying', 0), ('telling-truth', 3)), ('not', ('telling-truth', 1)), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 1)))", "index": 665}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Scarlett, Aiden, Abigail, Mason, and Sebastian. In a statement by Mia: \"Scarlett is a knave and Aiden is a knight\". In a statement by Scarlett: \"Mason is a knight or Aiden is a knave\". Aiden asserted: \"Mason is a knave and Abigail is a knight\". Abigail stated, \"Aiden is a knave if and only if Scarlett is a knave\". Mason noted, \"Abigail is a knight if and only if Mia is a knave\". As Sebastian put it, \"Abigail is a knave if and only if Abigail is a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Scarlett", "Aiden", "Abigail", "Mason", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false], "solution_text": "Mia is a knave, Scarlett is a knight, Aiden is a knave, Abigail is a knave, Mason is a knave, and Sebastian is a knave.", "solution_text_format": "(1) Mia is a knave\n(2) Scarlett is a knight\n(3) Aiden is a knave\n(4) Abigail is a knave\n(5) Mason is a knave\n(6) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Scarlett is a knave and Aiden is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Mia that Scarlett is a knave and Aiden is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Mason is a knight or Aiden is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Scarlett that Mason is a knight or Aiden is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Mia is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Scarlett is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Abigail that Aiden is a knave if and only if Scarlett is a knave.", "Aiden cannot be a knave, because this would contradict the claim of Mia that Scarlett is a knave and Aiden is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of Mason that Abigail is a knight if and only if Mia is a knave.", "We have exhausted all possibilities for Abigail, Mason, and Scarlett, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Scarlett is a knave and Aiden is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Mason is a knight or Aiden is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Mia is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Scarlett is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Abigail is a knight.", "Aiden cannot be a knave, because this would contradict the claim of Abigail that Aiden is a knave if and only if Scarlett is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Mason that Abigail is a knight if and only if Mia is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Mia is a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Mason that Abigail is a knight if and only if Mia is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Scarlett is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Scarlett that Mason is a knight or Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Mason is a knave and Abigail is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Abigail is a knave if and only if Abigail is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('lying', 2)), ('and', ('lying', 4), ('telling-truth', 3)), ('<=>', ('lying', 2), ('lying', 1)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('<=>', ('lying', 3), ('telling-truth', 3)))", "index": 666}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Aurora, David, Jack, Elizabeth, and Ethan. As Isabella put it, \"Elizabeth is a knight or Ethan is a knight\". Aurora was heard saying, \"David is not a knave\". David noted, \"Elizabeth is a knave and Aurora is a knave\". Jack said that Isabella is a knight and Ethan is a knight. Elizabeth was heard saying, \"Jack is not a knight\". Ethan asserted: \"Aurora is a knight and Isabella is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Aurora", "David", "Jack", "Elizabeth", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false], "solution_text": "Isabella is a knight, Aurora is a knave, David is a knave, Jack is a knave, Elizabeth is a knight, and Ethan is a knave.", "solution_text_format": "(1) Isabella is a knight\n(2) Aurora is a knave\n(3) David is a knave\n(4) Jack is a knave\n(5) Elizabeth is a knight\n(6) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Elizabeth is a knight or Ethan is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Jack is not a knight.", "Jack cannot be a knight, because this would contradict the claim of Elizabeth that Jack is not a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Isabella is a knight and Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Jack that Isabella is a knight and Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Aurora is a knight and Isabella is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that David is not a knave.", "David cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Aurora is a knave.", "David cannot be a knave, because this would contradict the claim of Aurora that David is not a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that David is not a knave.", "David cannot be a knight, because this would contradict the false claim of Aurora that David is not a knave.", "Assume David is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('lying', 2)), ('and', ('lying', 4), ('lying', 1)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 1), ('lying', 0)))", "index": 667}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Owen, Harper, Samuel, Emily, and Lucas. Daniel remarked, \"Owen is a knight or Owen is a knave\". Owen stated, \"If Daniel is a knave then Emily is a knave\". \"Samuel is not a knight\" - Harper. As Samuel put it, \"Lucas is a knave and Emily is a knight\". Emily was heard saying, \"Lucas is a knight\". In Lucas's words: \"Harper is not a knave\". So who is a knight and who is a knave?", "names": ["Daniel", "Owen", "Harper", "Samuel", "Emily", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Daniel is a knight, Owen is a knight, Harper is a knight, Samuel is a knave, Emily is a knight, and Lucas is a knight.", "solution_text_format": "(1) Daniel is a knight\n(2) Owen is a knight\n(3) Harper is a knight\n(4) Samuel is a knave\n(5) Emily is a knight\n(6) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Owen is a knight or Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Daniel is a knave then Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Harper is not a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Harper that Samuel is not a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Lucas is a knave and Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 1)), ('->', ('lying', 0), ('lying', 4)), ('not', ('telling-truth', 3)), ('and', ('lying', 5), ('telling-truth', 4)), ('telling-truth', 5), ('not', ('lying', 2)))", "index": 668}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Chloe, Mia, Mason, Riley, and William. Elizabeth commented, \"Riley is a knight and Mia is a knight\". Chloe remarked, \"Mia is not a knight\". Mia remarked, \"William is a knight and Riley is a knave\". In a statement by Mason: \"Elizabeth is a knight or Chloe is a knight\". \"If Elizabeth is a knave then Mia is a knight\" - Riley. William commented, \"Mason is not a knight\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Chloe", "Mia", "Mason", "Riley", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false], "solution_text": "Elizabeth is a knave, Chloe is a knight, Mia is a knave, Mason is a knight, Riley is a knave, and William is a knave.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Chloe is a knight\n(3) Mia is a knave\n(4) Mason is a knight\n(5) Riley is a knave\n(6) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Riley is a knight and Mia is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that William is a knight and Riley is a knave.", "Mia cannot be a knave, because this would contradict the claim of Elizabeth that Riley is a knight and Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the claim of Elizabeth that Riley is a knight and Mia is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Riley is a knight and Mia is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Elizabeth that Riley is a knight and Mia is a knight.", "Mia cannot be a knave, because this would contradict the claim of Riley that If Elizabeth is a knave then Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Riley that If Elizabeth is a knave then Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that William is a knight and Riley is a knave.", "William cannot be a knight, because this would contradict the false claim of Mia that William is a knight and Riley is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Mason is not a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Elizabeth is a knight or Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Mia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('telling-truth', 2)), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 5), ('lying', 4)), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('lying', 0), ('telling-truth', 2)), ('not', ('telling-truth', 3)))", "index": 669}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, James, Sebastian, Liam, Emma, and Grace. Lucas expressed that Sebastian is a knight or Grace is a knave. James noted, \"Sebastian is a knight and Grace is a knave\". Sebastian expressed that Emma is a knight and Grace is a knight. Liam noted, \"Emma is a knight if and only if Sebastian is a knave\". As Emma put it, \"Lucas is a knave\". According to Grace, \"Grace is a knight if and only if Sebastian is a knave\". So who is a knight and who is a knave?", "names": ["Lucas", "James", "Sebastian", "Liam", "Emma", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false], "solution_text": "Lucas is a knight, James is a knave, Sebastian is a knave, Liam is a knave, Emma is a knave, and Grace is a knave.", "solution_text_format": "(1) Lucas is a knight\n(2) James is a knave\n(3) Sebastian is a knave\n(4) Liam is a knave\n(5) Emma is a knave\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Sebastian is a knight or Grace is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Emma is a knight and Grace is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Lucas is a knave.", "Emma cannot be a knave, because this would contradict the claim of Sebastian that Emma is a knight and Grace is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Emma is a knight and Grace is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Lucas is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Grace cannot be a knight, because this would contradict the claim of Lucas that Sebastian is a knight or Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Sebastian is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Grace is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Sebastian is a knight and Grace is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Emma is a knight if and only if Sebastian is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Emma is a knight if and only if Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 5)), ('and', ('telling-truth', 2), ('lying', 5)), ('and', ('telling-truth', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 4), ('lying', 2)), ('lying', 0), ('<=>', ('telling-truth', 5), ('lying', 2)))", "index": 670}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Penelope, Avery, Owen, Ethan, and Noah. \"Noah is a knight,\" Lucas claimed. Penelope said that Avery is a knave and Penelope is a knight. Avery expressed that If Ethan is a knight then Ethan is a knave. Owen commented, \"Ethan is a knave\". In a statement by Ethan: \"Penelope is a knight if and only if Lucas is a knave\". Noah noted, \"Lucas is a knight if and only if Owen is a knight\". So who is a knight and who is a knave?", "names": ["Lucas", "Penelope", "Avery", "Owen", "Ethan", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Lucas is a knave, Penelope is a knave, Avery is a knight, Owen is a knight, Ethan is a knave, and Noah is a knave.", "solution_text_format": "(1) Lucas is a knave\n(2) Penelope is a knave\n(3) Avery is a knight\n(4) Owen is a knight\n(5) Ethan is a knave\n(6) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Owen that Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Lucas is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Avery is a knave and Penelope is a knight.", "Avery cannot be a knight, because this would contradict the claim of Penelope that Avery is a knave and Penelope is a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that If Ethan is a knight then Ethan is a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the false claim of Ethan that Penelope is a knight if and only if Lucas is a knave.", "We have exhausted all possibilities for Penelope and Ethan, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Noah that Lucas is a knight if and only if Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the claim of Lucas that Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Lucas that Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Owen that Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Lucas is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Ethan that Penelope is a knight if and only if Lucas is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Avery is a knave and Penelope is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Ethan is a knight then Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('and', ('lying', 2), ('telling-truth', 1)), ('->', ('telling-truth', 4), ('lying', 4)), ('lying', 4), ('<=>', ('telling-truth', 1), ('lying', 0)), ('<=>', ('telling-truth', 0), ('telling-truth', 3)))", "index": 671}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Alexander, Emily, Noah, Lucas, and Oliver. Mason told you that Oliver is not a knave. \"Lucas is not a knave\" - Alexander. As Emily put it, \"If Lucas is a knave then Emily is a knight\". Noah asserted: \"Emily is a knight\". Lucas stated, \"Mason is not a knight\". In Oliver's words: \"Noah is a knave if and only if Emily is a knight\". So who is a knight and who is a knave?", "names": ["Mason", "Alexander", "Emily", "Noah", "Lucas", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Mason is a knave, Alexander is a knight, Emily is a knight, Noah is a knight, Lucas is a knight, and Oliver is a knave.", "solution_text_format": "(1) Mason is a knave\n(2) Alexander is a knight\n(3) Emily is a knight\n(4) Noah is a knight\n(5) Lucas is a knight\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Oliver is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Noah is a knave if and only if Emily is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of Oliver that Noah is a knave if and only if Emily is a knight.", "Emily cannot be a knave, because this would contradict the claim of Noah that Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Noah that Emily is a knight.", "Emily cannot be a knave, because this would contradict the claim of Oliver that Noah is a knave if and only if Emily is a knight.", "We have exhausted all possibilities for Emily and Noah, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Mason that Oliver is not a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Oliver is not a knave.", "Oliver cannot be a knight, because this would contradict the false claim of Mason that Oliver is not a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Emily is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Lucas is a knave then Emily is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Mason is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Lucas is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('not', ('lying', 4)), ('->', ('lying', 4), ('telling-truth', 2)), ('telling-truth', 2), ('not', ('telling-truth', 0)), ('<=>', ('lying', 3), ('telling-truth', 2)))", "index": 672}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Zoey, Samuel, Mason, Scarlett, Noah, and Liam. As Zoey put it, \"If Liam is a knave then Samuel is a knave\". Samuel said that Zoey is a knave and Mason is a knight. Mason told you that Samuel is a knight if and only if Zoey is a knight. Scarlett stated, \"Samuel is a knave and Mason is a knave\". \"Scarlett is not a knight,\" Noah mentioned. Liam said that Scarlett is a knight. So who is a knight and who is a knave?", "names": ["Zoey", "Samuel", "Mason", "Scarlett", "Noah", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true], "solution_text": "Zoey is a knight, Samuel is a knave, Mason is a knave, Scarlett is a knight, Noah is a knave, and Liam is a knight.", "solution_text_format": "(1) Zoey is a knight\n(2) Samuel is a knave\n(3) Mason is a knave\n(4) Scarlett is a knight\n(5) Noah is a knave\n(6) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that If Liam is a knave then Samuel is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Samuel is a knave and Mason is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Zoey is a knave and Mason is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Zoey is a knave and Mason is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Samuel is a knight if and only if Zoey is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Zoey is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Scarlett is not a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Scarlett is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 1)), ('and', ('lying', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('lying', 1), ('lying', 2)), ('not', ('telling-truth', 3)), ('telling-truth', 3))", "index": 673}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Grace, Noah, Chloe, Olivia, and Charlotte. Jacob said, \"If Charlotte is a knave then Olivia is a knave.\" As Grace put it, \"If Noah is a knight then Olivia is a knave\". Noah said, \"Olivia is not a knight.\" Chloe commented, \"Grace is a knight\". As Olivia put it, \"Jacob is a knave if and only if Noah is a knight\". According to Charlotte, \"Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Jacob", "Grace", "Noah", "Chloe", "Olivia", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Jacob is a knight, Grace is a knight, Noah is a knight, Chloe is a knight, Olivia is a knave, and Charlotte is a knave.", "solution_text_format": "(1) Jacob is a knight\n(2) Grace is a knight\n(3) Noah is a knight\n(4) Chloe is a knight\n(5) Olivia is a knave\n(6) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that If Charlotte is a knave then Olivia is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Jacob is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Jacob that If Charlotte is a knave then Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Jacob is a knave if and only if Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Olivia is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Noah is a knight then Olivia is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 4)), ('->', ('telling-truth', 2), ('lying', 4)), ('not', ('telling-truth', 4)), ('telling-truth', 1), ('<=>', ('lying', 0), ('telling-truth', 2)), ('lying', 0))", "index": 674}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Oliver, Emily, Henry, David, and Lucas. Chloe commented, \"Oliver is a knave or Emily is a knight\". As Oliver put it, \"David is a knight or Emily is a knave\". In a statement by Emily: \"Emily is a knight or Lucas is a knave\". Henry told you that David is a knight if and only if Oliver is a knave. As David put it, \"Henry is a knave and Emily is a knight\". Lucas noted, \"Emily is a knight or Oliver is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Oliver", "Emily", "Henry", "David", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Chloe is a knight, Oliver is a knight, Emily is a knight, Henry is a knave, David is a knight, and Lucas is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Oliver is a knight\n(3) Emily is a knight\n(4) Henry is a knave\n(5) David is a knight\n(6) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Oliver is a knave or Emily is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that David is a knight or Emily is a knave.", "Assume David is a knight. No contradiction is found in their claim that Henry is a knave and Emily is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that David is a knight if and only if Oliver is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that David is a knight if and only if Oliver is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Emily is a knight or Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Emily is a knight or Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('lying', 2)), ('or', ('telling-truth', 2), ('lying', 5)), ('<=>', ('telling-truth', 4), ('lying', 1)), ('and', ('lying', 3), ('telling-truth', 2)), ('or', ('telling-truth', 2), ('lying', 1)))", "index": 675}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, James, Daniel, Owen, Henry, and Oliver. Samuel said, \"James is a knave or James is a knight.\" James commented, \"Oliver is a knave or Samuel is a knave\". Daniel commented, \"Owen is not a knight\". Owen expressed that Henry is a knave and Oliver is a knight. Henry told you that James is a knave. Oliver remarked, \"Samuel is a knight if and only if Owen is a knave\". So who is a knight and who is a knave?", "names": ["Samuel", "James", "Daniel", "Owen", "Henry", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Samuel is a knight, James is a knave, Daniel is a knight, Owen is a knave, Henry is a knight, and Oliver is a knight.", "solution_text_format": "(1) Samuel is a knight\n(2) James is a knave\n(3) Daniel is a knight\n(4) Owen is a knave\n(5) Henry is a knight\n(6) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that James is a knave or James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Oliver is a knave or Samuel is a knave.", "Oliver cannot be a knight, because this would contradict the claim of James that Oliver is a knave or Samuel is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Oliver is a knight.", "Owen cannot be a knave, because this would contradict the false claim of Oliver that Samuel is a knight if and only if Owen is a knave.", "We have exhausted all possibilities for Owen and Oliver, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Oliver is a knave or Samuel is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Oliver that Samuel is a knight if and only if Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Henry is a knave and Oliver is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that James is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Owen is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('or', ('lying', 5), ('lying', 0)), ('not', ('telling-truth', 3)), ('and', ('lying', 4), ('telling-truth', 5)), ('lying', 1), ('<=>', ('telling-truth', 0), ('lying', 3)))", "index": 676}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Elizabeth, Mia, Sophia, Grace, and Noah. In a statement by Henry: \"Noah is a knight\". Elizabeth noted, \"Sophia is not a knight\". \"Henry is not a knight,\" Mia claimed. In Sophia's words: \"Noah is a knave\". Grace said, \"Elizabeth is not a knight.\" Noah noted, \"Mia is a knave if and only if Grace is a knight\". So who is a knight and who is a knave?", "names": ["Henry", "Elizabeth", "Mia", "Sophia", "Grace", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Henry is a knave, Elizabeth is a knave, Mia is a knight, Sophia is a knight, Grace is a knight, and Noah is a knave.", "solution_text_format": "(1) Henry is a knave\n(2) Elizabeth is a knave\n(3) Mia is a knight\n(4) Sophia is a knight\n(5) Grace is a knight\n(6) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Mia is a knave if and only if Grace is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Henry is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Grace that Elizabeth is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Noah is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of Elizabeth that Sophia is not a knight.", "We have exhausted all possibilities for Sophia and Elizabeth, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Noah that Mia is a knave if and only if Grace is a knight.", "We have exhausted all possibilities for Grace and Mia, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the claim of Henry that Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Henry that Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Grace is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Henry is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Grace that Elizabeth is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('not', ('telling-truth', 3)), ('not', ('telling-truth', 0)), ('lying', 5), ('not', ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 4)))", "index": 677}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Lily, Emma, James, Ella, and Matthew. \"James is a knave or Matthew is a knave,\" Victoria mentioned. Lily told you that Emma is a knight and James is a knight. In Emma's words: \"Ella is a knight\". In a statement by James: \"Matthew is a knight\". Ella told you that James is a knight if and only if Matthew is a knave. Matthew told you that Emma is not a knave. So who is a knight and who is a knave?", "names": ["Victoria", "Lily", "Emma", "James", "Ella", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false], "solution_text": "Victoria is a knight, Lily is a knave, Emma is a knave, James is a knave, Ella is a knave, and Matthew is a knave.", "solution_text_format": "(1) Victoria is a knight\n(2) Lily is a knave\n(3) Emma is a knave\n(4) James is a knave\n(5) Ella is a knave\n(6) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that James is a knave or Matthew is a knave.", "Assume James is a knight. No contradiction is found in their claim that Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of Victoria that James is a knave or Matthew is a knave.", "Matthew cannot be a knave, because this would contradict the claim of James that Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of James that Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Emma is not a knave.", "Emma cannot be a knight, because this would contradict the false claim of Matthew that Emma is not a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Emma that Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that James is a knight if and only if Matthew is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Emma is a knight and James is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Emma is a knight and James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 5)), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('telling-truth', 4), ('telling-truth', 5), ('<=>', ('telling-truth', 3), ('lying', 5)), ('not', ('lying', 2)))", "index": 678}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Charlotte, William, Aria, Noah, and Logan. \"Noah is a knave or William is a knave,\" Jacob claimed. As Charlotte put it, \"Charlotte is a knight and Aria is a knave\". William was heard saying, \"If Aria is a knave then Charlotte is a knight\". In a statement by Aria: \"Charlotte is a knight\". According to Noah, \"William is a knave or William is a knight\". \"Jacob is a knight if and only if Aria is a knight,\" Logan claimed. So who is a knight and who is a knave?", "names": ["Jacob", "Charlotte", "William", "Aria", "Noah", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false], "solution_text": "Jacob is a knight, Charlotte is a knave, William is a knave, Aria is a knave, Noah is a knight, and Logan is a knave.", "solution_text_format": "(1) Jacob is a knight\n(2) Charlotte is a knave\n(3) William is a knave\n(4) Aria is a knave\n(5) Noah is a knight\n(6) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Noah is a knave or William is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that William is a knave or William is a knight.", "William cannot be a knight, because this would contradict the claim of Jacob that Noah is a knave or William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that If Aria is a knave then Charlotte is a knight.", "Aria cannot be a knight, because this would contradict the false claim of William that If Aria is a knave then Charlotte is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of William that If Aria is a knave then Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Charlotte is a knight and Aria is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Jacob is a knight if and only if Aria is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('lying', 2)), ('and', ('telling-truth', 1), ('lying', 3)), ('->', ('lying', 3), ('telling-truth', 1)), ('telling-truth', 1), ('or', ('lying', 2), ('telling-truth', 2)), ('<=>', ('telling-truth', 0), ('telling-truth', 3)))", "index": 679}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Noah, David, Avery, Chloe, and Owen. Aiden said that David is a knave. According to Noah, \"Aiden is a knave and Aiden is a knight\". David was heard saying, \"Noah is a knave if and only if Noah is a knight\". Avery noted, \"David is a knave or David is a knight\". Chloe was heard saying, \"David is a knight or Avery is a knave\". Owen commented, \"Chloe is not a knight\". So who is a knight and who is a knave?", "names": ["Aiden", "Noah", "David", "Avery", "Chloe", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true], "solution_text": "Aiden is a knight, Noah is a knave, David is a knave, Avery is a knight, Chloe is a knave, and Owen is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Noah is a knave\n(3) David is a knave\n(4) Avery is a knight\n(5) Chloe is a knave\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Aiden that David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Noah is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Aiden is a knave and Aiden is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Aiden is a knave and Aiden is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that David is a knave or David is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that David is a knight or Avery is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that David is a knight or Avery is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Chloe is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('and', ('lying', 0), ('telling-truth', 0)), ('<=>', ('lying', 1), ('telling-truth', 1)), ('or', ('lying', 2), ('telling-truth', 2)), ('or', ('telling-truth', 2), ('lying', 3)), ('not', ('telling-truth', 4)))", "index": 680}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Joseph, Avery, Lily, Noah, and Ava. Mia expressed that Joseph is a knight or Lily is a knight. \"Ava is a knave and Ava is a knight,\" Joseph claimed. \"Mia is a knight,\" Avery mentioned. \"Noah is a knave and Avery is a knight\" - Lily. Noah remarked, \"Avery is a knight and Lily is a knight\". \"Lily is not a knight,\" Ava declared. So who is a knight and who is a knave?", "names": ["Mia", "Joseph", "Avery", "Lily", "Noah", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true], "solution_text": "Mia is a knave, Joseph is a knave, Avery is a knave, Lily is a knave, Noah is a knave, and Ava is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Joseph is a knave\n(3) Avery is a knave\n(4) Lily is a knave\n(5) Noah is a knave\n(6) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Joseph is a knight or Lily is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Ava is a knave and Ava is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ava is a knave and Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Ava that Lily is not a knight.", "Lily cannot be a knave, because this would contradict the claim of Mia that Joseph is a knight or Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Noah is a knave and Avery is a knight.", "Noah cannot be a knight, because this would contradict the claim of Lily that Noah is a knave and Avery is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Avery is a knight and Lily is a knight.", "Avery cannot be a knight, because this would contradict the false claim of Noah that Avery is a knight and Lily is a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that Mia is a knight.", "We have exhausted all possibilities for Avery and Noah, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the claim of Mia that Joseph is a knight or Lily is a knight.", "We have exhausted all possibilities for Lily, Ava, and Joseph, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Joseph is a knight or Lily is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Mia that Joseph is a knight or Lily is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ava is a knave and Ava is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the false claim of Mia that Joseph is a knight or Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Noah is a knave and Avery is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Lily is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Avery is a knight and Lily is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Mia is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('telling-truth', 3)), ('and', ('lying', 5), ('telling-truth', 5)), ('telling-truth', 0), ('and', ('lying', 4), ('telling-truth', 2)), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('telling-truth', 3)))", "index": 681}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Abigail, Ava, Sofia, Avery, and Aiden. In Elizabeth's words: \"If Sofia is a knight then Sofia is a knave\". According to Abigail, \"Elizabeth is a knave and Sofia is a knight\". \"If Elizabeth is a knave then Sofia is a knight,\" Ava mentioned. In a statement by Sofia: \"Sofia is a knight or Aiden is a knight\". Avery commented, \"Sofia is a knight\". According to Aiden, \"Sofia is not a knight\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Abigail", "Ava", "Sofia", "Avery", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Elizabeth is a knave, Abigail is a knight, Ava is a knight, Sofia is a knight, Avery is a knight, and Aiden is a knave.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Abigail is a knight\n(3) Ava is a knight\n(4) Sofia is a knight\n(5) Avery is a knight\n(6) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that If Sofia is a knight then Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Elizabeth that If Sofia is a knight then Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Sofia is a knight or Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Sofia that Sofia is a knight or Aiden is a knight.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Sofia is not a knight.", "We have exhausted all possibilities for Aiden and Sofia, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that If Sofia is a knight then Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Sofia is a knight or Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Sofia is not a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Sofia is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Elizabeth is a knave and Sofia is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Sofia is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Sofia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 3)), ('and', ('lying', 0), ('telling-truth', 3)), ('->', ('lying', 0), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('telling-truth', 5)), ('telling-truth', 3), ('not', ('telling-truth', 3)))", "index": 682}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Jack, David, Elizabeth, Logan, and Sebastian. \"Jack is a knave or Logan is a knave,\" Olivia claimed. According to Jack, \"Logan is not a knight\". David asserted: \"Sebastian is a knave if and only if David is a knight\". In a statement by Elizabeth: \"If Sebastian is a knight then Logan is a knight\". According to Logan, \"David is not a knave\". Sebastian was heard saying, \"Logan is a knight\". So who is a knight and who is a knave?", "names": ["Olivia", "Jack", "David", "Elizabeth", "Logan", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Olivia is a knight, Jack is a knight, David is a knave, Elizabeth is a knight, Logan is a knave, and Sebastian is a knave.", "solution_text_format": "(1) Olivia is a knight\n(2) Jack is a knight\n(3) David is a knave\n(4) Elizabeth is a knight\n(5) Logan is a knave\n(6) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Jack is a knave or Logan is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Logan is not a knight.", "Logan cannot be a knight, because this would contradict the claim of Olivia that Jack is a knave or Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that David is not a knave.", "David cannot be a knight, because this would contradict the false claim of Logan that David is not a knave.", "Assume David is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if David is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of David that Sebastian is a knave if and only if David is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Logan is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Sebastian is a knight then Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('lying', 4)), ('not', ('telling-truth', 4)), ('<=>', ('lying', 5), ('telling-truth', 2)), ('->', ('telling-truth', 5), ('telling-truth', 4)), ('not', ('lying', 2)), ('telling-truth', 4))", "index": 683}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, James, Sophia, Sofia, Liam, and Ella. \"James is a knave and Liam is a knight\" - Owen. James noted, \"If Ella is a knight then Owen is a knave\". Sophia expressed that Ella is a knight or Sofia is a knight. Sofia remarked, \"If Liam is a knave then Sophia is a knight\". Liam stated, \"Sophia is not a knight\". \"Liam is a knight and Liam is a knave,\" Ella claimed. So who is a knight and who is a knave?", "names": ["Owen", "James", "Sophia", "Sofia", "Liam", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Owen is a knave, James is a knight, Sophia is a knight, Sofia is a knight, Liam is a knave, and Ella is a knave.", "solution_text_format": "(1) Owen is a knave\n(2) James is a knight\n(3) Sophia is a knight\n(4) Sofia is a knight\n(5) Liam is a knave\n(6) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that James is a knave and Liam is a knight.", "James cannot be a knight, because this would contradict the claim of Owen that James is a knave and Liam is a knight.", "Assume James is a knave. No contradiction is found in their false claim that If Ella is a knight then Owen is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Liam is a knight and Liam is a knave.", "Ella cannot be a knave, because this would contradict the false claim of James that If Ella is a knight then Owen is a knave.", "We have exhausted all possibilities for Ella and James, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that James is a knave and Liam is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Ella is a knight then Owen is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Liam is a knight and Liam is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Liam is a knight and Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Sophia is not a knight.", "Sophia cannot be a knight, because this would contradict the claim of Liam that Sophia is not a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Ella is a knight or Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Sophia that Ella is a knight or Sofia is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Liam is a knave then Sophia is a knight.", "We have exhausted all possibilities for Sofia and Sophia, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Sophia is not a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Ella is a knight or Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Liam is a knave then Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 4)), ('->', ('telling-truth', 5), ('lying', 0)), ('or', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('lying', 4), ('telling-truth', 2)), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 4), ('lying', 4)))", "index": 684}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Henry, Samuel, Abigail, Joseph, and William. In Aurora's words: \"Samuel is a knight and Abigail is a knight\". \"If Abigail is a knave then Joseph is a knave,\" Henry claimed. \"William is a knight if and only if Abigail is a knight,\" Samuel declared. Abigail was heard saying, \"Henry is a knight if and only if Aurora is a knight\". \"Samuel is a knight if and only if Abigail is a knight,\" Joseph mentioned. As William put it, \"Abigail is a knave if and only if Joseph is a knave\". So who is a knight and who is a knave?", "names": ["Aurora", "Henry", "Samuel", "Abigail", "Joseph", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Aurora is a knight, Henry is a knight, Samuel is a knight, Abigail is a knight, Joseph is a knight, and William is a knight.", "solution_text_format": "(1) Aurora is a knight\n(2) Henry is a knight\n(3) Samuel is a knight\n(4) Abigail is a knight\n(5) Joseph is a knight\n(6) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Samuel is a knight and Abigail is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that William is a knight if and only if Abigail is a knight.", "Assume William is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Joseph is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Henry is a knight if and only if Aurora is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Abigail is a knave then Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 3)), ('->', ('lying', 3), ('lying', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('lying', 3), ('lying', 4)))", "index": 685}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Harper, Aurora, Sebastian, Victoria, and David. Mason expressed that Victoria is a knight and Sebastian is a knight. Harper was heard saying, \"If Sebastian is a knight then David is a knight\". Aurora remarked, \"Harper is a knight if and only if David is a knave\". In Sebastian's words: \"Mason is a knight and Victoria is a knight\". As Victoria put it, \"David is not a knave\". In David's words: \"Mason is a knave\". So who is a knight and who is a knave?", "names": ["Mason", "Harper", "Aurora", "Sebastian", "Victoria", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true], "solution_text": "Mason is a knave, Harper is a knight, Aurora is a knave, Sebastian is a knave, Victoria is a knight, and David is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Harper is a knight\n(3) Aurora is a knave\n(4) Sebastian is a knave\n(5) Victoria is a knight\n(6) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Victoria is a knight and Sebastian is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that David is not a knave.", "David cannot be a knight, because this would contradict the claim of their own that Mason is a knave.", "David cannot be a knave, because this would contradict the claim of Victoria that David is not a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the claim of Mason that Victoria is a knight and Sebastian is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Victoria is a knight and Sebastian is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that David is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Mason is a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Mason that Victoria is a knight and Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Mason is a knight and Victoria is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Sebastian is a knight then David is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Harper is a knight if and only if David is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Harper is a knight if and only if David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('telling-truth', 5)), ('<=>', ('telling-truth', 1), ('lying', 5)), ('and', ('telling-truth', 0), ('telling-truth', 4)), ('not', ('lying', 5)), ('lying', 0))", "index": 686}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, James, Noah, Jacob, Zoey, and Emily. As Riley put it, \"Emily is a knave or Noah is a knave\". James said, \"Emily is a knight and Noah is a knight.\" \"If James is a knight then Riley is a knave,\" Noah claimed. Jacob commented, \"Zoey is a knave if and only if James is a knave\". Zoey asserted: \"James is a knave and Emily is a knave\". In a statement by Emily: \"If Noah is a knave then James is a knave\". So who is a knight and who is a knave?", "names": ["Riley", "James", "Noah", "Jacob", "Zoey", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Riley is a knave, James is a knight, Noah is a knight, Jacob is a knave, Zoey is a knave, and Emily is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) James is a knight\n(3) Noah is a knight\n(4) Jacob is a knave\n(5) Zoey is a knave\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Emily is a knave or Noah is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Noah is a knave then James is a knave.", "Noah cannot be a knight, because this would contradict the claim of Riley that Emily is a knave or Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that If James is a knight then Riley is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Noah is a knight.", "James cannot be a knave, because this would contradict the false claim of Noah that If James is a knight then Riley is a knave.", "We have exhausted all possibilities for James and Noah, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that If Noah is a knave then James is a knave.", "Noah cannot be a knight, because this would contradict the false claim of Emily that If Noah is a knave then James is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that If James is a knight then Riley is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Emily is a knight and Noah is a knight.", "James cannot be a knave, because this would contradict the false claim of Noah that If James is a knight then Riley is a knave.", "We have exhausted all possibilities for James, Noah, and Emily, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Emily is a knave or Noah is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Noah is a knave then James is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If James is a knight then Riley is a knave.", "Assume James is a knight. No contradiction is found in their claim that Emily is a knight and Noah is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Zoey is a knave if and only if James is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that James is a knave and Emily is a knave.", "Zoey cannot be a knave, because this would contradict the claim of Jacob that Zoey is a knave if and only if James is a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if James is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Jacob that Zoey is a knave if and only if James is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that James is a knave and Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('lying', 2)), ('and', ('telling-truth', 5), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('lying', 0)), ('<=>', ('lying', 4), ('lying', 1)), ('and', ('lying', 1), ('lying', 5)), ('->', ('lying', 2), ('lying', 1)))", "index": 687}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Henry, James, Noah, Jack, and Jackson. Avery was heard saying, \"If James is a knight then Henry is a knight\". Henry remarked, \"If Jack is a knave then Avery is a knave\". James remarked, \"Henry is a knight if and only if Jackson is a knave\". In Noah's words: \"Jackson is a knight and James is a knave\". According to Jack, \"Jackson is a knight\". Jackson said that Noah is a knight and Avery is a knave. So who is a knight and who is a knave?", "names": ["Avery", "Henry", "James", "Noah", "Jack", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false], "solution_text": "Avery is a knight, Henry is a knave, James is a knave, Noah is a knave, Jack is a knave, and Jackson is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Henry is a knave\n(3) James is a knave\n(4) Noah is a knave\n(5) Jack is a knave\n(6) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that If James is a knight then Henry is a knight.", "Assume James is a knight. No contradiction is found in their claim that Henry is a knight if and only if Jackson is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Jack is a knave then Avery is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the claim of James that Henry is a knight if and only if Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the claim of Jack that Jackson is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Henry that If Jack is a knave then Avery is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Henry.", "Henry cannot be a knave, because this would contradict the claim of Avery that If James is a knight then Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Jackson is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Jack is a knave then Avery is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Noah is a knight and Avery is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of James that Henry is a knight if and only if Jackson is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Henry that If Jack is a knave then Avery is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that If Jack is a knave then Avery is a knave.", "Jack cannot be a knight, because this would contradict the false claim of Henry that If Jack is a knave then Avery is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of James that Henry is a knight if and only if Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Noah is a knight and Avery is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Jackson is a knight and James is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Jackson is a knight and James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('lying', 4), ('lying', 0)), ('<=>', ('telling-truth', 1), ('lying', 5)), ('and', ('telling-truth', 5), ('lying', 2)), ('telling-truth', 5), ('and', ('telling-truth', 3), ('lying', 0)))", "index": 688}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Owen, Zoey, Henry, Chloe, and Lily. As Riley put it, \"Henry is a knave if and only if Owen is a knight\". Owen expressed that Henry is a knave or Owen is a knight. According to Zoey, \"Chloe is not a knave\". Henry noted, \"Henry is a knight or Zoey is a knight\". Chloe expressed that Owen is a knave or Zoey is a knave. In a statement by Lily: \"Zoey is a knight or Henry is a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Owen", "Zoey", "Henry", "Chloe", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Riley is a knight, Owen is a knave, Zoey is a knight, Henry is a knight, Chloe is a knight, and Lily is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Owen is a knave\n(3) Zoey is a knight\n(4) Henry is a knight\n(5) Chloe is a knight\n(6) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Henry is a knave if and only if Owen is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Henry is a knight or Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Chloe is not a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Owen is a knave or Zoey is a knave.", "Owen cannot be a knight, because this would contradict the claim of Riley that Henry is a knave if and only if Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Henry is a knave or Owen is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Zoey is a knight or Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 1)), ('or', ('lying', 3), ('telling-truth', 1)), ('not', ('lying', 4)), ('or', ('telling-truth', 3), ('telling-truth', 2)), ('or', ('lying', 1), ('lying', 2)), ('or', ('telling-truth', 2), ('lying', 3)))", "index": 689}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Sebastian, Luke, Alexander, Emily, and Olivia. Jacob remarked, \"Sebastian is not a knight\". \"If Alexander is a knave then Olivia is a knave,\" Sebastian mentioned. Luke said that Sebastian is a knight if and only if Jacob is a knave. Alexander said, \"Sebastian is a knave and Jacob is a knight.\" In a statement by Emily: \"If Sebastian is a knight then Olivia is a knave\". Olivia stated, \"Emily is a knave if and only if Luke is a knight\". So who is a knight and who is a knave?", "names": ["Jacob", "Sebastian", "Luke", "Alexander", "Emily", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false], "solution_text": "Jacob is a knave, Sebastian is a knight, Luke is a knight, Alexander is a knave, Emily is a knight, and Olivia is a knave.", "solution_text_format": "(1) Jacob is a knave\n(2) Sebastian is a knight\n(3) Luke is a knight\n(4) Alexander is a knave\n(5) Emily is a knight\n(6) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Sebastian is not a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Jacob that Sebastian is not a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Alexander is a knave then Olivia is a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Sebastian that If Alexander is a knave then Olivia is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knave and Jacob is a knight.", "We have exhausted all possibilities for Alexander and Sebastian, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Alexander is a knave then Olivia is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Jacob is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Sebastian is a knave and Jacob is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Sebastian that If Alexander is a knave then Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Luke is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Sebastian is a knight then Olivia is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('->', ('lying', 3), ('lying', 5)), ('<=>', ('telling-truth', 1), ('lying', 0)), ('and', ('lying', 1), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('lying', 5)), ('<=>', ('lying', 4), ('telling-truth', 2)))", "index": 690}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Sofia, Sophia, William, Lucas, and Henry. \"If Sophia is a knight then Henry is a knave,\" Jack claimed. Sofia expressed that Jack is not a knight. In a statement by Sophia: \"Jack is not a knight\". As William put it, \"Henry is not a knight\". According to Lucas, \"If William is a knave then Henry is a knave\". Henry commented, \"Henry is a knight if and only if Sophia is a knight\". So who is a knight and who is a knave?", "names": ["Jack", "Sofia", "Sophia", "William", "Lucas", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Jack is a knave, Sofia is a knight, Sophia is a knight, William is a knave, Lucas is a knave, and Henry is a knight.", "solution_text_format": "(1) Jack is a knave\n(2) Sofia is a knight\n(3) Sophia is a knight\n(4) William is a knave\n(5) Lucas is a knave\n(6) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that If Sophia is a knight then Henry is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Jack is not a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Henry is a knight if and only if Sophia is a knight.", "Henry cannot be a knave, because this would contradict the false claim of their own that Henry is a knight if and only if Sophia is a knight.", "We have exhausted all possibilities for Henry and Sophia, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that If Sophia is a knight then Henry is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Jack is not a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Henry is a knight if and only if Sophia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Jack is not a knight.", "William cannot be a knight, because this would contradict the claim of their own that Henry is not a knight.", "Assume William is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that If William is a knave then Henry is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that If William is a knave then Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 5)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 5)), ('->', ('lying', 3), ('lying', 5)), ('<=>', ('telling-truth', 5), ('telling-truth', 2)))", "index": 691}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Aria, Liam, Ethan, Emily, and Riley. \"Riley is a knight and Emily is a knight,\" Elizabeth declared. \"Ethan is a knave or Emily is a knight,\" Aria mentioned. Liam commented, \"Riley is a knight if and only if Ethan is a knave\". Ethan asserted: \"Liam is a knave and Riley is a knave\". \"Riley is a knight or Aria is a knave,\" Emily claimed. Riley remarked, \"Emily is not a knave\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Aria", "Liam", "Ethan", "Emily", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Elizabeth is a knight, Aria is a knight, Liam is a knight, Ethan is a knave, Emily is a knight, and Riley is a knight.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Aria is a knight\n(3) Liam is a knight\n(4) Ethan is a knave\n(5) Emily is a knight\n(6) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Riley is a knight and Emily is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Riley is a knight or Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Ethan is a knave or Emily is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Liam is a knave and Riley is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Liam is a knave and Riley is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Riley is a knight if and only if Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 4)), ('or', ('lying', 3), ('telling-truth', 4)), ('<=>', ('telling-truth', 5), ('lying', 3)), ('and', ('lying', 2), ('lying', 5)), ('or', ('telling-truth', 5), ('lying', 1)), ('not', ('lying', 4)))", "index": 692}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Alexander, Luke, Penelope, Ethan, and William. Logan stated, \"Ethan is a knight and Alexander is a knave\". \"Luke is a knight and William is a knight,\" Alexander mentioned. Luke noted, \"Penelope is not a knight\". \"Logan is a knight and William is a knave,\" Penelope mentioned. \"Logan is a knave,\" Ethan mentioned. \"Penelope is a knave or Alexander is a knave\" - William. So who is a knight and who is a knave?", "names": ["Logan", "Alexander", "Luke", "Penelope", "Ethan", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Logan is a knave, Alexander is a knight, Luke is a knight, Penelope is a knave, Ethan is a knight, and William is a knight.", "solution_text_format": "(1) Logan is a knave\n(2) Alexander is a knight\n(3) Luke is a knight\n(4) Penelope is a knave\n(5) Ethan is a knight\n(6) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Ethan is a knight and Alexander is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Logan is a knave.", "Ethan cannot be a knave, because this would contradict the claim of Logan that Ethan is a knight and Alexander is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Ethan is a knight and Alexander is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Logan is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Luke is a knight and William is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Luke that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Logan is a knight and William is a knave.", "Assume William is a knight. No contradiction is found in their claim that Penelope is a knave or Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 1)), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 0), ('lying', 5)), ('lying', 0), ('or', ('lying', 3), ('lying', 1)))", "index": 693}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Avery, Jack, James, William, and Oliver. Aiden noted, \"Avery is a knight if and only if James is a knave\". In Avery's words: \"Aiden is a knave if and only if Oliver is a knight\". Jack told you that Oliver is a knave or Aiden is a knight. \"Aiden is a knight\" - James. William commented, \"Jack is a knave\". In a statement by Oliver: \"William is a knight if and only if Avery is a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Avery", "Jack", "James", "William", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false], "solution_text": "Aiden is a knave, Avery is a knave, Jack is a knight, James is a knave, William is a knave, and Oliver is a knave.", "solution_text_format": "(1) Aiden is a knave\n(2) Avery is a knave\n(3) Jack is a knight\n(4) James is a knave\n(5) William is a knave\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Avery is a knight if and only if James is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Avery that Aiden is a knave if and only if Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that William is a knight if and only if Avery is a knave.", "Assume William is a knight. No contradiction is found in their claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of William that Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that Oliver is a knave or Aiden is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the false claim of Oliver that William is a knight if and only if Avery is a knave.", "We have exhausted all possibilities for William and Oliver, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that William is a knight if and only if Avery is a knave.", "Assume William is a knight. No contradiction is found in their claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of William that Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that Oliver is a knave or Aiden is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Oliver that William is a knight if and only if Avery is a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the false claim of Avery that Aiden is a knave if and only if Oliver is a knight.", "We have exhausted all possibilities for Oliver and Avery, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Avery is a knight if and only if James is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that William is a knight if and only if Avery is a knave.", "William cannot be a knight, because this would contradict the claim of Oliver that William is a knight if and only if Avery is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Oliver is a knave or Aiden is a knight.", "Jack cannot be a knave, because this would contradict the false claim of William that Jack is a knave.", "We have exhausted all possibilities for Jack and William, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Avery that Aiden is a knave if and only if Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Avery that Aiden is a knave if and only if Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that William is a knight if and only if Avery is a knave.", "William cannot be a knight, because this would contradict the false claim of Oliver that William is a knight if and only if Avery is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Oliver is a knave or Aiden is a knight.", "James cannot be a knight, because this would contradict the false claim of Aiden that Avery is a knight if and only if James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 3)), ('<=>', ('lying', 0), ('telling-truth', 5)), ('or', ('lying', 5), ('telling-truth', 0)), ('telling-truth', 0), ('lying', 2), ('<=>', ('telling-truth', 4), ('lying', 1)))", "index": 694}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Liam, Avery, Abigail, David, and Charlotte. Ava stated, \"Abigail is a knight or David is a knave\". \"Charlotte is a knave if and only if Charlotte is a knight,\" Liam claimed. Avery said, \"Abigail is not a knave.\" According to Abigail, \"If Avery is a knave then David is a knight\". David asserted: \"Charlotte is a knave if and only if Liam is a knave\". Charlotte remarked, \"Ava is not a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Liam", "Avery", "Abigail", "David", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Ava is a knight, Liam is a knave, Avery is a knight, Abigail is a knight, David is a knight, and Charlotte is a knave.", "solution_text_format": "(1) Ava is a knight\n(2) Liam is a knave\n(3) Avery is a knight\n(4) Abigail is a knight\n(5) David is a knight\n(6) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Abigail is a knight or David is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Avery is a knave then David is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume David is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Liam is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Ava is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Liam cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave if and only if Charlotte is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('lying', 4)), ('<=>', ('lying', 5), ('telling-truth', 5)), ('not', ('lying', 3)), ('->', ('lying', 2), ('telling-truth', 4)), ('<=>', ('lying', 5), ('lying', 1)), ('not', ('telling-truth', 0)))", "index": 695}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Matthew, Amelia, James, Chloe, and Olivia. Benjamin expressed that James is a knight if and only if Olivia is a knave. Matthew said that Chloe is a knight and James is a knave. Amelia stated, \"Olivia is a knave or Chloe is a knight\". James commented, \"Matthew is a knight if and only if Matthew is a knave\". \"Benjamin is not a knave\" - Chloe. \"Matthew is a knave and Matthew is a knight,\" Olivia declared. So who is a knight and who is a knave?", "names": ["Benjamin", "Matthew", "Amelia", "James", "Chloe", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false], "solution_text": "Benjamin is a knave, Matthew is a knave, Amelia is a knight, James is a knave, Chloe is a knave, and Olivia is a knave.", "solution_text_format": "(1) Benjamin is a knave\n(2) Matthew is a knave\n(3) Amelia is a knight\n(4) James is a knave\n(5) Chloe is a knave\n(6) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that James is a knight if and only if Olivia is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Matthew is a knight if and only if Matthew is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Chloe is a knight and James is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Matthew is a knave and Matthew is a knight.", "Olivia cannot be a knave, because this would contradict the claim of Benjamin that James is a knight if and only if Olivia is a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Matthew that Chloe is a knight and James is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Chloe is a knight and James is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Matthew that Chloe is a knight and James is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Benjamin is not a knave.", "We have exhausted all possibilities for Chloe, Matthew, and James, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that James is a knight if and only if Olivia is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Matthew is a knight if and only if Matthew is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Chloe is a knight and James is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knave.", "Chloe cannot be a knave, because this would contradict the claim of Matthew that Chloe is a knight and James is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Chloe is a knight and James is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Matthew that Chloe is a knight and James is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Olivia cannot be a knight, because this would contradict the false claim of Benjamin that James is a knight if and only if Olivia is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Matthew is a knave and Matthew is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Olivia is a knave or Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 5)), ('and', ('telling-truth', 4), ('lying', 3)), ('or', ('lying', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('not', ('lying', 0)), ('and', ('lying', 1), ('telling-truth', 1)))", "index": 696}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Evelyn, Lily, Jack, Zoey, and Luke. \"Luke is a knight if and only if Evelyn is a knight,\" Scarlett mentioned. Evelyn expressed that Zoey is a knight and Luke is a knave. Lily said that Evelyn is a knight if and only if Scarlett is a knight. Jack told you that Lily is a knave. In a statement by Zoey: \"If Evelyn is a knight then Lily is a knave\". \"Scarlett is not a knave,\" Luke claimed. So who is a knight and who is a knave?", "names": ["Scarlett", "Evelyn", "Lily", "Jack", "Zoey", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Scarlett is a knave, Evelyn is a knight, Lily is a knave, Jack is a knight, Zoey is a knight, and Luke is a knave.", "solution_text_format": "(1) Scarlett is a knave\n(2) Evelyn is a knight\n(3) Lily is a knave\n(4) Jack is a knight\n(5) Zoey is a knight\n(6) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Luke is a knight if and only if Evelyn is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Zoey is a knight and Luke is a knave.", "Evelyn cannot be a knave, because this would contradict the claim of Scarlett that Luke is a knight if and only if Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the false claim of their own that Scarlett is not a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Evelyn is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Scarlett is not a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Scarlett is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Zoey is a knight and Luke is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Evelyn is a knight then Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight if and only if Scarlett is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Scarlett is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('and', ('telling-truth', 4), ('lying', 5)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('lying', 2), ('->', ('telling-truth', 1), ('lying', 2)), ('not', ('lying', 0)))", "index": 697}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Lucas, David, Michael, Harper, and Owen. Mia expressed that David is a knave. \"David is a knight or Lucas is a knight,\" Lucas mentioned. In a statement by David: \"Owen is a knight or Owen is a knave\". \"Lucas is a knave and Mia is a knave,\" Michael claimed. Harper told you that Michael is a knight or Mia is a knave. \"David is a knight,\" Owen claimed. So who is a knight and who is a knave?", "names": ["Mia", "Lucas", "David", "Michael", "Harper", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Mia is a knave, Lucas is a knight, David is a knight, Michael is a knave, Harper is a knight, and Owen is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Lucas is a knight\n(3) David is a knight\n(4) Michael is a knave\n(5) Harper is a knight\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Mia that David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that Owen is a knight or Owen is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Owen is a knight or Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that David is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that David is a knight or Lucas is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Mia is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Lucas is a knave and Mia is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Michael is a knight or Mia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('or', ('telling-truth', 5), ('lying', 5)), ('and', ('lying', 1), ('lying', 0)), ('or', ('telling-truth', 3), ('lying', 0)), ('telling-truth', 2))", "index": 698}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, James, Abigail, Aria, Mason, and Penelope. Oliver told you that Mason is a knight. James said, \"Mason is a knave if and only if Abigail is a knight.\" \"If Mason is a knight then Oliver is a knave,\" Abigail declared. \"If Abigail is a knave then Mason is a knight,\" Aria declared. As Mason put it, \"James is not a knight\". In a statement by Penelope: \"Abigail is a knight if and only if Oliver is a knave\". So who is a knight and who is a knave?", "names": ["Oliver", "James", "Abigail", "Aria", "Mason", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Oliver is a knave, James is a knight, Abigail is a knight, Aria is a knight, Mason is a knave, and Penelope is a knight.", "solution_text_format": "(1) Oliver is a knave\n(2) James is a knight\n(3) Abigail is a knight\n(4) Aria is a knight\n(5) Mason is a knave\n(6) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that James is not a knight.", "James cannot be a knight, because this would contradict the claim of Mason that James is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Abigail is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that If Mason is a knight then Oliver is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of James that Mason is a knave if and only if Abigail is a knight.", "We have exhausted all possibilities for Abigail and James, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Oliver that Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Mason is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Oliver that Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that James is not a knight.", "Assume James is a knight. No contradiction is found in their claim that Mason is a knave if and only if Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Mason is a knight then Oliver is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Abigail is a knave then Mason is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('<=>', ('lying', 4), ('telling-truth', 2)), ('->', ('telling-truth', 4), ('lying', 0)), ('->', ('lying', 2), ('telling-truth', 4)), ('not', ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('lying', 0)))", "index": 699}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Ava, Aurora, Samuel, Isabella, and Mia. Daniel told you that Isabella is a knave and Samuel is a knight. Ava was heard saying, \"Aurora is a knight and Isabella is a knight\". Aurora noted, \"Mia is a knight if and only if Mia is a knave\". Samuel stated, \"Daniel is a knave if and only if Aurora is a knave\". Isabella said, \"Aurora is a knight if and only if Mia is a knight.\" According to Mia, \"Ava is a knave and Daniel is a knight\". So who is a knight and who is a knave?", "names": ["Daniel", "Ava", "Aurora", "Samuel", "Isabella", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false], "solution_text": "Daniel is a knave, Ava is a knave, Aurora is a knave, Samuel is a knight, Isabella is a knight, and Mia is a knave.", "solution_text_format": "(1) Daniel is a knave\n(2) Ava is a knave\n(3) Aurora is a knave\n(4) Samuel is a knight\n(5) Isabella is a knight\n(6) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Isabella is a knave and Samuel is a knight.", "Isabella cannot be a knight, because this would contradict the claim of Daniel that Isabella is a knave and Samuel is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Mia is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Mia is a knight if and only if Mia is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Ava is a knave and Daniel is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Isabella is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Aurora is a knight and Isabella is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Daniel is a knave if and only if Aurora is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Daniel that Isabella is a knave and Samuel is a knight.", "We have exhausted all possibilities for Samuel and Ava, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of Isabella that Aurora is a knight if and only if Mia is a knight.", "We have exhausted all possibilities for Mia, Aurora, and Isabella, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Isabella is a knave and Samuel is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Mia is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Mia is a knight if and only if Mia is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Mia is a knight if and only if Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of Isabella that Aurora is a knight if and only if Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Ava is a knave and Daniel is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Isabella is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Aurora is a knight and Isabella is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('telling-truth', 5), ('lying', 5)), ('<=>', ('lying', 0), ('lying', 2)), ('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('and', ('lying', 1), ('telling-truth', 0)))", "index": 700}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Riley, Jackson, Mia, Samuel, and Alexander. Scarlett stated, \"Samuel is a knight\". Riley said, \"Mia is not a knight.\" \"Alexander is a knight\" - Jackson. Mia told you that Jackson is a knave if and only if Riley is a knave. Samuel was heard saying, \"Mia is a knave\". \"Scarlett is a knave or Samuel is a knave,\" Alexander declared. So who is a knight and who is a knave?", "names": ["Scarlett", "Riley", "Jackson", "Mia", "Samuel", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false], "solution_text": "Scarlett is a knight, Riley is a knight, Jackson is a knave, Mia is a knave, Samuel is a knight, and Alexander is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Riley is a knight\n(3) Jackson is a knave\n(4) Mia is a knave\n(5) Samuel is a knight\n(6) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of Samuel that Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Riley is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave or Samuel is a knave.", "Alexander cannot be a knave, because this would contradict the claim of Jackson that Alexander is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Jackson that Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Scarlett is a knave or Samuel is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Mia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('not', ('telling-truth', 3)), ('telling-truth', 5), ('<=>', ('lying', 2), ('lying', 1)), ('lying', 3), ('or', ('lying', 0), ('lying', 4)))", "index": 701}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Lucas, Logan, Mia, Sophia, and Isabella. Ethan commented, \"Logan is a knight\". \"Sophia is a knave\" - Lucas. \"Mia is a knave if and only if Isabella is a knave,\" Logan mentioned. Mia noted, \"Sophia is a knight and Sophia is a knave\". Sophia commented, \"Isabella is a knight if and only if Ethan is a knave\". According to Isabella, \"If Logan is a knight then Sophia is a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Lucas", "Logan", "Mia", "Sophia", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Ethan is a knave, Lucas is a knave, Logan is a knave, Mia is a knave, Sophia is a knight, and Isabella is a knight.", "solution_text_format": "(1) Ethan is a knave\n(2) Lucas is a knave\n(3) Logan is a knave\n(4) Mia is a knave\n(5) Sophia is a knight\n(6) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Mia is a knave if and only if Isabella is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Sophia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Sophia is a knight and Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Ethan is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Logan that Mia is a knave if and only if Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that If Logan is a knight then Sophia is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Ethan is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Logan that Mia is a knave if and only if Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of Sophia that Isabella is a knight if and only if Ethan is a knave.", "We have exhausted all possibilities for Isabella, Sophia, and Mia, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Ethan that Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Logan is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Ethan that Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Isabella is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Sophia is a knight and Sophia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Sophia is a knight and Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Ethan is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Logan is a knight then Sophia is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Sophia is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('lying', 4), ('<=>', ('lying', 3), ('lying', 5)), ('and', ('telling-truth', 4), ('lying', 4)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('->', ('telling-truth', 2), ('telling-truth', 4)))", "index": 702}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Charlotte, Owen, Ethan, James, and Logan. Jack expressed that James is a knave and Charlotte is a knight. As Charlotte put it, \"If Ethan is a knave then Logan is a knight\". Owen commented, \"James is a knave\". In a statement by Ethan: \"James is a knave\". In James's words: \"Jack is a knight or Charlotte is a knave\". Logan told you that Charlotte is a knight or James is a knave. So who is a knight and who is a knave?", "names": ["Jack", "Charlotte", "Owen", "Ethan", "James", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false], "solution_text": "Jack is a knave, Charlotte is a knave, Owen is a knave, Ethan is a knave, James is a knight, and Logan is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Charlotte is a knave\n(3) Owen is a knave\n(4) Ethan is a knave\n(5) James is a knight\n(6) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that James is a knave and Charlotte is a knight.", "James cannot be a knight, because this would contradict the claim of Jack that James is a knave and Charlotte is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that Jack is a knight or Charlotte is a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that James is a knave and Charlotte is a knight.", "Assume James is a knight. No contradiction is found in their claim that Jack is a knight or Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of James that Jack is a knight or Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Ethan is a knave then Logan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Charlotte that If Ethan is a knave then Logan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that James is a knave.", "Logan cannot be a knight, because this would contradict the false claim of Charlotte that If Ethan is a knave then Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Charlotte is a knight or James is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that James is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 1)), ('->', ('lying', 3), ('telling-truth', 5)), ('lying', 4), ('lying', 4), ('or', ('telling-truth', 0), ('lying', 1)), ('or', ('telling-truth', 1), ('lying', 4)))", "index": 703}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Emma, Owen, Aria, Samuel, and Zoey. Jackson asserted: \"Emma is a knight if and only if Aria is a knave\". Emma said that Owen is a knight and Zoey is a knave. \"Emma is a knight\" - Owen. Aria noted, \"Zoey is a knight and Emma is a knight\". Samuel remarked, \"Zoey is a knight if and only if Jackson is a knave\". Zoey stated, \"Samuel is a knave or Aria is a knave\". So who is a knight and who is a knave?", "names": ["Jackson", "Emma", "Owen", "Aria", "Samuel", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Jackson is a knave, Emma is a knave, Owen is a knave, Aria is a knave, Samuel is a knight, and Zoey is a knight.", "solution_text_format": "(1) Jackson is a knave\n(2) Emma is a knave\n(3) Owen is a knave\n(4) Aria is a knave\n(5) Samuel is a knight\n(6) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Emma is a knight if and only if Aria is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Owen is a knight and Zoey is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Emma is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Emma that Owen is a knight and Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Samuel is a knave or Aria is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Jackson is a knave.", "Aria cannot be a knight, because this would contradict the claim of Jackson that Emma is a knight if and only if Aria is a knave.", "Aria cannot be a knave, because this would contradict the false claim of Zoey that Samuel is a knave or Aria is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Zoey is a knight if and only if Jackson is a knave.", "We have exhausted all possibilities for Samuel and Zoey, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Emma that Owen is a knight and Zoey is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Owen is a knight and Zoey is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Emma is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Emma is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Samuel is a knave or Aria is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Zoey is a knight if and only if Jackson is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Jackson is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Zoey is a knight and Emma is a knight.", "Aria cannot be a knave, because this would contradict the claim of Jackson that Emma is a knight if and only if Aria is a knave.", "We have exhausted all possibilities for Aria and Samuel, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Samuel is a knave or Aria is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Jackson is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Zoey is a knight and Emma is a knight.", "Aria cannot be a knave, because this would contradict the claim of Jackson that Emma is a knight if and only if Aria is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Zoey is a knight if and only if Jackson is a knave.", "We have exhausted all possibilities for Samuel, Zoey, Owen, and Emma, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Emma is a knight if and only if Aria is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Owen is a knight and Zoey is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Emma is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Emma that Owen is a knight and Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Samuel is a knave or Aria is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Zoey is a knight if and only if Jackson is a knave.", "Samuel cannot be a knave, because this would contradict the false claim of Zoey that Samuel is a knave or Aria is a knave.", "We have exhausted all possibilities for Samuel and Zoey, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Emma that Owen is a knight and Zoey is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Owen is a knight and Zoey is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Emma is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Emma is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Samuel is a knave or Aria is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Jackson is a knave.", "Aria cannot be a knight, because this would contradict the false claim of Jackson that Emma is a knight if and only if Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Zoey is a knight and Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 3)), ('and', ('telling-truth', 2), ('lying', 5)), ('telling-truth', 1), ('and', ('telling-truth', 5), ('telling-truth', 1)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('or', ('lying', 4), ('lying', 3)))", "index": 704}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Alexander, Riley, Sophia, Ella, and Liam. Victoria said, \"Alexander is not a knave.\" Alexander commented, \"Ella is a knave and Sophia is a knave\". \"Riley is a knight,\" Riley declared. Sophia said, \"Victoria is a knight or Alexander is a knight.\" As Ella put it, \"Riley is a knight if and only if Sophia is a knight\". Liam expressed that If Riley is a knight then Ella is a knight. So who is a knight and who is a knave?", "names": ["Victoria", "Alexander", "Riley", "Sophia", "Ella", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Victoria is a knave, Alexander is a knave, Riley is a knave, Sophia is a knave, Ella is a knight, and Liam is a knight.", "solution_text_format": "(1) Victoria is a knave\n(2) Alexander is a knave\n(3) Riley is a knave\n(4) Sophia is a knave\n(5) Ella is a knight\n(6) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Ella is a knave and Sophia is a knave.", "Ella cannot be a knight, because this would contradict the claim of Alexander that Ella is a knave and Sophia is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Sophia is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Alexander that Ella is a knave and Sophia is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Victoria is a knight or Alexander is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Riley is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Alexander that Ella is a knave and Sophia is a knave.", "Sophia cannot be a knave, because this would contradict the false claim of their own that Victoria is a knight or Alexander is a knight.", "We have exhausted all possibilities for Sophia, Riley, and Ella, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Victoria that Alexander is not a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Alexander is not a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Victoria that Alexander is not a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ella is a knave and Sophia is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Riley is a knight if and only if Sophia is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Riley is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Victoria is a knight or Alexander is a knight.", "Sophia cannot be a knave, because this would contradict the claim of Ella that Riley is a knight if and only if Sophia is a knight.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Riley is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Victoria is a knight or Alexander is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Victoria is a knight or Alexander is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Riley is a knight then Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('and', ('lying', 4), ('lying', 3)), ('telling-truth', 2), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('->', ('telling-truth', 2), ('telling-truth', 4)))", "index": 705}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Michael, Owen, Jacob, Logan, and Riley. Mia asserted: \"Michael is not a knight\". Michael noted, \"If Jacob is a knave then Logan is a knave\". \"Mia is a knight\" - Owen. \"Riley is a knave and Mia is a knight,\" Jacob declared. Logan asserted: \"Riley is a knight and Jacob is a knight\". \"If Owen is a knave then Michael is a knight,\" Riley mentioned. So who is a knight and who is a knave?", "names": ["Mia", "Michael", "Owen", "Jacob", "Logan", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true], "solution_text": "Mia is a knave, Michael is a knight, Owen is a knave, Jacob is a knave, Logan is a knave, and Riley is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Michael is a knight\n(3) Owen is a knave\n(4) Jacob is a knave\n(5) Logan is a knave\n(6) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Mia that Michael is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that If Jacob is a knave then Logan is a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Michael that If Jacob is a knave then Logan is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Riley is a knave and Mia is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Owen is a knave then Michael is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Mia is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Riley is a knight and Jacob is a knight.", "Logan cannot be a knave, because this would contradict the false claim of Michael that If Jacob is a knave then Logan is a knave.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of their own that Mia is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of Jacob that Riley is a knave and Mia is a knight.", "We have exhausted all possibilities for Riley, Jacob, and Michael, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Jacob is a knave then Logan is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Mia is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Riley is a knave and Mia is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Owen is a knave then Michael is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Mia is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Mia is a knight.", "Logan cannot be a knight, because this would contradict the claim of Michael that If Jacob is a knave then Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Riley is a knight and Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('->', ('lying', 3), ('lying', 4)), ('telling-truth', 0), ('and', ('lying', 5), ('telling-truth', 0)), ('and', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('lying', 2), ('telling-truth', 1)))", "index": 706}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, Samuel, Sofia, Daniel, Chloe, and Zoey. Penelope said, \"Samuel is not a knight.\" As Samuel put it, \"Penelope is a knave\". Sofia noted, \"Chloe is a knight if and only if Penelope is a knave\". Daniel asserted: \"Penelope is not a knight\". \"Sofia is a knight and Zoey is a knave,\" Chloe mentioned. As Zoey put it, \"Daniel is a knight and Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Penelope", "Samuel", "Sofia", "Daniel", "Chloe", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true], "solution_text": "Penelope is a knave, Samuel is a knight, Sofia is a knave, Daniel is a knight, Chloe is a knave, and Zoey is a knight.", "solution_text_format": "(1) Penelope is a knave\n(2) Samuel is a knight\n(3) Sofia is a knave\n(4) Daniel is a knight\n(5) Chloe is a knave\n(6) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Samuel is not a knight.", "Samuel cannot be a knight, because this would contradict the claim of Penelope that Samuel is not a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Penelope is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Sofia that Chloe is a knight if and only if Penelope is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Sofia is a knight and Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Daniel is a knight and Penelope is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of Chloe that Sofia is a knight and Zoey is a knave.", "We have exhausted all possibilities for Zoey and Chloe, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Penelope is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Zoey is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of Sofia that Chloe is a knight if and only if Penelope is a knave.", "We have exhausted all possibilities for Chloe, Sofia, and Samuel, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Samuel is not a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Penelope is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Penelope is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Sofia is a knight and Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Chloe that Sofia is a knight and Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Daniel is a knight and Penelope is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Zoey that Daniel is a knight and Penelope is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Penelope is not a knight.", "We have exhausted all possibilities for Daniel and Zoey, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Sofia that Chloe is a knight if and only if Penelope is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Penelope is a knave.", "Chloe cannot be a knight, because this would contradict the false claim of Sofia that Chloe is a knight if and only if Penelope is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Sofia is a knight and Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Daniel is a knight and Penelope is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Penelope is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('lying', 0), ('<=>', ('telling-truth', 4), ('lying', 0)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 2), ('lying', 5)), ('and', ('telling-truth', 3), ('lying', 0)))", "index": 707}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Harper, Abigail, Michael, Olivia, and Aurora. Benjamin remarked, \"Aurora is a knight and Michael is a knight\". According to Harper, \"Michael is a knight and Aurora is a knave\". Abigail asserted: \"Aurora is a knave if and only if Benjamin is a knave\". Michael commented, \"Benjamin is not a knave\". Olivia commented, \"Michael is not a knight\". According to Aurora, \"Olivia is not a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Harper", "Abigail", "Michael", "Olivia", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Benjamin is a knave, Harper is a knave, Abigail is a knave, Michael is a knave, Olivia is a knight, and Aurora is a knight.", "solution_text_format": "(1) Benjamin is a knave\n(2) Harper is a knave\n(3) Abigail is a knave\n(4) Michael is a knave\n(5) Olivia is a knight\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Aurora is a knight and Michael is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Olivia that Michael is not a knight.", "Michael cannot be a knave, because this would contradict the claim of Benjamin that Aurora is a knight and Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the claim of Aurora that Olivia is not a knave.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Benjamin that Aurora is a knight and Michael is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Aurora is a knight and Michael is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the false claim of Benjamin that Aurora is a knight and Michael is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Benjamin is not a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Aurora is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Michael is a knight and Aurora is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Aurora is a knave if and only if Benjamin is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 3)), ('and', ('telling-truth', 3), ('lying', 5)), ('<=>', ('lying', 5), ('lying', 0)), ('not', ('lying', 0)), ('not', ('telling-truth', 3)), ('not', ('lying', 4)))", "index": 708}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, James, Harper, Aiden, Noah, and Emma. Jack said that If Aiden is a knave then James is a knave. \"Harper is a knight or Noah is a knave,\" James declared. Harper said that Noah is a knight or Emma is a knight. According to Aiden, \"Harper is a knight or Noah is a knight\". \"Aiden is a knave if and only if Jack is a knave,\" Noah mentioned. Emma expressed that Harper is a knave and Aiden is a knight. So who is a knight and who is a knave?", "names": ["Jack", "James", "Harper", "Aiden", "Noah", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Jack is a knight, James is a knight, Harper is a knight, Aiden is a knight, Noah is a knight, and Emma is a knave.", "solution_text_format": "(1) Jack is a knight\n(2) James is a knight\n(3) Harper is a knight\n(4) Aiden is a knight\n(5) Noah is a knight\n(6) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that If Aiden is a knave then James is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Harper is a knight or Noah is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Noah is a knight or Emma is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Jack is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Aiden is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Harper is a knave and Aiden is a knight.", "Assume James is a knight. No contradiction is found in their claim that Harper is a knight or Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 1)), ('or', ('telling-truth', 2), ('lying', 4)), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('or', ('telling-truth', 2), ('telling-truth', 4)), ('<=>', ('lying', 3), ('lying', 0)), ('and', ('lying', 2), ('telling-truth', 3)))", "index": 709}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Sebastian, Ella, Lucas, Amelia, and Isabella. Olivia asserted: \"Isabella is a knight or Lucas is a knave\". \"If Amelia is a knight then Ella is a knight,\" Sebastian mentioned. Ella commented, \"If Isabella is a knight then Ella is a knight\". In a statement by Lucas: \"Olivia is not a knight\". \"If Lucas is a knave then Isabella is a knave,\" Amelia declared. \"Lucas is a knight,\" Isabella claimed. So who is a knight and who is a knave?", "names": ["Olivia", "Sebastian", "Ella", "Lucas", "Amelia", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Olivia is a knight, Sebastian is a knight, Ella is a knight, Lucas is a knave, Amelia is a knight, and Isabella is a knave.", "solution_text_format": "(1) Olivia is a knight\n(2) Sebastian is a knight\n(3) Ella is a knight\n(4) Lucas is a knave\n(5) Amelia is a knight\n(6) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Isabella is a knight or Lucas is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Olivia is not a knight.", "Lucas cannot be a knave, because this would contradict the claim of Isabella that Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Olivia that Isabella is a knight or Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Olivia is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Amelia is a knight then Ella is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Lucas is a knave then Isabella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Isabella is a knight then Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('lying', 3)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('->', ('telling-truth', 5), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('->', ('lying', 3), ('lying', 5)), ('telling-truth', 3))", "index": 710}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Abigail, Emma, Aurora, Jack, and Sofia. Matthew was heard saying, \"Jack is a knight or Sofia is a knight\". As Abigail put it, \"Sofia is not a knave\". Emma stated, \"Abigail is a knight or Sofia is a knave\". Aurora said that If Matthew is a knave then Abigail is a knight. Jack told you that Matthew is not a knight. \"Aurora is not a knave,\" Sofia mentioned. So who is a knight and who is a knave?", "names": ["Matthew", "Abigail", "Emma", "Aurora", "Jack", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Matthew is a knight, Abigail is a knight, Emma is a knight, Aurora is a knight, Jack is a knave, and Sofia is a knight.", "solution_text_format": "(1) Matthew is a knight\n(2) Abigail is a knight\n(3) Emma is a knight\n(4) Aurora is a knight\n(5) Jack is a knave\n(6) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Jack is a knight or Sofia is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Matthew is not a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Matthew is not a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Matthew is a knave then Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Abigail is a knight or Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('lying', 5)), ('or', ('telling-truth', 1), ('lying', 5)), ('->', ('lying', 0), ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('not', ('lying', 3)))", "index": 711}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Scarlett, Jack, Harper, Emily, and Aria. \"Harper is a knave and Aria is a knight,\" Jacob claimed. According to Scarlett, \"Jacob is a knight and Aria is a knight\". Jack expressed that Jacob is a knight and Jacob is a knave. According to Harper, \"Jack is not a knight\". Emily commented, \"Scarlett is a knight\". According to Aria, \"Emily is not a knave\". So who is a knight and who is a knave?", "names": ["Jacob", "Scarlett", "Jack", "Harper", "Emily", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false], "solution_text": "Jacob is a knave, Scarlett is a knave, Jack is a knave, Harper is a knight, Emily is a knave, and Aria is a knave.", "solution_text_format": "(1) Jacob is a knave\n(2) Scarlett is a knave\n(3) Jack is a knave\n(4) Harper is a knight\n(5) Emily is a knave\n(6) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Harper is a knave and Aria is a knight.", "Harper cannot be a knight, because this would contradict the claim of Jacob that Harper is a knave and Aria is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Jacob is a knave.", "Jack cannot be a knave, because this would contradict the false claim of Harper that Jack is not a knight.", "We have exhausted all possibilities for Jack and Harper, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Harper is a knave and Aria is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Jack is not a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Jacob is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Jacob is a knight and Jacob is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Aria is a knight.", "Scarlett cannot be a knave, because this would contradict the claim of Emily that Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Aria that Emily is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Aria that Emily is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Aria is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Jacob is a knight and Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('lying', 0)), ('not', ('telling-truth', 2)), ('telling-truth', 1), ('not', ('lying', 4)))", "index": 712}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Daniel, Amelia, Benjamin, Scarlett, and Chloe. \"Daniel is a knight\" - Elizabeth. Daniel commented, \"Benjamin is a knave or Amelia is a knight\". Amelia stated, \"Daniel is a knight\". Benjamin said, \"Elizabeth is a knave and Daniel is a knight.\" Scarlett said that Amelia is a knave and Daniel is a knave. Chloe said that Daniel is a knave or Amelia is a knight. So who is a knight and who is a knave?", "names": ["Elizabeth", "Daniel", "Amelia", "Benjamin", "Scarlett", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Elizabeth is a knight, Daniel is a knight, Amelia is a knight, Benjamin is a knave, Scarlett is a knave, and Chloe is a knight.", "solution_text_format": "(1) Elizabeth is a knight\n(2) Daniel is a knight\n(3) Amelia is a knight\n(4) Benjamin is a knave\n(5) Scarlett is a knave\n(6) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Benjamin is a knave or Amelia is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Daniel is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Daniel is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Daniel is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Daniel is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Amelia is a knave and Daniel is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Daniel is a knave or Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('or', ('lying', 3), ('telling-truth', 2)), ('telling-truth', 1), ('and', ('lying', 0), ('telling-truth', 1)), ('and', ('lying', 2), ('lying', 1)), ('or', ('lying', 1), ('telling-truth', 2)))", "index": 713}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Avery, Penelope, Scarlett, Chloe, and Luke. According to Liam, \"Avery is a knave if and only if Liam is a knight\". Avery told you that Chloe is a knight. Penelope said, \"Avery is a knave.\" Scarlett expressed that Luke is a knave. According to Chloe, \"Luke is a knight\". \"Liam is a knave or Luke is a knight,\" Luke claimed. So who is a knight and who is a knave?", "names": ["Liam", "Avery", "Penelope", "Scarlett", "Chloe", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false], "solution_text": "Liam is a knight, Avery is a knave, Penelope is a knight, Scarlett is a knight, Chloe is a knave, and Luke is a knave.", "solution_text_format": "(1) Liam is a knight\n(2) Avery is a knave\n(3) Penelope is a knight\n(4) Scarlett is a knight\n(5) Chloe is a knave\n(6) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Avery is a knave if and only if Liam is a knight.", "Avery cannot be a knight, because this would contradict the claim of Liam that Avery is a knave if and only if Liam is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Avery that Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Chloe that Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Liam is a knave or Luke is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Avery is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 0)), ('telling-truth', 4), ('lying', 1), ('lying', 5), ('telling-truth', 5), ('or', ('lying', 0), ('telling-truth', 5)))", "index": 714}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Samuel, Grace, Aiden, Mason, and Lily. \"Mason is a knave or Samuel is a knight,\" Matthew declared. In Samuel's words: \"If Aiden is a knight then Samuel is a knight\". According to Grace, \"Lily is a knight if and only if Samuel is a knave\". \"Grace is a knight,\" Aiden mentioned. Mason said that Lily is a knight or Matthew is a knight. In Lily's words: \"Aiden is a knight\". So who is a knight and who is a knave?", "names": ["Matthew", "Samuel", "Grace", "Aiden", "Mason", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Matthew is a knave, Samuel is a knave, Grace is a knight, Aiden is a knight, Mason is a knight, and Lily is a knight.", "solution_text_format": "(1) Matthew is a knave\n(2) Samuel is a knave\n(3) Grace is a knight\n(4) Aiden is a knight\n(5) Mason is a knight\n(6) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Mason is a knave or Samuel is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Lily is a knight or Matthew is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Lily is a knight if and only if Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Grace that Lily is a knight if and only if Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Matthew that Mason is a knave or Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Aiden that Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Lily that Aiden is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Lily that Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Aiden that Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Grace that Lily is a knight if and only if Samuel is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Matthew that Mason is a knave or Samuel is a knight.", "We have exhausted all possibilities for Samuel, Grace, Aiden, and Lily, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the false claim of their own that Lily is a knight or Matthew is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Mason is a knave or Samuel is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Lily is a knight or Matthew is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Lily is a knight if and only if Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Matthew that Mason is a knave or Samuel is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that If Aiden is a knight then Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 1)), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('<=>', ('telling-truth', 5), ('lying', 1)), ('telling-truth', 2), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('telling-truth', 3))", "index": 715}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Grace, Sebastian, James, Harper, and David. Abigail noted, \"Sebastian is not a knight\". \"Harper is a knight and Sebastian is a knight\" - Grace. According to Sebastian, \"Grace is a knave or James is a knave\". James said that Grace is a knight. \"James is a knave and Sebastian is a knave,\" Harper claimed. According to David, \"Harper is not a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Grace", "Sebastian", "James", "Harper", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true], "solution_text": "Abigail is a knave, Grace is a knave, Sebastian is a knight, James is a knave, Harper is a knave, and David is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Grace is a knave\n(3) Sebastian is a knight\n(4) James is a knave\n(5) Harper is a knave\n(6) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Sebastian is not a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Abigail that Sebastian is not a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Grace is a knave or James is a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Sebastian is a knight.", "Grace cannot be a knave, because this would contradict the false claim of Sebastian that Grace is a knave or James is a knave.", "We have exhausted all possibilities for Grace and Sebastian, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Grace is a knave or James is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Harper is a knight and Sebastian is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that James is a knave and Sebastian is a knave.", "Harper cannot be a knave, because this would contradict the claim of Grace that Harper is a knight and Sebastian is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Harper is a knight and Sebastian is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Grace that Harper is a knight and Sebastian is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that James is a knave and Sebastian is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Grace is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Grace is a knight.", "Assume David is a knight. No contradiction is found in their claim that Harper is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('and', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('lying', 1), ('lying', 3)), ('telling-truth', 1), ('and', ('lying', 3), ('lying', 2)), ('not', ('telling-truth', 4)))", "index": 716}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, David, Evelyn, Joseph, Ella, and Matthew. According to Emily, \"If David is a knave then Joseph is a knave\". David said that Emily is a knight. Evelyn remarked, \"Joseph is a knave and Matthew is a knave\". According to Joseph, \"David is a knave\". In Ella's words: \"Evelyn is not a knight\". Matthew asserted: \"Ella is a knave and Evelyn is a knight\". So who is a knight and who is a knave?", "names": ["Emily", "David", "Evelyn", "Joseph", "Ella", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false], "solution_text": "Emily is a knave, David is a knave, Evelyn is a knave, Joseph is a knight, Ella is a knight, and Matthew is a knave.", "solution_text_format": "(1) Emily is a knave\n(2) David is a knave\n(3) Evelyn is a knave\n(4) Joseph is a knight\n(5) Ella is a knight\n(6) Matthew is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that If David is a knave then Joseph is a knave.", "Assume David is a knight. No contradiction is found in their claim that Emily is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that David is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that David is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Joseph is a knave and Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Evelyn that Joseph is a knave and Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Ella is a knave and Evelyn is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Evelyn is not a knight.", "Ella cannot be a knave, because this would contradict the false claim of Matthew that Ella is a knave and Evelyn is a knight.", "We have exhausted all possibilities for Ella and Matthew, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Joseph is a knave and Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Evelyn is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of Evelyn that Joseph is a knave and Matthew is a knave.", "We have exhausted all possibilities for Matthew, Evelyn, and Joseph, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of their own that Emily is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that If David is a knave then Joseph is a knave.", "David cannot be a knight, because this would contradict the false claim of Emily that If David is a knave then Joseph is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Emily is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that David is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Joseph is a knave and Matthew is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Joseph is a knave and Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Evelyn is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Ella is a knave and Evelyn is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Evelyn is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('lying', 3)), ('telling-truth', 0), ('and', ('lying', 3), ('lying', 5)), ('lying', 1), ('not', ('telling-truth', 2)), ('and', ('lying', 4), ('telling-truth', 2)))", "index": 717}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Ella, Mia, Ava, Matthew, and Lily. \"If Mia is a knight then Ella is a knight,\" Aiden claimed. Ella said that Ava is not a knave. Mia asserted: \"If Ella is a knave then Lily is a knave\". Ava expressed that Mia is a knight if and only if Ella is a knight. Matthew remarked, \"Mia is a knave if and only if Mia is a knight\". \"Matthew is a knave or Aiden is a knave,\" Lily declared. So who is a knight and who is a knave?", "names": ["Aiden", "Ella", "Mia", "Ava", "Matthew", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Aiden is a knight, Ella is a knight, Mia is a knight, Ava is a knight, Matthew is a knave, and Lily is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Ella is a knight\n(3) Mia is a knight\n(4) Ava is a knight\n(5) Matthew is a knave\n(6) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that If Mia is a knight then Ella is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Ella is a knave then Lily is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Ava is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Mia is a knight if and only if Ella is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Matthew is a knave or Aiden is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Mia is a knave if and only if Mia is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 1)), ('not', ('lying', 3)), ('->', ('lying', 1), ('lying', 5)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 2)), ('or', ('lying', 4), ('lying', 0)))", "index": 718}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, James, Mason, Avery, Scarlett, and Riley. Victoria noted, \"Victoria is a knight or Avery is a knight\". James expressed that If Mason is a knight then Victoria is a knight. \"If Avery is a knight then James is a knight,\" Mason declared. \"Victoria is a knave and Scarlett is a knight\" - Avery. Scarlett said, \"If James is a knave then Victoria is a knave.\" \"Mason is a knight,\" Riley mentioned. So who is a knight and who is a knave?", "names": ["Victoria", "James", "Mason", "Avery", "Scarlett", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Victoria is a knight, James is a knight, Mason is a knight, Avery is a knave, Scarlett is a knight, and Riley is a knight.", "solution_text_format": "(1) Victoria is a knight\n(2) James is a knight\n(3) Mason is a knight\n(4) Avery is a knave\n(5) Scarlett is a knight\n(6) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Victoria is a knight or Avery is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Victoria is a knave and Scarlett is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Victoria is a knave and Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If James is a knave then Victoria is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Mason is a knight then Victoria is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that If Avery is a knight then James is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 3)), ('->', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('and', ('lying', 0), ('telling-truth', 4)), ('->', ('lying', 1), ('lying', 0)), ('telling-truth', 2))", "index": 719}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Daniel, Ethan, Matthew, Aurora, and Aria. \"Ethan is a knight if and only if Matthew is a knight,\" Chloe mentioned. \"Aurora is a knave if and only if Daniel is a knight,\" Daniel mentioned. \"Aurora is a knight if and only if Daniel is a knight,\" Ethan declared. Matthew was heard saying, \"Chloe is a knave or Daniel is a knight\". Aurora expressed that Matthew is not a knight. Aria commented, \"Ethan is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Daniel", "Ethan", "Matthew", "Aurora", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true], "solution_text": "Chloe is a knave, Daniel is a knight, Ethan is a knave, Matthew is a knight, Aurora is a knave, and Aria is a knight.", "solution_text_format": "(1) Chloe is a knave\n(2) Daniel is a knight\n(3) Ethan is a knave\n(4) Matthew is a knight\n(5) Aurora is a knave\n(6) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Matthew is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Daniel is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of Aurora that Matthew is not a knight.", "Matthew cannot be a knave, because this would contradict the claim of Chloe that Ethan is a knight if and only if Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Matthew is not a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Chloe is a knave or Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the claim of Ethan that Aurora is a knight if and only if Daniel is a knight.", "Daniel cannot be a knave, because this would contradict the claim of Matthew that Chloe is a knave or Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Chloe that Ethan is a knight if and only if Matthew is a knight.", "We have exhausted all possibilities for Matthew and Aurora, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Daniel is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of Chloe that Ethan is a knight if and only if Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Chloe is a knave or Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Aurora is a knave if and only if Daniel is a knight.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Aurora is a knave if and only if Daniel is a knight.", "We have exhausted all possibilities for Daniel and Matthew, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of Chloe that Ethan is a knight if and only if Matthew is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of Aurora that Matthew is not a knight.", "We have exhausted all possibilities for Matthew, Aurora, and Ethan, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Matthew is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Daniel is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Chloe that Ethan is a knight if and only if Matthew is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave or Daniel is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Chloe that Ethan is a knight if and only if Matthew is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave or Daniel is a knight.", "We have exhausted all possibilities for Matthew and Aurora, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Daniel is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of Aurora that Matthew is not a knight.", "Matthew cannot be a knave, because this would contradict the false claim of Chloe that Ethan is a knight if and only if Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Matthew is not a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Chloe is a knave or Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Daniel is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('lying', 4), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('or', ('lying', 0), ('telling-truth', 1)), ('not', ('telling-truth', 3)), ('lying', 2))", "index": 720}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Sofia, Matthew, Victoria, Ethan, and Isabella. Lily expressed that If Sofia is a knight then Sofia is a knave. \"If Matthew is a knight then Ethan is a knight,\" Sofia claimed. In Matthew's words: \"Lily is a knight\". In Victoria's words: \"Matthew is not a knight\". \"If Sofia is a knave then Victoria is a knave,\" Ethan declared. In Isabella's words: \"If Ethan is a knight then Matthew is a knight\". So who is a knight and who is a knave?", "names": ["Lily", "Sofia", "Matthew", "Victoria", "Ethan", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Lily is a knave, Sofia is a knight, Matthew is a knave, Victoria is a knight, Ethan is a knight, and Isabella is a knave.", "solution_text_format": "(1) Lily is a knave\n(2) Sofia is a knight\n(3) Matthew is a knave\n(4) Victoria is a knight\n(5) Ethan is a knight\n(6) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that If Sofia is a knight then Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Lily that If Sofia is a knight then Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Matthew is a knight then Ethan is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Lily is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Sofia that If Matthew is a knight then Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Sofia is a knave then Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Matthew is not a knight.", "Victoria cannot be a knave, because this would contradict the false claim of Ethan that If Sofia is a knave then Victoria is a knave.", "We have exhausted all possibilities for Victoria and Ethan, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of Sofia that If Matthew is a knight then Ethan is a knight.", "We have exhausted all possibilities for Matthew and Sofia, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that If Sofia is a knight then Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Matthew is a knight then Ethan is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Lily is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Sofia is a knave then Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that If Ethan is a knight then Matthew is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Ethan is a knight then Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('lying', 1)), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('telling-truth', 0), ('not', ('telling-truth', 2)), ('->', ('lying', 1), ('lying', 3)), ('->', ('telling-truth', 4), ('telling-truth', 2)))", "index": 721}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Luke, Penelope, Ava, Mia, and Zoey. \"Luke is a knight,\" Alexander claimed. Luke expressed that Penelope is a knight. \"Mia is not a knave,\" Penelope mentioned. Ava said, \"Zoey is not a knight.\" \"Penelope is a knave if and only if Ava is a knave,\" Mia declared. \"Penelope is a knight or Luke is a knight\" - Zoey. So who is a knight and who is a knave?", "names": ["Alexander", "Luke", "Penelope", "Ava", "Mia", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false], "solution_text": "Alexander is a knave, Luke is a knave, Penelope is a knave, Ava is a knight, Mia is a knave, and Zoey is a knave.", "solution_text_format": "(1) Alexander is a knave\n(2) Luke is a knave\n(3) Penelope is a knave\n(4) Ava is a knight\n(5) Mia is a knave\n(6) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Luke is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Mia is not a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Ava that Zoey is not a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Penelope is a knight or Luke is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Mia that Penelope is a knave if and only if Ava is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Penelope that Mia is not a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Luke that Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Alexander that Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Alexander that Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the false claim of Luke that Penelope is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the false claim of Penelope that Mia is not a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Ava that Zoey is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Penelope is a knight or Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('telling-truth', 2), ('not', ('lying', 4)), ('not', ('telling-truth', 5)), ('<=>', ('lying', 2), ('lying', 3)), ('or', ('telling-truth', 2), ('telling-truth', 1)))", "index": 722}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Liam, Jack, Samuel, Sebastian, and Ava. As Aurora put it, \"If Ava is a knave then Sebastian is a knave\". Liam said, \"If Ava is a knave then Samuel is a knave.\" Jack remarked, \"Aurora is a knight or Samuel is a knave\". Samuel asserted: \"Sebastian is not a knave\". \"Liam is a knight,\" Sebastian declared. Ava noted, \"Jack is not a knave\". So who is a knight and who is a knave?", "names": ["Aurora", "Liam", "Jack", "Samuel", "Sebastian", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Aurora is a knight, Liam is a knight, Jack is a knight, Samuel is a knight, Sebastian is a knight, and Ava is a knight.", "solution_text_format": "(1) Aurora is a knight\n(2) Liam is a knight\n(3) Jack is a knight\n(4) Samuel is a knight\n(5) Sebastian is a knight\n(6) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that If Ava is a knave then Sebastian is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Aurora is a knight or Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Ava is a knave then Samuel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('lying', 4)), ('->', ('lying', 5), ('lying', 3)), ('or', ('telling-truth', 0), ('lying', 3)), ('not', ('lying', 4)), ('telling-truth', 1), ('not', ('lying', 2)))", "index": 723}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Zoey, Noah, Grace, Lily, and Liam. As Riley put it, \"Liam is a knight and Lily is a knave\". In a statement by Zoey: \"Grace is a knave or Riley is a knight\". Noah commented, \"Grace is a knight if and only if Liam is a knave\". Grace was heard saying, \"Liam is a knight\". Lily said that If Noah is a knight then Zoey is a knave. \"Lily is a knight and Noah is a knight\" - Liam. So who is a knight and who is a knave?", "names": ["Riley", "Zoey", "Noah", "Grace", "Lily", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "Riley is a knave, Zoey is a knight, Noah is a knave, Grace is a knave, Lily is a knight, and Liam is a knave.", "solution_text_format": "(1) Riley is a knave\n(2) Zoey is a knight\n(3) Noah is a knave\n(4) Grace is a knave\n(5) Lily is a knight\n(6) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Liam is a knight and Lily is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Lily is a knight and Noah is a knight.", "Lily cannot be a knight, because this would contradict the claim of Riley that Liam is a knight and Lily is a knave.", "Lily cannot be a knave, because this would contradict the claim of Liam that Lily is a knight and Noah is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Riley that Liam is a knight and Lily is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Liam is a knight and Lily is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Lily is a knight and Noah is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Noah is a knight then Zoey is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Grace is a knight if and only if Liam is a knave.", "Grace cannot be a knight, because this would contradict the claim of Noah that Grace is a knight if and only if Liam is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Liam is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the claim of Liam that Lily is a knight and Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of Riley that Liam is a knight and Lily is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Lily is a knight and Noah is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Noah is a knight then Zoey is a knave.", "Noah cannot be a knight, because this would contradict the false claim of Liam that Lily is a knight and Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Liam is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Noah that Grace is a knight if and only if Liam is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Liam is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Grace is a knave or Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 4)), ('or', ('lying', 3), ('telling-truth', 0)), ('<=>', ('telling-truth', 3), ('lying', 5)), ('telling-truth', 5), ('->', ('telling-truth', 2), ('lying', 1)), ('and', ('telling-truth', 4), ('telling-truth', 2)))", "index": 724}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Jacob, Sofia, Benjamin, Alexander, and Michael. Harper said, \"Benjamin is a knave or Jacob is a knave.\" \"Harper is a knave if and only if Michael is a knight\" - Jacob. Sofia was heard saying, \"Benjamin is a knight if and only if Jacob is a knave\". Benjamin stated, \"Michael is a knave\". Alexander said that Jacob is a knave and Benjamin is a knave. Michael told you that If Michael is a knight then Benjamin is a knave. So who is a knight and who is a knave?", "names": ["Harper", "Jacob", "Sofia", "Benjamin", "Alexander", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true], "solution_text": "Harper is a knight, Jacob is a knave, Sofia is a knave, Benjamin is a knave, Alexander is a knight, and Michael is a knight.", "solution_text_format": "(1) Harper is a knight\n(2) Jacob is a knave\n(3) Sofia is a knave\n(4) Benjamin is a knave\n(5) Alexander is a knight\n(6) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Benjamin is a knave or Jacob is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Benjamin that Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that If Michael is a knight then Benjamin is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Michael is a knight then Benjamin is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Harper is a knave if and only if Michael is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Michael is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Jacob is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Jacob is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Jacob is a knave and Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 1)), ('<=>', ('lying', 0), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 1)), ('lying', 5), ('and', ('lying', 1), ('lying', 3)), ('->', ('telling-truth', 5), ('lying', 3)))", "index": 725}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Elizabeth, Amelia, Mia, Aria, and Oliver. David was heard saying, \"Amelia is a knave or Elizabeth is a knight\". According to Elizabeth, \"Mia is a knight\". Amelia stated, \"Mia is a knave or Aria is a knight\". Mia asserted: \"Amelia is a knave if and only if Amelia is a knight\". Aria expressed that Elizabeth is a knave. Oliver asserted: \"Amelia is a knight and Mia is a knight\". So who is a knight and who is a knave?", "names": ["David", "Elizabeth", "Amelia", "Mia", "Aria", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "David is a knave, Elizabeth is a knave, Amelia is a knight, Mia is a knave, Aria is a knight, and Oliver is a knave.", "solution_text_format": "(1) David is a knave\n(2) Elizabeth is a knave\n(3) Amelia is a knight\n(4) Mia is a knave\n(5) Aria is a knight\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Amelia is a knave or Elizabeth is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Mia is a knave or Aria is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Amelia is a knave if and only if Amelia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Amelia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Mia is a knight.", "Elizabeth cannot be a knave, because this would contradict the claim of David that Amelia is a knave or Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Mia is a knight.", "Elizabeth cannot be a knave, because this would contradict the claim of David that Amelia is a knave or Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, Aria, and Mia, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Mia is a knave or Aria is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Amelia is a knave if and only if Amelia is a knight.", "Mia cannot be a knave, because this would contradict the false claim of Amelia that Mia is a knave or Aria is a knight.", "We have exhausted all possibilities for Mia and Amelia, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Amelia is a knave or Elizabeth is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Mia is a knave or Aria is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Amelia is a knave if and only if Amelia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Amelia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of David that Amelia is a knave or Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Mia is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Amelia is a knight and Mia is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Amelia is a knight and Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 1)), ('telling-truth', 3), ('or', ('lying', 3), ('telling-truth', 4)), ('<=>', ('lying', 2), ('telling-truth', 2)), ('lying', 1), ('and', ('telling-truth', 2), ('telling-truth', 3)))", "index": 726}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Abigail, Emma, Owen, Ethan, and Scarlett. In a statement by Logan: \"Emma is a knight if and only if Abigail is a knave\". In Abigail's words: \"Emma is not a knight\". Emma told you that Scarlett is a knave. Owen expressed that Ethan is a knave and Ethan is a knight. According to Ethan, \"Ethan is a knight if and only if Logan is a knight\". Scarlett said that Ethan is a knight and Emma is a knight. So who is a knight and who is a knave?", "names": ["Logan", "Abigail", "Emma", "Owen", "Ethan", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Logan is a knight, Abigail is a knave, Emma is a knight, Owen is a knave, Ethan is a knave, and Scarlett is a knave.", "solution_text_format": "(1) Logan is a knight\n(2) Abigail is a knave\n(3) Emma is a knight\n(4) Owen is a knave\n(5) Ethan is a knave\n(6) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Emma is a knight if and only if Abigail is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Emma that Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Ethan is a knight and Emma is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Scarlett that Ethan is a knight and Emma is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Logan is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Logan that Emma is a knight if and only if Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Ethan is a knave and Ethan is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Ethan is a knave and Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 1)), ('not', ('telling-truth', 2)), ('lying', 5), ('and', ('lying', 4), ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('telling-truth', 4), ('telling-truth', 2)))", "index": 727}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Daniel, Logan, Zoey, Sophia, and Amelia. Mia asserted: \"Sophia is a knight if and only if Logan is a knave\". \"Amelia is a knight,\" Daniel declared. \"Amelia is not a knave,\" Logan claimed. Zoey asserted: \"Daniel is a knight if and only if Amelia is a knave\". Sophia told you that Amelia is a knight if and only if Logan is a knight. Amelia remarked, \"Mia is a knight and Sophia is a knave\". So who is a knight and who is a knave?", "names": ["Mia", "Daniel", "Logan", "Zoey", "Sophia", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false], "solution_text": "Mia is a knight, Daniel is a knave, Logan is a knave, Zoey is a knave, Sophia is a knight, and Amelia is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Daniel is a knave\n(3) Logan is a knave\n(4) Zoey is a knave\n(5) Sophia is a knight\n(6) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Logan is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Logan is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Sophia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Mia is a knight and Sophia is a knave.", "Logan cannot be a knight, because this would contradict the claim of Mia that Sophia is a knight if and only if Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Amelia is not a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Amelia is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Amelia is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Amelia is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('lying', 2)), ('telling-truth', 5), ('not', ('lying', 5)), ('<=>', ('telling-truth', 1), ('lying', 5)), ('<=>', ('telling-truth', 5), ('telling-truth', 2)), ('and', ('telling-truth', 0), ('lying', 4)))", "index": 728}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Evelyn, Michael, Matthew, Avery, and Isabella. Aiden commented, \"Evelyn is a knave or Isabella is a knight\". According to Evelyn, \"Aiden is not a knave\". According to Michael, \"Avery is a knight and Matthew is a knight\". Matthew asserted: \"Aiden is not a knave\". \"Evelyn is not a knight,\" Avery declared. Isabella told you that Michael is a knave and Aiden is a knight. So who is a knight and who is a knave?", "names": ["Aiden", "Evelyn", "Michael", "Matthew", "Avery", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Aiden is a knight, Evelyn is a knight, Michael is a knave, Matthew is a knight, Avery is a knave, and Isabella is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Evelyn is a knight\n(3) Michael is a knave\n(4) Matthew is a knight\n(5) Avery is a knave\n(6) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Evelyn is a knave or Isabella is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Michael is a knave and Aiden is a knight.", "Michael cannot be a knight, because this would contradict the claim of Isabella that Michael is a knave and Aiden is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Avery is a knight and Matthew is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Evelyn is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Aiden is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 5)), ('not', ('lying', 0)), ('and', ('telling-truth', 4), ('telling-truth', 3)), ('not', ('lying', 0)), ('not', ('telling-truth', 1)), ('and', ('lying', 2), ('telling-truth', 0)))", "index": 729}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Jackson, Liam, Aurora, David, and Scarlett. \"Scarlett is not a knave,\" Ava claimed. Jackson expressed that Liam is a knave or Scarlett is a knave. In a statement by Liam: \"If David is a knight then Ava is a knave\". Aurora said, \"If Jackson is a knight then Scarlett is a knave.\" David stated, \"Jackson is not a knave\". Scarlett told you that Aurora is not a knave. So who is a knight and who is a knave?", "names": ["Ava", "Jackson", "Liam", "Aurora", "David", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "Ava is a knight, Jackson is a knave, Liam is a knight, Aurora is a knight, David is a knave, and Scarlett is a knight.", "solution_text_format": "(1) Ava is a knight\n(2) Jackson is a knave\n(3) Liam is a knight\n(4) Aurora is a knight\n(5) David is a knave\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Jackson is a knight then Scarlett is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Aurora that If Jackson is a knight then Scarlett is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Liam is a knave or Scarlett is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If David is a knight then Ava is a knave.", "David cannot be a knight, because this would contradict the claim of Liam that If David is a knight then Ava is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Jackson is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('or', ('lying', 2), ('lying', 5)), ('->', ('telling-truth', 4), ('lying', 0)), ('->', ('telling-truth', 1), ('lying', 5)), ('not', ('lying', 1)), ('not', ('lying', 3)))", "index": 730}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Daniel, Aria, Sophia, Alexander, and Logan. Liam was heard saying, \"Aria is a knave if and only if Sophia is a knave\". Daniel said, \"Logan is a knight or Sophia is a knight.\" According to Aria, \"If Sophia is a knight then Logan is a knave\". According to Sophia, \"Alexander is not a knave\". Alexander was heard saying, \"Alexander is a knight if and only if Sophia is a knight\". \"Alexander is a knave,\" Logan claimed. So who is a knight and who is a knave?", "names": ["Liam", "Daniel", "Aria", "Sophia", "Alexander", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Liam is a knight, Daniel is a knight, Aria is a knight, Sophia is a knight, Alexander is a knight, and Logan is a knave.", "solution_text_format": "(1) Liam is a knight\n(2) Daniel is a knight\n(3) Aria is a knight\n(4) Sophia is a knight\n(5) Alexander is a knight\n(6) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Aria is a knave if and only if Sophia is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Sophia is a knight then Logan is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Sophia is a knight.", "Logan cannot be a knight, because this would contradict the claim of Aria that If Sophia is a knight then Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Logan is a knight or Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 3)), ('or', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('lying', 5)), ('not', ('lying', 4)), ('<=>', ('telling-truth', 4), ('telling-truth', 3)), ('lying', 4))", "index": 731}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Aiden, Ava, Jacob, Logan, and Elizabeth. In Lily's words: \"Ava is not a knave\". \"Logan is a knight or Logan is a knave,\" Aiden claimed. Ava told you that Lily is a knave if and only if Jacob is a knave. \"Lily is a knave if and only if Aiden is a knave,\" Jacob declared. Logan said, \"Lily is a knight or Jacob is a knave.\" As Elizabeth put it, \"Jacob is a knave or Aiden is a knave\". So who is a knight and who is a knave?", "names": ["Lily", "Aiden", "Ava", "Jacob", "Logan", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Lily is a knight, Aiden is a knight, Ava is a knight, Jacob is a knight, Logan is a knight, and Elizabeth is a knave.", "solution_text_format": "(1) Lily is a knight\n(2) Aiden is a knight\n(3) Ava is a knight\n(4) Jacob is a knight\n(5) Logan is a knight\n(6) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Ava is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Lily is a knave if and only if Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Lily is a knave if and only if Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Logan is a knight or Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Lily is a knight or Jacob is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Jacob is a knave or Aiden is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Jacob is a knave or Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('or', ('telling-truth', 4), ('lying', 4)), ('<=>', ('lying', 0), ('lying', 3)), ('<=>', ('lying', 0), ('lying', 1)), ('or', ('telling-truth', 0), ('lying', 3)), ('or', ('lying', 3), ('lying', 1)))", "index": 732}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Chloe, Sebastian, Emily, Aurora, and Grace. Charlotte said, \"If Emily is a knight then Chloe is a knight.\" Chloe commented, \"Charlotte is a knight or Aurora is a knave\". \"Sebastian is a knight if and only if Grace is a knave\" - Sebastian. Emily noted, \"If Chloe is a knave then Grace is a knave\". Aurora remarked, \"Chloe is a knight\". \"Sebastian is a knight and Chloe is a knight,\" Grace mentioned. So who is a knight and who is a knave?", "names": ["Charlotte", "Chloe", "Sebastian", "Emily", "Aurora", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "Charlotte is a knight, Chloe is a knight, Sebastian is a knave, Emily is a knight, Aurora is a knight, and Grace is a knave.", "solution_text_format": "(1) Charlotte is a knight\n(2) Chloe is a knight\n(3) Sebastian is a knave\n(4) Emily is a knight\n(5) Aurora is a knight\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that If Emily is a knight then Chloe is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Chloe is a knave then Grace is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Charlotte is a knight or Aurora is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Chloe is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Sebastian is a knight and Chloe is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight if and only if Grace is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knight if and only if Grace is a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Sebastian is a knight and Chloe is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Grace that Sebastian is a knight and Chloe is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('lying', 4)), ('<=>', ('telling-truth', 2), ('lying', 5)), ('->', ('lying', 1), ('lying', 5)), ('telling-truth', 1), ('and', ('telling-truth', 2), ('telling-truth', 1)))", "index": 733}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Logan, Matthew, Sophia, Victoria, and Riley. \"Victoria is not a knight\" - Harper. Logan told you that Matthew is a knight or Sophia is a knave. Matthew commented, \"If Riley is a knight then Victoria is a knave\". In a statement by Sophia: \"If Victoria is a knave then Matthew is a knave\". Victoria stated, \"If Sophia is a knave then Harper is a knight\". Riley told you that Matthew is a knight or Harper is a knave. So who is a knight and who is a knave?", "names": ["Harper", "Logan", "Matthew", "Sophia", "Victoria", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Harper is a knave, Logan is a knave, Matthew is a knave, Sophia is a knight, Victoria is a knight, and Riley is a knight.", "solution_text_format": "(1) Harper is a knave\n(2) Logan is a knave\n(3) Matthew is a knave\n(4) Sophia is a knight\n(5) Victoria is a knight\n(6) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of Harper that Victoria is not a knight.", "Victoria cannot be a knave, because this would contradict the false claim of their own that If Sophia is a knave then Harper is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Sophia is a knave then Harper is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Victoria is a knave then Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Riley is a knight then Victoria is a knave.", "Riley cannot be a knight, because this would contradict the claim of Matthew that If Riley is a knight then Victoria is a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that Matthew is a knight or Harper is a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that If Riley is a knight then Victoria is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Matthew is a knight or Harper is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Matthew is a knight or Sophia is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Matthew is a knight or Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('or', ('telling-truth', 2), ('lying', 3)), ('->', ('telling-truth', 5), ('lying', 4)), ('->', ('lying', 4), ('lying', 2)), ('->', ('lying', 3), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('lying', 0)))", "index": 734}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, Riley, Olivia, Liam, Emily, and Jackson. \"If Riley is a knave then Olivia is a knave,\" Penelope claimed. In Riley's words: \"If Liam is a knave then Penelope is a knight\". Olivia told you that Liam is a knight and Penelope is a knave. \"Riley is not a knave\" - Liam. Emily said that Riley is a knave. Jackson said that Riley is not a knave. So who is a knight and who is a knave?", "names": ["Penelope", "Riley", "Olivia", "Liam", "Emily", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Penelope is a knight, Riley is a knight, Olivia is a knave, Liam is a knight, Emily is a knave, and Jackson is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) Riley is a knight\n(3) Olivia is a knave\n(4) Liam is a knight\n(5) Emily is a knave\n(6) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that If Riley is a knave then Olivia is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Liam is a knave then Penelope is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Riley is not a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Liam is a knight and Penelope is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Liam is a knight and Penelope is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Riley is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Riley is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Riley is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('lying', 2)), ('->', ('lying', 3), ('telling-truth', 0)), ('and', ('telling-truth', 3), ('lying', 0)), ('not', ('lying', 1)), ('lying', 1), ('not', ('lying', 1)))", "index": 735}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, William, Benjamin, Elizabeth, Evelyn, and Isabella. Sofia commented, \"William is a knave if and only if Benjamin is a knave\". \"If Elizabeth is a knight then Isabella is a knight,\" William claimed. Benjamin stated, \"If William is a knight then William is a knave\". Elizabeth said, \"If William is a knight then William is a knave.\" As Evelyn put it, \"Isabella is a knight and Benjamin is a knave\". In a statement by Isabella: \"Evelyn is a knight or Evelyn is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "William", "Benjamin", "Elizabeth", "Evelyn", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true], "solution_text": "Sofia is a knave, William is a knight, Benjamin is a knave, Elizabeth is a knave, Evelyn is a knight, and Isabella is a knight.", "solution_text_format": "(1) Sofia is a knave\n(2) William is a knight\n(3) Benjamin is a knave\n(4) Elizabeth is a knave\n(5) Evelyn is a knight\n(6) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that William is a knave if and only if Benjamin is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Isabella is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that If William is a knight then William is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that If William is a knight then William is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Evelyn is a knight or Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Isabella is a knight and Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that If William is a knight then William is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Sofia that William is a knave if and only if Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Isabella is a knight and Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that If William is a knight then William is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Sofia that William is a knave if and only if Benjamin is a knave.", "We have exhausted all possibilities for Benjamin and Evelyn, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Evelyn is a knight or Evelyn is a knave.", "We have exhausted all possibilities for Isabella and Elizabeth, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that If Elizabeth is a knight then Isabella is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If William is a knight then William is a knave.", "Isabella cannot be a knight, because this would contradict the false claim of William that If Elizabeth is a knight then Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Evelyn is a knight or Evelyn is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the false claim of William that If Elizabeth is a knight then Isabella is a knight.", "We have exhausted all possibilities for Elizabeth and William, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that William is a knave if and only if Benjamin is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Isabella is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that If William is a knight then William is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that If William is a knight then William is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Evelyn is a knight or Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Isabella is a knight and Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Sofia that William is a knave if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that If William is a knight then William is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 2)), ('->', ('telling-truth', 3), ('telling-truth', 5)), ('->', ('telling-truth', 1), ('lying', 1)), ('->', ('telling-truth', 1), ('lying', 1)), ('and', ('telling-truth', 5), ('lying', 2)), ('or', ('telling-truth', 4), ('lying', 4)))", "index": 736}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Joseph, Aria, Mia, Lily, and Emily. Sofia said, \"Lily is a knave.\" Joseph stated, \"Mia is not a knave\". \"If Emily is a knight then Sofia is a knight,\" Aria claimed. Mia commented, \"Emily is a knave\". Lily remarked, \"Lily is a knight or Aria is a knight\". As Emily put it, \"Lily is a knight if and only if Lily is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Joseph", "Aria", "Mia", "Lily", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Sofia is a knave, Joseph is a knight, Aria is a knight, Mia is a knight, Lily is a knight, and Emily is a knave.", "solution_text_format": "(1) Sofia is a knave\n(2) Joseph is a knight\n(3) Aria is a knight\n(4) Mia is a knight\n(5) Lily is a knight\n(6) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Sofia that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Lily is a knight or Aria is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Lily that Lily is a knight or Aria is a knight.", "Aria cannot be a knave, because this would contradict the false claim of their own that If Emily is a knight then Sofia is a knight.", "We have exhausted all possibilities for Aria and Lily, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Lily is a knight or Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that If Emily is a knight then Sofia is a knight.", "Emily cannot be a knight, because this would contradict the claim of Aria that If Emily is a knight then Sofia is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Lily is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Mia is not a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('not', ('lying', 3)), ('->', ('telling-truth', 5), ('telling-truth', 0)), ('lying', 5), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('lying', 4)))", "index": 737}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, Charlotte, Aiden, Riley, Joseph, and Oliver. According to Penelope, \"If Charlotte is a knave then Charlotte is a knight\". Charlotte remarked, \"Aiden is a knave\". In Aiden's words: \"Charlotte is a knight and Riley is a knave\". As Riley put it, \"If Penelope is a knave then Oliver is a knight\". Joseph asserted: \"Aiden is a knight or Penelope is a knight\". Oliver commented, \"Charlotte is not a knight\". So who is a knight and who is a knave?", "names": ["Penelope", "Charlotte", "Aiden", "Riley", "Joseph", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "Penelope is a knight, Charlotte is a knight, Aiden is a knave, Riley is a knight, Joseph is a knight, and Oliver is a knave.", "solution_text_format": "(1) Penelope is a knight\n(2) Charlotte is a knight\n(3) Aiden is a knave\n(4) Riley is a knight\n(5) Joseph is a knight\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that If Charlotte is a knave then Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Charlotte that Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Charlotte is a knight and Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Penelope is a knave then Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Aiden is a knight or Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 1)), ('lying', 2), ('and', ('telling-truth', 1), ('lying', 3)), ('->', ('lying', 0), ('telling-truth', 5)), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('not', ('telling-truth', 1)))", "index": 738}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Emily, Mia, Charlotte, Elizabeth, and Jacob. According to Abigail, \"Jacob is not a knight\". Emily was heard saying, \"Charlotte is not a knave\". \"Charlotte is a knave if and only if Abigail is a knave,\" Mia declared. \"If Abigail is a knave then Abigail is a knight,\" Charlotte declared. According to Elizabeth, \"Mia is a knave and Emily is a knave\". Jacob noted, \"Emily is a knave and Elizabeth is a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Emily", "Mia", "Charlotte", "Elizabeth", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Abigail is a knight, Emily is a knight, Mia is a knight, Charlotte is a knight, Elizabeth is a knave, and Jacob is a knave.", "solution_text_format": "(1) Abigail is a knight\n(2) Emily is a knight\n(3) Mia is a knight\n(4) Charlotte is a knight\n(5) Elizabeth is a knave\n(6) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Jacob is not a knight.", "Jacob cannot be a knight, because this would contradict the claim of Abigail that Jacob is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Emily is a knave and Elizabeth is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Charlotte is not a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Abigail is a knave then Abigail is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Emily is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Mia is a knave and Emily is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('not', ('lying', 3)), ('<=>', ('lying', 3), ('lying', 0)), ('->', ('lying', 0), ('telling-truth', 0)), ('and', ('lying', 2), ('lying', 1)), ('and', ('lying', 1), ('telling-truth', 4)))", "index": 739}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Mia, Joseph, Luke, Sebastian, and Jack. Samuel told you that Sebastian is a knave. \"Joseph is a knave and Joseph is a knight\" - Mia. Joseph expressed that Jack is a knight if and only if Mia is a knight. Luke expressed that Samuel is a knave and Joseph is a knave. Sebastian told you that Jack is not a knight. \"Samuel is a knave and Joseph is a knave\" - Jack. So who is a knight and who is a knave?", "names": ["Samuel", "Mia", "Joseph", "Luke", "Sebastian", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "Samuel is a knave, Mia is a knave, Joseph is a knight, Luke is a knave, Sebastian is a knight, and Jack is a knave.", "solution_text_format": "(1) Samuel is a knave\n(2) Mia is a knave\n(3) Joseph is a knight\n(4) Luke is a knave\n(5) Sebastian is a knight\n(6) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Samuel that Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Samuel is a knave and Joseph is a knave.", "Jack cannot be a knave, because this would contradict the false claim of Sebastian that Jack is not a knight.", "We have exhausted all possibilities for Jack and Sebastian, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jack is not a knight.", "Jack cannot be a knight, because this would contradict the claim of Sebastian that Jack is not a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Samuel is a knave and Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Jack is a knight if and only if Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Joseph is a knave and Joseph is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Joseph is a knave and Joseph is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Samuel is a knave and Joseph is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Samuel is a knave and Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('and', ('lying', 2), ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('and', ('lying', 0), ('lying', 2)), ('not', ('telling-truth', 5)), ('and', ('lying', 0), ('lying', 2)))", "index": 740}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Penelope, Joseph, Emma, Grace, and Scarlett. Ella expressed that Scarlett is a knave or Scarlett is a knight. In a statement by Penelope: \"Joseph is a knave\". Joseph said, \"Ella is a knight or Joseph is a knight.\" Emma commented, \"Penelope is a knave and Grace is a knave\". Grace stated, \"Penelope is a knave or Ella is a knight\". In a statement by Scarlett: \"Joseph is a knave\". So who is a knight and who is a knave?", "names": ["Ella", "Penelope", "Joseph", "Emma", "Grace", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false], "solution_text": "Ella is a knight, Penelope is a knave, Joseph is a knight, Emma is a knave, Grace is a knight, and Scarlett is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Penelope is a knave\n(3) Joseph is a knight\n(4) Emma is a knave\n(5) Grace is a knight\n(6) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Scarlett is a knave or Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Scarlett that Joseph is a knave.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Ella is a knight or Joseph is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Joseph is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Penelope is a knave and Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Emma that Penelope is a knave and Grace is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Penelope is a knave or Ella is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Penelope is a knave and Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Penelope is a knave or Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 5)), ('lying', 2), ('or', ('telling-truth', 0), ('telling-truth', 2)), ('and', ('lying', 1), ('lying', 4)), ('or', ('lying', 1), ('telling-truth', 0)), ('lying', 2))", "index": 741}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Daniel, Jack, Noah, Joseph, and Sofia. In Owen's words: \"Noah is a knight\". As Daniel put it, \"Jack is a knight and Noah is a knight\". \"Daniel is a knight,\" Jack declared. As Noah put it, \"Sofia is a knave if and only if Daniel is a knight\". In Joseph's words: \"Noah is a knight or Jack is a knight\". Sofia told you that Owen is a knave. So who is a knight and who is a knave?", "names": ["Owen", "Daniel", "Jack", "Noah", "Joseph", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Owen is a knight, Daniel is a knight, Jack is a knight, Noah is a knight, Joseph is a knight, and Sofia is a knave.", "solution_text_format": "(1) Owen is a knight\n(2) Daniel is a knight\n(3) Jack is a knight\n(4) Noah is a knight\n(5) Joseph is a knight\n(6) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Daniel is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Owen is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Owen is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Jack is a knight and Noah is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Noah is a knight or Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('telling-truth', 1), ('<=>', ('lying', 5), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('telling-truth', 2)), ('lying', 0))", "index": 742}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Ethan, Mason, Jack, Emma, and Riley. According to Jacob, \"Emma is a knave and Mason is a knight\". Ethan said, \"Jacob is a knight if and only if Emma is a knight.\" Mason said that If Mason is a knight then Emma is a knave. In a statement by Jack: \"Riley is a knight and Jack is a knight\". According to Emma, \"Ethan is a knight and Jack is a knave\". In Riley's words: \"Mason is a knave\". So who is a knight and who is a knave?", "names": ["Jacob", "Ethan", "Mason", "Jack", "Emma", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Jacob is a knight, Ethan is a knave, Mason is a knight, Jack is a knave, Emma is a knave, and Riley is a knave.", "solution_text_format": "(1) Jacob is a knight\n(2) Ethan is a knave\n(3) Mason is a knight\n(4) Jack is a knave\n(5) Emma is a knave\n(6) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Emma is a knave and Mason is a knight.", "Emma cannot be a knight, because this would contradict the claim of Jacob that Emma is a knave and Mason is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Ethan is a knight and Jack is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Jacob is a knight if and only if Emma is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Emma is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Riley is a knight and Jack is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Riley that Mason is a knave.", "Mason cannot be a knave, because this would contradict the claim of Jacob that Emma is a knave and Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the claim of Jack that Riley is a knight and Jack is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Riley is a knight and Jack is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Riley that Mason is a knave.", "Mason cannot be a knave, because this would contradict the claim of Jacob that Emma is a knave and Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Mason is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Mason is a knight then Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 2)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('->', ('telling-truth', 2), ('lying', 4)), ('and', ('telling-truth', 5), ('telling-truth', 3)), ('and', ('telling-truth', 1), ('lying', 3)), ('lying', 2))", "index": 743}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Owen, Harper, Olivia, Aiden, and Zoey. Joseph asserted: \"If Olivia is a knave then Owen is a knight\". As Owen put it, \"If Harper is a knight then Aiden is a knave\". In Harper's words: \"Zoey is a knave\". Olivia noted, \"Aiden is a knight or Olivia is a knight\". Aiden told you that If Harper is a knave then Aiden is a knight. Zoey said, \"Aiden is a knight.\" So who is a knight and who is a knave?", "names": ["Joseph", "Owen", "Harper", "Olivia", "Aiden", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Joseph is a knight, Owen is a knight, Harper is a knave, Olivia is a knight, Aiden is a knight, and Zoey is a knight.", "solution_text_format": "(1) Joseph is a knight\n(2) Owen is a knight\n(3) Harper is a knave\n(4) Olivia is a knight\n(5) Aiden is a knight\n(6) Zoey is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that If Olivia is a knave then Owen is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Aiden is a knight or Olivia is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Harper is a knave then Aiden is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Harper that Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Aiden is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Harper is a knight then Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 1)), ('->', ('telling-truth', 2), ('lying', 4)), ('lying', 5), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('->', ('lying', 2), ('telling-truth', 4)), ('telling-truth', 4))", "index": 744}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Owen, Logan, Emma, Ella, and Joseph. Sophia asserted: \"Logan is a knave or Sophia is a knight\". According to Owen, \"Ella is a knave or Logan is a knave\". Logan asserted: \"Emma is a knave and Owen is a knave\". Emma stated, \"Sophia is a knight and Joseph is a knight\". In a statement by Ella: \"Joseph is a knight\". \"If Owen is a knave then Ella is a knave,\" Joseph claimed. So who is a knight and who is a knave?", "names": ["Sophia", "Owen", "Logan", "Emma", "Ella", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Sophia is a knight, Owen is a knight, Logan is a knave, Emma is a knight, Ella is a knight, and Joseph is a knight.", "solution_text_format": "(1) Sophia is a knight\n(2) Owen is a knight\n(3) Logan is a knave\n(4) Emma is a knight\n(5) Ella is a knight\n(6) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Logan is a knave or Sophia is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Emma is a knave and Owen is a knave.", "Emma cannot be a knight, because this would contradict the claim of Logan that Emma is a knave and Owen is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Sophia is a knight and Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Emma that Sophia is a knight and Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Owen is a knave then Ella is a knave.", "Owen cannot be a knight, because this would contradict the claim of Logan that Emma is a knave and Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Ella is a knave or Logan is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Joseph is a knight.", "Ella cannot be a knave, because this would contradict the false claim of Owen that Ella is a knave or Logan is a knave.", "We have exhausted all possibilities for Ella, Owen, Joseph, and Emma, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Emma is a knave and Owen is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Sophia is a knight and Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Owen is a knave then Ella is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Ella is a knave or Logan is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 0)), ('or', ('lying', 4), ('lying', 2)), ('and', ('lying', 3), ('lying', 1)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('telling-truth', 5), ('->', ('lying', 1), ('lying', 4)))", "index": 745}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Benjamin, Logan, Lucas, Matthew, and Penelope. Ethan said, \"Penelope is a knave if and only if Lucas is a knave.\" Benjamin noted, \"If Matthew is a knight then Penelope is a knight\". Logan was heard saying, \"If Lucas is a knight then Penelope is a knight\". \"Penelope is a knight and Logan is a knave,\" Lucas declared. Matthew commented, \"If Logan is a knight then Benjamin is a knight\". In a statement by Penelope: \"Matthew is a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Benjamin", "Logan", "Lucas", "Matthew", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Ethan is a knave, Benjamin is a knight, Logan is a knight, Lucas is a knave, Matthew is a knight, and Penelope is a knight.", "solution_text_format": "(1) Ethan is a knave\n(2) Benjamin is a knight\n(3) Logan is a knight\n(4) Lucas is a knave\n(5) Matthew is a knight\n(6) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Lucas is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Logan is a knight then Benjamin is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Lucas is a knight then Penelope is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Penelope is a knight and Logan is a knave.", "Lucas cannot be a knave, because this would contradict the claim of Ethan that Penelope is a knave if and only if Lucas is a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of their own that If Lucas is a knight then Penelope is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Penelope that Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Penelope that Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that If Logan is a knight then Benjamin is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Lucas is a knight then Penelope is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Ethan that Penelope is a knave if and only if Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Penelope is a knight and Logan is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Matthew that If Logan is a knight then Benjamin is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knight then Penelope is a knight.", "We have exhausted all possibilities for Benjamin and Lucas, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the false claim of Matthew that If Logan is a knight then Benjamin is a knight.", "We have exhausted all possibilities for Logan, Matthew, and Penelope, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Lucas is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Logan is a knight then Benjamin is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Lucas is a knight then Penelope is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Ethan that Penelope is a knave if and only if Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Penelope is a knight and Logan is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Matthew is a knight then Penelope is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 3)), ('->', ('telling-truth', 4), ('telling-truth', 5)), ('->', ('telling-truth', 3), ('telling-truth', 5)), ('and', ('telling-truth', 5), ('lying', 2)), ('->', ('telling-truth', 2), ('telling-truth', 1)), ('telling-truth', 4))", "index": 746}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Jack, Sophia, Noah, Charlotte, and Harper. \"Noah is a knave if and only if Harper is a knave,\" Emily claimed. Jack stated, \"Emily is not a knave\". \"Emily is a knave and Jack is a knave,\" Sophia declared. Noah told you that If Charlotte is a knave then Harper is a knave. Charlotte was heard saying, \"Jack is a knave\". According to Harper, \"Noah is a knight and Sophia is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Jack", "Sophia", "Noah", "Charlotte", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Emily is a knave, Jack is a knave, Sophia is a knight, Noah is a knight, Charlotte is a knight, and Harper is a knave.", "solution_text_format": "(1) Emily is a knave\n(2) Jack is a knave\n(3) Sophia is a knight\n(4) Noah is a knight\n(5) Charlotte is a knight\n(6) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Noah is a knave if and only if Harper is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Charlotte is a knave then Harper is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Charlotte that Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that Emily is not a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Emily is not a knave.", "Harper cannot be a knight, because this would contradict the claim of Noah that If Charlotte is a knave then Harper is a knave.", "Harper cannot be a knave, because this would contradict the claim of Emily that Noah is a knave if and only if Harper is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of their own that Emily is not a knave.", "We have exhausted all possibilities for Jack and Charlotte, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that If Charlotte is a knave then Harper is a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Noah that If Charlotte is a knave then Harper is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Emily is not a knave.", "Harper cannot be a knight, because this would contradict the claim of Emily that Noah is a knave if and only if Harper is a knave.", "Harper cannot be a knave, because this would contradict the false claim of Noah that If Charlotte is a knave then Harper is a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of their own that Emily is not a knave.", "We have exhausted all possibilities for Jack, Charlotte, and Noah, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Harper is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Charlotte is a knave then Harper is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Emily is not a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Emily that Noah is a knave if and only if Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Noah is a knight and Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Emily is a knave and Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 5)), ('not', ('lying', 0)), ('and', ('lying', 0), ('lying', 1)), ('->', ('lying', 4), ('lying', 5)), ('lying', 1), ('and', ('telling-truth', 3), ('lying', 2)))", "index": 747}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Victoria, Isabella, Sophia, Aiden, and Emily. Liam expressed that Isabella is a knight if and only if Sophia is a knave. Victoria asserted: \"If Sophia is a knight then Sophia is a knave\". Isabella told you that If Sophia is a knight then Aiden is a knight. Sophia noted, \"If Aiden is a knave then Liam is a knave\". \"Sophia is a knight if and only if Liam is a knave,\" Aiden mentioned. According to Emily, \"Victoria is a knight if and only if Liam is a knight\". So who is a knight and who is a knave?", "names": ["Liam", "Victoria", "Isabella", "Sophia", "Aiden", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Liam is a knave, Victoria is a knave, Isabella is a knight, Sophia is a knight, Aiden is a knight, and Emily is a knight.", "solution_text_format": "(1) Liam is a knave\n(2) Victoria is a knave\n(3) Isabella is a knight\n(4) Sophia is a knight\n(5) Aiden is a knight\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Sophia is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Sophia is a knight then Aiden is a knight.", "Sophia cannot be a knight, because this would contradict the claim of Liam that Isabella is a knight if and only if Sophia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Aiden is a knave then Liam is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Sophia that If Aiden is a knave then Liam is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight if and only if Liam is a knave.", "We have exhausted all possibilities for Aiden and Sophia, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that If Sophia is a knight then Aiden is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Aiden is a knave then Liam is a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Isabella that If Sophia is a knight then Aiden is a knight.", "Aiden cannot be a knave, because this would contradict the claim of Sophia that If Aiden is a knave then Liam is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Liam that Isabella is a knight if and only if Sophia is a knave.", "We have exhausted all possibilities for Sophia and Isabella, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Sophia is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that If Sophia is a knight then Aiden is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Aiden is a knave then Liam is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Liam is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that If Sophia is a knight then Sophia is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Sophia is a knight then Sophia is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 3)), ('->', ('telling-truth', 3), ('lying', 3)), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('lying', 4), ('lying', 0)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)))", "index": 748}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Harper, Noah, Ella, Mia, and Zoey. \"Ella is a knight or Harper is a knight\" - Emily. In a statement by Harper: \"If Noah is a knave then Emily is a knight\". Noah remarked, \"Ella is a knight or Noah is a knight\". Ella told you that Noah is a knave. Mia was heard saying, \"Noah is a knight if and only if Ella is a knight\". Zoey said that If Mia is a knave then Noah is a knave. So who is a knight and who is a knave?", "names": ["Emily", "Harper", "Noah", "Ella", "Mia", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Emily is a knight, Harper is a knight, Noah is a knight, Ella is a knave, Mia is a knave, and Zoey is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Harper is a knight\n(3) Noah is a knight\n(4) Ella is a knave\n(5) Mia is a knave\n(6) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Ella is a knight or Harper is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Ella that Noah is a knave.", "Noah cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Noah is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Ella is a knight or Noah is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Noah is a knave then Emily is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Noah is a knight if and only if Ella is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Ella is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that If Mia is a knave then Noah is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Mia is a knave then Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 1)), ('->', ('lying', 2), ('telling-truth', 0)), ('or', ('telling-truth', 3), ('telling-truth', 2)), ('lying', 2), ('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('->', ('lying', 4), ('lying', 2)))", "index": 749}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Chloe, Emma, William, James, and Olivia. \"Olivia is not a knight\" - Samuel. Chloe noted, \"William is a knight\". \"Olivia is not a knight,\" Emma mentioned. In William's words: \"Samuel is a knight and Samuel is a knave\". James stated, \"William is not a knave\". Olivia told you that James is a knight and Emma is a knight. So who is a knight and who is a knave?", "names": ["Samuel", "Chloe", "Emma", "William", "James", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Samuel is a knight, Chloe is a knave, Emma is a knight, William is a knave, James is a knave, and Olivia is a knave.", "solution_text_format": "(1) Samuel is a knight\n(2) Chloe is a knave\n(3) Emma is a knight\n(4) William is a knave\n(5) James is a knave\n(6) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Olivia is not a knight.", "Olivia cannot be a knight, because this would contradict the claim of Samuel that Olivia is not a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that James is a knight and Emma is a knight.", "Assume James is a knight. No contradiction is found in their claim that William is not a knave.", "William cannot be a knight, because this would contradict the claim of their own that Samuel is a knight and Samuel is a knave.", "William cannot be a knave, because this would contradict the claim of James that William is not a knave.", "We have exhausted all possibilities for William, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that William is not a knave.", "William cannot be a knight, because this would contradict the claim of their own that Samuel is a knight and Samuel is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Samuel is a knight and Samuel is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Olivia is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that William is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('telling-truth', 3), ('not', ('telling-truth', 5)), ('and', ('telling-truth', 0), ('lying', 0)), ('not', ('lying', 3)), ('and', ('telling-truth', 4), ('telling-truth', 2)))", "index": 750}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Emily, Daniel, Mia, Henry, and Jackson. According to Sophia, \"Emily is a knight\". \"If Sophia is a knave then Mia is a knave,\" Emily mentioned. Daniel said that If Emily is a knave then Emily is a knight. \"If Jackson is a knight then Emily is a knave,\" Mia mentioned. Henry expressed that Henry is a knight or Mia is a knight. Jackson asserted: \"Mia is a knight or Daniel is a knave\". So who is a knight and who is a knave?", "names": ["Sophia", "Emily", "Daniel", "Mia", "Henry", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Sophia is a knave, Emily is a knave, Daniel is a knave, Mia is a knight, Henry is a knight, and Jackson is a knight.", "solution_text_format": "(1) Sophia is a knave\n(2) Emily is a knave\n(3) Daniel is a knave\n(4) Mia is a knight\n(5) Henry is a knight\n(6) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Sophia is a knave then Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Jackson is a knight then Emily is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Mia that If Jackson is a knight then Emily is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Mia is a knight or Daniel is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that If Jackson is a knight then Emily is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Mia is a knight or Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Jackson that Mia is a knight or Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Emily is a knave then Emily is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the false claim of Mia that If Jackson is a knight then Emily is a knave.", "We have exhausted all possibilities for Jackson and Mia, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Sophia that Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Sophia that Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that If Sophia is a knave then Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Jackson is a knight then Emily is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Mia is a knight or Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that If Emily is a knave then Emily is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that If Emily is a knave then Emily is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Henry is a knight or Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('->', ('lying', 0), ('lying', 3)), ('->', ('lying', 1), ('telling-truth', 1)), ('->', ('telling-truth', 5), ('lying', 1)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('or', ('telling-truth', 3), ('lying', 2)))", "index": 751}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Isabella, Ava, Benjamin, Logan, and Alexander. Victoria remarked, \"Benjamin is a knave and Alexander is a knave\". Isabella commented, \"Benjamin is a knave or Victoria is a knight\". \"Benjamin is a knave or Logan is a knave,\" Ava mentioned. Benjamin told you that Victoria is a knave or Logan is a knight. According to Logan, \"Alexander is a knight and Ava is a knave\". \"Alexander is a knight if and only if Benjamin is a knave,\" Alexander mentioned. So who is a knight and who is a knave?", "names": ["Victoria", "Isabella", "Ava", "Benjamin", "Logan", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Victoria is a knight, Isabella is a knight, Ava is a knight, Benjamin is a knave, Logan is a knave, and Alexander is a knave.", "solution_text_format": "(1) Victoria is a knight\n(2) Isabella is a knight\n(3) Ava is a knight\n(4) Benjamin is a knave\n(5) Logan is a knave\n(6) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Benjamin is a knave and Alexander is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Victoria that Benjamin is a knave and Alexander is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Victoria is a knave or Logan is a knight.", "Logan cannot be a knight, because this would contradict the false claim of Benjamin that Victoria is a knave or Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Alexander is a knight and Ava is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Victoria that Benjamin is a knave and Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Benjamin is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Benjamin is a knave or Logan is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Benjamin is a knave or Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 5)), ('or', ('lying', 3), ('telling-truth', 0)), ('or', ('lying', 3), ('lying', 4)), ('or', ('lying', 0), ('telling-truth', 4)), ('and', ('telling-truth', 5), ('lying', 2)), ('<=>', ('telling-truth', 5), ('lying', 3)))", "index": 752}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Sebastian, Matthew, Charlotte, Aiden, and Harper. Lucas said that If Charlotte is a knave then Harper is a knight. Sebastian stated, \"Harper is a knave and Lucas is a knave\". \"Lucas is a knight,\" Matthew mentioned. As Charlotte put it, \"Sebastian is a knight if and only if Lucas is a knight\". Aiden said, \"Charlotte is a knight.\" \"Aiden is a knight if and only if Aiden is a knave,\" Harper declared. So who is a knight and who is a knave?", "names": ["Lucas", "Sebastian", "Matthew", "Charlotte", "Aiden", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false], "solution_text": "Lucas is a knave, Sebastian is a knight, Matthew is a knave, Charlotte is a knave, Aiden is a knave, and Harper is a knave.", "solution_text_format": "(1) Lucas is a knave\n(2) Sebastian is a knight\n(3) Matthew is a knave\n(4) Charlotte is a knave\n(5) Aiden is a knave\n(6) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that If Charlotte is a knave then Harper is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Lucas is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Lucas is a knave.", "Sebastian cannot be a knave, because this would contradict the claim of Charlotte that Sebastian is a knight if and only if Lucas is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Lucas is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Lucas is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Harper is a knave and Lucas is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Aiden is a knight if and only if Aiden is a knave.", "Harper cannot be a knave, because this would contradict the claim of Lucas that If Charlotte is a knave then Harper is a knight.", "We have exhausted all possibilities for Harper, Sebastian, and Charlotte, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Charlotte is a knave then Harper is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Lucas that If Charlotte is a knave then Harper is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Lucas is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Harper is a knave and Lucas is a knave.", "Harper cannot be a knight, because this would contradict the false claim of Lucas that If Charlotte is a knave then Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Lucas is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 5)), ('and', ('lying', 5), ('lying', 0)), ('telling-truth', 0), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('telling-truth', 3), ('<=>', ('telling-truth', 4), ('lying', 4)))", "index": 753}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Oliver, Benjamin, Matthew, Aurora, and Scarlett. Abigail told you that Matthew is a knight and Aurora is a knave. \"Benjamin is a knight if and only if Scarlett is a knight,\" Oliver declared. In a statement by Benjamin: \"Oliver is a knight and Aurora is a knight\". Matthew expressed that Aurora is a knave and Benjamin is a knight. Aurora said, \"Abigail is not a knight.\" Scarlett commented, \"Oliver is a knight if and only if Aurora is a knave\". So who is a knight and who is a knave?", "names": ["Abigail", "Oliver", "Benjamin", "Matthew", "Aurora", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Abigail is a knave, Oliver is a knave, Benjamin is a knave, Matthew is a knave, Aurora is a knight, and Scarlett is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Oliver is a knave\n(3) Benjamin is a knave\n(4) Matthew is a knave\n(5) Aurora is a knight\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Matthew is a knight and Aurora is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Aurora is a knave and Benjamin is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Abigail that Matthew is a knight and Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Oliver is a knight and Aurora is a knight.", "Benjamin cannot be a knave, because this would contradict the claim of Matthew that Aurora is a knave and Benjamin is a knight.", "We have exhausted all possibilities for Benjamin and Aurora, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Abigail that Matthew is a knight and Aurora is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Matthew is a knight and Aurora is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Aurora is a knave and Benjamin is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Matthew that Aurora is a knave and Benjamin is a knight.", "Aurora cannot be a knave, because this would contradict the false claim of Abigail that Matthew is a knight and Aurora is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Aurora is a knave and Benjamin is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Oliver is a knight and Aurora is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Oliver is a knight if and only if Aurora is a knave.", "Scarlett cannot be a knave, because this would contradict the claim of Oliver that Benjamin is a knight if and only if Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Benjamin that Oliver is a knight and Aurora is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Oliver is a knight and Aurora is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Benjamin that Oliver is a knight and Aurora is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 4)), ('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('and', ('telling-truth', 1), ('telling-truth', 4)), ('and', ('lying', 4), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('lying', 4)))", "index": 754}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Ethan, Penelope, Jack, Riley, and Sebastian. \"Sebastian is not a knight,\" Ava declared. \"Riley is a knight,\" Ethan mentioned. Penelope noted, \"If Sebastian is a knave then Riley is a knave\". Jack remarked, \"Riley is a knight if and only if Sebastian is a knave\". Riley was heard saying, \"Sebastian is a knight if and only if Ethan is a knave\". In a statement by Sebastian: \"If Penelope is a knave then Jack is a knave\". So who is a knight and who is a knave?", "names": ["Ava", "Ethan", "Penelope", "Jack", "Riley", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "Ava is a knight, Ethan is a knight, Penelope is a knave, Jack is a knight, Riley is a knight, and Sebastian is a knave.", "solution_text_format": "(1) Ava is a knight\n(2) Ethan is a knight\n(3) Penelope is a knave\n(4) Jack is a knight\n(5) Riley is a knight\n(6) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Sebastian is not a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Ava that Sebastian is not a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Penelope is a knave then Jack is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Sebastian that If Penelope is a knave then Jack is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Sebastian is a knave then Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Riley is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Riley is a knight if and only if Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('telling-truth', 4), ('->', ('lying', 5), ('lying', 4)), ('<=>', ('telling-truth', 4), ('lying', 5)), ('<=>', ('telling-truth', 5), ('lying', 1)), ('->', ('lying', 2), ('lying', 3)))", "index": 755}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Logan, Ella, Jacob, Emma, and Chloe. Daniel was heard saying, \"If Logan is a knave then Emma is a knave\". \"Ella is a knave\" - Logan. Ella remarked, \"Daniel is a knight\". Jacob was heard saying, \"If Emma is a knight then Chloe is a knave\". In a statement by Emma: \"Emma is a knight or Logan is a knight\". Chloe noted, \"Jacob is a knight or Emma is a knave\". So who is a knight and who is a knave?", "names": ["Daniel", "Logan", "Ella", "Jacob", "Emma", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "Daniel is a knight, Logan is a knave, Ella is a knight, Jacob is a knight, Emma is a knave, and Chloe is a knight.", "solution_text_format": "(1) Daniel is a knight\n(2) Logan is a knave\n(3) Ella is a knight\n(4) Jacob is a knight\n(5) Emma is a knave\n(6) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that If Logan is a knave then Emma is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Logan that Ella is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Daniel is a knight.", "Emma cannot be a knight, because this would contradict the claim of Daniel that If Logan is a knave then Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Emma is a knight or Logan is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Emma is a knight then Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Jacob is a knight or Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('lying', 4)), ('lying', 2), ('telling-truth', 0), ('->', ('telling-truth', 4), ('lying', 5)), ('or', ('telling-truth', 4), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('lying', 4)))", "index": 756}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Owen, Aurora, Mason, Ella, and Oliver. \"Aurora is a knave or Owen is a knave\" - Emily. Owen said that If Oliver is a knave then Mason is a knave. \"Oliver is a knight if and only if Oliver is a knave,\" Aurora declared. Mason expressed that Ella is not a knave. \"If Emily is a knave then Oliver is a knave,\" Ella declared. Oliver said, \"Mason is a knave and Emily is a knight.\" So who is a knight and who is a knave?", "names": ["Emily", "Owen", "Aurora", "Mason", "Ella", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false], "solution_text": "Emily is a knight, Owen is a knave, Aurora is a knave, Mason is a knight, Ella is a knight, and Oliver is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Owen is a knave\n(3) Aurora is a knave\n(4) Mason is a knight\n(5) Ella is a knight\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Aurora is a knave or Owen is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Oliver is a knight if and only if Oliver is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Mason is a knave and Emily is a knight.", "Mason cannot be a knight, because this would contradict the claim of Oliver that Mason is a knave and Emily is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the false claim of Mason that Ella is not a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Emily is a knave then Oliver is a knave.", "We have exhausted all possibilities for Ella and Mason, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Mason is a knave and Emily is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Emily is a knave then Oliver is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that If Oliver is a knave then Mason is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that If Oliver is a knave then Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('lying', 1)), ('->', ('lying', 5), ('lying', 3)), ('<=>', ('telling-truth', 5), ('lying', 5)), ('not', ('lying', 4)), ('->', ('lying', 0), ('lying', 5)), ('and', ('lying', 3), ('telling-truth', 0)))", "index": 757}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Mason, Jacob, Noah, William, and Ava. David stated, \"If Ava is a knight then Ava is a knave\". According to Mason, \"Jacob is not a knave\". \"William is a knight if and only if Noah is a knight,\" Jacob mentioned. Noah said that William is not a knave. In William's words: \"Jacob is a knave\". Ava stated, \"Mason is a knight and William is a knight\". So who is a knight and who is a knave?", "names": ["David", "Mason", "Jacob", "Noah", "William", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "David is a knight, Mason is a knight, Jacob is a knight, Noah is a knave, William is a knave, and Ava is a knave.", "solution_text_format": "(1) David is a knight\n(2) Mason is a knight\n(3) Jacob is a knight\n(4) Noah is a knave\n(5) William is a knave\n(6) Ava is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that If Ava is a knight then Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of David that If Ava is a knight then Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Mason is a knight and William is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Jacob is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that William is a knight if and only if Noah is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Jacob is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Noah cannot be a knight, because this would contradict the claim of Jacob that William is a knight if and only if Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that William is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 5)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 3)), ('not', ('lying', 4)), ('lying', 2), ('and', ('telling-truth', 1), ('telling-truth', 4)))", "index": 758}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Ava, Daniel, Isabella, Ella, and Amelia. \"Isabella is a knave,\" Benjamin mentioned. In a statement by Ava: \"Amelia is a knave or Benjamin is a knight\". \"Benjamin is a knave and Amelia is a knave,\" Daniel mentioned. Isabella said that Amelia is a knave and Benjamin is a knight. Ella commented, \"If Benjamin is a knave then Isabella is a knave\". Amelia was heard saying, \"Ella is a knight or Ella is a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Ava", "Daniel", "Isabella", "Ella", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "Benjamin is a knight, Ava is a knight, Daniel is a knave, Isabella is a knave, Ella is a knight, and Amelia is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Ava is a knight\n(3) Daniel is a knave\n(4) Isabella is a knave\n(5) Ella is a knight\n(6) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Benjamin that Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Amelia is a knave and Benjamin is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Ella is a knight or Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Benjamin is a knave then Isabella is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Amelia is a knave or Benjamin is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave and Amelia is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Benjamin is a knave and Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('or', ('lying', 5), ('telling-truth', 0)), ('and', ('lying', 0), ('lying', 5)), ('and', ('lying', 5), ('telling-truth', 0)), ('->', ('lying', 0), ('lying', 3)), ('or', ('telling-truth', 4), ('lying', 4)))", "index": 759}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Sebastian, Jackson, Emma, Penelope, and Alexander. As Riley put it, \"Jackson is a knave\". Sebastian commented, \"Penelope is a knight and Jackson is a knight\". In Jackson's words: \"Penelope is not a knight\". Emma was heard saying, \"Sebastian is a knave or Riley is a knave\". Penelope expressed that Sebastian is a knight and Riley is a knight. In a statement by Alexander: \"Alexander is a knight or Riley is a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Sebastian", "Jackson", "Emma", "Penelope", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Riley is a knave, Sebastian is a knave, Jackson is a knight, Emma is a knight, Penelope is a knave, and Alexander is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Sebastian is a knave\n(3) Jackson is a knight\n(4) Emma is a knight\n(5) Penelope is a knave\n(6) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Riley that Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Sebastian is a knight and Riley is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Penelope is a knight and Jackson is a knight.", "Sebastian cannot be a knave, because this would contradict the claim of Penelope that Sebastian is a knight and Riley is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the false claim of Jackson that Penelope is not a knight.", "We have exhausted all possibilities for Penelope and Jackson, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Jackson that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sebastian is a knight and Riley is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Penelope is a knight and Jackson is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Penelope is a knight and Jackson is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Sebastian is a knave or Riley is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Alexander is a knight or Riley is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('and', ('telling-truth', 4), ('telling-truth', 2)), ('not', ('telling-truth', 4)), ('or', ('lying', 1), ('lying', 0)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 5), ('lying', 0)))", "index": 760}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Daniel, William, Sofia, Grace, and Jacob. \"Sofia is a knave,\" Mason mentioned. Daniel stated, \"Jacob is a knight or Mason is a knave\". William expressed that Mason is a knave or Grace is a knave. \"William is not a knight\" - Sofia. Grace noted, \"Sofia is a knight\". Jacob told you that Grace is a knight or William is a knave. So who is a knight and who is a knave?", "names": ["Mason", "Daniel", "William", "Sofia", "Grace", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Mason is a knight, Daniel is a knave, William is a knight, Sofia is a knave, Grace is a knave, and Jacob is a knave.", "solution_text_format": "(1) Mason is a knight\n(2) Daniel is a knave\n(3) William is a knight\n(4) Sofia is a knave\n(5) Grace is a knave\n(6) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Mason that Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that William is not a knight.", "Assume William is a knight. No contradiction is found in their claim that Mason is a knave or Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of William that Mason is a knave or Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Sofia is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Jacob is a knight or Mason is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Grace is a knight or William is a knave.", "Jacob cannot be a knave, because this would contradict the claim of Daniel that Jacob is a knight or Mason is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Jacob is a knight or Mason is a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Daniel that Jacob is a knight or Mason is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Grace is a knight or William is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('or', ('telling-truth', 5), ('lying', 0)), ('or', ('lying', 0), ('lying', 4)), ('not', ('telling-truth', 2)), ('telling-truth', 3), ('or', ('telling-truth', 4), ('lying', 2)))", "index": 761}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Grace, Lily, Samuel, David, and Daniel. \"Grace is a knight or David is a knave\" - James. Grace told you that If David is a knave then Samuel is a knave. Lily said that If James is a knight then Daniel is a knight. Samuel asserted: \"Samuel is a knight and Grace is a knave\". David stated, \"Lily is a knave or Samuel is a knight\". Daniel said that David is a knave and James is a knave. So who is a knight and who is a knave?", "names": ["James", "Grace", "Lily", "Samuel", "David", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false], "solution_text": "James is a knight, Grace is a knight, Lily is a knave, Samuel is a knave, David is a knight, and Daniel is a knave.", "solution_text_format": "(1) James is a knight\n(2) Grace is a knight\n(3) Lily is a knave\n(4) Samuel is a knave\n(5) David is a knight\n(6) Daniel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Grace is a knight or David is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If David is a knave then Samuel is a knave.", "Assume David is a knight. No contradiction is found in their claim that Lily is a knave or Samuel is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If James is a knight then Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that David is a knave and James is a knave.", "Daniel cannot be a knave, because this would contradict the claim of Lily that If James is a knight then Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that If James is a knight then Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Lily that If James is a knight then Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that David is a knave and James is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Samuel is a knight and Grace is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Samuel is a knight and Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 4)), ('->', ('lying', 4), ('lying', 3)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('telling-truth', 3), ('lying', 1)), ('or', ('lying', 2), ('telling-truth', 3)), ('and', ('lying', 4), ('lying', 0)))", "index": 762}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Abigail, Charlotte, Benjamin, Chloe, and Scarlett. Alexander noted, \"Abigail is not a knave\". \"If Charlotte is a knight then Scarlett is a knight,\" Abigail mentioned. Charlotte expressed that Alexander is not a knight. In Benjamin's words: \"Benjamin is a knight and Abigail is a knave\". \"Abigail is a knave and Charlotte is a knight,\" Chloe declared. According to Scarlett, \"Chloe is a knight and Alexander is a knave\". So who is a knight and who is a knave?", "names": ["Alexander", "Abigail", "Charlotte", "Benjamin", "Chloe", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Alexander is a knight, Abigail is a knight, Charlotte is a knave, Benjamin is a knave, Chloe is a knave, and Scarlett is a knave.", "solution_text_format": "(1) Alexander is a knight\n(2) Abigail is a knight\n(3) Charlotte is a knave\n(4) Benjamin is a knave\n(5) Chloe is a knave\n(6) Scarlett is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Charlotte is a knight then Scarlett is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Alexander is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Chloe is a knight and Alexander is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Chloe is a knight and Alexander is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Charlotte is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Abigail is a knave and Charlotte is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight and Abigail is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Benjamin is a knight and Abigail is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('->', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 3), ('lying', 1)), ('and', ('lying', 1), ('telling-truth', 2)), ('and', ('telling-truth', 4), ('lying', 0)))", "index": 763}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Amelia, Emily, Elizabeth, Mason, and Jacob. \"Jacob is a knight or Amelia is a knave,\" Aria declared. According to Amelia, \"Elizabeth is not a knight\". Emily expressed that Aria is a knight or Elizabeth is a knight. Elizabeth expressed that Mason is a knight or Jacob is a knave. Mason stated, \"If Aria is a knight then Jacob is a knight\". \"If Emily is a knave then Aria is a knave,\" Jacob declared. So who is a knight and who is a knave?", "names": ["Aria", "Amelia", "Emily", "Elizabeth", "Mason", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Aria is a knight, Amelia is a knave, Emily is a knight, Elizabeth is a knight, Mason is a knight, and Jacob is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) Amelia is a knave\n(3) Emily is a knight\n(4) Elizabeth is a knight\n(5) Mason is a knight\n(6) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Jacob is a knight or Amelia is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Emily is a knave then Aria is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Aria is a knight or Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Mason is a knight or Jacob is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Aria is a knight then Jacob is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Elizabeth is not a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Elizabeth is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('lying', 1)), ('not', ('telling-truth', 3)), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('telling-truth', 4), ('lying', 5)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('->', ('lying', 2), ('lying', 0)))", "index": 764}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Michael, Aurora, Grace, Daniel, and Avery. Logan said that Grace is a knight if and only if Michael is a knave. \"If Avery is a knave then Aurora is a knight,\" Michael mentioned. As Aurora put it, \"If Logan is a knave then Avery is a knave\". Grace remarked, \"Avery is a knight if and only if Daniel is a knave\". Daniel commented, \"Michael is not a knave\". In Avery's words: \"If Michael is a knight then Aurora is a knave\". So who is a knight and who is a knave?", "names": ["Logan", "Michael", "Aurora", "Grace", "Daniel", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Logan is a knave, Michael is a knight, Aurora is a knight, Grace is a knight, Daniel is a knight, and Avery is a knave.", "solution_text_format": "(1) Logan is a knave\n(2) Michael is a knight\n(3) Aurora is a knight\n(4) Grace is a knight\n(5) Daniel is a knight\n(6) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Grace is a knight if and only if Michael is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Avery is a knight if and only if Daniel is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Michael is a knight then Aurora is a knave.", "Michael cannot be a knight, because this would contradict the claim of Logan that Grace is a knight if and only if Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that If Avery is a knave then Aurora is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Michael is a knight then Aurora is a knave.", "Michael cannot be a knight, because this would contradict the claim of Logan that Grace is a knight if and only if Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of Avery that If Michael is a knight then Aurora is a knave.", "We have exhausted all possibilities for Michael and Avery, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Daniel is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Michael is a knight then Aurora is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Avery is a knave then Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Avery that If Michael is a knight then Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Logan is a knave then Avery is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Logan that Grace is a knight if and only if Michael is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Michael is a knight then Aurora is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Avery is a knave then Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Logan is a knave then Avery is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Grace that Avery is a knight if and only if Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Michael is not a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Michael that If Avery is a knave then Aurora is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the claim of Logan that Grace is a knight if and only if Michael is a knave.", "We have exhausted all possibilities for Michael, Avery, and Grace, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Michael is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Avery is a knight if and only if Daniel is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Michael is a knight then Aurora is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Avery is a knave then Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that If Logan is a knave then Avery is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that If Logan is a knave then Avery is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Grace that Avery is a knight if and only if Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Michael is not a knave.", "We have exhausted all possibilities for Daniel and Aurora, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the false claim of Logan that Grace is a knight if and only if Michael is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that If Michael is a knight then Aurora is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Avery is a knave then Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Logan is a knave then Avery is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Michael is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 1)), ('->', ('lying', 5), ('telling-truth', 2)), ('->', ('lying', 0), ('lying', 5)), ('<=>', ('telling-truth', 5), ('lying', 4)), ('not', ('lying', 1)), ('->', ('telling-truth', 1), ('lying', 2)))", "index": 765}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Isabella, Scarlett, Logan, Liam, and William. According to Mia, \"Logan is a knight if and only if Isabella is a knight\". Isabella was heard saying, \"Mia is a knave if and only if Isabella is a knight\". \"Mia is a knave,\" Scarlett claimed. Logan noted, \"If Mia is a knight then Logan is a knight\". \"Scarlett is a knight or Logan is a knight,\" Liam declared. William stated, \"William is a knight or Liam is a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Isabella", "Scarlett", "Logan", "Liam", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Mia is a knave, Isabella is a knave, Scarlett is a knight, Logan is a knight, Liam is a knight, and William is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Isabella is a knave\n(3) Scarlett is a knight\n(4) Logan is a knight\n(5) Liam is a knight\n(6) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Logan is a knight if and only if Isabella is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Mia is a knight then Logan is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Mia is a knave if and only if Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the claim of Mia that Logan is a knight if and only if Isabella is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that If Mia is a knight then Logan is a knight.", "Isabella cannot be a knight, because this would contradict the claim of Mia that Logan is a knight if and only if Isabella is a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Mia is a knave if and only if Isabella is a knight.", "We have exhausted all possibilities for Isabella and Logan, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Isabella is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Mia is a knight then Logan is a knight.", "Isabella cannot be a knight, because this would contradict the false claim of Mia that Logan is a knight if and only if Isabella is a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Isabella is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Mia is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Scarlett is a knight or Logan is a knight.", "Assume William is a knight. No contradiction is found in their claim that William is a knight or Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('telling-truth', 1)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('lying', 0), ('->', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('telling-truth', 2), ('telling-truth', 3)), ('or', ('telling-truth', 5), ('telling-truth', 4)))", "index": 766}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Penelope, William, Alexander, Elizabeth, and Emma. Mia remarked, \"Elizabeth is a knave or William is a knave\". Penelope asserted: \"William is a knight if and only if William is a knave\". \"Mia is a knight,\" William claimed. Alexander said, \"Mia is a knight and Mia is a knave.\" Elizabeth commented, \"William is a knight if and only if Penelope is a knight\". \"William is a knight and Penelope is a knave,\" Emma declared. So who is a knight and who is a knave?", "names": ["Mia", "Penelope", "William", "Alexander", "Elizabeth", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Mia is a knight, Penelope is a knave, William is a knight, Alexander is a knave, Elizabeth is a knave, and Emma is a knight.", "solution_text_format": "(1) Mia is a knight\n(2) Penelope is a knave\n(3) William is a knight\n(4) Alexander is a knave\n(5) Elizabeth is a knave\n(6) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Elizabeth is a knave or William is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that William is a knight if and only if Penelope is a knight.", "William cannot be a knight, because this would contradict the claim of Mia that Elizabeth is a knave or William is a knave.", "William cannot be a knave, because this would contradict the false claim of their own that Mia is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that William is a knight if and only if Penelope is a knight.", "Assume William is a knight. No contradiction is found in their claim that Mia is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that William is a knight if and only if William is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that William is a knight if and only if William is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Mia is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Mia is a knight and Mia is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that William is a knight and Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('lying', 2)), ('<=>', ('telling-truth', 2), ('lying', 2)), ('telling-truth', 0), ('and', ('telling-truth', 0), ('lying', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('and', ('telling-truth', 2), ('lying', 1)))", "index": 767}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Aurora, David, Sophia, Victoria, and Matthew. Jack said, \"Matthew is a knight.\" According to Aurora, \"Matthew is a knight and Victoria is a knave\". In David's words: \"Sophia is not a knave\". Sophia expressed that Victoria is a knave. Victoria stated, \"Matthew is a knave and Aurora is a knave\". Matthew noted, \"Victoria is a knight or Victoria is a knave\". So who is a knight and who is a knave?", "names": ["Jack", "Aurora", "David", "Sophia", "Victoria", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Jack is a knight, Aurora is a knight, David is a knight, Sophia is a knight, Victoria is a knave, and Matthew is a knight.", "solution_text_format": "(1) Jack is a knight\n(2) Aurora is a knight\n(3) David is a knight\n(4) Sophia is a knight\n(5) Victoria is a knave\n(6) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Victoria is a knight or Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of their own that Matthew is a knave and Aurora is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Matthew is a knave and Aurora is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Matthew is a knight and Victoria is a knave.", "Assume David is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Victoria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('and', ('telling-truth', 5), ('lying', 4)), ('not', ('lying', 3)), ('lying', 4), ('and', ('lying', 5), ('lying', 1)), ('or', ('telling-truth', 4), ('lying', 4)))", "index": 768}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Jack, Luke, Benjamin, Avery, and Joseph. Chloe said, \"Luke is not a knight.\" \"Benjamin is a knave or Benjamin is a knight,\" Jack declared. Luke stated, \"Joseph is a knave\". In a statement by Benjamin: \"Luke is not a knight\". According to Avery, \"If Luke is a knave then Luke is a knight\". \"Luke is a knave if and only if Benjamin is a knight\" - Joseph. So who is a knight and who is a knave?", "names": ["Chloe", "Jack", "Luke", "Benjamin", "Avery", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Chloe is a knight, Jack is a knight, Luke is a knave, Benjamin is a knight, Avery is a knave, and Joseph is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Jack is a knight\n(3) Luke is a knave\n(4) Benjamin is a knight\n(5) Avery is a knave\n(6) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Chloe that Luke is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Luke is a knave if and only if Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Luke is not a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Benjamin is a knave or Benjamin is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that If Luke is a knave then Luke is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that If Luke is a knave then Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('or', ('lying', 3), ('telling-truth', 3)), ('lying', 5), ('not', ('telling-truth', 2)), ('->', ('lying', 2), ('telling-truth', 2)), ('<=>', ('lying', 2), ('telling-truth', 3)))", "index": 769}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Scarlett, Ella, Daniel, Amelia, and Aurora. Victoria said that Scarlett is a knight. Scarlett said, \"Ella is a knave.\" \"Amelia is a knave\" - Ella. Daniel commented, \"Aurora is a knave if and only if Victoria is a knave\". Amelia expressed that Scarlett is a knave if and only if Victoria is a knight. Aurora told you that Victoria is a knight and Ella is a knave. So who is a knight and who is a knave?", "names": ["Victoria", "Scarlett", "Ella", "Daniel", "Amelia", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Victoria is a knave, Scarlett is a knave, Ella is a knight, Daniel is a knight, Amelia is a knave, and Aurora is a knave.", "solution_text_format": "(1) Victoria is a knave\n(2) Scarlett is a knave\n(3) Ella is a knight\n(4) Daniel is a knight\n(5) Amelia is a knave\n(6) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Scarlett that Ella is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave if and only if Victoria is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of Ella that Amelia is a knave.", "We have exhausted all possibilities for Amelia and Ella, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of Victoria that Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Victoria that Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Ella that Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Victoria is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Victoria is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Daniel that Aurora is a knave if and only if Victoria is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Victoria is a knight and Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('lying', 2), ('lying', 4), ('<=>', ('lying', 5), ('lying', 0)), ('<=>', ('lying', 1), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('lying', 2)))", "index": 770}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Sofia, Amelia, Jack, Zoey, and Daniel. \"Sofia is a knave if and only if Daniel is a knave\" - Matthew. Sofia said that Matthew is a knight. Amelia expressed that Zoey is a knave. According to Jack, \"Matthew is a knave and Sofia is a knight\". Zoey asserted: \"Matthew is not a knave\". Daniel stated, \"Matthew is a knight or Sofia is a knight\". So who is a knight and who is a knave?", "names": ["Matthew", "Sofia", "Amelia", "Jack", "Zoey", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "Matthew is a knight, Sofia is a knight, Amelia is a knave, Jack is a knave, Zoey is a knight, and Daniel is a knight.", "solution_text_format": "(1) Matthew is a knight\n(2) Sofia is a knight\n(3) Amelia is a knave\n(4) Jack is a knave\n(5) Zoey is a knight\n(6) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Daniel is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Matthew is a knight or Sofia is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Amelia that Zoey is a knave.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Matthew is not a knave.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Matthew is a knave and Sofia is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Matthew is a knave and Sofia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 5)), ('telling-truth', 0), ('lying', 4), ('and', ('lying', 0), ('telling-truth', 1)), ('not', ('lying', 0)), ('or', ('telling-truth', 0), ('telling-truth', 1)))", "index": 771}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Ava, Mason, Logan, Riley, and Ella. \"Logan is a knave and Ava is a knight,\" Lucas claimed. Ava said that If Logan is a knight then Riley is a knight. Mason told you that Ella is a knave if and only if Logan is a knight. Logan commented, \"If Ella is a knight then Ava is a knight\". \"Lucas is not a knave,\" Riley declared. Ella asserted: \"Riley is a knave if and only if Ava is a knight\". So who is a knight and who is a knave?", "names": ["Lucas", "Ava", "Mason", "Logan", "Riley", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Lucas is a knave, Ava is a knave, Mason is a knight, Logan is a knight, Riley is a knave, and Ella is a knave.", "solution_text_format": "(1) Lucas is a knave\n(2) Ava is a knave\n(3) Mason is a knight\n(4) Logan is a knight\n(5) Riley is a knave\n(6) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Logan is a knave and Ava is a knight.", "Logan cannot be a knight, because this would contradict the claim of Lucas that Logan is a knave and Ava is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that If Ella is a knight then Ava is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Riley is a knave if and only if Ava is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Ava cannot be a knight, because this would contradict the false claim of Logan that If Ella is a knight then Ava is a knight.", "Ava cannot be a knave, because this would contradict the claim of Lucas that Logan is a knave and Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Riley.", "Riley cannot be a knave, because this would contradict the false claim of their own that Lucas is not a knave.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of Logan that If Ella is a knight then Ava is a knight.", "We have exhausted all possibilities for Ella and Logan, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Logan is a knave and Ava is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Ella is a knight then Ava is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Riley is a knave if and only if Ava is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Lucas is not a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that If Logan is a knight then Riley is a knight.", "Ava cannot be a knave, because this would contradict the claim of Logan that If Ella is a knight then Ava is a knight.", "We have exhausted all possibilities for Ava and Riley, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Ava is a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Lucas is not a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that If Logan is a knight then Riley is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that If Logan is a knight then Riley is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Ella is a knave if and only if Logan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 1)), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('<=>', ('lying', 5), ('telling-truth', 3)), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('not', ('lying', 0)), ('<=>', ('lying', 4), ('telling-truth', 1)))", "index": 772}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Emma, Evelyn, Aiden, Daniel, and Benjamin. \"If James is a knight then Emma is a knight\" - James. \"Evelyn is a knave and Aiden is a knave,\" Emma mentioned. Evelyn asserted: \"If Emma is a knight then Evelyn is a knight\". Aiden was heard saying, \"Aiden is a knight and Emma is a knave\". Daniel told you that If Evelyn is a knight then Aiden is a knight. Benjamin expressed that Evelyn is a knave if and only if James is a knight. So who is a knight and who is a knave?", "names": ["James", "Emma", "Evelyn", "Aiden", "Daniel", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "James is a knight, Emma is a knight, Evelyn is a knave, Aiden is a knave, Daniel is a knight, and Benjamin is a knight.", "solution_text_format": "(1) James is a knight\n(2) Emma is a knight\n(3) Evelyn is a knave\n(4) Aiden is a knave\n(5) Daniel is a knight\n(6) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that If James is a knight then Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Evelyn is a knave and Aiden is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Emma that Evelyn is a knave and Aiden is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Emma is a knight then Evelyn is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Emma that Evelyn is a knave and Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aiden is a knight and Emma is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that If Evelyn is a knight then Aiden is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if James is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('and', ('lying', 2), ('lying', 3)), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('telling-truth', 3), ('lying', 1)), ('->', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('lying', 2), ('telling-truth', 0)))", "index": 773}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Chloe, Jack, Abigail, Joseph, and Ella. \"If Ella is a knight then Jack is a knight,\" Aria mentioned. \"Jack is a knight or Ella is a knave,\" Chloe mentioned. As Jack put it, \"Chloe is a knave and Ella is a knave\". In Abigail's words: \"Aria is a knave and Chloe is a knight\". Joseph noted, \"Chloe is a knight\". Ella remarked, \"Ella is a knight or Aria is a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Chloe", "Jack", "Abigail", "Joseph", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true], "solution_text": "Aria is a knave, Chloe is a knave, Jack is a knave, Abigail is a knave, Joseph is a knave, and Ella is a knight.", "solution_text_format": "(1) Aria is a knave\n(2) Chloe is a knave\n(3) Jack is a knave\n(4) Abigail is a knave\n(5) Joseph is a knave\n(6) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that If Ella is a knight then Jack is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Ella is a knight or Aria is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Chloe is a knave and Ella is a knave.", "Jack cannot be a knave, because this would contradict the claim of Aria that If Ella is a knight then Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Aria is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that If Ella is a knight then Jack is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Ella is a knight or Aria is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Aria that If Ella is a knight then Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Chloe is a knave and Ella is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that Jack is a knight or Ella is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Jack is a knight or Ella is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Aria is a knave and Chloe is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aria is a knave and Chloe is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Chloe is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('telling-truth', 2), ('lying', 5)), ('and', ('lying', 1), ('lying', 5)), ('and', ('lying', 0), ('telling-truth', 1)), ('telling-truth', 1), ('or', ('telling-truth', 5), ('telling-truth', 0)))", "index": 774}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Jackson, William, Penelope, Evelyn, and Matthew. Samuel stated, \"Penelope is a knight\". \"If Penelope is a knight then Evelyn is a knight,\" Jackson mentioned. William asserted: \"Jackson is a knave if and only if Jackson is a knight\". Penelope expressed that William is a knave or Matthew is a knight. In Evelyn's words: \"Matthew is a knave\". Matthew stated, \"Samuel is a knight\". So who is a knight and who is a knave?", "names": ["Samuel", "Jackson", "William", "Penelope", "Evelyn", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true], "solution_text": "Samuel is a knight, Jackson is a knave, William is a knave, Penelope is a knight, Evelyn is a knave, and Matthew is a knight.", "solution_text_format": "(1) Samuel is a knight\n(2) Jackson is a knave\n(3) William is a knave\n(4) Penelope is a knight\n(5) Evelyn is a knave\n(6) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that William is a knave or Matthew is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Jackson is a knave if and only if Jackson is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Penelope is a knight then Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Evelyn that Matthew is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Jackson that If Penelope is a knight then Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Penelope is a knight then Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Jackson that If Penelope is a knight then Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('<=>', ('lying', 1), ('telling-truth', 1)), ('or', ('lying', 2), ('telling-truth', 5)), ('lying', 5), ('telling-truth', 0))", "index": 775}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Aiden, Chloe, Aria, James, and Harper. Avery was heard saying, \"Aria is a knave or Aria is a knight\". Aiden asserted: \"Aiden is a knight or Aria is a knight\". \"James is not a knight,\" Chloe mentioned. Aria said, \"Aiden is a knave if and only if Aria is a knight.\" In a statement by James: \"If Aria is a knight then Harper is a knight\". Harper asserted: \"Aria is not a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Aiden", "Chloe", "Aria", "James", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false], "solution_text": "Avery is a knight, Aiden is a knave, Chloe is a knave, Aria is a knave, James is a knight, and Harper is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Aiden is a knave\n(3) Chloe is a knave\n(4) Aria is a knave\n(5) James is a knight\n(6) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Aria is a knave or Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Aria is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Aria that Aiden is a knave if and only if Aria is a knight.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Aiden is a knight or Aria is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Aria is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Aria that Aiden is a knave if and only if Aria is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aiden is a knight or Aria is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that James is not a knight.", "James cannot be a knight, because this would contradict the claim of Chloe that James is not a knight.", "James cannot be a knave, because this would contradict the false claim of their own that If Aria is a knight then Harper is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that James is not a knight.", "Assume James is a knight. No contradiction is found in their claim that If Aria is a knight then Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Aria is not a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Aria is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 3)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('not', ('telling-truth', 4)), ('<=>', ('lying', 1), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('telling-truth', 5)), ('not', ('lying', 3)))", "index": 776}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Jackson, Charlotte, Joseph, Aiden, and Grace. Scarlett remarked, \"Jackson is a knave or Charlotte is a knight\". Jackson was heard saying, \"If Charlotte is a knave then Grace is a knight\". Charlotte asserted: \"Charlotte is a knight and Scarlett is a knave\". According to Joseph, \"Aiden is a knight if and only if Jackson is a knave\". Aiden noted, \"If Grace is a knave then Joseph is a knave\". Grace said that Grace is a knight if and only if Scarlett is a knave. So who is a knight and who is a knave?", "names": ["Scarlett", "Jackson", "Charlotte", "Joseph", "Aiden", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true], "solution_text": "Scarlett is a knave, Jackson is a knight, Charlotte is a knave, Joseph is a knave, Aiden is a knight, and Grace is a knight.", "solution_text_format": "(1) Scarlett is a knave\n(2) Jackson is a knight\n(3) Charlotte is a knave\n(4) Joseph is a knave\n(5) Aiden is a knight\n(6) Grace is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Jackson is a knave or Charlotte is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Charlotte is a knave then Grace is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight and Scarlett is a knave.", "Charlotte cannot be a knave, because this would contradict the claim of Scarlett that Jackson is a knave or Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Charlotte is a knave then Grace is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Jackson that If Charlotte is a knave then Grace is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Charlotte is a knight and Scarlett is a knave.", "Grace cannot be a knight, because this would contradict the false claim of Jackson that If Charlotte is a knave then Grace is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that Grace is a knight if and only if Scarlett is a knave.", "We have exhausted all possibilities for Grace, Charlotte, and Jackson, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Jackson is a knave or Charlotte is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Charlotte is a knave then Grace is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Scarlett that Jackson is a knave or Charlotte is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Charlotte is a knight and Scarlett is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Grace is a knight if and only if Scarlett is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Jackson is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Joseph that Aiden is a knight if and only if Jackson is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that If Grace is a knave then Joseph is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Jackson is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Grace is a knave then Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 2)), ('->', ('lying', 2), ('telling-truth', 5)), ('and', ('telling-truth', 2), ('lying', 0)), ('<=>', ('telling-truth', 4), ('lying', 1)), ('->', ('lying', 5), ('lying', 3)), ('<=>', ('telling-truth', 5), ('lying', 0)))", "index": 777}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Noah, Evelyn, Ethan, James, and Michael. Samuel commented, \"Ethan is a knave and Noah is a knight\". Noah commented, \"Noah is a knight if and only if Evelyn is a knight\". Evelyn remarked, \"Samuel is a knight if and only if Michael is a knave\". In a statement by Ethan: \"Samuel is a knight or Noah is a knave\". \"Noah is not a knave,\" James declared. Michael noted, \"Evelyn is a knight or Ethan is a knight\". So who is a knight and who is a knave?", "names": ["Samuel", "Noah", "Evelyn", "Ethan", "James", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Samuel is a knave, Noah is a knave, Evelyn is a knight, Ethan is a knight, James is a knave, and Michael is a knight.", "solution_text_format": "(1) Samuel is a knave\n(2) Noah is a knave\n(3) Evelyn is a knight\n(4) Ethan is a knight\n(5) James is a knave\n(6) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Ethan is a knave and Noah is a knight.", "Ethan cannot be a knight, because this would contradict the claim of Samuel that Ethan is a knave and Noah is a knight.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight or Noah is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Ethan is a knave and Noah is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Samuel is a knight or Noah is a knave.", "Noah cannot be a knight, because this would contradict the claim of Ethan that Samuel is a knight or Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Evelyn is a knight or Ethan is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Noah is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Noah is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('<=>', ('telling-truth', 0), ('lying', 5)), ('or', ('telling-truth', 0), ('lying', 1)), ('not', ('lying', 1)), ('or', ('telling-truth', 2), ('telling-truth', 3)))", "index": 778}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Charlotte, Ella, Michael, Oliver, and Zoey. Mia expressed that Michael is a knight. \"Mia is not a knight\" - Charlotte. Ella expressed that Charlotte is a knight. \"Oliver is a knave or Oliver is a knight,\" Michael claimed. \"Mia is a knight if and only if Zoey is a knave,\" Oliver claimed. As Zoey put it, \"Ella is not a knave\". So who is a knight and who is a knave?", "names": ["Mia", "Charlotte", "Ella", "Michael", "Oliver", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false], "solution_text": "Mia is a knight, Charlotte is a knave, Ella is a knave, Michael is a knight, Oliver is a knight, and Zoey is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Charlotte is a knave\n(3) Ella is a knave\n(4) Michael is a knight\n(5) Oliver is a knight\n(6) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Oliver is a knave or Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Mia is a knight if and only if Zoey is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Oliver that Mia is a knight if and only if Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the false claim of Zoey that Ella is not a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Mia is not a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Mia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('not', ('telling-truth', 0)), ('telling-truth', 1), ('or', ('lying', 4), ('telling-truth', 4)), ('<=>', ('telling-truth', 0), ('lying', 5)), ('not', ('lying', 2)))", "index": 779}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Joseph, Grace, Sebastian, Benjamin, and Aiden. \"Benjamin is a knave,\" Henry claimed. According to Joseph, \"Sebastian is a knight and Sebastian is a knave\". As Grace put it, \"Sebastian is a knight and Aiden is a knave\". Sebastian told you that Joseph is not a knight. \"Henry is a knave if and only if Benjamin is a knight,\" Benjamin mentioned. Aiden told you that Henry is a knave if and only if Joseph is a knave. So who is a knight and who is a knave?", "names": ["Henry", "Joseph", "Grace", "Sebastian", "Benjamin", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Henry is a knave, Joseph is a knave, Grace is a knave, Sebastian is a knight, Benjamin is a knight, and Aiden is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Joseph is a knave\n(3) Grace is a knave\n(4) Sebastian is a knight\n(5) Benjamin is a knight\n(6) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Henry that Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Henry is a knave if and only if Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Benjamin is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Henry is a knave if and only if Benjamin is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Sebastian is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Sebastian is a knight and Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Joseph is not a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Sebastian is a knight and Aiden is a knave.", "Aiden cannot be a knight, because this would contradict the claim of Grace that Sebastian is a knight and Aiden is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Henry is a knave if and only if Joseph is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Sebastian is a knight and Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Henry is a knave if and only if Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('and', ('telling-truth', 3), ('lying', 3)), ('and', ('telling-truth', 3), ('lying', 5)), ('not', ('telling-truth', 1)), ('<=>', ('lying', 0), ('telling-truth', 4)), ('<=>', ('lying', 0), ('lying', 1)))", "index": 780}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Michael, Chloe, Daniel, Lucas, and Samuel. Mia said, \"Michael is a knight or Chloe is a knave.\" Michael told you that Chloe is a knight if and only if Samuel is a knight. As Chloe put it, \"Lucas is not a knave\". Daniel asserted: \"If Lucas is a knight then Samuel is a knave\". In a statement by Lucas: \"Samuel is a knave if and only if Michael is a knave\". Samuel remarked, \"Daniel is a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Michael", "Chloe", "Daniel", "Lucas", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true], "solution_text": "Mia is a knight, Michael is a knave, Chloe is a knave, Daniel is a knight, Lucas is a knave, and Samuel is a knight.", "solution_text_format": "(1) Mia is a knight\n(2) Michael is a knave\n(3) Chloe is a knave\n(4) Daniel is a knight\n(5) Lucas is a knave\n(6) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Michael is a knight or Chloe is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Samuel is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Michael is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that If Lucas is a knight then Samuel is a knave.", "Daniel cannot be a knave, because this would contradict the claim of Samuel that Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the claim of Michael that Chloe is a knight if and only if Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Chloe that Lucas is not a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Chloe that Lucas is not a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Michael is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Michael that Chloe is a knight if and only if Samuel is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Samuel that Daniel is a knight.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Lucas is a knight then Samuel is a knave.", "We have exhausted all possibilities for Daniel, Samuel, Lucas, and Chloe, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Samuel is a knight.", "Chloe cannot be a knight, because this would contradict the claim of Mia that Michael is a knight or Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Chloe that Lucas is not a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Michael is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Lucas is a knight then Samuel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 2)), ('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('lying', 4)), ('->', ('telling-truth', 4), ('lying', 5)), ('<=>', ('lying', 5), ('lying', 1)), ('telling-truth', 3))", "index": 781}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Benjamin, Harper, Ella, Sebastian, and Luke. \"If Sebastian is a knave then Sebastian is a knight,\" William claimed. \"Sebastian is a knave,\" Benjamin mentioned. Harper noted, \"If Luke is a knight then Benjamin is a knight\". \"Luke is a knight if and only if William is a knight\" - Ella. Sebastian expressed that Ella is not a knave. Luke said, \"Harper is a knight and Luke is a knight.\" So who is a knight and who is a knave?", "names": ["William", "Benjamin", "Harper", "Ella", "Sebastian", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "William is a knave, Benjamin is a knight, Harper is a knight, Ella is a knave, Sebastian is a knave, and Luke is a knight.", "solution_text_format": "(1) William is a knave\n(2) Benjamin is a knight\n(3) Harper is a knight\n(4) Ella is a knave\n(5) Sebastian is a knave\n(6) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that If Sebastian is a knave then Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Luke is a knight if and only if William is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Harper is a knight and Luke is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Luke is a knight then Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Harper that If Luke is a knight then Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Luke that Harper is a knight and Luke is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Ella that Luke is a knight if and only if William is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Sebastian that Ella is not a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of William that If Sebastian is a knave then Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that If Sebastian is a knave then Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of William that If Sebastian is a knave then Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the false claim of Sebastian that Ella is not a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Luke is a knight if and only if William is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Harper is a knight and Luke is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Luke is a knight then Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('telling-truth', 4)), ('lying', 4), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('<=>', ('telling-truth', 5), ('telling-truth', 0)), ('not', ('lying', 3)), ('and', ('telling-truth', 2), ('telling-truth', 5)))", "index": 782}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Lily, Alexander, Sofia, Ava, and Matthew. \"Matthew is a knave,\" Evelyn mentioned. Lily said, \"Ava is a knight if and only if Matthew is a knave.\" Alexander was heard saying, \"Matthew is a knave if and only if Ava is a knight\". \"Ava is a knight if and only if Matthew is a knave,\" Sofia claimed. In Ava's words: \"Sofia is a knave or Evelyn is a knight\". Matthew said, \"Alexander is a knight.\" So who is a knight and who is a knave?", "names": ["Evelyn", "Lily", "Alexander", "Sofia", "Ava", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Evelyn is a knave, Lily is a knight, Alexander is a knight, Sofia is a knight, Ava is a knave, and Matthew is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Lily is a knight\n(3) Alexander is a knight\n(4) Sofia is a knight\n(5) Ava is a knave\n(6) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Evelyn that Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Matthew that Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Ava is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Alexander that Matthew is a knave if and only if Ava is a knight.", "Ava cannot be a knave, because this would contradict the false claim of their own that Sofia is a knave or Evelyn is a knight.", "We have exhausted all possibilities for Ava, Alexander, and Matthew, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Ava is a knight.", "Ava cannot be a knight, because this would contradict the claim of Alexander that Matthew is a knave if and only if Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Sofia is a knave or Evelyn is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Ava is a knight if and only if Matthew is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Ava is a knight if and only if Matthew is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('<=>', ('telling-truth', 4), ('lying', 5)), ('<=>', ('lying', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('lying', 5)), ('or', ('lying', 3), ('telling-truth', 0)), ('telling-truth', 2))", "index": 783}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Aurora, Isabella, Amelia, Ava, and Emily. Sophia stated, \"Amelia is a knight or Emily is a knight\". In Aurora's words: \"Sophia is not a knave\". \"Aurora is a knave or Amelia is a knight,\" Isabella claimed. Amelia was heard saying, \"Ava is a knave\". As Ava put it, \"Aurora is not a knight\". Emily expressed that Sophia is a knave or Aurora is a knave. So who is a knight and who is a knave?", "names": ["Sophia", "Aurora", "Isabella", "Amelia", "Ava", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Sophia is a knight, Aurora is a knight, Isabella is a knight, Amelia is a knight, Ava is a knave, and Emily is a knave.", "solution_text_format": "(1) Sophia is a knight\n(2) Aurora is a knight\n(3) Isabella is a knight\n(4) Amelia is a knight\n(5) Ava is a knave\n(6) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Amelia is a knight or Emily is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Amelia that Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Sophia is a knave or Aurora is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Sophia is a knave or Aurora is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Aurora is a knave or Amelia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 5)), ('not', ('lying', 0)), ('or', ('lying', 1), ('telling-truth', 3)), ('lying', 4), ('not', ('telling-truth', 1)), ('or', ('lying', 0), ('lying', 1)))", "index": 784}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Michael, Amelia, Evelyn, Jacob, and Sophia. \"Evelyn is a knight if and only if Amelia is a knave,\" Henry declared. Michael said, \"Sophia is a knave or Michael is a knight.\" Amelia was heard saying, \"Michael is a knight\". \"If Sophia is a knave then Amelia is a knave,\" Evelyn claimed. As Jacob put it, \"Amelia is a knave and Henry is a knight\". Sophia was heard saying, \"Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Henry", "Michael", "Amelia", "Evelyn", "Jacob", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Henry is a knave, Michael is a knight, Amelia is a knight, Evelyn is a knight, Jacob is a knave, and Sophia is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Michael is a knight\n(3) Amelia is a knight\n(4) Evelyn is a knight\n(5) Jacob is a knave\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Amelia is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Sophia is a knave then Amelia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Sophia that Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Amelia is a knave and Henry is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Henry that Evelyn is a knight if and only if Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of Jacob that Amelia is a knave and Henry is a knight.", "We have exhausted all possibilities for Amelia and Jacob, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Amelia is a knave and Henry is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Henry that Evelyn is a knight if and only if Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Michael is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Amelia that Michael is a knight.", "Michael cannot be a knave, because this would contradict the false claim of their own that Sophia is a knave or Michael is a knight.", "We have exhausted all possibilities for Michael and Amelia, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of Sophia that Jacob is a knave.", "We have exhausted all possibilities for Jacob and Sophia, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Sophia is a knave then Amelia is a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Evelyn that If Sophia is a knave then Amelia is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Amelia is a knave and Henry is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Jacob that Amelia is a knave and Henry is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Henry that Evelyn is a knight if and only if Amelia is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the false claim of Sophia that Jacob is a knave.", "We have exhausted all possibilities for Jacob, Sophia, and Evelyn, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Amelia is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Sophia is a knave then Amelia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Amelia is a knave and Henry is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Amelia is a knave and Henry is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Sophia is a knave or Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 2)), ('or', ('lying', 5), ('telling-truth', 1)), ('telling-truth', 1), ('->', ('lying', 5), ('lying', 2)), ('and', ('lying', 2), ('telling-truth', 0)), ('lying', 4))", "index": 785}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Lily, Oliver, Emily, Jacob, and Liam. In a statement by Grace: \"If Lily is a knave then Oliver is a knight\". \"If Oliver is a knave then Grace is a knave\" - Lily. Oliver expressed that If Liam is a knave then Emily is a knave. Emily asserted: \"If Lily is a knave then Jacob is a knave\". Jacob expressed that Emily is a knight. Liam noted, \"Oliver is a knight or Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Lily", "Oliver", "Emily", "Jacob", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Grace is a knight, Lily is a knight, Oliver is a knight, Emily is a knight, Jacob is a knight, and Liam is a knight.", "solution_text_format": "(1) Grace is a knight\n(2) Lily is a knight\n(3) Oliver is a knight\n(4) Emily is a knight\n(5) Jacob is a knight\n(6) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that If Lily is a knave then Oliver is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Oliver is a knave then Grace is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Liam is a knave then Emily is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Oliver is a knight or Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Lily is a knave then Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 1), ('telling-truth', 2)), ('->', ('lying', 2), ('lying', 0)), ('->', ('lying', 5), ('lying', 3)), ('->', ('lying', 1), ('lying', 4)), ('telling-truth', 3), ('or', ('telling-truth', 2), ('lying', 4)))", "index": 786}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Ella, Jack, Daniel, Aiden, and Aurora. Grace said that Daniel is not a knight. According to Ella, \"Aurora is not a knight\". According to Jack, \"Ella is a knight or Grace is a knight\". \"Ella is a knave or Aiden is a knight,\" Daniel mentioned. Aiden was heard saying, \"Grace is a knight if and only if Ella is a knave\". Aurora told you that Aiden is a knave or Ella is a knight. So who is a knight and who is a knave?", "names": ["Grace", "Ella", "Jack", "Daniel", "Aiden", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "Grace is a knave, Ella is a knave, Jack is a knave, Daniel is a knight, Aiden is a knave, and Aurora is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Ella is a knave\n(3) Jack is a knave\n(4) Daniel is a knight\n(5) Aiden is a knave\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Daniel cannot be a knight, because this would contradict the claim of Grace that Daniel is not a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ella is a knave or Aiden is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Aurora is not a knight.", "Aurora cannot be a knight, because this would contradict the claim of Ella that Aurora is not a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Aiden is a knave or Ella is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of Daniel that Ella is a knave or Aiden is a knight.", "We have exhausted all possibilities for Ella and Daniel, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Ella is a knave or Aiden is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Aurora is not a knight.", "Aurora cannot be a knight, because this would contradict the claim of Ella that Aurora is not a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Aiden is a knave or Ella is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Aiden is a knave or Ella is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Grace is a knight if and only if Ella is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Ella is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Ella is a knight or Grace is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Ella is a knight or Grace is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('not', ('telling-truth', 5)), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('lying', 1), ('telling-truth', 4)), ('<=>', ('telling-truth', 0), ('lying', 1)), ('or', ('lying', 4), ('telling-truth', 1)))", "index": 787}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Aiden, James, William, Scarlett, and Sebastian. \"Sebastian is a knight,\" Ava mentioned. Aiden commented, \"James is not a knight\". James told you that Sebastian is not a knight. \"Sebastian is a knave or Ava is a knight\" - William. Scarlett said that James is not a knave. Sebastian told you that If Scarlett is a knight then James is a knight. So who is a knight and who is a knave?", "names": ["Ava", "Aiden", "James", "William", "Scarlett", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Ava is a knight, Aiden is a knight, James is a knave, William is a knight, Scarlett is a knave, and Sebastian is a knight.", "solution_text_format": "(1) Ava is a knight\n(2) Aiden is a knight\n(3) James is a knave\n(4) William is a knight\n(5) Scarlett is a knave\n(6) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Scarlett is a knight then James is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that James is not a knave.", "James cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight.", "James cannot be a knave, because this would contradict the claim of Scarlett that James is not a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that James is not a knave.", "James cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that James is not a knight.", "Assume William is a knight. No contradiction is found in their claim that Sebastian is a knave or Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('not', ('telling-truth', 2)), ('not', ('telling-truth', 5)), ('or', ('lying', 5), ('telling-truth', 0)), ('not', ('lying', 2)), ('->', ('telling-truth', 4), ('telling-truth', 2)))", "index": 788}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Michael, Amelia, Ava, Mason, and Mia. Ethan expressed that Michael is a knight or Ava is a knave. According to Michael, \"Ethan is a knave\". \"Mia is a knave or Ava is a knight,\" Amelia mentioned. According to Ava, \"Amelia is a knave and Michael is a knight\". \"Ethan is a knave and Ethan is a knight\" - Mason. \"Ethan is a knave or Mason is a knave,\" Mia declared. So who is a knight and who is a knave?", "names": ["Ethan", "Michael", "Amelia", "Ava", "Mason", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true], "solution_text": "Ethan is a knight, Michael is a knave, Amelia is a knave, Ava is a knave, Mason is a knave, and Mia is a knight.", "solution_text_format": "(1) Ethan is a knight\n(2) Michael is a knave\n(3) Amelia is a knave\n(4) Ava is a knave\n(5) Mason is a knave\n(6) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Michael is a knight or Ava is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Ethan is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Ethan is a knave.", "Ava cannot be a knight, because this would contradict the claim of Ethan that Michael is a knight or Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Amelia is a knave and Michael is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Mia is a knave or Ava is a knight.", "Mia cannot be a knight, because this would contradict the claim of Amelia that Mia is a knave or Ava is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Ethan is a knave or Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Ethan is a knave and Ethan is a knight.", "Mason cannot be a knave, because this would contradict the false claim of Mia that Ethan is a knave or Mason is a knave.", "We have exhausted all possibilities for Mason and Mia, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Mia is a knave or Ava is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Ethan is a knave or Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Ethan is a knave and Ethan is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Ethan is a knave and Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 3)), ('lying', 0), ('or', ('lying', 5), ('telling-truth', 3)), ('and', ('lying', 2), ('telling-truth', 1)), ('and', ('lying', 0), ('telling-truth', 0)), ('or', ('lying', 0), ('lying', 4)))", "index": 789}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, James, Ava, Lucas, Mia, and Penelope. Sebastian said, \"If Sebastian is a knight then Penelope is a knight.\" In a statement by James: \"Lucas is not a knight\". Ava told you that If James is a knave then Mia is a knight. Lucas said, \"Ava is a knave.\" Mia stated, \"James is not a knave\". Penelope noted, \"Lucas is a knight and Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "James", "Ava", "Lucas", "Mia", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true], "solution_text": "Sebastian is a knight, James is a knave, Ava is a knave, Lucas is a knight, Mia is a knave, and Penelope is a knight.", "solution_text_format": "(1) Sebastian is a knight\n(2) James is a knave\n(3) Ava is a knave\n(4) Lucas is a knight\n(5) Mia is a knave\n(6) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that If Sebastian is a knight then Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Lucas is a knight and Penelope is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Lucas that Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that If James is a knave then Mia is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Lucas is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Mia cannot be a knight, because this would contradict the false claim of Ava that If James is a knave then Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that James is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 5)), ('not', ('telling-truth', 3)), ('->', ('lying', 1), ('telling-truth', 4)), ('lying', 2), ('not', ('lying', 1)), ('and', ('telling-truth', 3), ('telling-truth', 5)))", "index": 790}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Abigail, David, Aria, Oliver, and Evelyn. Aurora told you that Abigail is a knight and Evelyn is a knave. Abigail was heard saying, \"David is a knight\". In David's words: \"Abigail is a knave if and only if David is a knight\". Aria was heard saying, \"Evelyn is a knight or Oliver is a knight\". Oliver noted, \"Evelyn is not a knave\". \"If Aria is a knave then Oliver is a knave,\" Evelyn claimed. So who is a knight and who is a knave?", "names": ["Aurora", "Abigail", "David", "Aria", "Oliver", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Aurora is a knave, Abigail is a knave, David is a knave, Aria is a knight, Oliver is a knight, and Evelyn is a knight.", "solution_text_format": "(1) Aurora is a knave\n(2) Abigail is a knave\n(3) David is a knave\n(4) Aria is a knight\n(5) Oliver is a knight\n(6) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Abigail is a knight and Evelyn is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that David is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Abigail is a knave if and only if David is a knight.", "David cannot be a knave, because this would contradict the claim of Abigail that David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Aurora that Abigail is a knight and Evelyn is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Abigail is a knight and Evelyn is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that David is a knight.", "David cannot be a knight, because this would contradict the claim of their own that Abigail is a knave if and only if David is a knight.", "David cannot be a knave, because this would contradict the claim of Abigail that David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that David is a knight.", "David cannot be a knight, because this would contradict the false claim of Abigail that David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if David is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Aria is a knave then Oliver is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Evelyn is a knight or Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Evelyn is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 5)), ('telling-truth', 2), ('<=>', ('lying', 1), ('telling-truth', 2)), ('or', ('telling-truth', 5), ('telling-truth', 4)), ('not', ('lying', 5)), ('->', ('lying', 3), ('lying', 4)))", "index": 791}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Sebastian, Evelyn, Liam, Isabella, and Samuel. Daniel commented, \"Samuel is a knight and Liam is a knight\". Sebastian asserted: \"If Daniel is a knave then Daniel is a knight\". Evelyn noted, \"Sebastian is a knave if and only if Sebastian is a knight\". Liam asserted: \"Evelyn is a knave\". Isabella stated, \"Daniel is not a knave\". In a statement by Samuel: \"If Liam is a knight then Liam is a knave\". So who is a knight and who is a knave?", "names": ["Daniel", "Sebastian", "Evelyn", "Liam", "Isabella", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false], "solution_text": "Daniel is a knave, Sebastian is a knave, Evelyn is a knave, Liam is a knight, Isabella is a knave, and Samuel is a knave.", "solution_text_format": "(1) Daniel is a knave\n(2) Sebastian is a knave\n(3) Evelyn is a knave\n(4) Liam is a knight\n(5) Isabella is a knave\n(6) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Samuel is a knight and Liam is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Liam is a knight then Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Samuel that If Liam is a knight then Liam is a knave.", "Liam cannot be a knave, because this would contradict the claim of Daniel that Samuel is a knight and Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the claim of Daniel that Samuel is a knight and Liam is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Samuel is a knight and Liam is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Liam is a knight then Liam is a knave.", "Liam cannot be a knight, because this would contradict the false claim of Daniel that Samuel is a knight and Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave if and only if Sebastian is a knight.", "Evelyn cannot be a knave, because this would contradict the false claim of Liam that Evelyn is a knave.", "We have exhausted all possibilities for Evelyn and Liam, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that If Liam is a knight then Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave if and only if Sebastian is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Sebastian is a knave if and only if Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that If Daniel is a knave then Daniel is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Daniel is a knave then Daniel is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Daniel is not a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Daniel is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('lying', 0), ('telling-truth', 0)), ('<=>', ('lying', 1), ('telling-truth', 1)), ('lying', 2), ('not', ('lying', 0)), ('->', ('telling-truth', 3), ('lying', 3)))", "index": 792}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Amelia, Emma, Evelyn, Ava, and Mason. Jackson asserted: \"Jackson is a knight if and only if Mason is a knave\". As Amelia put it, \"Emma is a knave and Ava is a knave\". In Emma's words: \"Evelyn is a knight and Emma is a knight\". Evelyn said, \"Jackson is a knight if and only if Emma is a knave.\" As Ava put it, \"Mason is a knight or Emma is a knave\". Mason expressed that If Emma is a knight then Mason is a knight. So who is a knight and who is a knave?", "names": ["Jackson", "Amelia", "Emma", "Evelyn", "Ava", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Jackson is a knave, Amelia is a knave, Emma is a knight, Evelyn is a knight, Ava is a knave, and Mason is a knave.", "solution_text_format": "(1) Jackson is a knave\n(2) Amelia is a knave\n(3) Emma is a knight\n(4) Evelyn is a knight\n(5) Ava is a knave\n(6) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Mason is a knave.", "Mason cannot be a knight, because this would contradict the claim of Jackson that Jackson is a knight if and only if Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that If Emma is a knight then Mason is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Evelyn is a knight and Emma is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Jackson is a knight if and only if Emma is a knave.", "Evelyn cannot be a knave, because this would contradict the claim of Emma that Evelyn is a knight and Emma is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Emma.", "Emma cannot be a knave, because this would contradict the false claim of Mason that If Emma is a knight then Mason is a knight.", "We have exhausted all possibilities for Emma and Mason, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Mason is a knave.", "Mason cannot be a knight, because this would contradict the false claim of Jackson that Jackson is a knight if and only if Mason is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that If Emma is a knight then Mason is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Evelyn is a knight and Emma is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Emma is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Ava is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Emma is a knave and Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Mason is a knight or Emma is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Mason is a knight or Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 5)), ('and', ('lying', 2), ('lying', 4)), ('and', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('telling-truth', 0), ('lying', 2)), ('or', ('telling-truth', 5), ('lying', 2)), ('->', ('telling-truth', 2), ('telling-truth', 5)))", "index": 793}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Sofia, Owen, Jackson, James, and Henry. \"If Henry is a knave then Jackson is a knight,\" Evelyn declared. \"Owen is a knight or Henry is a knave,\" Sofia declared. Owen commented, \"Henry is a knave\". As Jackson put it, \"James is a knight if and only if Sofia is a knight\". James was heard saying, \"Sofia is a knave if and only if Evelyn is a knight\". \"If Sofia is a knight then Henry is a knight,\" Henry claimed. So who is a knight and who is a knave?", "names": ["Evelyn", "Sofia", "Owen", "Jackson", "James", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true], "solution_text": "Evelyn is a knight, Sofia is a knave, Owen is a knave, Jackson is a knave, James is a knight, and Henry is a knight.", "solution_text_format": "(1) Evelyn is a knight\n(2) Sofia is a knave\n(3) Owen is a knave\n(4) Jackson is a knave\n(5) James is a knight\n(6) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that If Henry is a knave then Jackson is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Sofia is a knight then Henry is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Owen is a knight or Henry is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Henry is a knave.", "Owen cannot be a knave, because this would contradict the claim of Sofia that Owen is a knight or Henry is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Owen is a knight or Henry is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Sofia that Owen is a knight or Henry is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that James is a knight if and only if Sofia is a knight.", "James cannot be a knight, because this would contradict the claim of Jackson that James is a knight if and only if Sofia is a knight.", "James cannot be a knave, because this would contradict the false claim of their own that Sofia is a knave if and only if Evelyn is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that James is a knight if and only if Sofia is a knight.", "Assume James is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 3)), ('or', ('telling-truth', 2), ('lying', 5)), ('lying', 5), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('<=>', ('lying', 1), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('telling-truth', 5)))", "index": 794}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Benjamin, Owen, Michael, Liam, and Charlotte. In Oliver's words: \"If Owen is a knight then Benjamin is a knave\". \"Michael is not a knight\" - Benjamin. \"Charlotte is a knight and Benjamin is a knight,\" Owen declared. Michael stated, \"Liam is a knave if and only if Owen is a knave\". According to Liam, \"Charlotte is a knave and Benjamin is a knave\". \"Owen is a knave,\" Charlotte declared. So who is a knight and who is a knave?", "names": ["Oliver", "Benjamin", "Owen", "Michael", "Liam", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true], "solution_text": "Oliver is a knight, Benjamin is a knave, Owen is a knave, Michael is a knight, Liam is a knave, and Charlotte is a knight.", "solution_text_format": "(1) Oliver is a knight\n(2) Benjamin is a knave\n(3) Owen is a knave\n(4) Michael is a knight\n(5) Liam is a knave\n(6) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that If Owen is a knight then Benjamin is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Charlotte is a knight and Benjamin is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Owen is a knave.", "Charlotte cannot be a knave, because this would contradict the claim of Owen that Charlotte is a knight and Benjamin is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Charlotte is a knight and Benjamin is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Owen is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Owen that Charlotte is a knight and Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Liam is a knave if and only if Owen is a knave.", "Liam cannot be a knight, because this would contradict the claim of Michael that Liam is a knave if and only if Owen is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Charlotte is a knave and Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 1)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 5), ('telling-truth', 1)), ('<=>', ('lying', 4), ('lying', 2)), ('and', ('lying', 5), ('lying', 1)), ('lying', 2))", "index": 795}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Aria, Olivia, Liam, Evelyn, and Samuel. \"If Liam is a knave then Aria is a knave,\" David declared. Aria stated, \"Samuel is a knave or Liam is a knight\". According to Olivia, \"Liam is a knight if and only if Evelyn is a knight\". Liam said that Evelyn is a knave or Aria is a knave. Evelyn said that Olivia is a knave if and only if Evelyn is a knight. Samuel stated, \"Evelyn is not a knave\". So who is a knight and who is a knave?", "names": ["David", "Aria", "Olivia", "Liam", "Evelyn", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "David is a knight, Aria is a knight, Olivia is a knave, Liam is a knight, Evelyn is a knave, and Samuel is a knave.", "solution_text_format": "(1) David is a knight\n(2) Aria is a knight\n(3) Olivia is a knave\n(4) Liam is a knight\n(5) Evelyn is a knave\n(6) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that If Liam is a knave then Aria is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Evelyn is a knave or Aria is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Evelyn is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Evelyn that Olivia is a knave if and only if Evelyn is a knight.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Liam is a knight if and only if Evelyn is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Evelyn is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Liam is a knight if and only if Evelyn is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Evelyn is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Samuel is a knave or Liam is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Evelyn is not a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Evelyn is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 1)), ('or', ('lying', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 3), ('telling-truth', 4)), ('or', ('lying', 4), ('lying', 1)), ('<=>', ('lying', 2), ('telling-truth', 4)), ('not', ('lying', 4)))", "index": 796}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Owen, Evelyn, Lucas, Jacob, and Logan. \"Jacob is a knight and Owen is a knight,\" David mentioned. In a statement by Owen: \"Logan is not a knight\". In a statement by Evelyn: \"Owen is a knight and Evelyn is a knight\". \"Logan is a knight if and only if Owen is a knight,\" Lucas mentioned. Jacob asserted: \"Logan is a knight\". \"If Owen is a knight then Lucas is a knave,\" Logan claimed. So who is a knight and who is a knave?", "names": ["David", "Owen", "Evelyn", "Lucas", "Jacob", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "David is a knave, Owen is a knave, Evelyn is a knave, Lucas is a knave, Jacob is a knight, and Logan is a knight.", "solution_text_format": "(1) David is a knave\n(2) Owen is a knave\n(3) Evelyn is a knave\n(4) Lucas is a knave\n(5) Jacob is a knight\n(6) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Jacob is a knight and Owen is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Owen is a knight then Lucas is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Logan is not a knight.", "Owen cannot be a knave, because this would contradict the claim of David that Jacob is a knight and Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Jacob that Logan is a knight.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of David that Jacob is a knight and Owen is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Jacob is a knight and Owen is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Owen is a knight then Lucas is a knave.", "Owen cannot be a knight, because this would contradict the false claim of David that Jacob is a knight and Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Logan is not a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that Logan is a knight if and only if Owen is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Owen is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Owen is a knight and Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('telling-truth', 5)), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('telling-truth', 5), ('->', ('telling-truth', 1), ('lying', 3)))", "index": 797}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Elizabeth, Michael, Henry, Lucas, and Ella. According to Aurora, \"If Lucas is a knave then Ella is a knight\". Elizabeth asserted: \"Aurora is a knight or Aurora is a knave\". Michael said, \"Henry is a knight if and only if Henry is a knave.\" \"Elizabeth is a knight if and only if Lucas is a knave\" - Henry. Lucas asserted: \"Ella is a knight if and only if Henry is a knight\". \"Henry is not a knight,\" Ella mentioned. So who is a knight and who is a knave?", "names": ["Aurora", "Elizabeth", "Michael", "Henry", "Lucas", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false], "solution_text": "Aurora is a knave, Elizabeth is a knight, Michael is a knave, Henry is a knight, Lucas is a knave, and Ella is a knave.", "solution_text_format": "(1) Aurora is a knave\n(2) Elizabeth is a knight\n(3) Michael is a knave\n(4) Henry is a knight\n(5) Lucas is a knave\n(6) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that If Lucas is a knave then Ella is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Ella is a knight if and only if Henry is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of Ella that Henry is not a knight.", "Henry cannot be a knave, because this would contradict the claim of Lucas that Ella is a knight if and only if Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of Lucas that Ella is a knight if and only if Henry is a knight.", "Henry cannot be a knave, because this would contradict the false claim of Ella that Henry is not a knight.", "We have exhausted all possibilities for Henry and Ella, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Henry is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the false claim of Lucas that Ella is a knight if and only if Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if Lucas is a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Henry that Elizabeth is a knight if and only if Lucas is a knave.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight or Aurora is a knave.", "We have exhausted all possibilities for Elizabeth and Henry, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the claim of Aurora that If Lucas is a knave then Ella is a knight.", "We have exhausted all possibilities for Ella and Lucas, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that If Lucas is a knave then Ella is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Aurora that If Lucas is a knave then Ella is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Henry is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Aurora that If Lucas is a knave then Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if Lucas is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Aurora is a knight or Aurora is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Henry is a knight if and only if Henry is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('telling-truth', 5)), ('or', ('telling-truth', 0), ('lying', 0)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('<=>', ('telling-truth', 1), ('lying', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 3)), ('not', ('telling-truth', 3)))", "index": 798}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Oliver, Sophia, Matthew, Scarlett, and Jack. Ava told you that If Sophia is a knight then Matthew is a knave. \"If Matthew is a knight then Jack is a knave,\" Oliver declared. \"Jack is a knave,\" Sophia claimed. Matthew noted, \"Jack is a knave\". Scarlett stated, \"Matthew is a knight if and only if Jack is a knight\". Jack expressed that Scarlett is a knight. So who is a knight and who is a knave?", "names": ["Ava", "Oliver", "Sophia", "Matthew", "Scarlett", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Ava is a knave, Oliver is a knight, Sophia is a knight, Matthew is a knight, Scarlett is a knave, and Jack is a knave.", "solution_text_format": "(1) Ava is a knave\n(2) Oliver is a knight\n(3) Sophia is a knight\n(4) Matthew is a knight\n(5) Scarlett is a knave\n(6) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that If Sophia is a knight then Matthew is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Sophia that Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Jack that Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Jack is a knight.", "Matthew cannot be a knight, because this would contradict the claim of Ava that If Sophia is a knight then Matthew is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Jack is a knave.", "We have exhausted all possibilities for Matthew, Scarlett, and Jack, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Jack is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Jack is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Jack is a knave.", "Matthew cannot be a knave, because this would contradict the claim of Scarlett that Matthew is a knight if and only if Jack is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the claim of Jack that Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the false claim of Sophia that Jack is a knave.", "We have exhausted all possibilities for Jack and Sophia, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that If Sophia is a knight then Matthew is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Sophia that Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Jack that Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Jack is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Jack is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Matthew is a knight then Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 3)), ('->', ('telling-truth', 3), ('lying', 5)), ('lying', 5), ('lying', 5), ('<=>', ('telling-truth', 3), ('telling-truth', 5)), ('telling-truth', 4))", "index": 799}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Victoria, Chloe, Olivia, Michael, and Lucas. \"Chloe is a knight and Olivia is a knave,\" Samuel mentioned. Victoria expressed that If Samuel is a knight then Chloe is a knave. \"Chloe is a knight and Michael is a knave,\" Chloe claimed. Olivia commented, \"Samuel is not a knave\". Michael remarked, \"Olivia is a knave if and only if Victoria is a knight\". Lucas said that Victoria is a knight and Chloe is a knight. So who is a knight and who is a knave?", "names": ["Samuel", "Victoria", "Chloe", "Olivia", "Michael", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "Samuel is a knave, Victoria is a knight, Chloe is a knave, Olivia is a knave, Michael is a knight, and Lucas is a knave.", "solution_text_format": "(1) Samuel is a knave\n(2) Victoria is a knight\n(3) Chloe is a knave\n(4) Olivia is a knave\n(5) Michael is a knight\n(6) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Chloe is a knight and Olivia is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Chloe is a knight and Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Chloe that Chloe is a knight and Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Victoria is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Samuel that Chloe is a knight and Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Samuel is not a knave.", "We have exhausted all possibilities for Olivia and Michael, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the claim of Samuel that Chloe is a knight and Olivia is a knave.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Chloe is a knight and Olivia is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Chloe is a knight and Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Chloe that Chloe is a knight and Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Victoria is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Samuel is not a knave.", "Olivia cannot be a knave, because this would contradict the false claim of Samuel that Chloe is a knight and Olivia is a knave.", "We have exhausted all possibilities for Olivia and Michael, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Chloe is a knight and Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Victoria is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Samuel is not a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Samuel is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Samuel is a knight then Chloe is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Chloe is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Victoria is a knight and Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('lying', 3)), ('->', ('telling-truth', 0), ('lying', 2)), ('and', ('telling-truth', 2), ('lying', 4)), ('not', ('lying', 0)), ('<=>', ('lying', 3), ('telling-truth', 1)), ('and', ('telling-truth', 1), ('telling-truth', 2)))", "index": 800}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Mason, Samuel, Aiden, Benjamin, and Lucas. Oliver was heard saying, \"Lucas is a knight if and only if Benjamin is a knave\". Mason said that Aiden is not a knave. Samuel expressed that Mason is a knave if and only if Oliver is a knave. Aiden said, \"Samuel is a knight if and only if Benjamin is a knave.\" Benjamin expressed that Oliver is a knight if and only if Aiden is a knave. According to Lucas, \"Samuel is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Mason", "Samuel", "Aiden", "Benjamin", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Oliver is a knight, Mason is a knight, Samuel is a knight, Aiden is a knight, Benjamin is a knave, and Lucas is a knight.", "solution_text_format": "(1) Oliver is a knight\n(2) Mason is a knight\n(3) Samuel is a knight\n(4) Aiden is a knight\n(5) Benjamin is a knave\n(6) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Benjamin is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Samuel is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Mason is a knave if and only if Oliver is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Oliver that Lucas is a knight if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('lying', 4)), ('not', ('lying', 3)), ('<=>', ('lying', 1), ('lying', 0)), ('<=>', ('telling-truth', 2), ('lying', 4)), ('<=>', ('telling-truth', 0), ('lying', 3)), ('telling-truth', 2))", "index": 801}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Isabella, Alexander, Jacob, Luke, and Henry. In a statement by Michael: \"Jacob is a knight or Henry is a knave\". \"Michael is a knight if and only if Henry is a knave,\" Isabella mentioned. Alexander said, \"Henry is a knight or Jacob is a knight.\" In a statement by Jacob: \"If Henry is a knight then Alexander is a knight\". As Luke put it, \"If Jacob is a knight then Alexander is a knave\". Henry asserted: \"Alexander is not a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Isabella", "Alexander", "Jacob", "Luke", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Michael is a knight, Isabella is a knight, Alexander is a knight, Jacob is a knight, Luke is a knave, and Henry is a knave.", "solution_text_format": "(1) Michael is a knight\n(2) Isabella is a knight\n(3) Alexander is a knight\n(4) Jacob is a knight\n(5) Luke is a knave\n(6) Henry is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Jacob is a knight or Henry is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Henry is a knight then Alexander is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Henry that Alexander is not a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Henry is a knight or Jacob is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Alexander is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Henry is a knight or Jacob is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Michael is a knight if and only if Henry is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that If Jacob is a knight then Alexander is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that If Jacob is a knight then Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('lying', 5)), ('<=>', ('telling-truth', 0), ('lying', 5)), ('or', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('telling-truth', 5), ('telling-truth', 2)), ('->', ('telling-truth', 3), ('lying', 2)), ('not', ('telling-truth', 2)))", "index": 802}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Aurora, Lucas, Chloe, Victoria, and Aria. Mason said that Mason is a knight or Victoria is a knave. \"Mason is a knave if and only if Aria is a knave,\" Aurora declared. \"If Mason is a knight then Chloe is a knave\" - Lucas. According to Chloe, \"If Chloe is a knight then Lucas is a knight\". \"Aurora is a knave if and only if Mason is a knave,\" Victoria mentioned. Aria said, \"If Victoria is a knave then Mason is a knave.\" So who is a knight and who is a knave?", "names": ["Mason", "Aurora", "Lucas", "Chloe", "Victoria", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Mason is a knave, Aurora is a knave, Lucas is a knight, Chloe is a knight, Victoria is a knight, and Aria is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Aurora is a knave\n(3) Lucas is a knight\n(4) Chloe is a knight\n(5) Victoria is a knight\n(6) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Mason is a knight or Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Mason is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Mason is a knave if and only if Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Victoria is a knave then Mason is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Mason is a knight then Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Lucas that If Mason is a knight then Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that If Chloe is a knight then Lucas is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Mason is a knight then Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that If Chloe is a knight then Lucas is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of Lucas that If Mason is a knight then Chloe is a knave.", "We have exhausted all possibilities for Chloe and Lucas, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Aurora that Mason is a knave if and only if Aria is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Victoria that Aurora is a knave if and only if Mason is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Mason is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Victoria that Aurora is a knave if and only if Mason is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Aria is a knave.", "Aria cannot be a knight, because this would contradict the false claim of Aurora that Mason is a knave if and only if Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that If Victoria is a knave then Mason is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Mason is a knight then Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of Lucas that If Mason is a knight then Chloe is a knave.", "Chloe cannot be a knave, because this would contradict the false claim of their own that If Chloe is a knight then Lucas is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Mason is a knight then Chloe is a knave.", "Chloe cannot be a knight, because this would contradict the claim of their own that If Chloe is a knight then Lucas is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of Lucas that If Mason is a knight then Chloe is a knave.", "We have exhausted all possibilities for Chloe, Lucas, Aria, Aurora, and Victoria, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Mason is a knight or Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Mason is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Victoria that Aurora is a knave if and only if Mason is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Victoria is a knave then Mason is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Mason is a knight then Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Chloe is a knight then Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('lying', 4)), ('<=>', ('lying', 0), ('lying', 5)), ('->', ('telling-truth', 0), ('lying', 3)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('lying', 1), ('lying', 0)), ('->', ('lying', 4), ('lying', 0)))", "index": 803}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Chloe, Lucas, Zoey, James, and Joseph. Ella expressed that Zoey is a knave or Zoey is a knight. Chloe told you that If James is a knight then Zoey is a knave. Lucas was heard saying, \"James is a knight and Zoey is a knight\". Zoey expressed that Lucas is a knave and James is a knight. According to James, \"Joseph is a knight if and only if Zoey is a knave\". According to Joseph, \"Zoey is a knight and Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Ella", "Chloe", "Lucas", "Zoey", "James", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Ella is a knight, Chloe is a knight, Lucas is a knave, Zoey is a knave, James is a knave, and Joseph is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Chloe is a knight\n(3) Lucas is a knave\n(4) Zoey is a knave\n(5) James is a knave\n(6) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Zoey is a knave or Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Lucas is a knave and James is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Zoey that Lucas is a knave and James is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that James is a knight and Zoey is a knight.", "James cannot be a knight, because this would contradict the false claim of Lucas that James is a knight and Zoey is a knight.", "James cannot be a knave, because this would contradict the claim of Zoey that Lucas is a knave and James is a knight.", "We have exhausted all possibilities for James and Lucas, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Lucas is a knave and James is a knight.", "Lucas cannot be a knight, because this would contradict the claim of their own that James is a knight and Zoey is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that James is a knight and Zoey is a knight.", "James cannot be a knight, because this would contradict the false claim of Zoey that Lucas is a knave and James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Zoey is a knave.", "Joseph cannot be a knight, because this would contradict the false claim of James that Joseph is a knight if and only if Zoey is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Zoey is a knight and Joseph is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If James is a knight then Zoey is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 3)), ('->', ('telling-truth', 4), ('lying', 3)), ('and', ('telling-truth', 4), ('telling-truth', 3)), ('and', ('lying', 2), ('telling-truth', 4)), ('<=>', ('telling-truth', 5), ('lying', 3)), ('and', ('telling-truth', 3), ('telling-truth', 5)))", "index": 804}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Lily, Riley, Aria, Daniel, and William. Jackson commented, \"Daniel is a knave\". In Lily's words: \"Jackson is a knight\". Riley said that Aria is a knight and Jackson is a knight. Aria said that Daniel is a knight or Riley is a knight. \"Aria is not a knight,\" Daniel declared. \"Aria is a knight and Daniel is a knight,\" William mentioned. So who is a knight and who is a knave?", "names": ["Jackson", "Lily", "Riley", "Aria", "Daniel", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Jackson is a knight, Lily is a knight, Riley is a knight, Aria is a knight, Daniel is a knave, and William is a knave.", "solution_text_format": "(1) Jackson is a knight\n(2) Lily is a knight\n(3) Riley is a knight\n(4) Aria is a knight\n(5) Daniel is a knave\n(6) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of Jackson that Daniel is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Daniel is a knight or Riley is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Aria is a knight and Jackson is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Jackson is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Aria is a knight and Daniel is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Aria is a knight and Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('telling-truth', 0), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 3), ('telling-truth', 4)))", "index": 805}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Zoey, Oliver, Luke, Olivia, Scarlett, and Avery. \"Oliver is a knight and Olivia is a knight\" - Zoey. Oliver said, \"Olivia is a knave.\" As Luke put it, \"Zoey is not a knave\". \"Avery is a knight or Oliver is a knight,\" Olivia claimed. Scarlett noted, \"Zoey is a knight and Oliver is a knave\". Avery asserted: \"Luke is not a knight\". So who is a knight and who is a knave?", "names": ["Zoey", "Oliver", "Luke", "Olivia", "Scarlett", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "Zoey is a knave, Oliver is a knave, Luke is a knave, Olivia is a knight, Scarlett is a knave, and Avery is a knight.", "solution_text_format": "(1) Zoey is a knave\n(2) Oliver is a knave\n(3) Luke is a knave\n(4) Olivia is a knight\n(5) Scarlett is a knave\n(6) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Oliver is a knight and Olivia is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Oliver that Olivia is a knave.", "Olivia cannot be a knave, because this would contradict the claim of Zoey that Oliver is a knight and Olivia is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Zoey that Oliver is a knight and Olivia is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Oliver is a knight and Olivia is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Olivia is a knave.", "Olivia cannot be a knight, because this would contradict the false claim of Zoey that Oliver is a knight and Olivia is a knight.", "Olivia cannot be a knave, because this would contradict the false claim of their own that Avery is a knight or Oliver is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Avery is a knight or Oliver is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Zoey is not a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Zoey is not a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Zoey is a knight and Oliver is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Zoey is a knight and Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 3)), ('lying', 3), ('not', ('lying', 0)), ('or', ('telling-truth', 5), ('telling-truth', 1)), ('and', ('telling-truth', 0), ('lying', 1)), ('not', ('telling-truth', 2)))", "index": 806}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Ethan, Logan, Owen, Matthew, and Sophia. Daniel commented, \"Logan is a knave or Ethan is a knave\". \"Logan is not a knave,\" Ethan declared. Logan remarked, \"Logan is a knight if and only if Ethan is a knight\". Owen stated, \"Ethan is a knight\". Matthew asserted: \"Logan is not a knave\". \"Owen is a knave and Sophia is a knight,\" Sophia declared. So who is a knight and who is a knave?", "names": ["Daniel", "Ethan", "Logan", "Owen", "Matthew", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Daniel is a knave, Ethan is a knight, Logan is a knight, Owen is a knight, Matthew is a knight, and Sophia is a knave.", "solution_text_format": "(1) Daniel is a knave\n(2) Ethan is a knight\n(3) Logan is a knight\n(4) Owen is a knight\n(5) Matthew is a knight\n(6) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Logan is a knave or Ethan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight if and only if Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the claim of Daniel that Logan is a knave or Ethan is a knave.", "Ethan cannot be a knave, because this would contradict the false claim of their own that Logan is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Logan is not a knave.", "Ethan cannot be a knave, because this would contradict the false claim of Logan that Logan is a knight if and only if Ethan is a knight.", "We have exhausted all possibilities for Ethan and Logan, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Logan is a knave or Ethan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight if and only if Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Logan is not a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Logan is not a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Owen is a knave and Sophia is a knight.", "Assume Sophia is a knave. No contradiction is found in their false claim that Owen is a knave and Sophia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('lying', 1)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('telling-truth', 1), ('not', ('lying', 2)), ('and', ('lying', 3), ('telling-truth', 5)))", "index": 807}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Grace, Amelia, Oliver, Scarlett, and Jacob. Riley noted, \"Amelia is a knight and Riley is a knight\". \"If Oliver is a knight then Amelia is a knave,\" Grace declared. \"Jacob is a knight,\" Amelia declared. \"If Amelia is a knave then Grace is a knave,\" Oliver claimed. Scarlett told you that Riley is not a knave. \"Scarlett is a knight or Grace is a knight\" - Jacob. So who is a knight and who is a knave?", "names": ["Riley", "Grace", "Amelia", "Oliver", "Scarlett", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Riley is a knight, Grace is a knave, Amelia is a knight, Oliver is a knight, Scarlett is a knight, and Jacob is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Grace is a knave\n(3) Amelia is a knight\n(4) Oliver is a knight\n(5) Scarlett is a knight\n(6) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Amelia is a knight and Riley is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is a knight or Grace is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Riley is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Oliver is a knight then Amelia is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Grace that If Oliver is a knight then Amelia is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of their own that If Amelia is a knave then Grace is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that If Oliver is a knight then Amelia is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Amelia is a knave then Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('lying', 2)), ('telling-truth', 5), ('->', ('lying', 2), ('lying', 1)), ('not', ('lying', 0)), ('or', ('telling-truth', 4), ('telling-truth', 1)))", "index": 808}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Harper, Samuel, Jacob, Zoey, and Aurora. \"Aurora is a knight and Samuel is a knight\" - Alexander. As Harper put it, \"Zoey is a knave if and only if Samuel is a knight\". \"Jacob is a knight or Zoey is a knight,\" Samuel claimed. \"If Aurora is a knight then Jacob is a knight,\" Jacob declared. Zoey commented, \"Samuel is not a knave\". \"Alexander is a knight if and only if Jacob is a knave\" - Aurora. So who is a knight and who is a knave?", "names": ["Alexander", "Harper", "Samuel", "Jacob", "Zoey", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Alexander is a knight, Harper is a knave, Samuel is a knight, Jacob is a knave, Zoey is a knight, and Aurora is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Harper is a knave\n(3) Samuel is a knight\n(4) Jacob is a knave\n(5) Zoey is a knight\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Aurora is a knight and Samuel is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Aurora that Alexander is a knight if and only if Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Aurora is a knight then Jacob is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Jacob is a knight or Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Zoey is a knave if and only if Samuel is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 2)), ('<=>', ('lying', 4), ('telling-truth', 2)), ('or', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 0), ('lying', 3)))", "index": 809}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Abigail, Luke, William, Alexander, and Aria. As Michael put it, \"Abigail is not a knight\". In a statement by Abigail: \"If Aria is a knight then Luke is a knight\". As Luke put it, \"Abigail is a knave or Michael is a knight\". William expressed that Luke is not a knight. Alexander told you that If William is a knave then William is a knight. \"Luke is a knight if and only if Alexander is a knight\" - Aria. So who is a knight and who is a knave?", "names": ["Michael", "Abigail", "Luke", "William", "Alexander", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Michael is a knave, Abigail is a knight, Luke is a knave, William is a knight, Alexander is a knight, and Aria is a knave.", "solution_text_format": "(1) Michael is a knave\n(2) Abigail is a knight\n(3) Luke is a knave\n(4) William is a knight\n(5) Alexander is a knight\n(6) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of Michael that Abigail is not a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Aria is a knight then Luke is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Luke is a knight if and only if Alexander is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Abigail that If Aria is a knight then Luke is a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that Abigail is a knave or Michael is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the false claim of Abigail that If Aria is a knight then Luke is a knight.", "We have exhausted all possibilities for Aria and Abigail, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Abigail is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Aria is a knight then Luke is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Luke is a knight if and only if Alexander is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Abigail is a knave or Michael is a knight.", "Luke cannot be a knave, because this would contradict the claim of Abigail that If Aria is a knight then Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Alexander is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Abigail is a knave or Michael is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Abigail is a knave or Michael is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If William is a knave then William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Luke is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('->', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('lying', 1), ('telling-truth', 0)), ('not', ('telling-truth', 2)), ('->', ('lying', 3), ('telling-truth', 3)), ('<=>', ('telling-truth', 2), ('telling-truth', 4)))", "index": 810}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Liam, Ella, Avery, Daniel, and Scarlett. Joseph told you that Daniel is a knight and Scarlett is a knave. \"Avery is a knave and Ella is a knave,\" Liam mentioned. In Ella's words: \"Joseph is a knave if and only if Avery is a knave\". \"Joseph is a knave if and only if Avery is a knight,\" Avery claimed. In a statement by Daniel: \"Avery is a knave\". As Scarlett put it, \"Ella is a knave if and only if Liam is a knave\". So who is a knight and who is a knave?", "names": ["Joseph", "Liam", "Ella", "Avery", "Daniel", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "Joseph is a knave, Liam is a knave, Ella is a knave, Avery is a knight, Daniel is a knave, and Scarlett is a knight.", "solution_text_format": "(1) Joseph is a knave\n(2) Liam is a knave\n(3) Ella is a knave\n(4) Avery is a knight\n(5) Daniel is a knave\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Daniel is a knight and Scarlett is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Joseph is a knave if and only if Avery is a knight.", "Avery cannot be a knave, because this would contradict the false claim of their own that Joseph is a knave if and only if Avery is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Joseph that Daniel is a knight and Scarlett is a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Daniel is a knight and Scarlett is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Daniel that Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Avery is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Ella is a knave if and only if Liam is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Avery is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Ella is a knave.", "Liam cannot be a knave, because this would contradict the claim of Scarlett that Ella is a knave if and only if Liam is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that Joseph is a knave if and only if Avery is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of Joseph that Daniel is a knight and Scarlett is a knave.", "We have exhausted all possibilities for Scarlett and Avery, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Avery is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Ella is a knave if and only if Liam is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Joseph is a knave if and only if Avery is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Avery is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Ella is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Avery is a knave and Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 5)), ('and', ('lying', 3), ('lying', 2)), ('<=>', ('lying', 0), ('lying', 3)), ('<=>', ('lying', 0), ('telling-truth', 3)), ('lying', 3), ('<=>', ('lying', 2), ('lying', 1)))", "index": 811}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Alexander, Jacob, James, Benjamin, and Lucas. Liam said that James is a knave if and only if Alexander is a knight. \"Jacob is not a knave,\" Alexander declared. Jacob stated, \"Alexander is a knight or Lucas is a knight\". \"Alexander is a knight and Alexander is a knave,\" James declared. Benjamin said, \"Liam is a knight and James is a knave.\" Lucas said, \"If Benjamin is a knight then Alexander is a knave.\" So who is a knight and who is a knave?", "names": ["Liam", "Alexander", "Jacob", "James", "Benjamin", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Liam is a knight, Alexander is a knight, Jacob is a knight, James is a knave, Benjamin is a knight, and Lucas is a knave.", "solution_text_format": "(1) Liam is a knight\n(2) Alexander is a knight\n(3) Jacob is a knight\n(4) James is a knave\n(5) Benjamin is a knight\n(6) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that James is a knave if and only if Alexander is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Alexander is a knight and Alexander is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Alexander is a knight and Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Jacob is not a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Alexander is a knight or Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Benjamin is a knight then Alexander is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Lucas that If Benjamin is a knight then Alexander is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Liam is a knight and James is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Alexander is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Liam is a knight and James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 1)), ('not', ('lying', 2)), ('or', ('telling-truth', 1), ('telling-truth', 5)), ('and', ('telling-truth', 1), ('lying', 1)), ('and', ('telling-truth', 0), ('lying', 3)), ('->', ('telling-truth', 4), ('lying', 1)))", "index": 812}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, James, Victoria, Lucas, Emily, and Sofia. As Joseph put it, \"Lucas is a knave if and only if Lucas is a knight\". James said that Joseph is a knave. Victoria noted, \"James is a knave if and only if Lucas is a knight\". Lucas told you that Emily is a knave if and only if Joseph is a knight. \"Joseph is not a knave\" - Emily. According to Sofia, \"Lucas is not a knave\". So who is a knight and who is a knave?", "names": ["Joseph", "James", "Victoria", "Lucas", "Emily", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Joseph is a knave, James is a knight, Victoria is a knight, Lucas is a knave, Emily is a knave, and Sofia is a knave.", "solution_text_format": "(1) Joseph is a knave\n(2) James is a knight\n(3) Victoria is a knight\n(4) Lucas is a knave\n(5) Emily is a knave\n(6) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Joseph cannot be a knight, because this would contradict the claim of their own that Lucas is a knave if and only if Lucas is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Emily is a knave if and only if Joseph is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Joseph is not a knave.", "Emily cannot be a knave, because this would contradict the claim of Lucas that Emily is a knave if and only if Joseph is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Joseph is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Lucas that Emily is a knave if and only if Joseph is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Joseph is not a knave.", "Assume James is a knight. No contradiction is found in their claim that Joseph is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that James is a knave if and only if Lucas is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Lucas is not a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Lucas is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 3)), ('lying', 0), ('<=>', ('lying', 1), ('telling-truth', 3)), ('<=>', ('lying', 4), ('telling-truth', 0)), ('not', ('lying', 0)), ('not', ('lying', 3)))", "index": 813}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Aria, Victoria, Amelia, Mia, and Joseph. Chloe told you that Aria is a knight or Aria is a knave. Aria told you that Chloe is a knave or Joseph is a knave. Victoria said, \"Mia is a knight if and only if Joseph is a knight.\" As Amelia put it, \"Aria is not a knave\". \"Joseph is not a knave,\" Mia claimed. \"Amelia is a knave if and only if Joseph is a knight,\" Joseph mentioned. So who is a knight and who is a knave?", "names": ["Chloe", "Aria", "Victoria", "Amelia", "Mia", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Chloe is a knight, Aria is a knave, Victoria is a knight, Amelia is a knave, Mia is a knight, and Joseph is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Aria is a knave\n(3) Victoria is a knight\n(4) Amelia is a knave\n(5) Mia is a knight\n(6) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Aria is a knight or Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Chloe is a knave or Joseph is a knave.", "Joseph cannot be a knight, because this would contradict the claim of Aria that Chloe is a knave or Joseph is a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Joseph is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Joseph that Amelia is a knave if and only if Joseph is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Aria is not a knave.", "We have exhausted all possibilities for Amelia and Joseph, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Chloe is a knave or Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Joseph is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Aria is not a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Aria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Mia is a knight if and only if Joseph is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Joseph is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 1)), ('or', ('lying', 0), ('lying', 5)), ('<=>', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('lying', 1)), ('not', ('lying', 5)), ('<=>', ('lying', 3), ('telling-truth', 5)))", "index": 814}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Harper, Alexander, Michael, Ava, and David. \"David is a knave if and only if Alexander is a knave,\" Oliver claimed. Harper was heard saying, \"Ava is not a knight\". \"David is a knave,\" Alexander declared. \"Harper is a knave,\" Michael claimed. \"Alexander is a knight if and only if David is a knave\" - Ava. David told you that If Harper is a knight then Michael is a knave. So who is a knight and who is a knave?", "names": ["Oliver", "Harper", "Alexander", "Michael", "Ava", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Oliver is a knave, Harper is a knave, Alexander is a knave, Michael is a knight, Ava is a knight, and David is a knight.", "solution_text_format": "(1) Oliver is a knave\n(2) Harper is a knave\n(3) Alexander is a knave\n(4) Michael is a knight\n(5) Ava is a knight\n(6) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that David is a knave if and only if Alexander is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Harper is a knight then Michael is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Harper that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if David is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that David is a knave.", "Alexander cannot be a knave, because this would contradict the claim of Oliver that David is a knave if and only if Alexander is a knave.", "We have exhausted all possibilities for Alexander and Ava, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Alexander is a knight if and only if David is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that David is a knave.", "Alexander cannot be a knave, because this would contradict the claim of Oliver that David is a knave if and only if Alexander is a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of Harper that Ava is not a knight.", "We have exhausted all possibilities for Ava and Harper, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that If Harper is a knight then Michael is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Harper that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if David is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Oliver that David is a knave if and only if Alexander is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that David is a knave.", "We have exhausted all possibilities for Alexander and Ava, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the false claim of David that If Harper is a knight then Michael is a knave.", "We have exhausted all possibilities for Harper and David, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that David is a knave if and only if Alexander is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Harper is a knight then Michael is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Harper that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if David is a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Oliver that David is a knave if and only if Alexander is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of Ava that Alexander is a knight if and only if David is a knave.", "We have exhausted all possibilities for Alexander and Ava, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Alexander is a knight if and only if David is a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Oliver that David is a knave if and only if Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that David is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 2)), ('not', ('telling-truth', 4)), ('lying', 5), ('lying', 1), ('<=>', ('telling-truth', 2), ('lying', 5)), ('->', ('telling-truth', 1), ('lying', 3)))", "index": 815}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Olivia, Luke, Samuel, Harper, and James. Jack commented, \"Olivia is a knave and James is a knave\". Olivia said, \"Jack is a knave or James is a knave.\" Luke stated, \"If Luke is a knight then Jack is a knave\". \"Harper is a knave,\" Samuel claimed. Harper stated, \"Luke is a knight if and only if Luke is a knave\". James stated, \"Harper is a knight if and only if Samuel is a knight\". So who is a knight and who is a knave?", "names": ["Jack", "Olivia", "Luke", "Samuel", "Harper", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Jack is a knave, Olivia is a knight, Luke is a knight, Samuel is a knight, Harper is a knave, and James is a knave.", "solution_text_format": "(1) Jack is a knave\n(2) Olivia is a knight\n(3) Luke is a knight\n(4) Samuel is a knight\n(5) Harper is a knave\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Olivia is a knave and James is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Jack that Olivia is a knave and James is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Jack is a knave or James is a knave.", "James cannot be a knight, because this would contradict the claim of Jack that Olivia is a knave and James is a knave.", "James cannot be a knave, because this would contradict the false claim of Olivia that Jack is a knave or James is a knave.", "We have exhausted all possibilities for James and Olivia, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Olivia is a knave and James is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Jack is a knave or James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Harper is a knight if and only if Samuel is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Luke is a knight if and only if Luke is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Luke is a knight then Jack is a knave.", "Samuel cannot be a knight, because this would contradict the claim of James that Harper is a knight if and only if Samuel is a knight.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Harper is a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the false claim of their own that If Luke is a knight then Jack is a knave.", "We have exhausted all possibilities for Luke and Harper, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Samuel is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Luke is a knight if and only if Luke is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Luke is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Luke is a knight then Jack is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('lying', 5)), ('or', ('lying', 0), ('lying', 5)), ('->', ('telling-truth', 2), ('lying', 0)), ('lying', 4), ('<=>', ('telling-truth', 2), ('lying', 2)), ('<=>', ('telling-truth', 4), ('telling-truth', 3)))", "index": 816}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Amelia, Lucas, Elizabeth, Sofia, and Aiden. Oliver was heard saying, \"Lucas is not a knave\". According to Amelia, \"If Elizabeth is a knave then Oliver is a knave\". Lucas commented, \"Elizabeth is a knight\". As Elizabeth put it, \"Sofia is a knight if and only if Sofia is a knave\". Sofia said that Lucas is a knight. Aiden commented, \"Oliver is a knave or Elizabeth is a knave\". So who is a knight and who is a knave?", "names": ["Oliver", "Amelia", "Lucas", "Elizabeth", "Sofia", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true], "solution_text": "Oliver is a knave, Amelia is a knight, Lucas is a knave, Elizabeth is a knave, Sofia is a knave, and Aiden is a knight.", "solution_text_format": "(1) Oliver is a knave\n(2) Amelia is a knight\n(3) Lucas is a knave\n(4) Elizabeth is a knave\n(5) Sofia is a knave\n(6) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Sofia is a knight if and only if Sofia is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Lucas that Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Oliver that Lucas is not a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Lucas is not a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Oliver that Lucas is not a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Lucas that Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Lucas is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Oliver is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Oliver is a knave or Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('->', ('lying', 3), ('lying', 0)), ('telling-truth', 3), ('<=>', ('telling-truth', 4), ('lying', 4)), ('telling-truth', 2), ('or', ('lying', 0), ('lying', 3)))", "index": 817}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Matthew, Mason, Grace, Henry, and William. Daniel said that Matthew is a knight if and only if Daniel is a knight. Matthew commented, \"William is a knight\". According to Mason, \"William is not a knight\". According to Grace, \"Daniel is a knight\". Henry told you that If Mason is a knight then Matthew is a knave. William remarked, \"Grace is not a knave\". So who is a knight and who is a knave?", "names": ["Daniel", "Matthew", "Mason", "Grace", "Henry", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Daniel is a knight, Matthew is a knight, Mason is a knave, Grace is a knight, Henry is a knight, and William is a knight.", "solution_text_format": "(1) Daniel is a knight\n(2) Matthew is a knight\n(3) Mason is a knave\n(4) Grace is a knight\n(5) Henry is a knight\n(6) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Daniel is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Grace is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Daniel is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that William is not a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that William is not a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If Mason is a knight then Matthew is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('telling-truth', 5), ('not', ('telling-truth', 5)), ('telling-truth', 0), ('->', ('telling-truth', 2), ('lying', 1)), ('not', ('lying', 3)))", "index": 818}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, David, Grace, Liam, Henry, and Scarlett. \"Aiden is a knight and David is a knight,\" Aiden mentioned. According to David, \"If Scarlett is a knight then Liam is a knight\". \"If Henry is a knave then David is a knave,\" Grace claimed. \"Henry is a knave\" - Liam. In a statement by Henry: \"If Aiden is a knight then Scarlett is a knight\". Scarlett expressed that If Aiden is a knight then David is a knight. So who is a knight and who is a knave?", "names": ["Aiden", "David", "Grace", "Liam", "Henry", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true], "solution_text": "Aiden is a knave, David is a knave, Grace is a knight, Liam is a knave, Henry is a knight, and Scarlett is a knight.", "solution_text_format": "(1) Aiden is a knave\n(2) David is a knave\n(3) Grace is a knight\n(4) Liam is a knave\n(5) Henry is a knight\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Aiden is a knight and David is a knight.", "Assume David is a knight. No contradiction is found in their claim that If Scarlett is a knight then Liam is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Aiden is a knight then David is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Liam that Henry is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knight then Scarlett is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of David that If Scarlett is a knight then Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knight then David is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Aiden that Aiden is a knight and David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aiden is a knight and David is a knight.", "Assume David is a knight. No contradiction is found in their claim that If Scarlett is a knight then Liam is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Aiden is a knight then David is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Liam that Henry is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knight then Scarlett is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of David that If Scarlett is a knight then Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knight then David is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that If Scarlett is a knight then Liam is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Aiden is a knight then David is a knight.", "Liam cannot be a knight, because this would contradict the false claim of David that If Scarlett is a knight then Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Aiden is a knight then Scarlett is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Henry is a knave then David is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('lying', 4), ('lying', 1)), ('lying', 4), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('->', ('telling-truth', 0), ('telling-truth', 1)))", "index": 819}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Zoey, Alexander, Daniel, Sebastian, Amelia, and Owen. \"Owen is a knight and Zoey is a knight,\" Zoey claimed. Alexander remarked, \"If Daniel is a knight then Alexander is a knight\". Daniel remarked, \"Amelia is a knight if and only if Alexander is a knight\". Sebastian commented, \"Alexander is a knight\". Amelia said that Daniel is a knight if and only if Owen is a knave. Owen remarked, \"Sebastian is a knight or Zoey is a knight\". So who is a knight and who is a knave?", "names": ["Zoey", "Alexander", "Daniel", "Sebastian", "Amelia", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Zoey is a knight, Alexander is a knave, Daniel is a knight, Sebastian is a knave, Amelia is a knave, and Owen is a knight.", "solution_text_format": "(1) Zoey is a knight\n(2) Alexander is a knave\n(3) Daniel is a knight\n(4) Sebastian is a knave\n(5) Amelia is a knave\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that Owen is a knight and Zoey is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Sebastian is a knight or Zoey is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Daniel is a knight then Alexander is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Alexander is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Owen is a knave.", "Amelia cannot be a knave, because this would contradict the claim of Daniel that Amelia is a knight if and only if Alexander is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Alexander is a knight.", "Amelia cannot be a knight, because this would contradict the false claim of Daniel that Amelia is a knight if and only if Alexander is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight if and only if Owen is a knave.", "We have exhausted all possibilities for Amelia and Daniel, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Sebastian that Alexander is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Sebastian that Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Daniel is a knight then Alexander is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Alexander is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Daniel that Amelia is a knight if and only if Alexander is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 0)), ('->', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('telling-truth', 1), ('<=>', ('telling-truth', 2), ('lying', 5)), ('or', ('telling-truth', 3), ('telling-truth', 0)))", "index": 820}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Liam, Daniel, Riley, Zoey, and Ethan. Aiden remarked, \"Liam is a knight if and only if Ethan is a knight\". According to Liam, \"If Daniel is a knight then Aiden is a knight\". Daniel expressed that Ethan is a knave and Zoey is a knight. Riley stated, \"Aiden is a knight and Ethan is a knave\". \"Liam is not a knight,\" Zoey declared. Ethan expressed that Zoey is a knight or Riley is a knight. So who is a knight and who is a knave?", "names": ["Aiden", "Liam", "Daniel", "Riley", "Zoey", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false], "solution_text": "Aiden is a knave, Liam is a knight, Daniel is a knave, Riley is a knave, Zoey is a knave, and Ethan is a knave.", "solution_text_format": "(1) Aiden is a knave\n(2) Liam is a knight\n(3) Daniel is a knave\n(4) Riley is a knave\n(5) Zoey is a knave\n(6) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Liam is a knight if and only if Ethan is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Daniel is a knight then Aiden is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Ethan is a knave and Zoey is a knight.", "Ethan cannot be a knight, because this would contradict the claim of Daniel that Ethan is a knave and Zoey is a knight.", "Ethan cannot be a knave, because this would contradict the claim of Aiden that Liam is a knight if and only if Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ethan is a knave and Zoey is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Zoey is a knight or Riley is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Liam is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Ethan is a knave.", "Riley cannot be a knave, because this would contradict the claim of Ethan that Zoey is a knight or Riley is a knight.", "We have exhausted all possibilities for Riley and Zoey, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Aiden that Liam is a knight if and only if Ethan is a knight.", "We have exhausted all possibilities for Ethan and Daniel, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knight then Aiden is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Ethan is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Daniel is a knight then Aiden is a knight.", "Daniel cannot be a knight, because this would contradict the claim of Liam that If Daniel is a knight then Aiden is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Ethan is a knave and Zoey is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Aiden that Liam is a knight if and only if Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Zoey is a knight or Riley is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of Daniel that Ethan is a knave and Zoey is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Riley cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Ethan is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Aiden is a knight and Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 5)), ('->', ('telling-truth', 2), ('telling-truth', 0)), ('and', ('lying', 5), ('telling-truth', 4)), ('and', ('telling-truth', 0), ('lying', 5)), ('not', ('telling-truth', 1)), ('or', ('telling-truth', 4), ('telling-truth', 3)))", "index": 821}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Emma, Benjamin, Elizabeth, Samuel, and Aurora. Daniel said, \"Elizabeth is not a knight.\" Emma remarked, \"If Emma is a knight then Aurora is a knave\". \"Benjamin is a knight if and only if Daniel is a knave\" - Benjamin. As Elizabeth put it, \"Samuel is not a knave\". \"Benjamin is a knave if and only if Aurora is a knave,\" Samuel mentioned. Aurora noted, \"If Emma is a knight then Aurora is a knight\". So who is a knight and who is a knave?", "names": ["Daniel", "Emma", "Benjamin", "Elizabeth", "Samuel", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Daniel is a knave, Emma is a knight, Benjamin is a knave, Elizabeth is a knight, Samuel is a knight, and Aurora is a knave.", "solution_text_format": "(1) Daniel is a knave\n(2) Emma is a knight\n(3) Benjamin is a knave\n(4) Elizabeth is a knight\n(5) Samuel is a knight\n(6) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Daniel that Elizabeth is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Samuel is not a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Elizabeth that Samuel is not a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Aurora is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight if and only if Daniel is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knight if and only if Daniel is a knave.", "We have exhausted all possibilities for Benjamin, Samuel, and Elizabeth, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Elizabeth is not a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Aurora is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Daniel is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Emma is a knight then Aurora is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that If Emma is a knight then Aurora is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Aurora is a knave.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Samuel that Benjamin is a knave if and only if Aurora is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Daniel is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Samuel that Benjamin is a knave if and only if Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that If Emma is a knight then Aurora is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Emma is a knight then Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('->', ('telling-truth', 1), ('lying', 5)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('not', ('lying', 4)), ('<=>', ('lying', 2), ('lying', 5)), ('->', ('telling-truth', 1), ('telling-truth', 5)))", "index": 822}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Lily, Henry, Charlotte, Scarlett, and Lucas. Ella commented, \"Lily is a knave\". Lily said that Scarlett is a knave if and only if Charlotte is a knave. Henry stated, \"Lily is a knight if and only if Scarlett is a knight\". In a statement by Charlotte: \"Lucas is not a knave\". Scarlett was heard saying, \"Lucas is a knave or Henry is a knight\". Lucas was heard saying, \"Lily is a knight if and only if Ella is a knave\". So who is a knight and who is a knave?", "names": ["Ella", "Lily", "Henry", "Charlotte", "Scarlett", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Ella is a knave, Lily is a knight, Henry is a knight, Charlotte is a knight, Scarlett is a knight, and Lucas is a knight.", "solution_text_format": "(1) Ella is a knave\n(2) Lily is a knight\n(3) Henry is a knight\n(4) Charlotte is a knight\n(5) Scarlett is a knight\n(6) Lucas is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Ella that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Charlotte is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Lucas is a knave or Henry is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Lily is a knight if and only if Ella is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that Lily is a knight if and only if Scarlett is a knight.", "Henry cannot be a knave, because this would contradict the claim of Scarlett that Lucas is a knave or Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of their own that Lily is a knight if and only if Ella is a knave.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Lucas is a knave or Henry is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Lily is a knight if and only if Ella is a knave.", "Henry cannot be a knight, because this would contradict the false claim of Scarlett that Lucas is a knave or Henry is a knight.", "Henry cannot be a knave, because this would contradict the false claim of their own that Lily is a knight if and only if Scarlett is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the false claim of Scarlett that Lucas is a knave or Henry is a knight.", "We have exhausted all possibilities for Lucas, Scarlett, and Lily, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Charlotte is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Lucas is a knave or Henry is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Lily is a knight if and only if Ella is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Lily is a knight if and only if Scarlett is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Lucas is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('<=>', ('lying', 4), ('lying', 3)), ('<=>', ('telling-truth', 1), ('telling-truth', 4)), ('not', ('lying', 5)), ('or', ('lying', 5), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('lying', 0)))", "index": 823}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Mason, Jacob, Benjamin, Logan, and Daniel. Abigail remarked, \"Benjamin is a knave and Daniel is a knave\". In Mason's words: \"Logan is a knight or Abigail is a knave\". Jacob was heard saying, \"If Benjamin is a knight then Benjamin is a knave\". \"If Abigail is a knave then Mason is a knight,\" Benjamin claimed. Logan was heard saying, \"Jacob is a knight if and only if Daniel is a knave\". Daniel said that Jacob is a knave if and only if Mason is a knight. So who is a knight and who is a knave?", "names": ["Abigail", "Mason", "Jacob", "Benjamin", "Logan", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Abigail is a knave, Mason is a knight, Jacob is a knave, Benjamin is a knight, Logan is a knight, and Daniel is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Mason is a knight\n(3) Jacob is a knave\n(4) Benjamin is a knight\n(5) Logan is a knight\n(6) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Benjamin is a knave and Daniel is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Abigail that Benjamin is a knave and Daniel is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that If Abigail is a knave then Mason is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Benjamin is a knave and Daniel is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Abigail is a knave then Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Logan is a knight or Abigail is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Daniel is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that If Benjamin is a knight then Benjamin is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Benjamin is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 5)), ('or', ('telling-truth', 4), ('lying', 0)), ('->', ('telling-truth', 3), ('lying', 3)), ('->', ('lying', 0), ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('lying', 5)), ('<=>', ('lying', 2), ('telling-truth', 1)))", "index": 824}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Benjamin, Ava, Joseph, Emma, and Mia. Evelyn commented, \"Ava is a knave\". Benjamin commented, \"Ava is a knight or Evelyn is a knave\". Ava stated, \"If Joseph is a knave then Evelyn is a knight\". \"If Mia is a knight then Benjamin is a knight,\" Joseph declared. Emma expressed that Benjamin is a knave if and only if Mia is a knave. Mia expressed that Joseph is a knave. So who is a knight and who is a knave?", "names": ["Evelyn", "Benjamin", "Ava", "Joseph", "Emma", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Evelyn is a knave, Benjamin is a knight, Ava is a knight, Joseph is a knight, Emma is a knave, and Mia is a knave.", "solution_text_format": "(1) Evelyn is a knave\n(2) Benjamin is a knight\n(3) Ava is a knight\n(4) Joseph is a knight\n(5) Emma is a knave\n(6) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Evelyn that Ava is a knave.", "Ava cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knave then Evelyn is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Joseph is a knave then Evelyn is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Mia is a knight then Benjamin is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that Joseph is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Ava is a knight or Evelyn is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave if and only if Mia is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Mia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('or', ('telling-truth', 2), ('lying', 0)), ('->', ('lying', 3), ('telling-truth', 0)), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('<=>', ('lying', 1), ('lying', 5)), ('lying', 3))", "index": 825}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Victoria, Mason, Aiden, Aurora, and Jacob. Isabella was heard saying, \"Victoria is a knight if and only if Aiden is a knave\". As Victoria put it, \"If Aurora is a knight then Jacob is a knight\". \"Aurora is a knight and Aiden is a knight,\" Mason claimed. Aiden expressed that If Jacob is a knight then Victoria is a knight. Aurora commented, \"Mason is a knave and Jacob is a knight\". In a statement by Jacob: \"Victoria is not a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Victoria", "Mason", "Aiden", "Aurora", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false], "solution_text": "Isabella is a knave, Victoria is a knight, Mason is a knave, Aiden is a knight, Aurora is a knave, and Jacob is a knave.", "solution_text_format": "(1) Isabella is a knave\n(2) Victoria is a knight\n(3) Mason is a knave\n(4) Aiden is a knight\n(5) Aurora is a knave\n(6) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Aiden is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Aurora is a knight then Jacob is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Mason is a knave and Jacob is a knight.", "Mason cannot be a knight, because this would contradict the claim of Aurora that Mason is a knave and Jacob is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Aurora is a knight and Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Isabella that Victoria is a knight if and only if Aiden is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knight then Victoria is a knight.", "We have exhausted all possibilities for Aiden and Mason, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Mason is a knave and Jacob is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Aiden is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Aurora is a knight and Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Isabella that Victoria is a knight if and only if Aiden is a knave.", "Aiden cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knight then Victoria is a knight.", "We have exhausted all possibilities for Aiden, Mason, and Aurora, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Aurora is a knight then Jacob is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Mason is a knave and Jacob is a knight.", "Mason cannot be a knight, because this would contradict the claim of Aurora that Mason is a knave and Jacob is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Aurora is a knight and Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Mason that Aurora is a knight and Aiden is a knight.", "Aiden cannot be a knave, because this would contradict the claim of Isabella that Victoria is a knight if and only if Aiden is a knave.", "We have exhausted all possibilities for Aiden and Mason, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of Victoria that If Aurora is a knight then Jacob is a knight.", "We have exhausted all possibilities for Aurora and Victoria, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Aiden is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that If Aurora is a knight then Jacob is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Mason is a knave and Jacob is a knight.", "Mason cannot be a knight, because this would contradict the claim of Aurora that Mason is a knave and Jacob is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Aurora is a knight and Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Mason that Aurora is a knight and Aiden is a knight.", "Aiden cannot be a knave, because this would contradict the false claim of Isabella that Victoria is a knight if and only if Aiden is a knave.", "We have exhausted all possibilities for Aiden and Mason, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Mason is a knave and Jacob is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Aiden is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Aurora is a knight and Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Jacob is a knight then Victoria is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Aurora that Mason is a knave and Jacob is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Victoria is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 3)), ('->', ('telling-truth', 4), ('telling-truth', 5)), ('and', ('telling-truth', 4), ('telling-truth', 3)), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('and', ('lying', 2), ('telling-truth', 5)), ('not', ('telling-truth', 1)))", "index": 826}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Ella, Mason, Grace, Avery, and Emily. Mia commented, \"If Grace is a knight then Emily is a knave\". In a statement by Ella: \"Avery is a knight\". Mason said that Mia is a knight or Avery is a knave. \"If Avery is a knight then Grace is a knight\" - Grace. Avery commented, \"Grace is not a knave\". Emily remarked, \"If Avery is a knave then Emily is a knight\". So who is a knight and who is a knave?", "names": ["Mia", "Ella", "Mason", "Grace", "Avery", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Mia is a knave, Ella is a knight, Mason is a knave, Grace is a knight, Avery is a knight, and Emily is a knight.", "solution_text_format": "(1) Mia is a knave\n(2) Ella is a knight\n(3) Mason is a knave\n(4) Grace is a knight\n(5) Avery is a knight\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that If Grace is a knight then Emily is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Avery is a knight then Grace is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Grace is not a knave.", "Emily cannot be a knight, because this would contradict the claim of Mia that If Grace is a knight then Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that If Avery is a knave then Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the false claim of their own that Grace is not a knave.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that If Avery is a knight then Grace is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Grace is not a knave.", "Avery cannot be a knave, because this would contradict the false claim of Grace that If Avery is a knight then Grace is a knight.", "We have exhausted all possibilities for Avery and Grace, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that If Grace is a knight then Emily is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that If Avery is a knight then Grace is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Grace is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Avery is a knave then Emily is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Avery is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Mia is a knight or Avery is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Mia is a knight or Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('lying', 5)), ('telling-truth', 4), ('or', ('telling-truth', 0), ('lying', 4)), ('->', ('telling-truth', 4), ('telling-truth', 3)), ('not', ('lying', 3)), ('->', ('lying', 4), ('telling-truth', 5)))", "index": 827}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Aurora, James, Jack, Ella, and Sophia. Matthew remarked, \"Sophia is not a knave\". Aurora expressed that If Aurora is a knight then Jack is a knave. James was heard saying, \"Jack is a knight and Aurora is a knight\". Jack stated, \"Ella is a knight or Jack is a knight\". Ella stated, \"Aurora is a knave if and only if Jack is a knave\". Sophia noted, \"Matthew is a knight or James is a knave\". So who is a knight and who is a knave?", "names": ["Matthew", "Aurora", "James", "Jack", "Ella", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true], "solution_text": "Matthew is a knight, Aurora is a knight, James is a knave, Jack is a knave, Ella is a knave, and Sophia is a knight.", "solution_text_format": "(1) Matthew is a knight\n(2) Aurora is a knight\n(3) James is a knave\n(4) Jack is a knave\n(5) Ella is a knave\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Matthew is a knight or James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Jack is a knight and Aurora is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Ella is a knight or Jack is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Jack is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that If Aurora is a knight then Jack is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knight then Jack is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Jack is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that If Aurora is a knight then Jack is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knight then Jack is a knave.", "We have exhausted all possibilities for Aurora and Ella, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of James that Jack is a knight and Aurora is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Jack is a knight and Aurora is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Ella is a knight or Jack is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Jack is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that If Aurora is a knight then Jack is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knight then Jack is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Jack is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that If Aurora is a knight then Jack is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knight then Jack is a knave.", "We have exhausted all possibilities for Aurora and Ella, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Ella is a knight or Jack is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Jack that Ella is a knight or Jack is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Jack is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Aurora is a knight then Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('->', ('telling-truth', 1), ('lying', 3)), ('and', ('telling-truth', 3), ('telling-truth', 1)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('<=>', ('lying', 1), ('lying', 3)), ('or', ('telling-truth', 0), ('lying', 2)))", "index": 828}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Samuel, Luke, Amelia, Ava, and Noah. \"Samuel is a knave if and only if Ava is a knight,\" Avery claimed. Samuel expressed that Avery is a knight. \"Noah is not a knight,\" Luke claimed. \"Avery is not a knight,\" Amelia mentioned. Ava told you that Samuel is a knight and Noah is a knight. Noah commented, \"Avery is not a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Samuel", "Luke", "Amelia", "Ava", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Avery is a knave, Samuel is a knave, Luke is a knight, Amelia is a knight, Ava is a knave, and Noah is a knave.", "solution_text_format": "(1) Avery is a knave\n(2) Samuel is a knave\n(3) Luke is a knight\n(4) Amelia is a knight\n(5) Ava is a knave\n(6) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Ava is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Avery is a knight.", "Ava cannot be a knight, because this would contradict the claim of Avery that Samuel is a knave if and only if Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Samuel is a knight and Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Ava that Samuel is a knight and Noah is a knight.", "Noah cannot be a knave, because this would contradict the false claim of their own that Avery is not a knave.", "We have exhausted all possibilities for Noah and Ava, so let us go back and reconsider Samuel.", "Samuel cannot be a knave, because this would contradict the false claim of their own that Avery is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Ava is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Avery is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Avery is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Avery that Samuel is a knave if and only if Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Samuel is a knight and Noah is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that Avery is not a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Avery is not a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Noah is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Avery is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 4)), ('telling-truth', 0), ('not', ('telling-truth', 5)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 1), ('telling-truth', 5)), ('not', ('lying', 0)))", "index": 829}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Olivia, Alexander, Sofia, Aria, and Abigail. Ella remarked, \"Ella is a knight if and only if Sofia is a knight\". As Olivia put it, \"Alexander is a knave\". \"Sofia is a knight,\" Alexander mentioned. Sofia stated, \"Ella is not a knight\". Aria asserted: \"Ella is not a knight\". Abigail noted, \"Alexander is a knave\". So who is a knight and who is a knave?", "names": ["Ella", "Olivia", "Alexander", "Sofia", "Aria", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Ella is a knave, Olivia is a knave, Alexander is a knight, Sofia is a knight, Aria is a knight, and Abigail is a knave.", "solution_text_format": "(1) Ella is a knave\n(2) Olivia is a knave\n(3) Alexander is a knight\n(4) Sofia is a knight\n(5) Aria is a knight\n(6) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Ella is a knight if and only if Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Ella is not a knight.", "Sofia cannot be a knave, because this would contradict the claim of Ella that Ella is a knight if and only if Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Ella is not a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Olivia that Alexander is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Sofia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Ella is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Alexander is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('telling-truth', 3)), ('lying', 2), ('telling-truth', 3), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('lying', 2))", "index": 830}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Chloe, Benjamin, Aiden, Jackson, and Elizabeth. Mason told you that Elizabeth is a knave if and only if Elizabeth is a knight. \"If Aiden is a knight then Elizabeth is a knight\" - Chloe. According to Benjamin, \"If Jackson is a knave then Chloe is a knave\". In Aiden's words: \"If Chloe is a knight then Mason is a knight\". Jackson noted, \"Aiden is a knight or Elizabeth is a knight\". \"If Mason is a knight then Benjamin is a knight,\" Elizabeth declared. So who is a knight and who is a knave?", "names": ["Mason", "Chloe", "Benjamin", "Aiden", "Jackson", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Mason is a knave, Chloe is a knight, Benjamin is a knight, Aiden is a knave, Jackson is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Chloe is a knight\n(3) Benjamin is a knight\n(4) Aiden is a knave\n(5) Jackson is a knight\n(6) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Mason cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave if and only if Elizabeth is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Mason is a knight then Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Jackson is a knave then Chloe is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Aiden is a knight or Elizabeth is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Chloe is a knight then Mason is a knight.", "Chloe cannot be a knight, because this would contradict the claim of Aiden that If Chloe is a knight then Mason is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knight then Elizabeth is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Chloe is a knight then Mason is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Aiden is a knight then Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('telling-truth', 5)), ('->', ('telling-truth', 3), ('telling-truth', 5)), ('->', ('lying', 4), ('lying', 1)), ('->', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 3), ('telling-truth', 5)), ('->', ('telling-truth', 0), ('telling-truth', 2)))", "index": 831}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Luke, Scarlett, Zoey, Samuel, and Emma. Aria was heard saying, \"Emma is a knight and Emma is a knave\". \"Scarlett is a knave\" - Luke. As Scarlett put it, \"If Luke is a knave then Zoey is a knave\". \"Aria is a knight if and only if Scarlett is a knight,\" Zoey declared. Samuel expressed that Emma is a knave. \"Scarlett is a knight\" - Emma. So who is a knight and who is a knave?", "names": ["Aria", "Luke", "Scarlett", "Zoey", "Samuel", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true], "solution_text": "Aria is a knave, Luke is a knave, Scarlett is a knight, Zoey is a knave, Samuel is a knave, and Emma is a knight.", "solution_text_format": "(1) Aria is a knave\n(2) Luke is a knave\n(3) Scarlett is a knight\n(4) Zoey is a knave\n(5) Samuel is a knave\n(6) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Aria cannot be a knight, because this would contradict the claim of their own that Emma is a knight and Emma is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Emma is a knight and Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Luke is a knave then Zoey is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Scarlett is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Scarlett that If Luke is a knave then Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Scarlett is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Emma is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 5)), ('lying', 2), ('->', ('lying', 1), ('lying', 3)), ('<=>', ('telling-truth', 0), ('telling-truth', 2)), ('lying', 5), ('telling-truth', 2))", "index": 832}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Ella, Elizabeth, Noah, Aria, and Emily. \"If Aria is a knave then Noah is a knave,\" Samuel mentioned. \"Samuel is not a knave,\" Ella claimed. Elizabeth expressed that Aria is a knave or Samuel is a knight. \"Ella is a knight if and only if Samuel is a knight,\" Noah declared. Aria expressed that Noah is a knight or Ella is a knight. Emily stated, \"Noah is not a knave\". So who is a knight and who is a knave?", "names": ["Samuel", "Ella", "Elizabeth", "Noah", "Aria", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Samuel is a knight, Ella is a knight, Elizabeth is a knight, Noah is a knight, Aria is a knight, and Emily is a knight.", "solution_text_format": "(1) Samuel is a knight\n(2) Ella is a knight\n(3) Elizabeth is a knight\n(4) Noah is a knight\n(5) Aria is a knight\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that If Aria is a knave then Noah is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Noah is a knight or Ella is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Ella is a knight if and only if Samuel is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Aria is a knave or Samuel is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Noah is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('lying', 3)), ('not', ('lying', 0)), ('or', ('lying', 4), ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 3), ('telling-truth', 1)), ('not', ('lying', 3)))", "index": 833}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Elizabeth, Emily, Owen, Sebastian, and Joseph. Ethan told you that Emily is a knight. Elizabeth asserted: \"If Sebastian is a knight then Ethan is a knight\". Emily was heard saying, \"Ethan is a knave and Emily is a knight\". \"Sebastian is a knight or Ethan is a knight,\" Owen declared. Sebastian expressed that Emily is a knave and Emily is a knight. \"Sebastian is a knight or Owen is a knight\" - Joseph. So who is a knight and who is a knave?", "names": ["Ethan", "Elizabeth", "Emily", "Owen", "Sebastian", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false], "solution_text": "Ethan is a knave, Elizabeth is a knight, Emily is a knave, Owen is a knave, Sebastian is a knave, and Joseph is a knave.", "solution_text_format": "(1) Ethan is a knave\n(2) Elizabeth is a knight\n(3) Emily is a knave\n(4) Owen is a knave\n(5) Sebastian is a knave\n(6) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Ethan is a knave and Emily is a knight.", "Emily cannot be a knave, because this would contradict the claim of Ethan that Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Ethan that Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Ethan is a knave and Emily is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Sebastian is a knight then Ethan is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Elizabeth that If Sebastian is a knight then Ethan is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Emily is a knave and Emily is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight or Ethan is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Sebastian is a knight or Ethan is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight or Owen is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Sebastian is a knight or Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('lying', 0), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('lying', 2), ('telling-truth', 2)), ('or', ('telling-truth', 4), ('telling-truth', 3)))", "index": 834}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Riley, Jacob, Logan, Amelia, and Scarlett. \"Scarlett is a knight\" - Harper. \"Riley is a knight\" - Riley. Jacob expressed that Logan is a knave. Logan told you that Amelia is a knight if and only if Riley is a knight. Amelia noted, \"Harper is a knave and Jacob is a knight\". Scarlett said that Jacob is a knave if and only if Amelia is a knave. So who is a knight and who is a knave?", "names": ["Harper", "Riley", "Jacob", "Logan", "Amelia", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true], "solution_text": "Harper is a knight, Riley is a knave, Jacob is a knave, Logan is a knight, Amelia is a knave, and Scarlett is a knight.", "solution_text_format": "(1) Harper is a knight\n(2) Riley is a knave\n(3) Jacob is a knave\n(4) Logan is a knight\n(5) Amelia is a knave\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Jacob is a knave if and only if Amelia is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Jacob that Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Riley is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Jacob is a knight.", "Amelia cannot be a knave, because this would contradict the claim of Scarlett that Jacob is a knave if and only if Amelia is a knave.", "We have exhausted all possibilities for Amelia and Logan, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Riley is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Jacob is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Harper is a knave and Jacob is a knight.", "Riley cannot be a knight, because this would contradict the claim of Logan that Amelia is a knight if and only if Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('telling-truth', 1), ('lying', 3), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('and', ('lying', 0), ('telling-truth', 2)), ('<=>', ('lying', 2), ('lying', 4)))", "index": 835}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Sofia, Grace, James, Logan, and Noah. \"Sofia is a knight and Grace is a knave,\" Chloe claimed. \"Noah is a knave or James is a knave,\" Sofia declared. \"Logan is a knave and Chloe is a knave,\" Grace declared. James commented, \"If Logan is a knave then Noah is a knave\". According to Logan, \"James is a knave\". Noah was heard saying, \"Grace is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Sofia", "Grace", "James", "Logan", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Chloe is a knave, Sofia is a knight, Grace is a knight, James is a knight, Logan is a knave, and Noah is a knave.", "solution_text_format": "(1) Chloe is a knave\n(2) Sofia is a knight\n(3) Grace is a knight\n(4) James is a knight\n(5) Logan is a knave\n(6) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Sofia is a knight and Grace is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Noah is a knave or James is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Chloe that Sofia is a knight and Grace is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Logan is a knave and Chloe is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Sofia that Noah is a knave or James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that If Logan is a knave then Noah is a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Sofia that Noah is a knave or James is a knave.", "James cannot be a knave, because this would contradict the false claim of Logan that James is a knave.", "We have exhausted all possibilities for James, Logan, and Grace, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Chloe that Sofia is a knight and Grace is a knave.", "Grace cannot be a knave, because this would contradict the false claim of Noah that Grace is a knave.", "We have exhausted all possibilities for Grace and Noah, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of Chloe that Sofia is a knight and Grace is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Sofia is a knight and Grace is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Noah is a knave or James is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Noah that Grace is a knave.", "Grace cannot be a knave, because this would contradict the false claim of Chloe that Sofia is a knight and Grace is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Logan is a knave and Chloe is a knave.", "Logan cannot be a knight, because this would contradict the claim of Grace that Logan is a knave and Chloe is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that James is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Logan is a knave then Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 2)), ('or', ('lying', 5), ('lying', 3)), ('and', ('lying', 4), ('lying', 0)), ('->', ('lying', 4), ('lying', 5)), ('lying', 3), ('lying', 2))", "index": 836}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Aria, Logan, Lucas, Daniel, and Benjamin. In a statement by Alexander: \"Benjamin is a knight or Lucas is a knight\". In a statement by Aria: \"Logan is a knave\". According to Logan, \"Alexander is a knight\". According to Lucas, \"If Logan is a knight then Aria is a knave\". Daniel was heard saying, \"Logan is a knight if and only if Lucas is a knight\". Benjamin expressed that Lucas is a knave and Lucas is a knight. So who is a knight and who is a knave?", "names": ["Alexander", "Aria", "Logan", "Lucas", "Daniel", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Alexander is a knight, Aria is a knave, Logan is a knight, Lucas is a knight, Daniel is a knight, and Benjamin is a knave.", "solution_text_format": "(1) Alexander is a knight\n(2) Aria is a knave\n(3) Logan is a knight\n(4) Lucas is a knight\n(5) Daniel is a knight\n(6) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Benjamin is a knight or Lucas is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Lucas is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Lucas is a knave and Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Logan is a knight then Aria is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Alexander is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Logan is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Logan is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Logan is a knight if and only if Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 3)), ('lying', 2), ('telling-truth', 0), ('->', ('telling-truth', 2), ('lying', 1)), ('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('and', ('lying', 3), ('telling-truth', 3)))", "index": 837}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Olivia, Penelope, Oliver, Benjamin, and Scarlett. Ella was heard saying, \"Oliver is a knight\". Olivia remarked, \"Scarlett is a knave if and only if Penelope is a knight\". \"Oliver is a knave\" - Penelope. In a statement by Oliver: \"Olivia is a knight if and only if Penelope is a knight\". \"If Scarlett is a knave then Benjamin is a knight,\" Benjamin claimed. Scarlett noted, \"Olivia is a knave\". So who is a knight and who is a knave?", "names": ["Ella", "Olivia", "Penelope", "Oliver", "Benjamin", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true], "solution_text": "Ella is a knave, Olivia is a knave, Penelope is a knight, Oliver is a knave, Benjamin is a knight, and Scarlett is a knight.", "solution_text_format": "(1) Ella is a knave\n(2) Olivia is a knave\n(3) Penelope is a knight\n(4) Oliver is a knave\n(5) Benjamin is a knight\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Penelope is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Penelope is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Penelope cannot be a knave, because this would contradict the claim of Olivia that Scarlett is a knave if and only if Penelope is a knight.", "We have exhausted all possibilities for Penelope and Scarlett, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Penelope is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Olivia is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Oliver is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of Olivia that Scarlett is a knave if and only if Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Scarlett.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave.", "We have exhausted all possibilities for Scarlett and Olivia, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Ella that Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Ella that Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Penelope is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Penelope is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Oliver that Olivia is a knight if and only if Penelope is a knight.", "Penelope cannot be a knave, because this would contradict the claim of Olivia that Scarlett is a knave if and only if Penelope is a knight.", "We have exhausted all possibilities for Penelope and Scarlett, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Penelope is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Olivia is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Oliver is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Scarlett is a knave then Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('<=>', ('lying', 5), ('telling-truth', 2)), ('lying', 3), ('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('lying', 5), ('telling-truth', 4)), ('lying', 1))", "index": 838}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Matthew, Michael, Jacob, Lucas, and Charlotte. Aurora told you that Michael is not a knave. Matthew stated, \"Lucas is not a knave\". Michael expressed that Charlotte is a knight. \"If Matthew is a knight then Aurora is a knight,\" Jacob mentioned. Lucas stated, \"Michael is a knight\". Charlotte noted, \"If Aurora is a knave then Michael is a knave\". So who is a knight and who is a knave?", "names": ["Aurora", "Matthew", "Michael", "Jacob", "Lucas", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Aurora is a knight, Matthew is a knight, Michael is a knight, Jacob is a knight, Lucas is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Aurora is a knight\n(2) Matthew is a knight\n(3) Michael is a knight\n(4) Jacob is a knight\n(5) Lucas is a knight\n(6) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Michael is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Aurora is a knave then Michael is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Michael is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Matthew is a knight then Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('not', ('lying', 4)), ('telling-truth', 5), ('->', ('telling-truth', 1), ('telling-truth', 0)), ('telling-truth', 2), ('->', ('lying', 0), ('lying', 2)))", "index": 839}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Samuel, Henry, Mason, Aria, and William. In James's words: \"Aria is a knight\". Samuel was heard saying, \"Mason is a knave and Henry is a knave\". \"William is a knave if and only if Aria is a knight,\" Henry mentioned. According to Mason, \"Aria is a knight\". In Aria's words: \"Aria is a knight or William is a knight\". According to William, \"Mason is a knave or Aria is a knight\". So who is a knight and who is a knave?", "names": ["James", "Samuel", "Henry", "Mason", "Aria", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true], "solution_text": "James is a knight, Samuel is a knave, Henry is a knave, Mason is a knight, Aria is a knight, and William is a knight.", "solution_text_format": "(1) James is a knight\n(2) Samuel is a knave\n(3) Henry is a knave\n(4) Mason is a knight\n(5) Aria is a knight\n(6) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Aria is a knight or William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Mason is a knave or Aria is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Aria is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Henry is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Mason is a knave and Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of their own that William is a knave if and only if Aria is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that William is a knave if and only if Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('and', ('lying', 3), ('lying', 2)), ('<=>', ('lying', 5), ('telling-truth', 4)), ('telling-truth', 4), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('or', ('lying', 3), ('telling-truth', 4)))", "index": 840}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Evelyn, Jackson, Charlotte, Aurora, and Sofia. According to Logan, \"Aurora is a knight or Evelyn is a knight\". Evelyn said that Jackson is a knave or Sofia is a knave. \"Aurora is not a knave,\" Jackson declared. Charlotte expressed that Evelyn is a knight. In a statement by Aurora: \"Jackson is a knave and Sofia is a knight\". Sofia said that If Evelyn is a knight then Jackson is a knight. So who is a knight and who is a knave?", "names": ["Logan", "Evelyn", "Jackson", "Charlotte", "Aurora", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Logan is a knight, Evelyn is a knight, Jackson is a knave, Charlotte is a knight, Aurora is a knave, and Sofia is a knave.", "solution_text_format": "(1) Logan is a knight\n(2) Evelyn is a knight\n(3) Jackson is a knave\n(4) Charlotte is a knight\n(5) Aurora is a knave\n(6) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Aurora is a knight or Evelyn is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Jackson is a knave and Sofia is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Aurora that Jackson is a knave and Sofia is a knight.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Aurora is not a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Jackson is a knave and Sofia is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Aurora is not a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Aurora is not a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Aurora that Jackson is a knave and Sofia is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Jackson is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jackson is a knave or Sofia is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 1)), ('or', ('lying', 2), ('lying', 5)), ('not', ('lying', 4)), ('telling-truth', 1), ('and', ('lying', 2), ('telling-truth', 5)), ('->', ('telling-truth', 1), ('telling-truth', 2)))", "index": 841}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Jack, Amelia, Elizabeth, Oliver, and Sophia. \"Elizabeth is a knight\" - Lily. Jack remarked, \"Lily is a knight\". \"Sophia is a knave if and only if Sophia is a knight,\" Amelia mentioned. Elizabeth told you that If Oliver is a knave then Jack is a knave. Oliver said, \"If Jack is a knave then Elizabeth is a knave.\" Sophia stated, \"Amelia is a knight or Elizabeth is a knight\". So who is a knight and who is a knave?", "names": ["Lily", "Jack", "Amelia", "Elizabeth", "Oliver", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Lily is a knight, Jack is a knight, Amelia is a knave, Elizabeth is a knight, Oliver is a knight, and Sophia is a knight.", "solution_text_format": "(1) Lily is a knight\n(2) Jack is a knight\n(3) Amelia is a knave\n(4) Elizabeth is a knight\n(5) Oliver is a knight\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Oliver is a knave then Jack is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Jack is a knave then Elizabeth is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Lily is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Sophia is a knave if and only if Sophia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Amelia is a knight or Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('telling-truth', 0), ('<=>', ('lying', 5), ('telling-truth', 5)), ('->', ('lying', 4), ('lying', 1)), ('->', ('lying', 1), ('lying', 3)), ('or', ('telling-truth', 2), ('telling-truth', 3)))", "index": 842}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Jack, James, Grace, Luke, and Avery. As Aria put it, \"Grace is a knave and Luke is a knave\". Jack commented, \"Luke is a knave if and only if James is a knight\". James remarked, \"Aria is not a knight\". Grace commented, \"James is a knight or Aria is a knight\". Luke said, \"Grace is a knave if and only if Grace is a knight.\" Avery commented, \"Jack is not a knave\". So who is a knight and who is a knave?", "names": ["Aria", "Jack", "James", "Grace", "Luke", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Aria is a knave, Jack is a knight, James is a knight, Grace is a knight, Luke is a knave, and Avery is a knight.", "solution_text_format": "(1) Aria is a knave\n(2) Jack is a knight\n(3) James is a knight\n(4) Grace is a knight\n(5) Luke is a knave\n(6) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Grace is a knave and Luke is a knave.", "Grace cannot be a knight, because this would contradict the claim of Aria that Grace is a knave and Luke is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that James is a knight or Aria is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Grace is a knave and Luke is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that James is a knight or Aria is a knight.", "Assume James is a knight. No contradiction is found in their claim that Aria is not a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Grace is a knave if and only if Grace is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Grace is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Luke is a knave if and only if James is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Jack is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 4)), ('<=>', ('lying', 4), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('<=>', ('lying', 3), ('telling-truth', 3)), ('not', ('lying', 1)))", "index": 843}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Logan, Sebastian, Daniel, Penelope, and Lucas. Isabella told you that Isabella is a knight or Lucas is a knight. \"If Lucas is a knight then Lucas is a knave\" - Logan. In Sebastian's words: \"Lucas is a knight or Isabella is a knight\". Daniel told you that Sebastian is a knave. In Penelope's words: \"Logan is a knight if and only if Lucas is a knave\". Lucas commented, \"If Sebastian is a knight then Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Logan", "Sebastian", "Daniel", "Penelope", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Isabella is a knight, Logan is a knight, Sebastian is a knight, Daniel is a knave, Penelope is a knight, and Lucas is a knave.", "solution_text_format": "(1) Isabella is a knight\n(2) Logan is a knight\n(3) Sebastian is a knight\n(4) Daniel is a knave\n(5) Penelope is a knight\n(6) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Isabella is a knight or Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Sebastian is a knight then Penelope is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Lucas is a knight or Isabella is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Lucas that If Sebastian is a knight then Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Lucas is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that If Lucas is a knight then Lucas is a knave.", "Logan cannot be a knave, because this would contradict the false claim of Penelope that Logan is a knight if and only if Lucas is a knave.", "We have exhausted all possibilities for Logan and Penelope, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that Lucas is a knight or Isabella is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Penelope is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Lucas is a knight or Isabella is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Logan is a knight if and only if Lucas is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that If Lucas is a knight then Lucas is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('telling-truth', 5)), ('->', ('telling-truth', 5), ('lying', 5)), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('lying', 2), ('<=>', ('telling-truth', 1), ('lying', 5)), ('->', ('telling-truth', 2), ('lying', 4)))", "index": 844}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Elizabeth, Riley, Avery, Sofia, and Emma. In Aria's words: \"If Riley is a knave then Elizabeth is a knave\". Elizabeth commented, \"Elizabeth is a knight and Aria is a knight\". Riley was heard saying, \"Elizabeth is a knight\". \"Emma is a knave or Elizabeth is a knave,\" Avery mentioned. \"If Riley is a knave then Elizabeth is a knave,\" Sofia claimed. Emma noted, \"Avery is a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Elizabeth", "Riley", "Avery", "Sofia", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true], "solution_text": "Aria is a knight, Elizabeth is a knave, Riley is a knave, Avery is a knight, Sofia is a knight, and Emma is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) Elizabeth is a knave\n(3) Riley is a knave\n(4) Avery is a knight\n(5) Sofia is a knight\n(6) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that If Riley is a knave then Elizabeth is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Elizabeth is a knight and Aria is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Emma is a knave or Elizabeth is a knave.", "Emma cannot be a knight, because this would contradict the claim of Avery that Emma is a knave or Elizabeth is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that Avery is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Emma is a knave or Elizabeth is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Avery is a knight.", "Emma cannot be a knave, because this would contradict the false claim of Avery that Emma is a knave or Elizabeth is a knave.", "We have exhausted all possibilities for Emma and Avery, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Riley that Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Aria that If Riley is a knave then Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Aria is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Emma is a knave or Elizabeth is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Avery is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that If Riley is a knave then Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 1)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('telling-truth', 1), ('or', ('lying', 5), ('lying', 1)), ('->', ('lying', 2), ('lying', 1)), ('telling-truth', 3))", "index": 845}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Lily, Samuel, Ethan, Jacob, and Olivia. Emily was heard saying, \"If Samuel is a knave then Jacob is a knight\". Lily was heard saying, \"Emily is a knight or Samuel is a knave\". Samuel said that If Lily is a knave then Emily is a knight. Ethan was heard saying, \"If Samuel is a knave then Ethan is a knight\". Jacob noted, \"Lily is a knight\". Olivia expressed that Samuel is a knave if and only if Jacob is a knave. So who is a knight and who is a knave?", "names": ["Emily", "Lily", "Samuel", "Ethan", "Jacob", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Emily is a knight, Lily is a knight, Samuel is a knight, Ethan is a knight, Jacob is a knight, and Olivia is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Lily is a knight\n(3) Samuel is a knight\n(4) Ethan is a knight\n(5) Jacob is a knight\n(6) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that If Samuel is a knave then Jacob is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Lily is a knave then Emily is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Emily is a knight or Samuel is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Samuel is a knave then Ethan is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 4)), ('or', ('telling-truth', 0), ('lying', 2)), ('->', ('lying', 1), ('telling-truth', 0)), ('->', ('lying', 2), ('telling-truth', 3)), ('telling-truth', 1), ('<=>', ('lying', 2), ('lying', 4)))", "index": 846}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Scarlett, James, Logan, Harper, and Jacob. \"Harper is a knight or Scarlett is a knight,\" Avery claimed. Scarlett told you that Harper is a knave. \"If Logan is a knight then Harper is a knight\" - James. \"Scarlett is a knave\" - Logan. Harper said that If Jacob is a knight then Scarlett is a knight. \"Avery is not a knight\" - Jacob. So who is a knight and who is a knave?", "names": ["Avery", "Scarlett", "James", "Logan", "Harper", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Avery is a knight, Scarlett is a knave, James is a knight, Logan is a knight, Harper is a knight, and Jacob is a knave.", "solution_text_format": "(1) Avery is a knight\n(2) Scarlett is a knave\n(3) James is a knight\n(4) Logan is a knight\n(5) Harper is a knight\n(6) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Harper is a knight or Scarlett is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Jacob is a knight then Scarlett is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Avery is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Harper is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Harper is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Logan is a knight then Harper is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Scarlett is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 1)), ('lying', 4), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('lying', 1), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('not', ('telling-truth', 0)))", "index": 847}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Olivia, Jacob, Penelope, Michael, and Mia. Emma expressed that Mia is not a knight. \"Emma is not a knave\" - Olivia. \"Olivia is a knight,\" Jacob claimed. Penelope stated, \"If Emma is a knave then Jacob is a knight\". As Michael put it, \"Mia is not a knave\". Mia noted, \"Jacob is a knave and Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Emma", "Olivia", "Jacob", "Penelope", "Michael", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Emma is a knight, Olivia is a knight, Jacob is a knight, Penelope is a knight, Michael is a knave, and Mia is a knave.", "solution_text_format": "(1) Emma is a knight\n(2) Olivia is a knight\n(3) Jacob is a knight\n(4) Penelope is a knight\n(5) Michael is a knave\n(6) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Mia is not a knight.", "Mia cannot be a knight, because this would contradict the claim of Emma that Mia is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Jacob is a knave and Penelope is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Olivia is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Emma is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that If Emma is a knave then Jacob is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Mia is not a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Mia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('not', ('lying', 0)), ('telling-truth', 1), ('->', ('lying', 0), ('telling-truth', 2)), ('not', ('lying', 5)), ('and', ('lying', 2), ('telling-truth', 3)))", "index": 848}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Sebastian, Henry, Ella, Daniel, and Luke. \"Ella is a knave if and only if Alexander is a knight,\" Alexander declared. \"Henry is not a knave,\" Sebastian claimed. Henry stated, \"Alexander is a knight or Alexander is a knave\". In a statement by Ella: \"Daniel is a knight\". \"Alexander is a knight and Henry is a knight,\" Daniel mentioned. Luke stated, \"Daniel is a knight\". So who is a knight and who is a knave?", "names": ["Alexander", "Sebastian", "Henry", "Ella", "Daniel", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Alexander is a knave, Sebastian is a knight, Henry is a knight, Ella is a knave, Daniel is a knave, and Luke is a knave.", "solution_text_format": "(1) Alexander is a knave\n(2) Sebastian is a knight\n(3) Henry is a knight\n(4) Ella is a knave\n(5) Daniel is a knave\n(6) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Ella is a knave if and only if Alexander is a knight.", "Ella cannot be a knight, because this would contradict the claim of Alexander that Ella is a knave if and only if Alexander is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Ella that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Alexander is a knight and Henry is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Daniel that Alexander is a knight and Henry is a knight.", "Henry cannot be a knave, because this would contradict the false claim of their own that Alexander is a knight or Alexander is a knave.", "We have exhausted all possibilities for Henry, Daniel, and Ella, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Alexander is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Alexander that Ella is a knave if and only if Alexander is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Ella that Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Alexander is a knight and Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Alexander is a knight or Alexander is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Henry is not a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Daniel is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Daniel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('telling-truth', 0)), ('not', ('lying', 2)), ('or', ('telling-truth', 0), ('lying', 0)), ('telling-truth', 4), ('and', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 4))", "index": 849}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Ella, Luke, Scarlett, Logan, and Riley. William said that Ella is a knave if and only if Riley is a knight. In a statement by Ella: \"If Logan is a knight then Luke is a knight\". In Luke's words: \"Scarlett is a knight\". In Scarlett's words: \"If William is a knight then Ella is a knave\". Logan asserted: \"If Luke is a knave then Riley is a knight\". Riley remarked, \"Riley is a knight and Logan is a knave\". So who is a knight and who is a knave?", "names": ["William", "Ella", "Luke", "Scarlett", "Logan", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "William is a knight, Ella is a knight, Luke is a knave, Scarlett is a knave, Logan is a knave, and Riley is a knave.", "solution_text_format": "(1) William is a knight\n(2) Ella is a knight\n(3) Luke is a knave\n(4) Scarlett is a knave\n(5) Logan is a knave\n(6) Riley is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Ella is a knave if and only if Riley is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Logan is a knight then Luke is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Luke is a knave then Riley is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that If William is a knight then Ella is a knave.", "Scarlett cannot be a knave, because this would contradict the claim of Luke that Scarlett is a knight.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Ella that If Logan is a knight then Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that If Luke is a knave then Riley is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Logan that If Luke is a knave then Riley is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Scarlett cannot be a knight, because this would contradict the false claim of Luke that Scarlett is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that If William is a knight then Ella is a knave.", "Riley cannot be a knight, because this would contradict the claim of William that Ella is a knave if and only if Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Riley is a knight and Logan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 5)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('telling-truth', 3), ('->', ('telling-truth', 0), ('lying', 1)), ('->', ('lying', 2), ('telling-truth', 5)), ('and', ('telling-truth', 5), ('lying', 4)))", "index": 850}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Sophia, Mia, Abigail, Luke, and Aurora. Avery told you that Luke is not a knave. \"Luke is a knave,\" Sophia declared. Mia told you that Sophia is a knave if and only if Mia is a knight. Abigail expressed that Luke is not a knave. \"Mia is a knight,\" Luke declared. Aurora stated, \"Abigail is a knight or Mia is a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Sophia", "Mia", "Abigail", "Luke", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Avery is a knight, Sophia is a knave, Mia is a knight, Abigail is a knight, Luke is a knight, and Aurora is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Sophia is a knave\n(3) Mia is a knight\n(4) Abigail is a knight\n(5) Luke is a knight\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Luke is not a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Mia is a knight.", "Sophia cannot be a knight, because this would contradict the claim of their own that Luke is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Luke is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Luke is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Abigail is a knight or Mia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('lying', 4), ('<=>', ('lying', 1), ('telling-truth', 2)), ('not', ('lying', 4)), ('telling-truth', 2), ('or', ('telling-truth', 3), ('lying', 2)))", "index": 851}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Noah, Luke, Grace, Chloe, Henry, and Ava. Noah said, \"Grace is a knave and Grace is a knight.\" Luke told you that Noah is a knight. \"Henry is a knave\" - Grace. Chloe remarked, \"Henry is a knight if and only if Grace is a knave\". Henry expressed that If Chloe is a knave then Luke is a knight. Ava noted, \"Chloe is a knight\". So who is a knight and who is a knave?", "names": ["Noah", "Luke", "Grace", "Chloe", "Henry", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Noah is a knave, Luke is a knave, Grace is a knave, Chloe is a knight, Henry is a knight, and Ava is a knight.", "solution_text_format": "(1) Noah is a knave\n(2) Luke is a knave\n(3) Grace is a knave\n(4) Chloe is a knight\n(5) Henry is a knight\n(6) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Noah cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Grace is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Grace is a knave and Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Grace that Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that If Chloe is a knave then Luke is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Henry that If Chloe is a knave then Luke is a knight.", "Chloe cannot be a knave, because this would contradict the false claim of their own that Henry is a knight if and only if Grace is a knave.", "We have exhausted all possibilities for Chloe and Henry, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If Chloe is a knave then Luke is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Henry is a knight if and only if Grace is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Noah is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Noah is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('telling-truth', 2)), ('telling-truth', 0), ('lying', 4), ('<=>', ('telling-truth', 4), ('lying', 2)), ('->', ('lying', 3), ('telling-truth', 1)), ('telling-truth', 3))", "index": 852}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Avery, Emma, Owen, Alexander, and Luke. As Scarlett put it, \"Alexander is a knight or Owen is a knave\". Avery commented, \"Scarlett is a knave if and only if Alexander is a knight\". Emma stated, \"Luke is a knight or Avery is a knave\". Owen remarked, \"Luke is not a knight\". Alexander said that Scarlett is a knave or Avery is a knave. In Luke's words: \"Avery is a knave\". So who is a knight and who is a knave?", "names": ["Scarlett", "Avery", "Emma", "Owen", "Alexander", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Scarlett is a knight, Avery is a knave, Emma is a knight, Owen is a knave, Alexander is a knight, and Luke is a knight.", "solution_text_format": "(1) Scarlett is a knight\n(2) Avery is a knave\n(3) Emma is a knight\n(4) Owen is a knave\n(5) Alexander is a knight\n(6) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Alexander is a knight or Owen is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Scarlett is a knave or Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave if and only if Alexander is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Alexander is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Owen that Luke is not a knight.", "Luke cannot be a knave, because this would contradict the false claim of their own that Avery is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Luke is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that Avery is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Luke is a knight or Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('lying', 3)), ('<=>', ('lying', 0), ('telling-truth', 4)), ('or', ('telling-truth', 5), ('lying', 1)), ('not', ('telling-truth', 5)), ('or', ('lying', 0), ('lying', 1)), ('lying', 1))", "index": 853}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Penelope, Lucas, Benjamin, Owen, and Isabella. Victoria was heard saying, \"Penelope is not a knight\". According to Penelope, \"Isabella is a knave if and only if Owen is a knave\". Lucas said, \"Isabella is a knight and Penelope is a knave.\" As Benjamin put it, \"Isabella is not a knave\". \"Benjamin is a knight or Penelope is a knight,\" Owen mentioned. According to Isabella, \"Isabella is a knight or Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Victoria", "Penelope", "Lucas", "Benjamin", "Owen", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Victoria is a knave, Penelope is a knight, Lucas is a knave, Benjamin is a knight, Owen is a knight, and Isabella is a knight.", "solution_text_format": "(1) Victoria is a knave\n(2) Penelope is a knight\n(3) Lucas is a knave\n(4) Benjamin is a knight\n(5) Owen is a knight\n(6) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Victoria that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Owen is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Isabella is a knight or Penelope is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Penelope that Isabella is a knave if and only if Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Benjamin is a knight or Penelope is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Owen that Benjamin is a knight or Penelope is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Isabella is not a knave.", "We have exhausted all possibilities for Benjamin and Owen, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Isabella is a knight or Penelope is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Benjamin is a knight or Penelope is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Isabella is not a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Owen that Benjamin is a knight or Penelope is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of Penelope that Isabella is a knave if and only if Owen is a knave.", "We have exhausted all possibilities for Owen, Isabella, and Penelope, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Owen is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Isabella is a knight or Penelope is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Benjamin is a knight or Penelope is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Isabella is a knight and Penelope is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Isabella is a knight and Penelope is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 1)), ('<=>', ('lying', 5), ('lying', 4)), ('and', ('telling-truth', 5), ('lying', 1)), ('not', ('lying', 5)), ('or', ('telling-truth', 3), ('telling-truth', 1)), ('or', ('telling-truth', 5), ('telling-truth', 1)))", "index": 854}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Abigail, Penelope, James, Ava, and Sophia. Aria asserted: \"Sophia is a knight or Abigail is a knight\". \"James is a knave\" - Abigail. \"If Penelope is a knight then Ava is a knight,\" Penelope mentioned. James said, \"Ava is a knight and Penelope is a knight.\" Ava was heard saying, \"Penelope is a knight\". Sophia said, \"James is a knight if and only if Penelope is a knight.\" So who is a knight and who is a knave?", "names": ["Aria", "Abigail", "Penelope", "James", "Ava", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Aria is a knight, Abigail is a knave, Penelope is a knight, James is a knight, Ava is a knight, and Sophia is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) Abigail is a knave\n(3) Penelope is a knight\n(4) James is a knight\n(5) Ava is a knight\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Sophia is a knight or Abigail is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that James is a knight if and only if Penelope is a knight.", "Assume James is a knight. No contradiction is found in their claim that Ava is a knight and Penelope is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Penelope is a knight then Ava is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that James is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 1)), ('lying', 3), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('and', ('telling-truth', 4), ('telling-truth', 2)), ('telling-truth', 2), ('<=>', ('telling-truth', 3), ('telling-truth', 2)))", "index": 855}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Daniel, Victoria, Ella, Benjamin, and Aurora. William expressed that Daniel is a knave and Aurora is a knight. According to Daniel, \"Aurora is a knight or Benjamin is a knight\". Victoria expressed that William is not a knight. \"If Benjamin is a knave then Daniel is a knave,\" Ella declared. Benjamin asserted: \"Ella is a knight if and only if Victoria is a knave\". Aurora asserted: \"Daniel is not a knave\". So who is a knight and who is a knave?", "names": ["William", "Daniel", "Victoria", "Ella", "Benjamin", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "William is a knave, Daniel is a knave, Victoria is a knight, Ella is a knight, Benjamin is a knave, and Aurora is a knave.", "solution_text_format": "(1) William is a knave\n(2) Daniel is a knave\n(3) Victoria is a knight\n(4) Ella is a knight\n(5) Benjamin is a knave\n(6) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Daniel is a knave and Aurora is a knight.", "Daniel cannot be a knight, because this would contradict the claim of William that Daniel is a knave and Aurora is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Aurora is a knight or Benjamin is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Daniel that Aurora is a knight or Benjamin is a knight.", "Aurora cannot be a knave, because this would contradict the claim of William that Daniel is a knave and Aurora is a knight.", "We have exhausted all possibilities for Aurora and Daniel, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Daniel is a knave and Aurora is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Aurora is a knight or Benjamin is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Ella is a knight if and only if Victoria is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Benjamin is a knave then Daniel is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Benjamin that Ella is a knight if and only if Victoria is a knave.", "Victoria cannot be a knave, because this would contradict the false claim of their own that William is not a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Benjamin is a knave then Daniel is a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Victoria is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that If Benjamin is a knave then Daniel is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Daniel is a knave.", "Victoria cannot be a knight, because this would contradict the false claim of Benjamin that Ella is a knight if and only if Victoria is a knave.", "Victoria cannot be a knave, because this would contradict the false claim of their own that William is not a knight.", "We have exhausted all possibilities for Victoria, Ella, and Benjamin, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Daniel is not a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Aurora is a knight or Benjamin is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of William that Daniel is a knave and Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Daniel is not a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Daniel that Aurora is a knight or Benjamin is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Victoria is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Benjamin is a knave then Daniel is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that William is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 5)), ('or', ('telling-truth', 5), ('telling-truth', 4)), ('not', ('telling-truth', 0)), ('->', ('lying', 4), ('lying', 1)), ('<=>', ('telling-truth', 3), ('lying', 2)), ('not', ('lying', 1)))", "index": 856}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Isabella, Emma, Sofia, Riley, and Ethan. According to Ava, \"Emma is a knave\". \"Ethan is a knave and Emma is a knave,\" Isabella declared. Emma was heard saying, \"Ethan is not a knave\". Sofia told you that If Riley is a knave then Ava is a knave. In Riley's words: \"If Ethan is a knave then Isabella is a knight\". Ethan said that Isabella is a knave and Sofia is a knave. So who is a knight and who is a knave?", "names": ["Ava", "Isabella", "Emma", "Sofia", "Riley", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "Ava is a knight, Isabella is a knight, Emma is a knave, Sofia is a knight, Riley is a knight, and Ethan is a knave.", "solution_text_format": "(1) Ava is a knight\n(2) Isabella is a knight\n(3) Emma is a knave\n(4) Sofia is a knight\n(5) Riley is a knight\n(6) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Ava that Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Ethan is not a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Emma that Ethan is not a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Isabella is a knave and Sofia is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Ethan is a knave and Emma is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Riley is a knave then Ava is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Ethan is a knave then Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('and', ('lying', 5), ('lying', 2)), ('not', ('lying', 5)), ('->', ('lying', 4), ('lying', 0)), ('->', ('lying', 5), ('telling-truth', 1)), ('and', ('lying', 1), ('lying', 3)))", "index": 857}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Zoey, Penelope, Ella, Aria, and Abigail. Grace was heard saying, \"Ella is not a knight\". In Zoey's words: \"Abigail is a knave if and only if Ella is a knight\". Penelope told you that Abigail is a knave if and only if Abigail is a knight. Ella noted, \"Abigail is a knave or Aria is a knight\". In Aria's words: \"Abigail is a knight\". Abigail commented, \"Zoey is a knave or Ella is a knight\". So who is a knight and who is a knave?", "names": ["Grace", "Zoey", "Penelope", "Ella", "Aria", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Grace is a knave, Zoey is a knave, Penelope is a knave, Ella is a knight, Aria is a knight, and Abigail is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Zoey is a knave\n(3) Penelope is a knave\n(4) Ella is a knight\n(5) Aria is a knight\n(6) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Ella is not a knight.", "Ella cannot be a knight, because this would contradict the claim of Grace that Ella is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Abigail is a knave or Aria is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Zoey is a knave or Ella is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Abigail that Zoey is a knave or Ella is a knight.", "Zoey cannot be a knave, because this would contradict the false claim of their own that Abigail is a knave if and only if Ella is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of Ella that Abigail is a knave or Aria is a knight.", "We have exhausted all possibilities for Abigail and Ella, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Abigail is a knave or Aria is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Zoey is a knave or Ella is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Abigail is a knave if and only if Ella is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Ella is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Abigail is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Abigail is a knave if and only if Abigail is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('<=>', ('lying', 5), ('telling-truth', 3)), ('<=>', ('lying', 5), ('telling-truth', 5)), ('or', ('lying', 5), ('telling-truth', 4)), ('telling-truth', 5), ('or', ('lying', 1), ('telling-truth', 3)))", "index": 858}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Oliver, Aria, Aurora, Liam, and Luke. James commented, \"Luke is a knight and Aurora is a knave\". As Oliver put it, \"Liam is not a knight\". Aria said that Oliver is a knight or Aria is a knight. Aurora remarked, \"Liam is a knight and Oliver is a knight\". \"James is a knave if and only if Aurora is a knight,\" Liam mentioned. As Luke put it, \"Luke is a knight and Liam is a knave\". So who is a knight and who is a knave?", "names": ["James", "Oliver", "Aria", "Aurora", "Liam", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "James is a knave, Oliver is a knight, Aria is a knight, Aurora is a knave, Liam is a knave, and Luke is a knave.", "solution_text_format": "(1) James is a knave\n(2) Oliver is a knight\n(3) Aria is a knight\n(4) Aurora is a knave\n(5) Liam is a knave\n(6) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Luke is a knight and Aurora is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Luke is a knight and Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Luke that Luke is a knight and Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that James is a knave if and only if Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of James that Luke is a knight and Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of Liam that James is a knave if and only if Aurora is a knight.", "We have exhausted all possibilities for Aurora and Liam, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of James that Luke is a knight and Aurora is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Luke is a knight and Aurora is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Luke is a knight and Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Luke that Luke is a knight and Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that James is a knave if and only if Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Liam is a knight and Oliver is a knight.", "Aurora cannot be a knave, because this would contradict the false claim of James that Luke is a knight and Aurora is a knave.", "We have exhausted all possibilities for Aurora and Liam, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Luke is a knight and Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that James is a knave if and only if Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Liam is a knight and Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Liam is not a knight.", "Oliver cannot be a knave, because this would contradict the claim of Aurora that Liam is a knight and Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Liam that James is a knave if and only if Aurora is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that James is a knave if and only if Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Liam is a knight and Oliver is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Liam is a knight and Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Liam is not a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Oliver is a knight or Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 3)), ('not', ('telling-truth', 4)), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('<=>', ('lying', 0), ('telling-truth', 3)), ('and', ('telling-truth', 5), ('lying', 4)))", "index": 859}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Chloe, Benjamin, Elizabeth, Olivia, and Ava. \"Olivia is a knave or Benjamin is a knave,\" Alexander claimed. As Chloe put it, \"Benjamin is a knight and Benjamin is a knave\". In Benjamin's words: \"Olivia is a knave if and only if Alexander is a knight\". Elizabeth stated, \"Alexander is a knight or Ava is a knave\". In a statement by Olivia: \"Elizabeth is a knight if and only if Elizabeth is a knave\". Ava commented, \"Benjamin is not a knight\". So who is a knight and who is a knave?", "names": ["Alexander", "Chloe", "Benjamin", "Elizabeth", "Olivia", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false], "solution_text": "Alexander is a knight, Chloe is a knave, Benjamin is a knight, Elizabeth is a knight, Olivia is a knave, and Ava is a knave.", "solution_text_format": "(1) Alexander is a knight\n(2) Chloe is a knave\n(3) Benjamin is a knight\n(4) Elizabeth is a knight\n(5) Olivia is a knave\n(6) Ava is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Olivia is a knave or Benjamin is a knave.", "Olivia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight if and only if Elizabeth is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Alexander is a knight or Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Ava that Benjamin is not a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave if and only if Alexander is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Alexander is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight and Benjamin is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Benjamin is a knight and Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('lying', 2)), ('and', ('telling-truth', 2), ('lying', 2)), ('<=>', ('lying', 4), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 5)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('not', ('telling-truth', 2)))", "index": 860}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Aria, Isabella, William, Jack, and Logan. Oliver expressed that Aria is a knight and Jack is a knave. Aria said, \"Isabella is not a knight.\" Isabella was heard saying, \"William is a knight and William is a knave\". William was heard saying, \"If Jack is a knight then Isabella is a knight\". Jack said, \"If Jack is a knight then William is a knave.\" As Logan put it, \"If Oliver is a knight then Isabella is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Aria", "Isabella", "William", "Jack", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true], "solution_text": "Oliver is a knave, Aria is a knight, Isabella is a knave, William is a knave, Jack is a knight, and Logan is a knight.", "solution_text_format": "(1) Oliver is a knave\n(2) Aria is a knight\n(3) Isabella is a knave\n(4) William is a knave\n(5) Jack is a knight\n(6) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Aria is a knight and Jack is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Aria that Isabella is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that William is a knight and William is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Jack is a knight then Isabella is a knight.", "Jack cannot be a knight, because this would contradict the claim of Oliver that Aria is a knight and Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that If Jack is a knight then William is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that If Jack is a knight then Isabella is a knight.", "Jack cannot be a knight, because this would contradict the claim of Oliver that Aria is a knight and Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of William that If Jack is a knight then Isabella is a knight.", "We have exhausted all possibilities for Jack, William, and Isabella, so let us go back and reconsider Aria.", "Aria cannot be a knave, because this would contradict the claim of Oliver that Aria is a knight and Jack is a knave.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Aria is a knight and Jack is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Aria that Isabella is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that William is a knight and William is a knave.", "Assume William is a knight. No contradiction is found in their claim that If Jack is a knight then Isabella is a knight.", "Jack cannot be a knight, because this would contradict the claim of William that If Jack is a knight then Isabella is a knight.", "Jack cannot be a knave, because this would contradict the false claim of Oliver that Aria is a knight and Jack is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that If Jack is a knight then Isabella is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Jack is a knight then William is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that If Oliver is a knight then Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('lying', 4)), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 3), ('lying', 3)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('->', ('telling-truth', 4), ('lying', 3)), ('->', ('telling-truth', 0), ('telling-truth', 2)))", "index": 861}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Emma, Luke, Aurora, Alexander, and David. Mason commented, \"Alexander is a knight\". Emma was heard saying, \"Luke is a knave or Aurora is a knight\". Luke said, \"Mason is a knight if and only if Alexander is a knight.\" Aurora told you that Aurora is a knight and Alexander is a knight. Alexander told you that David is a knight and Luke is a knave. David stated, \"Luke is a knave and Alexander is a knave\". So who is a knight and who is a knave?", "names": ["Mason", "Emma", "Luke", "Aurora", "Alexander", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false], "solution_text": "Mason is a knave, Emma is a knave, Luke is a knight, Aurora is a knave, Alexander is a knave, and David is a knave.", "solution_text_format": "(1) Mason is a knave\n(2) Emma is a knave\n(3) Luke is a knight\n(4) Aurora is a knave\n(5) Alexander is a knave\n(6) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that David is a knight and Luke is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Alexander is a knave.", "David cannot be a knave, because this would contradict the claim of Alexander that David is a knight and Luke is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Mason that Alexander is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Mason that Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that David is a knight and Luke is a knave.", "Assume David is a knight. No contradiction is found in their claim that Luke is a knave and Alexander is a knave.", "Luke cannot be a knight, because this would contradict the claim of David that Luke is a knave and Alexander is a knave.", "Luke cannot be a knave, because this would contradict the false claim of their own that Mason is a knight if and only if Alexander is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Luke is a knave and Alexander is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Mason is a knight if and only if Alexander is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Luke is a knave or Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Alexander is a knight.", "Aurora cannot be a knave, because this would contradict the claim of Emma that Luke is a knave or Aurora is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Luke is a knave or Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Emma that Luke is a knave or Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Aurora is a knight and Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('or', ('lying', 2), ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('telling-truth', 4)), ('and', ('telling-truth', 3), ('telling-truth', 4)), ('and', ('telling-truth', 5), ('lying', 2)), ('and', ('lying', 2), ('lying', 4)))", "index": 862}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Sebastian, James, Grace, Ava, and Aurora. \"James is a knight if and only if Aurora is a knave\" - Mason. In Sebastian's words: \"If Mason is a knave then Ava is a knight\". \"Ava is a knave or Sebastian is a knave\" - James. Grace expressed that Sebastian is a knave. Ava was heard saying, \"Mason is not a knight\". Aurora remarked, \"Ava is not a knave\". So who is a knight and who is a knave?", "names": ["Mason", "Sebastian", "James", "Grace", "Ava", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Mason is a knight, Sebastian is a knight, James is a knight, Grace is a knave, Ava is a knave, and Aurora is a knave.", "solution_text_format": "(1) Mason is a knight\n(2) Sebastian is a knight\n(3) James is a knight\n(4) Grace is a knave\n(5) Ava is a knave\n(6) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that James is a knight if and only if Aurora is a knave.", "Assume James is a knight. No contradiction is found in their claim that Ava is a knave or Sebastian is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Mason is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Mason is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Mason is a knave then Ava is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Mason that James is a knight if and only if Aurora is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Ava is not a knave.", "Grace cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 5)), ('->', ('lying', 0), ('telling-truth', 4)), ('or', ('lying', 4), ('lying', 1)), ('lying', 1), ('not', ('telling-truth', 0)), ('not', ('lying', 4)))", "index": 863}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Abigail, Liam, Riley, James, and Ethan. In a statement by Aurora: \"James is a knave\". Abigail commented, \"Aurora is a knave and Liam is a knight\". Liam commented, \"Ethan is a knave if and only if James is a knave\". \"James is a knight or Aurora is a knave,\" Riley claimed. \"Abigail is a knave or Aurora is a knight,\" James mentioned. Ethan noted, \"If Abigail is a knave then Abigail is a knight\". So who is a knight and who is a knave?", "names": ["Aurora", "Abigail", "Liam", "Riley", "James", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false], "solution_text": "Aurora is a knave, Abigail is a knave, Liam is a knave, Riley is a knight, James is a knight, and Ethan is a knave.", "solution_text_format": "(1) Aurora is a knave\n(2) Abigail is a knave\n(3) Liam is a knave\n(4) Riley is a knight\n(5) James is a knight\n(6) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Aurora that James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that Abigail is a knave or Aurora is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Abigail is a knave or Aurora is a knight.", "Abigail cannot be a knight, because this would contradict the claim of James that Abigail is a knave or Aurora is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aurora is a knave and Liam is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Abigail that Aurora is a knave and Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if James is a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Liam that Ethan is a knave if and only if James is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Abigail is a knave then Abigail is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that James is a knight or Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('and', ('lying', 0), ('telling-truth', 2)), ('<=>', ('lying', 5), ('lying', 4)), ('or', ('telling-truth', 4), ('lying', 0)), ('or', ('lying', 1), ('telling-truth', 0)), ('->', ('lying', 1), ('telling-truth', 1)))", "index": 864}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Victoria, Logan, Sebastian, Emily, and Jacob. Jackson stated, \"Sebastian is not a knave\". Victoria was heard saying, \"Jackson is a knight or Jackson is a knave\". Logan said that Emily is a knave and Victoria is a knight. Sebastian commented, \"Emily is a knave\". Emily stated, \"Emily is a knight or Victoria is a knight\". \"Victoria is not a knight\" - Jacob. So who is a knight and who is a knave?", "names": ["Jackson", "Victoria", "Logan", "Sebastian", "Emily", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "Jackson is a knave, Victoria is a knight, Logan is a knave, Sebastian is a knave, Emily is a knight, and Jacob is a knave.", "solution_text_format": "(1) Jackson is a knave\n(2) Victoria is a knight\n(3) Logan is a knave\n(4) Sebastian is a knave\n(5) Emily is a knight\n(6) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Sebastian is not a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Sebastian that Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Emily is a knight or Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Emily that Emily is a knight or Victoria is a knight.", "Victoria cannot be a knave, because this would contradict the false claim of their own that Jackson is a knight or Jackson is a knave.", "We have exhausted all possibilities for Victoria and Emily, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Jackson that Sebastian is not a knave.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Sebastian is not a knave.", "Sebastian cannot be a knight, because this would contradict the false claim of Jackson that Sebastian is not a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Emily is a knight or Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Jackson is a knight or Jackson is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Emily is a knave and Victoria is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Emily is a knave and Victoria is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Victoria is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Victoria is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('or', ('telling-truth', 0), ('lying', 0)), ('and', ('lying', 4), ('telling-truth', 1)), ('lying', 4), ('or', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('telling-truth', 1)))", "index": 865}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Aurora, Benjamin, Amelia, Samuel, and Luke. Sebastian remarked, \"If Benjamin is a knave then Samuel is a knave\". According to Aurora, \"Sebastian is a knave\". In Benjamin's words: \"Luke is not a knight\". Amelia said, \"Luke is a knight if and only if Aurora is a knave.\" Samuel said that Amelia is a knight. Luke remarked, \"Aurora is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "Aurora", "Benjamin", "Amelia", "Samuel", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Sebastian is a knight, Aurora is a knave, Benjamin is a knight, Amelia is a knave, Samuel is a knave, and Luke is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Aurora is a knave\n(3) Benjamin is a knight\n(4) Amelia is a knave\n(5) Samuel is a knave\n(6) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that If Benjamin is a knave then Samuel is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Luke is not a knight.", "Luke cannot be a knight, because this would contradict the claim of Benjamin that Luke is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Sebastian is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Luke is a knight if and only if Aurora is a knave.", "Amelia cannot be a knave, because this would contradict the claim of Samuel that Amelia is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Amelia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Luke is a knight if and only if Aurora is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Aurora is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 4)), ('lying', 0), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 5), ('lying', 1)), ('telling-truth', 3), ('telling-truth', 1))", "index": 866}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Noah, Emily, Alexander, Oliver, Lily, and Ethan. Noah expressed that Ethan is a knight and Alexander is a knave. \"Lily is not a knight\" - Emily. Alexander said, \"Ethan is a knight or Noah is a knave.\" \"If Oliver is a knight then Noah is a knave\" - Oliver. Lily expressed that Noah is not a knight. Ethan said, \"Emily is a knight and Alexander is a knave.\" So who is a knight and who is a knave?", "names": ["Noah", "Emily", "Alexander", "Oliver", "Lily", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Noah is a knave, Emily is a knave, Alexander is a knight, Oliver is a knight, Lily is a knight, and Ethan is a knave.", "solution_text_format": "(1) Noah is a knave\n(2) Emily is a knave\n(3) Alexander is a knight\n(4) Oliver is a knight\n(5) Lily is a knight\n(6) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Ethan is a knight and Alexander is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Emily is a knight and Alexander is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Emily that Lily is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Alexander cannot be a knight, because this would contradict the claim of Noah that Ethan is a knight and Alexander is a knave.", "Alexander cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight or Noah is a knave.", "We have exhausted all possibilities for Alexander and Lily, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Ethan that Emily is a knight and Alexander is a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Noah that Ethan is a knight and Alexander is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Ethan is a knight and Alexander is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Emily is a knight and Alexander is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Emily that Lily is not a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Noah is not a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Ethan that Emily is a knight and Alexander is a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Emily is a knight and Alexander is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Lily is not a knight.", "Lily cannot be a knight, because this would contradict the claim of Emily that Lily is not a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Noah is not a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Noah is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Ethan is a knight or Noah is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Oliver is a knight then Noah is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 2)), ('not', ('telling-truth', 4)), ('or', ('telling-truth', 5), ('lying', 0)), ('->', ('telling-truth', 3), ('lying', 0)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 1), ('lying', 2)))", "index": 867}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Elizabeth, Aria, Amelia, Liam, and Sophia. Emma noted, \"If Aria is a knight then Emma is a knight\". Elizabeth said, \"Emma is not a knight.\" Aria said, \"Amelia is not a knight.\" According to Amelia, \"If Liam is a knight then Sophia is a knave\". \"If Aria is a knave then Elizabeth is a knave,\" Liam mentioned. In a statement by Sophia: \"Elizabeth is a knave and Emma is a knight\". So who is a knight and who is a knave?", "names": ["Emma", "Elizabeth", "Aria", "Amelia", "Liam", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Emma is a knight, Elizabeth is a knave, Aria is a knight, Amelia is a knave, Liam is a knight, and Sophia is a knight.", "solution_text_format": "(1) Emma is a knight\n(2) Elizabeth is a knave\n(3) Aria is a knight\n(4) Amelia is a knave\n(5) Liam is a knight\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that If Aria is a knight then Emma is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of Aria that Amelia is not a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that If Liam is a knight then Sophia is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Aria is a knave then Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Emma is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Emma is not a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Elizabeth is a knave and Emma is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 3)), ('->', ('telling-truth', 4), ('lying', 5)), ('->', ('lying', 2), ('lying', 1)), ('and', ('lying', 1), ('telling-truth', 0)))", "index": 868}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Emma, Lily, Sebastian, Avery, and Emily. As Aria put it, \"Sebastian is a knave and Lily is a knave\". Emma was heard saying, \"Emily is a knave or Sebastian is a knave\". In Lily's words: \"Avery is a knight and Aria is a knave\". In a statement by Sebastian: \"Avery is a knave\". Avery said that If Lily is a knave then Sebastian is a knight. Emily said, \"If Sebastian is a knave then Avery is a knave.\" So who is a knight and who is a knave?", "names": ["Aria", "Emma", "Lily", "Sebastian", "Avery", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false], "solution_text": "Aria is a knave, Emma is a knight, Lily is a knight, Sebastian is a knave, Avery is a knight, and Emily is a knave.", "solution_text_format": "(1) Aria is a knave\n(2) Emma is a knight\n(3) Lily is a knight\n(4) Sebastian is a knave\n(5) Avery is a knight\n(6) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Sebastian is a knave and Lily is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Aria that Sebastian is a knave and Lily is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Lily is a knave then Sebastian is a knight.", "Lily cannot be a knight, because this would contradict the claim of Aria that Sebastian is a knave and Lily is a knave.", "Lily cannot be a knave, because this would contradict the claim of Avery that If Lily is a knave then Sebastian is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the false claim of Sebastian that Avery is a knave.", "We have exhausted all possibilities for Avery and Sebastian, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Sebastian is a knave and Lily is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Sebastian that Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that If Lily is a knave then Sebastian is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Lily is a knave then Sebastian is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Avery is a knight and Aria is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Emily is a knave or Sebastian is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that If Sebastian is a knave then Avery is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that If Sebastian is a knave then Avery is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('lying', 2)), ('or', ('lying', 5), ('lying', 3)), ('and', ('telling-truth', 4), ('lying', 0)), ('lying', 4), ('->', ('lying', 2), ('telling-truth', 3)), ('->', ('lying', 3), ('lying', 4)))", "index": 869}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Ethan, Scarlett, Ella, Oliver, and Ava. In Sebastian's words: \"Ella is not a knight\". Ethan noted, \"Ella is not a knave\". In Scarlett's words: \"Sebastian is a knight if and only if Ella is a knave\". Ella remarked, \"Ava is a knave if and only if Sebastian is a knight\". Oliver was heard saying, \"Ava is a knave if and only if Ethan is a knave\". Ava stated, \"If Ella is a knave then Oliver is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "Ethan", "Scarlett", "Ella", "Oliver", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Sebastian is a knave, Ethan is a knight, Scarlett is a knight, Ella is a knight, Oliver is a knight, and Ava is a knight.", "solution_text_format": "(1) Sebastian is a knave\n(2) Ethan is a knight\n(3) Scarlett is a knight\n(4) Ella is a knight\n(5) Oliver is a knight\n(6) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Ella is not a knight.", "Ella cannot be a knight, because this would contradict the claim of Sebastian that Ella is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Sebastian is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Ella is a knave then Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Ava is a knave if and only if Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.", "Ethan cannot be a knave, because this would contradict the claim of Oliver that Ava is a knave if and only if Ethan is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Ava that If Ella is a knave then Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of Ella that Ava is a knave if and only if Sebastian is a knight.", "We have exhausted all possibilities for Ava and Ella, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Ava is a knave if and only if Sebastian is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Ella is a knave then Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Ava is a knave if and only if Ethan is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('not', ('lying', 3)), ('<=>', ('telling-truth', 0), ('lying', 3)), ('<=>', ('lying', 5), ('telling-truth', 0)), ('<=>', ('lying', 5), ('lying', 1)), ('->', ('lying', 3), ('telling-truth', 4)))", "index": 870}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Grace, Isabella, Daniel, Sophia, and Joseph. Jacob remarked, \"Sophia is a knave if and only if Isabella is a knave\". \"Daniel is a knave and Sophia is a knight,\" Grace mentioned. According to Isabella, \"Sophia is a knight\". In a statement by Daniel: \"If Daniel is a knight then Isabella is a knight\". Sophia asserted: \"Grace is a knight or Isabella is a knight\". In a statement by Joseph: \"Daniel is a knave and Joseph is a knight\". So who is a knight and who is a knave?", "names": ["Jacob", "Grace", "Isabella", "Daniel", "Sophia", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Jacob is a knight, Grace is a knave, Isabella is a knight, Daniel is a knight, Sophia is a knight, and Joseph is a knave.", "solution_text_format": "(1) Jacob is a knight\n(2) Grace is a knave\n(3) Isabella is a knight\n(4) Daniel is a knight\n(5) Sophia is a knight\n(6) Joseph is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Isabella is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Grace is a knight or Isabella is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Daniel is a knave and Sophia is a knight.", "Daniel cannot be a knight, because this would contradict the claim of Grace that Daniel is a knave and Sophia is a knight.", "Daniel cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knight then Isabella is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Daniel is a knave and Sophia is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Daniel is a knight then Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Sophia is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Daniel is a knave and Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('lying', 2)), ('and', ('lying', 3), ('telling-truth', 4)), ('telling-truth', 4), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('lying', 3), ('telling-truth', 5)))", "index": 871}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Michael, Avery, Emily, Henry, and Charlotte. Sophia told you that Charlotte is a knight or Avery is a knight. In Michael's words: \"Sophia is a knight or Avery is a knight\". Avery remarked, \"If Emily is a knave then Henry is a knave\". \"Charlotte is not a knight,\" Emily mentioned. Henry commented, \"Michael is a knight and Sophia is a knight\". Charlotte commented, \"Avery is a knight and Charlotte is a knight\". So who is a knight and who is a knave?", "names": ["Sophia", "Michael", "Avery", "Emily", "Henry", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Sophia is a knight, Michael is a knight, Avery is a knight, Emily is a knight, Henry is a knight, and Charlotte is a knave.", "solution_text_format": "(1) Sophia is a knight\n(2) Michael is a knight\n(3) Avery is a knight\n(4) Emily is a knight\n(5) Henry is a knight\n(6) Charlotte is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Charlotte is a knight or Avery is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Avery is a knight and Charlotte is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Emily is a knave then Henry is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Charlotte is not a knight.", "Henry cannot be a knight, because this would contradict the claim of Avery that If Emily is a knave then Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Michael is a knight and Sophia is a knight.", "Michael cannot be a knight, because this would contradict the false claim of Henry that Michael is a knight and Sophia is a knight.", "Michael cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight or Avery is a knight.", "We have exhausted all possibilities for Michael, Henry, and Emily, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the claim of Charlotte that Avery is a knight and Charlotte is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Avery is a knight and Charlotte is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Emily is a knave then Henry is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Charlotte is not a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Michael is a knight and Sophia is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Sophia is a knight or Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('telling-truth', 0), ('telling-truth', 2)), ('->', ('lying', 3), ('lying', 4)), ('not', ('telling-truth', 5)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('telling-truth', 2), ('telling-truth', 5)))", "index": 872}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Isabella, Jacob, Mia, Sebastian, and Harper. \"Mia is a knight and Isabella is a knave,\" Logan claimed. Isabella said that If Isabella is a knight then Sebastian is a knight. In Jacob's words: \"Isabella is not a knight\". In Mia's words: \"Isabella is a knight if and only if Jacob is a knight\". Sebastian stated, \"Jacob is a knave\". Harper asserted: \"Logan is a knave and Sebastian is a knight\". So who is a knight and who is a knave?", "names": ["Logan", "Isabella", "Jacob", "Mia", "Sebastian", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true], "solution_text": "Logan is a knave, Isabella is a knight, Jacob is a knave, Mia is a knave, Sebastian is a knight, and Harper is a knight.", "solution_text_format": "(1) Logan is a knave\n(2) Isabella is a knight\n(3) Jacob is a knave\n(4) Mia is a knave\n(5) Sebastian is a knight\n(6) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Mia is a knight and Isabella is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Jacob is a knight.", "Isabella cannot be a knight, because this would contradict the claim of Logan that Mia is a knight and Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that If Isabella is a knight then Sebastian is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Logan that Mia is a knight and Isabella is a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Mia is a knight and Isabella is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Jacob is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Isabella is a knight then Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Isabella is not a knight.", "Jacob cannot be a knave, because this would contradict the claim of Mia that Isabella is a knight if and only if Jacob is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Isabella that If Isabella is a knight then Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of Logan that Mia is a knight and Isabella is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Jacob is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Isabella is a knight then Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of their own that Isabella is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Logan is a knave and Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('lying', 1)), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('not', ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('lying', 2), ('and', ('lying', 0), ('telling-truth', 4)))", "index": 873}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Michael, Jackson, Lily, Victoria, and Mia. Sofia was heard saying, \"If Lily is a knight then Mia is a knight\". Michael commented, \"Sofia is a knave\". According to Jackson, \"Victoria is not a knight\". \"Sofia is a knave or Jackson is a knight,\" Lily mentioned. Victoria said, \"If Mia is a knave then Michael is a knave.\" According to Mia, \"Jackson is a knave if and only if Lily is a knave\". So who is a knight and who is a knave?", "names": ["Sofia", "Michael", "Jackson", "Lily", "Victoria", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true], "solution_text": "Sofia is a knight, Michael is a knave, Jackson is a knave, Lily is a knave, Victoria is a knight, and Mia is a knight.", "solution_text_format": "(1) Sofia is a knight\n(2) Michael is a knave\n(3) Jackson is a knave\n(4) Lily is a knave\n(5) Victoria is a knight\n(6) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that If Lily is a knight then Mia is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Sofia is a knave or Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of Jackson that Victoria is not a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Mia is a knave then Michael is a knave.", "Mia cannot be a knight, because this would contradict the false claim of Victoria that If Mia is a knave then Michael is a knave.", "Mia cannot be a knave, because this would contradict the claim of Sofia that If Lily is a knight then Mia is a knight.", "We have exhausted all possibilities for Mia and Victoria, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the claim of Lily that Sofia is a knave or Jackson is a knight.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Sofia is a knave or Jackson is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Lily that Sofia is a knave or Jackson is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Mia is a knave then Michael is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Lily is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Sofia is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Sofia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('telling-truth', 5)), ('lying', 0), ('not', ('telling-truth', 4)), ('or', ('lying', 0), ('telling-truth', 2)), ('->', ('lying', 5), ('lying', 1)), ('<=>', ('lying', 2), ('lying', 3)))", "index": 874}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Zoey, Evelyn, Harper, Mia, and Isabella. In David's words: \"If Mia is a knave then David is a knight\". Zoey commented, \"If Harper is a knight then Evelyn is a knight\". Evelyn told you that David is a knave. \"If Evelyn is a knight then Harper is a knight,\" Harper declared. In a statement by Mia: \"Isabella is a knave if and only if Harper is a knight\". \"Mia is not a knave,\" Isabella claimed. So who is a knight and who is a knave?", "names": ["David", "Zoey", "Evelyn", "Harper", "Mia", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "David is a knave, Zoey is a knight, Evelyn is a knight, Harper is a knave, Mia is a knave, and Isabella is a knave.", "solution_text_format": "(1) David is a knave\n(2) Zoey is a knight\n(3) Evelyn is a knight\n(4) Harper is a knave\n(5) Mia is a knave\n(6) Isabella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that If Mia is a knave then David is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Isabella is a knave if and only if Harper is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Mia is not a knave.", "Harper cannot be a knight, because this would contradict the claim of Mia that Isabella is a knave if and only if Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Harper is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that David is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of Harper that If Evelyn is a knight then Harper is a knight.", "We have exhausted all possibilities for Evelyn and Harper, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Mia is not a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Harper is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Mia is not a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Mia that Isabella is a knave if and only if Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Harper is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that David is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of Harper that If Evelyn is a knight then Harper is a knight.", "We have exhausted all possibilities for Evelyn, Harper, Isabella, and Mia, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that If Mia is a knave then David is a knight.", "Mia cannot be a knight, because this would contradict the false claim of David that If Mia is a knave then David is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Isabella is a knave if and only if Harper is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Mia is not a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Mia that Isabella is a knave if and only if Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Harper is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that David is a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that If Harper is a knight then Evelyn is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('lying', 0), ('->', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('lying', 5), ('telling-truth', 3)), ('not', ('lying', 4)))", "index": 875}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Luke, Liam, Lily, Grace, and Michael. Mason told you that Luke is a knight. In Luke's words: \"Lily is a knight and Mason is a knave\". Liam commented, \"Liam is a knight if and only if Mason is a knave\". Lily expressed that Liam is a knave. Grace stated, \"Liam is a knight or Lily is a knight\". Michael noted, \"Luke is a knight if and only if Luke is a knave\". So who is a knight and who is a knave?", "names": ["Mason", "Luke", "Liam", "Lily", "Grace", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "Mason is a knave, Luke is a knave, Liam is a knight, Lily is a knave, Grace is a knight, and Michael is a knave.", "solution_text_format": "(1) Mason is a knave\n(2) Luke is a knave\n(3) Liam is a knight\n(4) Lily is a knave\n(5) Grace is a knight\n(6) Michael is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Mason is a knave.", "Luke cannot be a knave, because this would contradict the claim of Mason that Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Luke is a knight.", "Luke cannot be a knight, because this would contradict the false claim of Mason that Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Lily is a knight and Mason is a knave.", "Lily cannot be a knight, because this would contradict the false claim of Luke that Lily is a knight and Mason is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight if and only if Mason is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Liam is a knight or Lily is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Luke is a knight if and only if Luke is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('and', ('telling-truth', 3), ('lying', 0)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('lying', 2), ('or', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('telling-truth', 1), ('lying', 1)))", "index": 876}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Emily, Evelyn, Riley, Sebastian, and Benjamin. \"Jacob is a knight if and only if Sebastian is a knave,\" Jacob declared. In a statement by Emily: \"Evelyn is not a knight\". Evelyn commented, \"Jacob is a knight or Jacob is a knave\". \"Benjamin is a knight if and only if Jacob is a knave,\" Riley declared. Sebastian remarked, \"Riley is not a knave\". Benjamin was heard saying, \"If Sebastian is a knight then Jacob is a knight\". So who is a knight and who is a knave?", "names": ["Jacob", "Emily", "Evelyn", "Riley", "Sebastian", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Jacob is a knight, Emily is a knave, Evelyn is a knight, Riley is a knave, Sebastian is a knave, and Benjamin is a knight.", "solution_text_format": "(1) Jacob is a knight\n(2) Emily is a knave\n(3) Evelyn is a knight\n(4) Riley is a knave\n(5) Sebastian is a knave\n(6) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Jacob is a knight if and only if Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Jacob that Jacob is a knight if and only if Sebastian is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Riley is not a knave.", "Riley cannot be a knight, because this would contradict the false claim of Sebastian that Riley is not a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Jacob is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Sebastian is a knight then Jacob is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Emily that Evelyn is not a knight.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Jacob is a knight or Jacob is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jacob is a knight or Jacob is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 4)), ('not', ('telling-truth', 2)), ('or', ('telling-truth', 0), ('lying', 0)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('not', ('lying', 3)), ('->', ('telling-truth', 4), ('telling-truth', 0)))", "index": 877}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Noah, Ella, Owen, Penelope, Riley, and Abigail. In Noah's words: \"Penelope is a knave if and only if Owen is a knave\". Ella stated, \"Penelope is a knight\". Owen was heard saying, \"Penelope is a knave or Riley is a knight\". Penelope remarked, \"Noah is a knave\". \"Owen is a knight\" - Riley. In Abigail's words: \"Penelope is a knight and Noah is a knight\". So who is a knight and who is a knave?", "names": ["Noah", "Ella", "Owen", "Penelope", "Riley", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false], "solution_text": "Noah is a knave, Ella is a knight, Owen is a knave, Penelope is a knight, Riley is a knave, and Abigail is a knave.", "solution_text_format": "(1) Noah is a knave\n(2) Ella is a knight\n(3) Owen is a knave\n(4) Penelope is a knight\n(5) Riley is a knave\n(6) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Noah is a knight. No contradiction is found in their claim that Penelope is a knave if and only if Owen is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Noah is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Noah is a knave.", "Owen cannot be a knight, because this would contradict the claim of Noah that Penelope is a knave if and only if Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that Penelope is a knave or Riley is a knight.", "We have exhausted all possibilities for Owen and Penelope, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Owen is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Noah is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Noah that Penelope is a knave if and only if Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Penelope is a knave or Riley is a knight.", "Riley cannot be a knight, because this would contradict the false claim of Owen that Penelope is a knave or Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Owen is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Penelope is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Penelope is a knight and Noah is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Penelope is a knight and Noah is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 2)), ('telling-truth', 3), ('or', ('lying', 3), ('telling-truth', 4)), ('lying', 0), ('telling-truth', 2), ('and', ('telling-truth', 3), ('telling-truth', 0)))", "index": 878}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, Alexander, Abigail, Michael, Evelyn, and Matthew. As Penelope put it, \"Evelyn is a knight and Alexander is a knight\". Alexander noted, \"If Evelyn is a knight then Michael is a knave\". Abigail stated, \"Alexander is a knight if and only if Alexander is a knave\". According to Michael, \"Abigail is a knight if and only if Penelope is a knave\". Evelyn said, \"If Alexander is a knight then Abigail is a knight.\" Matthew told you that If Michael is a knight then Evelyn is a knave. So who is a knight and who is a knave?", "names": ["Penelope", "Alexander", "Abigail", "Michael", "Evelyn", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true], "solution_text": "Penelope is a knave, Alexander is a knight, Abigail is a knave, Michael is a knave, Evelyn is a knave, and Matthew is a knight.", "solution_text_format": "(1) Penelope is a knave\n(2) Alexander is a knight\n(3) Abigail is a knave\n(4) Michael is a knave\n(5) Evelyn is a knave\n(6) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Evelyn is a knight and Alexander is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Alexander is a knight then Abigail is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Evelyn is a knight then Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Alexander that If Evelyn is a knight then Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Penelope is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Alexander is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of Michael that Abigail is a knight if and only if Penelope is a knave.", "We have exhausted all possibilities for Abigail and Michael, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Penelope that Evelyn is a knight and Alexander is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Penelope that Evelyn is a knight and Alexander is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Evelyn is a knight and Alexander is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Alexander is a knight then Abigail is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Penelope that Evelyn is a knight and Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Evelyn is a knight then Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Penelope is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Alexander is a knave.", "Abigail cannot be a knave, because this would contradict the claim of Michael that Abigail is a knight if and only if Penelope is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the false claim of Alexander that If Evelyn is a knight then Michael is a knave.", "We have exhausted all possibilities for Michael and Alexander, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Alexander is a knight then Abigail is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Evelyn is a knight then Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Penelope is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Alexander is a knave.", "Abigail cannot be a knave, because this would contradict the claim of Michael that Abigail is a knight if and only if Penelope is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Penelope is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Alexander is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Alexander is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Michael is a knight then Evelyn is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('telling-truth', 1)), ('->', ('telling-truth', 4), ('lying', 3)), ('<=>', ('telling-truth', 1), ('lying', 1)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('telling-truth', 3), ('lying', 4)))", "index": 879}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, David, William, Charlotte, Lucas, and Owen. In a statement by Aurora: \"Owen is a knave or William is a knave\". David said, \"Lucas is a knight or Aurora is a knave.\" In a statement by William: \"David is a knight\". In Charlotte's words: \"If Aurora is a knight then Lucas is a knight\". Lucas said, \"If William is a knave then Lucas is a knight.\" Owen noted, \"Aurora is not a knave\". So who is a knight and who is a knave?", "names": ["Aurora", "David", "William", "Charlotte", "Lucas", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true], "solution_text": "Aurora is a knight, David is a knave, William is a knave, Charlotte is a knave, Lucas is a knave, and Owen is a knight.", "solution_text_format": "(1) Aurora is a knight\n(2) David is a knave\n(3) William is a knave\n(4) Charlotte is a knave\n(5) Lucas is a knave\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Owen is a knave or William is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Aurora is not a knave.", "William cannot be a knight, because this would contradict the claim of Aurora that Owen is a knave or William is a knave.", "Assume William is a knave. No contradiction is found in their false claim that David is a knight.", "David cannot be a knight, because this would contradict the false claim of William that David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Lucas is a knight or Aurora is a knave.", "Lucas cannot be a knight, because this would contradict the false claim of David that Lucas is a knight or Aurora is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that If William is a knave then Lucas is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that If Aurora is a knight then Lucas is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Aurora is a knight then Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('lying', 2)), ('or', ('telling-truth', 4), ('lying', 0)), ('telling-truth', 1), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('->', ('lying', 2), ('telling-truth', 4)), ('not', ('lying', 0)))", "index": 880}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Daniel, William, Michael, Penelope, and Abigail. \"If Penelope is a knight then Daniel is a knave\" - Owen. Daniel noted, \"Abigail is a knight or Michael is a knight\". William said that If William is a knight then Abigail is a knight. In a statement by Michael: \"If Owen is a knight then Abigail is a knight\". \"Owen is a knight and Abigail is a knave\" - Penelope. Abigail told you that Daniel is a knave or Owen is a knight. So who is a knight and who is a knave?", "names": ["Owen", "Daniel", "William", "Michael", "Penelope", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Owen is a knight, Daniel is a knight, William is a knight, Michael is a knight, Penelope is a knave, and Abigail is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Daniel is a knight\n(3) William is a knight\n(4) Michael is a knight\n(5) Penelope is a knave\n(6) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that If Penelope is a knight then Daniel is a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Owen is a knight and Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Penelope that Owen is a knight and Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Daniel is a knave or Owen is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Owen is a knight and Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Daniel is a knave or Owen is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Abigail is a knight or Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Owen is a knight then Abigail is a knight.", "Assume William is a knight. No contradiction is found in their claim that If William is a knight then Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 1)), ('or', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('telling-truth', 2), ('telling-truth', 5)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('lying', 5)), ('or', ('lying', 1), ('telling-truth', 0)))", "index": 881}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Emily, Ethan, Noah, Aurora, and Victoria. Emma asserted: \"Emily is a knave and Aurora is a knight\". According to Emily, \"Aurora is a knight and Victoria is a knave\". Ethan was heard saying, \"Emily is a knight if and only if Noah is a knave\". \"If Emma is a knight then Aurora is a knight\" - Noah. Aurora commented, \"Aurora is a knight and Emily is a knight\". Victoria noted, \"Aurora is a knight if and only if Emma is a knave\". So who is a knight and who is a knave?", "names": ["Emma", "Emily", "Ethan", "Noah", "Aurora", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Emma is a knave, Emily is a knave, Ethan is a knight, Noah is a knight, Aurora is a knave, and Victoria is a knave.", "solution_text_format": "(1) Emma is a knave\n(2) Emily is a knave\n(3) Ethan is a knight\n(4) Noah is a knight\n(5) Aurora is a knave\n(6) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Emily is a knave and Aurora is a knight.", "Emily cannot be a knight, because this would contradict the claim of Emma that Emily is a knave and Aurora is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Aurora is a knight and Victoria is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Emily is a knight.", "Aurora cannot be a knave, because this would contradict the claim of Emma that Emily is a knave and Aurora is a knight.", "We have exhausted all possibilities for Aurora and Emily, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Emily is a knave and Aurora is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Aurora is a knight and Victoria is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Aurora is a knight and Emily is a knight.", "Victoria cannot be a knight, because this would contradict the claim of Emily that Aurora is a knight and Victoria is a knave.", "Victoria cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight if and only if Emma is a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Emily that Aurora is a knight and Victoria is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Aurora is a knight and Victoria is a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Emma that Emily is a knave and Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Aurora is a knight and Emily is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Aurora is a knight if and only if Emma is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Emma is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Emily is a knight if and only if Noah is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Emma is a knight then Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 4)), ('and', ('telling-truth', 4), ('lying', 5)), ('<=>', ('telling-truth', 1), ('lying', 3)), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('<=>', ('telling-truth', 4), ('lying', 0)))", "index": 882}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Avery, Jacob, Logan, Lucas, and Mason. Matthew said that Lucas is a knight or Jacob is a knight. \"Logan is a knave and Matthew is a knave,\" Avery claimed. Jacob remarked, \"Matthew is a knave if and only if Logan is a knight\". \"Lucas is a knight or Avery is a knight,\" Logan mentioned. In a statement by Lucas: \"Jacob is a knave and Logan is a knave\". According to Mason, \"Jacob is a knight and Matthew is a knight\". So who is a knight and who is a knave?", "names": ["Matthew", "Avery", "Jacob", "Logan", "Lucas", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Matthew is a knight, Avery is a knave, Jacob is a knight, Logan is a knave, Lucas is a knave, and Mason is a knight.", "solution_text_format": "(1) Matthew is a knight\n(2) Avery is a knave\n(3) Jacob is a knight\n(4) Logan is a knave\n(5) Lucas is a knave\n(6) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Lucas is a knight or Jacob is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Jacob is a knave and Logan is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Lucas that Jacob is a knave and Logan is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Logan is a knight.", "Logan cannot be a knight, because this would contradict the claim of Lucas that Jacob is a knave and Logan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of Jacob that Matthew is a knave if and only if Logan is a knight.", "We have exhausted all possibilities for Logan and Jacob, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Jacob is a knave and Logan is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Logan is a knight.", "Logan cannot be a knight, because this would contradict the claim of Jacob that Matthew is a knave if and only if Logan is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Lucas is a knight or Avery is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Matthew is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Logan is a knave and Matthew is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Jacob is a knight and Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 2)), ('and', ('lying', 3), ('lying', 0)), ('<=>', ('lying', 0), ('telling-truth', 3)), ('or', ('telling-truth', 4), ('telling-truth', 1)), ('and', ('lying', 2), ('lying', 3)), ('and', ('telling-truth', 2), ('telling-truth', 0)))", "index": 883}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Amelia, Abigail, Oliver, Isabella, and Matthew. In Scarlett's words: \"Isabella is a knave\". Amelia said that If Matthew is a knight then Amelia is a knight. \"Amelia is not a knave,\" Abigail claimed. As Oliver put it, \"Scarlett is not a knave\". Isabella expressed that Amelia is a knave. Matthew told you that Isabella is not a knight. So who is a knight and who is a knave?", "names": ["Scarlett", "Amelia", "Abigail", "Oliver", "Isabella", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Scarlett is a knight, Amelia is a knight, Abigail is a knight, Oliver is a knight, Isabella is a knave, and Matthew is a knight.", "solution_text_format": "(1) Scarlett is a knight\n(2) Amelia is a knight\n(3) Abigail is a knight\n(4) Oliver is a knight\n(5) Isabella is a knave\n(6) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Scarlett that Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that If Matthew is a knight then Amelia is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Scarlett is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('not', ('lying', 1)), ('not', ('lying', 0)), ('lying', 1), ('not', ('telling-truth', 4)))", "index": 884}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Sebastian, Harper, James, Riley, and Ethan. Isabella stated, \"Ethan is not a knight\". Sebastian expressed that If Sebastian is a knight then Isabella is a knight. \"Ethan is a knight if and only if Riley is a knight,\" Harper mentioned. James expressed that Ethan is a knave or Isabella is a knight. \"Sebastian is not a knight\" - Riley. As Ethan put it, \"Sebastian is a knight if and only if Ethan is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Sebastian", "Harper", "James", "Riley", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Isabella is a knight, Sebastian is a knight, Harper is a knight, James is a knight, Riley is a knave, and Ethan is a knave.", "solution_text_format": "(1) Isabella is a knight\n(2) Sebastian is a knight\n(3) Harper is a knight\n(4) James is a knight\n(5) Riley is a knave\n(6) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of Isabella that Ethan is not a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Ethan is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Sebastian is a knight then Isabella is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Riley is a knight.", "Riley cannot be a knight, because this would contradict the claim of Harper that Ethan is a knight if and only if Riley is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume James is a knight. No contradiction is found in their claim that Ethan is a knave or Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('->', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('or', ('lying', 5), ('telling-truth', 0)), ('not', ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 5)))", "index": 885}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Elizabeth, Joseph, Avery, James, and Aiden. \"Elizabeth is a knave,\" Olivia claimed. Elizabeth said, \"Joseph is not a knight.\" \"If Joseph is a knight then James is a knight\" - Joseph. According to Avery, \"Joseph is a knave\". James was heard saying, \"Joseph is a knight or Olivia is a knight\". \"If Elizabeth is a knight then Aiden is a knight,\" Aiden claimed. So who is a knight and who is a knave?", "names": ["Olivia", "Elizabeth", "Joseph", "Avery", "James", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Olivia is a knight, Elizabeth is a knave, Joseph is a knight, Avery is a knave, James is a knight, and Aiden is a knight.", "solution_text_format": "(1) Olivia is a knight\n(2) Elizabeth is a knave\n(3) Joseph is a knight\n(4) Avery is a knave\n(5) James is a knight\n(6) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Olivia that Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Joseph is not a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Joseph is a knight then James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Joseph is a knight or Olivia is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Joseph is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Joseph is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('not', ('telling-truth', 2)), ('->', ('telling-truth', 2), ('telling-truth', 4)), ('lying', 2), ('or', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('telling-truth', 5)))", "index": 886}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Jacob, William, Evelyn, James, and Mia. \"If William is a knave then James is a knave,\" Emily declared. According to Jacob, \"William is a knight if and only if William is a knave\". As William put it, \"Mia is a knave if and only if Jacob is a knight\". Evelyn was heard saying, \"Mia is a knave and James is a knight\". In a statement by James: \"Emily is a knave and James is a knight\". Mia expressed that James is a knight or Evelyn is a knight. So who is a knight and who is a knave?", "names": ["Emily", "Jacob", "William", "Evelyn", "James", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false], "solution_text": "Emily is a knight, Jacob is a knave, William is a knave, Evelyn is a knave, James is a knave, and Mia is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Jacob is a knave\n(3) William is a knave\n(4) Evelyn is a knave\n(5) James is a knave\n(6) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that If William is a knave then James is a knave.", "Assume William is a knight. No contradiction is found in their claim that Mia is a knave if and only if Jacob is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that James is a knight or Evelyn is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Emily is a knave and James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Emily is a knave and James is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Mia is a knave and James is a knight.", "Evelyn cannot be a knave, because this would contradict the claim of Mia that James is a knight or Evelyn is a knight.", "We have exhausted all possibilities for Evelyn and James, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that James is a knight or Evelyn is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Emily is a knave and James is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Emily is a knave and James is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Mia is a knave and James is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Mia is a knave and James is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that William is a knight if and only if William is a knave.", "Jacob cannot be a knave, because this would contradict the claim of William that Mia is a knave if and only if Jacob is a knight.", "We have exhausted all possibilities for Jacob, Evelyn, James, and Mia, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Jacob is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that James is a knight or Evelyn is a knight.", "James cannot be a knight, because this would contradict the claim of Emily that If William is a knave then James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Emily is a knave and James is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Mia is a knave and James is a knight.", "Evelyn cannot be a knave, because this would contradict the claim of Mia that James is a knight or Evelyn is a knight.", "We have exhausted all possibilities for Evelyn and James, so let us go back and reconsider Mia.", "Assume Mia is a knave. No contradiction is found in their false claim that James is a knight or Evelyn is a knight.", "James cannot be a knight, because this would contradict the claim of Emily that If William is a knave then James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Emily is a knave and James is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Mia is a knave and James is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Mia is a knave and James is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that William is a knight if and only if William is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that William is a knight if and only if William is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 4)), ('<=>', ('telling-truth', 2), ('lying', 2)), ('<=>', ('lying', 5), ('telling-truth', 1)), ('and', ('lying', 5), ('telling-truth', 4)), ('and', ('lying', 0), ('telling-truth', 4)), ('or', ('telling-truth', 4), ('telling-truth', 3)))", "index": 887}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Isabella, Oliver, Daniel, Sophia, and Sofia. Ella was heard saying, \"If Ella is a knight then Isabella is a knight\". \"Sophia is a knave or Sofia is a knave,\" Isabella declared. In a statement by Oliver: \"Daniel is not a knave\". Daniel expressed that Isabella is not a knight. Sophia noted, \"Oliver is a knave and Isabella is a knave\". According to Sofia, \"Daniel is a knight and Isabella is a knave\". So who is a knight and who is a knave?", "names": ["Ella", "Isabella", "Oliver", "Daniel", "Sophia", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Ella is a knight, Isabella is a knight, Oliver is a knave, Daniel is a knave, Sophia is a knave, and Sofia is a knave.", "solution_text_format": "(1) Ella is a knight\n(2) Isabella is a knight\n(3) Oliver is a knave\n(4) Daniel is a knave\n(5) Sophia is a knave\n(6) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that If Ella is a knight then Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Sophia is a knave or Sofia is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Oliver is a knave and Isabella is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Oliver is a knave and Isabella is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Isabella is not a knight.", "Daniel cannot be a knave, because this would contradict the claim of Oliver that Daniel is not a knave.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Daniel is not a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Oliver that Daniel is not a knave.", "Assume Daniel is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Daniel is a knight and Isabella is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Daniel is a knight and Isabella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('lying', 4), ('lying', 5)), ('not', ('lying', 3)), ('not', ('telling-truth', 1)), ('and', ('lying', 2), ('lying', 1)), ('and', ('telling-truth', 3), ('lying', 1)))", "index": 888}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Matthew, Mia, Luke, Elizabeth, and Victoria. As Benjamin put it, \"If Victoria is a knight then Elizabeth is a knight\". Matthew was heard saying, \"Victoria is a knight and Mia is a knave\". In a statement by Mia: \"Elizabeth is a knight or Matthew is a knight\". \"If Elizabeth is a knave then Benjamin is a knight,\" Luke declared. Elizabeth commented, \"Victoria is a knight and Victoria is a knave\". According to Victoria, \"Luke is a knave if and only if Elizabeth is a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Matthew", "Mia", "Luke", "Elizabeth", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false], "solution_text": "Benjamin is a knight, Matthew is a knave, Mia is a knave, Luke is a knight, Elizabeth is a knave, and Victoria is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Matthew is a knave\n(3) Mia is a knave\n(4) Luke is a knight\n(5) Elizabeth is a knave\n(6) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that If Victoria is a knight then Elizabeth is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Luke is a knave if and only if Elizabeth is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Benjamin is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Victoria is a knave.", "Elizabeth cannot be a knave, because this would contradict the claim of Benjamin that If Victoria is a knight then Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the false claim of their own that If Elizabeth is a knave then Benjamin is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Elizabeth is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Benjamin is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Victoria is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Victoria is a knight and Victoria is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Mia is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Victoria is a knight and Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight or Matthew is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Elizabeth is a knight or Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('telling-truth', 4)), ('and', ('telling-truth', 5), ('lying', 2)), ('or', ('telling-truth', 4), ('telling-truth', 1)), ('->', ('lying', 4), ('telling-truth', 0)), ('and', ('telling-truth', 5), ('lying', 5)), ('<=>', ('lying', 3), ('lying', 4)))", "index": 889}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Joseph, Liam, Alexander, Ella, and Aiden. Benjamin noted, \"If Aiden is a knight then Liam is a knave\". \"Alexander is a knight and Liam is a knave\" - Joseph. Liam said that Ella is a knight. Alexander stated, \"Joseph is a knight and Joseph is a knave\". Ella noted, \"Alexander is a knave and Aiden is a knave\". Aiden said that Joseph is not a knave. So who is a knight and who is a knave?", "names": ["Benjamin", "Joseph", "Liam", "Alexander", "Ella", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, false], "solution_text": "Benjamin is a knight, Joseph is a knave, Liam is a knight, Alexander is a knave, Ella is a knight, and Aiden is a knave.", "solution_text_format": "(1) Benjamin is a knight\n(2) Joseph is a knave\n(3) Liam is a knight\n(4) Alexander is a knave\n(5) Ella is a knight\n(6) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that If Aiden is a knight then Liam is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Joseph is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Alexander is a knight and Liam is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Joseph is a knave.", "Alexander cannot be a knave, because this would contradict the claim of Joseph that Alexander is a knight and Liam is a knave.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Aiden that Joseph is not a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Joseph is not a knave.", "Joseph cannot be a knight, because this would contradict the false claim of Aiden that Joseph is not a knave.", "Assume Joseph is a knave. No contradiction is found in their false claim that Alexander is a knight and Liam is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Joseph is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Joseph is a knight and Joseph is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Alexander is a knave and Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 2)), ('and', ('telling-truth', 3), ('lying', 2)), ('telling-truth', 4), ('and', ('telling-truth', 1), ('lying', 1)), ('and', ('lying', 3), ('lying', 5)), ('not', ('lying', 1)))", "index": 890}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Sofia, Owen, Evelyn, Aria, and Grace. Michael said that Owen is a knight and Aria is a knight. Sofia said, \"If Michael is a knave then Grace is a knight.\" \"Evelyn is a knave and Grace is a knave\" - Owen. Evelyn commented, \"Michael is a knight or Sofia is a knave\". \"Michael is a knight or Grace is a knave,\" Aria declared. Grace told you that Michael is a knight and Michael is a knave. So who is a knight and who is a knave?", "names": ["Michael", "Sofia", "Owen", "Evelyn", "Aria", "Grace"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false], "solution_text": "Michael is a knave, Sofia is a knave, Owen is a knave, Evelyn is a knight, Aria is a knight, and Grace is a knave.", "solution_text_format": "(1) Michael is a knave\n(2) Sofia is a knave\n(3) Owen is a knave\n(4) Evelyn is a knight\n(5) Aria is a knight\n(6) Grace is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Owen is a knight and Aria is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Evelyn is a knave and Grace is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Owen that Evelyn is a knave and Grace is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Michael is a knight or Sofia is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Michael that Owen is a knight and Aria is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Owen is a knight and Aria is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Evelyn is a knave and Grace is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Owen that Evelyn is a knave and Grace is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Michael is a knight or Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Michael is a knave then Grace is a knight.", "Grace cannot be a knight, because this would contradict the claim of Owen that Evelyn is a knave and Grace is a knave.", "Grace cannot be a knave, because this would contradict the claim of Sofia that If Michael is a knave then Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the false claim of Evelyn that Michael is a knight or Sofia is a knave.", "We have exhausted all possibilities for Sofia and Evelyn, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Evelyn is a knave and Grace is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Michael is a knight or Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Evelyn that Michael is a knight or Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Michael is a knave then Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Sofia that If Michael is a knave then Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Michael is a knight and Michael is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Michael is a knight or Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 4)), ('->', ('lying', 0), ('telling-truth', 5)), ('and', ('lying', 3), ('lying', 5)), ('or', ('telling-truth', 0), ('lying', 1)), ('or', ('telling-truth', 0), ('lying', 5)), ('and', ('telling-truth', 0), ('lying', 0)))", "index": 891}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Lucas, Evelyn, Benjamin, Samuel, and Harper. In Jack's words: \"If Jack is a knight then Harper is a knight\". Lucas commented, \"Evelyn is not a knave\". Evelyn remarked, \"Jack is not a knave\". \"Lucas is not a knave,\" Benjamin claimed. Samuel remarked, \"Benjamin is a knight\". \"Lucas is a knight,\" Harper declared. So who is a knight and who is a knave?", "names": ["Jack", "Lucas", "Evelyn", "Benjamin", "Samuel", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Jack is a knight, Lucas is a knight, Evelyn is a knight, Benjamin is a knight, Samuel is a knight, and Harper is a knight.", "solution_text_format": "(1) Jack is a knight\n(2) Lucas is a knight\n(3) Evelyn is a knight\n(4) Benjamin is a knight\n(5) Samuel is a knight\n(6) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that If Jack is a knight then Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Evelyn is not a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Lucas is not a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 5)), ('not', ('lying', 2)), ('not', ('lying', 0)), ('not', ('lying', 1)), ('telling-truth', 3), ('telling-truth', 1))", "index": 892}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Aurora, Logan, Matthew, Scarlett, and Oliver. Elizabeth stated, \"Scarlett is a knave and Oliver is a knight\". Aurora remarked, \"Elizabeth is a knave and Matthew is a knight\". According to Logan, \"Elizabeth is a knave and Elizabeth is a knight\". Matthew asserted: \"Elizabeth is a knave and Scarlett is a knight\". \"Matthew is a knight or Oliver is a knight,\" Scarlett declared. In a statement by Oliver: \"Matthew is not a knight\". So who is a knight and who is a knave?", "names": ["Elizabeth", "Aurora", "Logan", "Matthew", "Scarlett", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Elizabeth is a knave, Aurora is a knight, Logan is a knave, Matthew is a knight, Scarlett is a knight, and Oliver is a knave.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Aurora is a knight\n(3) Logan is a knave\n(4) Matthew is a knight\n(5) Scarlett is a knight\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Scarlett is a knave and Oliver is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Elizabeth that Scarlett is a knave and Oliver is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Matthew is a knight or Oliver is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Scarlett is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Scarlett is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Scarlett that Matthew is a knight or Oliver is a knight.", "Oliver cannot be a knave, because this would contradict the claim of Elizabeth that Scarlett is a knave and Oliver is a knight.", "We have exhausted all possibilities for Oliver, Matthew, and Scarlett, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Scarlett is a knave and Oliver is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Matthew is a knight or Oliver is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Elizabeth is a knave and Scarlett is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Matthew is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Matthew is not a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Elizabeth is a knave and Matthew is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Elizabeth is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 5)), ('and', ('lying', 0), ('telling-truth', 3)), ('and', ('lying', 0), ('telling-truth', 0)), ('and', ('lying', 0), ('telling-truth', 4)), ('or', ('telling-truth', 3), ('telling-truth', 5)), ('not', ('telling-truth', 3)))", "index": 893}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Aiden, Abigail, Sebastian, Ethan, and Daniel. \"Daniel is a knight or Abigail is a knight\" - Aria. In a statement by Aiden: \"Daniel is a knave\". \"If Aiden is a knight then Abigail is a knight,\" Abigail declared. Sebastian said that Ethan is not a knave. Ethan was heard saying, \"Daniel is a knave if and only if Aria is a knight\". \"If Sebastian is a knight then Ethan is a knight\" - Daniel. So who is a knight and who is a knave?", "names": ["Aria", "Aiden", "Abigail", "Sebastian", "Ethan", "Daniel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Aria is a knight, Aiden is a knave, Abigail is a knight, Sebastian is a knave, Ethan is a knave, and Daniel is a knight.", "solution_text_format": "(1) Aria is a knight\n(2) Aiden is a knave\n(3) Abigail is a knight\n(4) Sebastian is a knave\n(5) Ethan is a knave\n(6) Daniel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Daniel is a knight or Abigail is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Sebastian is a knight then Ethan is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Daniel is a knave if and only if Aria is a knight.", "Ethan cannot be a knave, because this would contradict the claim of Sebastian that Ethan is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Ethan is not a knave.", "Ethan cannot be a knight, because this would contradict the false claim of Sebastian that Ethan is not a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Aria is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Aiden is a knight then Abigail is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Daniel is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('telling-truth', 2)), ('lying', 5), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('not', ('lying', 4)), ('<=>', ('lying', 5), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('telling-truth', 4)))", "index": 894}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Charlotte, Owen, Elizabeth, Sofia, and Liam. \"Elizabeth is a knight or Owen is a knave,\" Victoria claimed. \"Sofia is a knight or Victoria is a knight,\" Charlotte mentioned. Owen told you that Victoria is a knave. Elizabeth remarked, \"If Liam is a knight then Charlotte is a knave\". Sofia remarked, \"If Owen is a knave then Owen is a knight\". Liam noted, \"Victoria is a knight and Sofia is a knave\". So who is a knight and who is a knave?", "names": ["Victoria", "Charlotte", "Owen", "Elizabeth", "Sofia", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true], "solution_text": "Victoria is a knight, Charlotte is a knight, Owen is a knave, Elizabeth is a knave, Sofia is a knave, and Liam is a knight.", "solution_text_format": "(1) Victoria is a knight\n(2) Charlotte is a knight\n(3) Owen is a knave\n(4) Elizabeth is a knave\n(5) Sofia is a knave\n(6) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Elizabeth is a knight or Owen is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Liam is a knight then Charlotte is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Victoria is a knight and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Liam that Victoria is a knight and Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Owen is a knave then Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Victoria is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Elizabeth that If Liam is a knight then Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight or Victoria is a knight.", "We have exhausted all possibilities for Charlotte, Owen, and Sofia, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Victoria is a knight and Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Owen is a knave then Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Victoria is a knave.", "Owen cannot be a knave, because this would contradict the claim of Sofia that If Owen is a knave then Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the false claim of Liam that Victoria is a knight and Sofia is a knave.", "We have exhausted all possibilities for Sofia and Liam, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that If Liam is a knight then Charlotte is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Victoria is a knight and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Liam that Victoria is a knight and Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that If Owen is a knave then Owen is a knight.", "Owen cannot be a knight, because this would contradict the claim of Victoria that Elizabeth is a knight or Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Sofia is a knight or Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('lying', 2)), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('lying', 0), ('->', ('telling-truth', 5), ('lying', 1)), ('->', ('lying', 2), ('telling-truth', 2)), ('and', ('telling-truth', 0), ('lying', 4)))", "index": 895}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Joseph, Isabella, Lucas, Grace, and Penelope. \"Penelope is a knave and Liam is a knight,\" Liam declared. Joseph remarked, \"Liam is a knave or Joseph is a knight\". Isabella noted, \"Joseph is a knight or Lucas is a knight\". As Lucas put it, \"Isabella is a knave and Liam is a knight\". \"Lucas is a knave or Joseph is a knight\" - Grace. Penelope commented, \"If Liam is a knave then Lucas is a knave\". So who is a knight and who is a knave?", "names": ["Liam", "Joseph", "Isabella", "Lucas", "Grace", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Liam is a knave, Joseph is a knight, Isabella is a knight, Lucas is a knave, Grace is a knight, and Penelope is a knight.", "solution_text_format": "(1) Liam is a knave\n(2) Joseph is a knight\n(3) Isabella is a knight\n(4) Lucas is a knave\n(5) Grace is a knight\n(6) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Penelope is a knave and Liam is a knight.", "Penelope cannot be a knight, because this would contradict the claim of Liam that Penelope is a knave and Liam is a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that If Liam is a knave then Lucas is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Penelope is a knave and Liam is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Liam is a knave then Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Liam is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Isabella is a knave and Liam is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Joseph is a knight or Lucas is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Liam is a knave or Joseph is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Lucas is a knave or Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 0)), ('or', ('lying', 0), ('telling-truth', 1)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('and', ('lying', 2), ('telling-truth', 0)), ('or', ('lying', 3), ('telling-truth', 1)), ('->', ('lying', 0), ('lying', 3)))", "index": 896}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Alexander, Lily, Michael, Jacob, and Olivia. \"Jacob is a knave and Alexander is a knave,\" Matthew mentioned. \"Michael is a knight and Matthew is a knight,\" Alexander declared. Lily expressed that Michael is a knight. Michael expressed that Jacob is not a knight. In Jacob's words: \"If Michael is a knight then Lily is a knight\". \"If Jacob is a knave then Alexander is a knave,\" Olivia claimed. So who is a knight and who is a knave?", "names": ["Matthew", "Alexander", "Lily", "Michael", "Jacob", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Matthew is a knave, Alexander is a knave, Lily is a knave, Michael is a knave, Jacob is a knight, and Olivia is a knight.", "solution_text_format": "(1) Matthew is a knave\n(2) Alexander is a knave\n(3) Lily is a knave\n(4) Michael is a knave\n(5) Jacob is a knight\n(6) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Jacob is a knave and Alexander is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Matthew that Jacob is a knave and Alexander is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Michael is a knight then Lily is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Jacob is not a knight.", "Lily cannot be a knight, because this would contradict the false claim of Jacob that If Michael is a knight then Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Michael is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Michael.", "Michael cannot be a knave, because this would contradict the false claim of their own that Jacob is not a knight.", "We have exhausted all possibilities for Michael and Jacob, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Jacob is a knave and Alexander is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Michael is a knight then Lily is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Jacob is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Michael is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Michael is a knight.", "Alexander cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Matthew is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Michael is a knight and Matthew is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Jacob is a knave then Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 1)), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('telling-truth', 3), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('->', ('lying', 4), ('lying', 1)))", "index": 897}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Matthew, Emma, Owen, Zoey, and William. Evelyn asserted: \"If Evelyn is a knight then Emma is a knight\". Matthew commented, \"Matthew is a knight and Emma is a knight\". In Emma's words: \"If Evelyn is a knight then Owen is a knave\". \"Matthew is a knight,\" Owen declared. Zoey remarked, \"Zoey is a knight and Emma is a knave\". As William put it, \"Emma is not a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "Matthew", "Emma", "Owen", "Zoey", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Evelyn is a knight, Matthew is a knave, Emma is a knight, Owen is a knave, Zoey is a knave, and William is a knave.", "solution_text_format": "(1) Evelyn is a knight\n(2) Matthew is a knave\n(3) Emma is a knight\n(4) Owen is a knave\n(5) Zoey is a knave\n(6) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that If Evelyn is a knight then Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that If Evelyn is a knight then Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Emma that If Evelyn is a knight then Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Owen that Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Matthew is a knight and Emma is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Zoey is a knight and Emma is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Zoey is a knight and Emma is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Emma is not a knight.", "Assume William is a knave. No contradiction is found in their false claim that Emma is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 2)), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('telling-truth', 0), ('lying', 3)), ('telling-truth', 1), ('and', ('telling-truth', 4), ('lying', 2)), ('not', ('telling-truth', 2)))", "index": 898}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Zoey, Victoria, Aiden, James, and Aurora. Jack commented, \"Zoey is a knave and Aiden is a knight\". Zoey remarked, \"Aiden is not a knave\". Victoria was heard saying, \"Aurora is a knave\". Aiden said that Victoria is a knave. James expressed that James is a knight or Jack is a knave. Aurora noted, \"James is a knight\". So who is a knight and who is a knave?", "names": ["Jack", "Zoey", "Victoria", "Aiden", "James", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Jack is a knave, Zoey is a knight, Victoria is a knave, Aiden is a knight, James is a knight, and Aurora is a knight.", "solution_text_format": "(1) Jack is a knave\n(2) Zoey is a knight\n(3) Victoria is a knave\n(4) Aiden is a knight\n(5) James is a knight\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Zoey is a knave and Aiden is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Jack that Zoey is a knave and Aiden is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Aiden is not a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Zoey that Aiden is not a knave.", "Aiden cannot be a knave, because this would contradict the claim of Jack that Zoey is a knave and Aiden is a knight.", "We have exhausted all possibilities for Aiden and Zoey, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Zoey is a knave and Aiden is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Aiden that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Aurora is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that James is a knight.", "Assume James is a knight. No contradiction is found in their claim that James is a knight or Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 1), ('telling-truth', 3)), ('not', ('lying', 3)), ('lying', 5), ('lying', 2), ('or', ('telling-truth', 4), ('lying', 0)), ('telling-truth', 4))", "index": 899}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Mason, Harper, Scarlett, Logan, and Elizabeth. Ethan stated, \"Mason is a knight\". Mason said that Logan is not a knave. In a statement by Harper: \"Mason is a knave or Ethan is a knave\". \"Elizabeth is a knight or Scarlett is a knight,\" Scarlett claimed. As Logan put it, \"Elizabeth is a knave and Scarlett is a knight\". Elizabeth commented, \"Harper is a knight if and only if Ethan is a knave\". So who is a knight and who is a knave?", "names": ["Ethan", "Mason", "Harper", "Scarlett", "Logan", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Ethan is a knave, Mason is a knave, Harper is a knight, Scarlett is a knight, Logan is a knave, and Elizabeth is a knight.", "solution_text_format": "(1) Ethan is a knave\n(2) Mason is a knave\n(3) Harper is a knight\n(4) Scarlett is a knight\n(5) Logan is a knave\n(6) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Logan is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Elizabeth is a knave and Scarlett is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Logan that Elizabeth is a knave and Scarlett is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Ethan is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Mason is a knave or Ethan is a knave.", "Harper cannot be a knave, because this would contradict the false claim of Elizabeth that Harper is a knight if and only if Ethan is a knave.", "We have exhausted all possibilities for Harper and Elizabeth, so let us go back and reconsider Logan.", "Logan cannot be a knave, because this would contradict the claim of Mason that Logan is not a knave.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Mason.", "Mason cannot be a knave, because this would contradict the claim of Ethan that Mason is a knight.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Mason is a knight.", "Mason cannot be a knight, because this would contradict the false claim of Ethan that Mason is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Logan is not a knave.", "Logan cannot be a knight, because this would contradict the false claim of Mason that Logan is not a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Scarlett is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Harper is a knight if and only if Ethan is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Mason is a knave or Ethan is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Elizabeth is a knight or Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('not', ('lying', 4)), ('or', ('lying', 1), ('lying', 0)), ('or', ('telling-truth', 5), ('telling-truth', 3)), ('and', ('lying', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 2), ('lying', 0)))", "index": 900}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Aurora, Abigail, Michael, Logan, and Luke. \"Logan is a knight or Abigail is a knight,\" Chloe declared. Aurora asserted: \"Michael is a knave or Logan is a knave\". Abigail expressed that If Chloe is a knave then Logan is a knight. Michael expressed that Luke is a knight and Chloe is a knave. \"Abigail is a knave,\" Logan claimed. In Luke's words: \"Logan is a knight and Chloe is a knight\". So who is a knight and who is a knave?", "names": ["Chloe", "Aurora", "Abigail", "Michael", "Logan", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Chloe is a knight, Aurora is a knight, Abigail is a knight, Michael is a knave, Logan is a knave, and Luke is a knave.", "solution_text_format": "(1) Chloe is a knight\n(2) Aurora is a knight\n(3) Abigail is a knight\n(4) Michael is a knave\n(5) Logan is a knave\n(6) Luke is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Logan is a knight or Abigail is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Logan that Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that If Chloe is a knave then Logan is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Chloe is a knave then Logan is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Michael is a knave or Logan is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Luke is a knight and Chloe is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Luke is a knight and Chloe is a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Chloe is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Logan is a knight and Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('lying', 3), ('lying', 4)), ('->', ('lying', 0), ('telling-truth', 4)), ('and', ('telling-truth', 5), ('lying', 0)), ('lying', 2), ('and', ('telling-truth', 4), ('telling-truth', 0)))", "index": 901}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Daniel, Lily, Aurora, Isabella, and Michael. Olivia told you that If Michael is a knave then Daniel is a knight. Daniel told you that Olivia is a knight or Olivia is a knave. Lily expressed that Daniel is a knave and Aurora is a knight. According to Aurora, \"Lily is a knight and Lily is a knave\". Isabella noted, \"Olivia is a knave\". In a statement by Michael: \"If Michael is a knight then Daniel is a knight\". So who is a knight and who is a knave?", "names": ["Olivia", "Daniel", "Lily", "Aurora", "Isabella", "Michael"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true], "solution_text": "Olivia is a knight, Daniel is a knight, Lily is a knave, Aurora is a knave, Isabella is a knave, and Michael is a knight.", "solution_text_format": "(1) Olivia is a knight\n(2) Daniel is a knight\n(3) Lily is a knave\n(4) Aurora is a knave\n(5) Isabella is a knave\n(6) Michael is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that If Michael is a knave then Daniel is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Michael is a knight then Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Olivia is a knight or Olivia is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Aurora is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Daniel is a knave and Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Lily is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Lily is a knight and Lily is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('lying', 0)), ('and', ('lying', 1), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('lying', 2)), ('lying', 0), ('->', ('telling-truth', 5), ('telling-truth', 1)))", "index": 902}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Abigail, Luke, Henry, Oliver, and Jackson. As Evelyn put it, \"Jackson is a knave and Luke is a knight\". Abigail said, \"Evelyn is not a knight.\" Luke stated, \"Abigail is a knave if and only if Evelyn is a knave\". Henry stated, \"Jackson is not a knight\". Oliver commented, \"If Abigail is a knight then Luke is a knight\". Jackson noted, \"Luke is a knight and Oliver is a knave\". So who is a knight and who is a knave?", "names": ["Evelyn", "Abigail", "Luke", "Henry", "Oliver", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false], "solution_text": "Evelyn is a knave, Abigail is a knight, Luke is a knave, Henry is a knight, Oliver is a knave, and Jackson is a knave.", "solution_text_format": "(1) Evelyn is a knave\n(2) Abigail is a knight\n(3) Luke is a knave\n(4) Henry is a knight\n(5) Oliver is a knave\n(6) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Jackson is a knave and Luke is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Evelyn that Jackson is a knave and Luke is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Luke is a knight and Oliver is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Evelyn is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Evelyn is not a knight.", "Abigail cannot be a knave, because this would contradict the claim of Luke that Abigail is a knave if and only if Evelyn is a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Evelyn that Jackson is a knave and Luke is a knight.", "We have exhausted all possibilities for Luke and Jackson, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Jackson is a knave and Luke is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Luke is a knight and Oliver is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Evelyn is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Luke that Abigail is a knave if and only if Evelyn is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Evelyn is not a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Luke.", "Luke cannot be a knave, because this would contradict the claim of Jackson that Luke is a knight and Oliver is a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Luke is a knight and Oliver is a knave.", "Luke cannot be a knight, because this would contradict the false claim of Evelyn that Jackson is a knave and Luke is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Evelyn is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that If Abigail is a knight then Luke is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Abigail is a knight then Luke is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Jackson is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('<=>', ('lying', 1), ('lying', 0)), ('not', ('telling-truth', 5)), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('telling-truth', 2), ('lying', 4)))", "index": 903}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Alexander, Henry, Aiden, Riley, and Elizabeth. David remarked, \"If Elizabeth is a knight then Henry is a knave\". \"David is a knave if and only if Henry is a knight,\" Alexander claimed. Henry said that Alexander is a knight. Aiden said, \"If Elizabeth is a knight then David is a knight.\" Riley asserted: \"If Henry is a knave then Elizabeth is a knave\". Elizabeth told you that Elizabeth is a knight or Henry is a knight. So who is a knight and who is a knave?", "names": ["David", "Alexander", "Henry", "Aiden", "Riley", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "David is a knave, Alexander is a knight, Henry is a knight, Aiden is a knave, Riley is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) David is a knave\n(2) Alexander is a knight\n(3) Henry is a knight\n(4) Aiden is a knave\n(5) Riley is a knight\n(6) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Henry is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Elizabeth is a knight or Henry is a knight.", "Henry cannot be a knight, because this would contradict the claim of David that If Elizabeth is a knight then Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Henry that Alexander is a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that David is a knave if and only if Henry is a knight.", "We have exhausted all possibilities for Alexander and Henry, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Elizabeth is a knight or Henry is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Elizabeth that Elizabeth is a knight or Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Alexander is a knight.", "Alexander cannot be a knight, because this would contradict the false claim of Henry that Alexander is a knight.", "Alexander cannot be a knave, because this would contradict the false claim of their own that David is a knave if and only if Henry is a knight.", "We have exhausted all possibilities for Alexander, Henry, and Elizabeth, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that If Elizabeth is a knight then Henry is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Elizabeth is a knight or Henry is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that David is a knave if and only if Henry is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that If Elizabeth is a knight then David is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Elizabeth is a knight then David is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that If Henry is a knave then Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 2)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('telling-truth', 1), ('->', ('telling-truth', 5), ('telling-truth', 0)), ('->', ('lying', 2), ('lying', 5)), ('or', ('telling-truth', 5), ('telling-truth', 2)))", "index": 904}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Lucas, Mason, Chloe, Harper, and Mia. According to Victoria, \"Victoria is a knight if and only if Lucas is a knave\". \"Harper is a knight\" - Lucas. Mason expressed that Victoria is a knave or Harper is a knight. Chloe commented, \"Victoria is not a knight\". \"Chloe is not a knight,\" Harper claimed. \"Victoria is a knave if and only if Harper is a knave,\" Mia mentioned. So who is a knight and who is a knave?", "names": ["Victoria", "Lucas", "Mason", "Chloe", "Harper", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Victoria is a knave, Lucas is a knave, Mason is a knight, Chloe is a knight, Harper is a knave, and Mia is a knight.", "solution_text_format": "(1) Victoria is a knave\n(2) Lucas is a knave\n(3) Mason is a knight\n(4) Chloe is a knight\n(5) Harper is a knave\n(6) Mia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Victoria that Victoria is a knight if and only if Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Harper is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Lucas that Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Victoria is not a knight.", "Chloe cannot be a knave, because this would contradict the false claim of Harper that Chloe is not a knight.", "We have exhausted all possibilities for Chloe, Harper, and Lucas, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Victoria that Victoria is a knight if and only if Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Harper is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Lucas that Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Chloe is not a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Victoria is a knave or Harper is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('telling-truth', 4), ('or', ('lying', 0), ('telling-truth', 4)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 3)), ('<=>', ('lying', 0), ('lying', 4)))", "index": 905}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Jackson, Mason, Harper, Avery, and Sofia. Isabella remarked, \"Sofia is a knave if and only if Mason is a knave\". Jackson was heard saying, \"Mason is a knave if and only if Harper is a knave\". According to Mason, \"Sofia is a knight or Jackson is a knight\". Harper told you that Avery is a knight. \"Isabella is a knight and Jackson is a knight,\" Avery declared. \"Avery is not a knave\" - Sofia. So who is a knight and who is a knave?", "names": ["Isabella", "Jackson", "Mason", "Harper", "Avery", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Isabella is a knight, Jackson is a knight, Mason is a knight, Harper is a knight, Avery is a knight, and Sofia is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Jackson is a knight\n(3) Mason is a knight\n(4) Harper is a knight\n(5) Avery is a knight\n(6) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Mason is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Avery is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Isabella is a knight and Jackson is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Mason is a knave if and only if Harper is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Sofia is a knight or Jackson is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 2)), ('<=>', ('lying', 2), ('lying', 3)), ('or', ('telling-truth', 5), ('telling-truth', 1)), ('telling-truth', 4), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('not', ('lying', 4)))", "index": 906}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Henry, Sophia, Emily, Aria, and Ella. As Grace put it, \"Sophia is a knight or Emily is a knave\". In Henry's words: \"Aria is a knight or Grace is a knight\". As Sophia put it, \"Emily is a knave\". \"Henry is a knave,\" Emily declared. Aria noted, \"Grace is a knave\". Ella told you that Henry is a knight. So who is a knight and who is a knave?", "names": ["Grace", "Henry", "Sophia", "Emily", "Aria", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Grace is a knight, Henry is a knight, Sophia is a knight, Emily is a knave, Aria is a knave, and Ella is a knight.", "solution_text_format": "(1) Grace is a knight\n(2) Henry is a knight\n(3) Sophia is a knight\n(4) Emily is a knave\n(5) Aria is a knave\n(6) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Sophia is a knight or Emily is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Sophia that Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Aria is a knight or Grace is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Grace is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 3)), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('lying', 3), ('lying', 1), ('lying', 0), ('telling-truth', 1))", "index": 907}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Elizabeth, Olivia, Scarlett, Owen, and Sebastian. Luke remarked, \"Elizabeth is a knave or Olivia is a knight\". Elizabeth said that If Owen is a knight then Scarlett is a knave. Olivia was heard saying, \"Sebastian is a knave or Scarlett is a knight\". Scarlett told you that Olivia is a knave. Owen told you that Scarlett is not a knight. In a statement by Sebastian: \"Luke is a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Elizabeth", "Olivia", "Scarlett", "Owen", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Luke is a knight, Elizabeth is a knight, Olivia is a knight, Scarlett is a knave, Owen is a knight, and Sebastian is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Elizabeth is a knight\n(3) Olivia is a knight\n(4) Scarlett is a knave\n(5) Owen is a knight\n(6) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Elizabeth is a knave or Olivia is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Owen is a knight then Scarlett is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Scarlett is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Elizabeth that If Owen is a knight then Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Sebastian is a knave or Scarlett is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Olivia that Sebastian is a knave or Scarlett is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 2)), ('->', ('telling-truth', 4), ('lying', 3)), ('or', ('lying', 5), ('telling-truth', 3)), ('lying', 2), ('not', ('telling-truth', 3)), ('lying', 0))", "index": 908}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Sebastian, Lucas, Owen, James, and Ava. Avery said that Sebastian is a knave if and only if Ava is a knight. Sebastian asserted: \"James is a knight and Lucas is a knave\". In Lucas's words: \"Owen is a knight if and only if Avery is a knight\". Owen stated, \"Sebastian is a knave and Lucas is a knight\". James commented, \"If James is a knight then Avery is a knight\". As Ava put it, \"If Avery is a knave then Sebastian is a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Sebastian", "Lucas", "Owen", "James", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Avery is a knight, Sebastian is a knave, Lucas is a knight, Owen is a knight, James is a knight, and Ava is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Sebastian is a knave\n(3) Lucas is a knight\n(4) Owen is a knight\n(5) James is a knight\n(6) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Ava is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that James is a knight and Lucas is a knave.", "Assume James is a knight. No contradiction is found in their claim that If James is a knight then Avery is a knight.", "Lucas cannot be a knight, because this would contradict the claim of Sebastian that James is a knight and Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Avery is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Lucas that Owen is a knight if and only if Avery is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Sebastian is a knave and Lucas is a knight.", "Ava cannot be a knight, because this would contradict the claim of Avery that Sebastian is a knave if and only if Ava is a knight.", "Ava cannot be a knave, because this would contradict the false claim of their own that If Avery is a knave then Sebastian is a knave.", "We have exhausted all possibilities for Ava, Owen, and Lucas, so let us go back and reconsider James.", "James cannot be a knave, because this would contradict the claim of Sebastian that James is a knight and Lucas is a knave.", "We have exhausted all possibilities for James, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that James is a knight and Lucas is a knave.", "Assume James is a knight. No contradiction is found in their claim that If James is a knight then Avery is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Owen is a knight if and only if Avery is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Sebastian is a knave and Lucas is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Avery is a knave then Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 5)), ('and', ('telling-truth', 4), ('lying', 2)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('and', ('lying', 1), ('telling-truth', 2)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('->', ('lying', 0), ('lying', 1)))", "index": 909}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Lily, Isabella, Noah, Grace, and Avery. Matthew noted, \"Grace is not a knave\". \"If Avery is a knave then Grace is a knight\" - Lily. Isabella was heard saying, \"Lily is a knave and Avery is a knave\". Noah noted, \"Avery is a knight if and only if Isabella is a knight\". Grace asserted: \"Lily is a knave if and only if Avery is a knave\". \"Avery is a knight or Lily is a knave,\" Avery declared. So who is a knight and who is a knave?", "names": ["Matthew", "Lily", "Isabella", "Noah", "Grace", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "Matthew is a knight, Lily is a knight, Isabella is a knave, Noah is a knave, Grace is a knight, and Avery is a knight.", "solution_text_format": "(1) Matthew is a knight\n(2) Lily is a knight\n(3) Isabella is a knave\n(4) Noah is a knave\n(5) Grace is a knight\n(6) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Grace is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Lily is a knave if and only if Avery is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Avery is a knave then Grace is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Avery is a knight or Lily is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Avery is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Lily is a knave and Avery is a knave.", "Noah cannot be a knight, because this would contradict the claim of their own that Avery is a knight if and only if Isabella is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Isabella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('->', ('lying', 5), ('telling-truth', 4)), ('and', ('lying', 1), ('lying', 5)), ('<=>', ('telling-truth', 5), ('telling-truth', 2)), ('<=>', ('lying', 1), ('lying', 5)), ('or', ('telling-truth', 5), ('lying', 1)))", "index": 910}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Aria, Victoria, Harper, Scarlett, and Owen. Daniel noted, \"Aria is a knight and Owen is a knight\". \"Daniel is not a knight\" - Aria. In a statement by Victoria: \"If Aria is a knave then Owen is a knight\". Harper stated, \"If Daniel is a knave then Scarlett is a knave\". Scarlett commented, \"Daniel is a knight and Harper is a knave\". Owen expressed that Daniel is a knight. So who is a knight and who is a knave?", "names": ["Daniel", "Aria", "Victoria", "Harper", "Scarlett", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, false], "solution_text": "Daniel is a knave, Aria is a knight, Victoria is a knight, Harper is a knight, Scarlett is a knave, and Owen is a knave.", "solution_text_format": "(1) Daniel is a knave\n(2) Aria is a knight\n(3) Victoria is a knight\n(4) Harper is a knight\n(5) Scarlett is a knave\n(6) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Aria is a knight and Owen is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Daniel is not a knight.", "Aria cannot be a knave, because this would contradict the claim of Daniel that Aria is a knight and Owen is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Aria is a knight and Owen is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Daniel is not a knight.", "Owen cannot be a knight, because this would contradict the false claim of Daniel that Aria is a knight and Owen is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Daniel is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Aria is a knave then Owen is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Daniel is a knave then Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Harper that If Daniel is a knave then Scarlett is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Daniel is a knight and Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 5)), ('not', ('telling-truth', 0)), ('->', ('lying', 1), ('telling-truth', 5)), ('->', ('lying', 0), ('lying', 4)), ('and', ('telling-truth', 0), ('lying', 3)), ('telling-truth', 0))", "index": 911}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Samuel, Ethan, Isabella, Michael, and Ava. Owen commented, \"If Samuel is a knight then Michael is a knave\". Samuel noted, \"Michael is not a knave\". Ethan remarked, \"Michael is a knave if and only if Isabella is a knight\". Isabella was heard saying, \"Owen is not a knight\". Michael remarked, \"If Isabella is a knight then Michael is a knight\". Ava remarked, \"Ethan is a knight and Owen is a knave\". So who is a knight and who is a knave?", "names": ["Owen", "Samuel", "Ethan", "Isabella", "Michael", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Owen is a knave, Samuel is a knight, Ethan is a knave, Isabella is a knight, Michael is a knight, and Ava is a knave.", "solution_text_format": "(1) Owen is a knave\n(2) Samuel is a knight\n(3) Ethan is a knave\n(4) Isabella is a knight\n(5) Michael is a knight\n(6) Ava is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that If Samuel is a knight then Michael is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Michael is not a knave.", "Michael cannot be a knight, because this would contradict the claim of Owen that If Samuel is a knight then Michael is a knave.", "Michael cannot be a knave, because this would contradict the claim of Samuel that Michael is not a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Michael is not a knave.", "Michael cannot be a knight, because this would contradict the false claim of Samuel that Michael is not a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that If Isabella is a knight then Michael is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Owen is not a knight.", "Isabella cannot be a knave, because this would contradict the false claim of Michael that If Isabella is a knight then Michael is a knight.", "We have exhausted all possibilities for Isabella, Michael, and Samuel, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that If Samuel is a knight then Michael is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Michael is not a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Isabella is a knight then Michael is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Owen is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Michael is a knave if and only if Isabella is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Isabella is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Ethan is a knight and Owen is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Ethan is a knight and Owen is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('lying', 4)), ('not', ('lying', 4)), ('<=>', ('lying', 4), ('telling-truth', 3)), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('and', ('telling-truth', 2), ('lying', 0)))", "index": 912}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Benjamin, Evelyn, Sofia, Zoey, and Abigail. \"Benjamin is a knave if and only if Sofia is a knave,\" Sebastian declared. Benjamin said that Sofia is a knave and Sebastian is a knave. Evelyn asserted: \"Sofia is a knight if and only if Abigail is a knave\". Sofia commented, \"Evelyn is a knight\". Zoey remarked, \"Evelyn is a knave\". In Abigail's words: \"Sebastian is a knight if and only if Benjamin is a knave\". So who is a knight and who is a knave?", "names": ["Sebastian", "Benjamin", "Evelyn", "Sofia", "Zoey", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Sebastian is a knave, Benjamin is a knave, Evelyn is a knight, Sofia is a knight, Zoey is a knave, and Abigail is a knave.", "solution_text_format": "(1) Sebastian is a knave\n(2) Benjamin is a knave\n(3) Evelyn is a knight\n(4) Sofia is a knight\n(5) Zoey is a knave\n(6) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Sofia is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Sebastian is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Sofia is a knave and Sebastian is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Sebastian that Benjamin is a knave if and only if Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Sofia that Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Evelyn that Sofia is a knight if and only if Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knight if and only if Benjamin is a knave.", "We have exhausted all possibilities for Abigail, Evelyn, Sofia, and Benjamin, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Sofia is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Sofia is a knave and Sebastian is a knave.", "Sofia cannot be a knight, because this would contradict the false claim of Sebastian that Benjamin is a knave if and only if Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Evelyn is a knight.", "Evelyn cannot be a knight, because this would contradict the false claim of Sofia that Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Evelyn that Sofia is a knight if and only if Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knight if and only if Benjamin is a knave.", "We have exhausted all possibilities for Abigail, Evelyn, and Sofia, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Sofia is a knave and Sebastian is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Evelyn that Sofia is a knight if and only if Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Benjamin is a knave.", "Zoey cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Evelyn is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 3)), ('and', ('lying', 3), ('lying', 0)), ('<=>', ('telling-truth', 3), ('lying', 5)), ('telling-truth', 2), ('lying', 2), ('<=>', ('telling-truth', 0), ('lying', 1)))", "index": 913}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jack, Logan, Evelyn, Harper, Jacob, and Benjamin. Jack noted, \"Jack is a knight or Logan is a knave\". Logan expressed that Jack is a knave if and only if Evelyn is a knave. Evelyn was heard saying, \"If Harper is a knight then Evelyn is a knight\". Harper commented, \"Logan is a knave if and only if Logan is a knight\". In Jacob's words: \"Logan is not a knave\". Benjamin noted, \"Harper is not a knave\". So who is a knight and who is a knave?", "names": ["Jack", "Logan", "Evelyn", "Harper", "Jacob", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Jack is a knight, Logan is a knight, Evelyn is a knight, Harper is a knave, Jacob is a knight, and Benjamin is a knave.", "solution_text_format": "(1) Jack is a knight\n(2) Logan is a knight\n(3) Evelyn is a knight\n(4) Harper is a knave\n(5) Jacob is a knight\n(6) Benjamin is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jack is a knight. No contradiction is found in their claim that Jack is a knight or Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Jack is a knave if and only if Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Harper is a knight then Evelyn is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Logan is a knave if and only if Logan is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Logan is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Logan is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Harper is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Harper is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('lying', 1)), ('<=>', ('lying', 0), ('lying', 2)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('lying', 1), ('telling-truth', 1)), ('not', ('lying', 1)), ('not', ('lying', 3)))", "index": 914}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Ava, Elizabeth, James, Mia, and Noah. As Lily put it, \"Noah is a knight and James is a knave\". In Ava's words: \"Lily is a knight or James is a knight\". Elizabeth expressed that James is a knave or Lily is a knave. James said, \"Ava is a knight.\" In Mia's words: \"Ava is a knight and James is a knight\". Noah told you that If Ava is a knave then Mia is a knave. So who is a knight and who is a knave?", "names": ["Lily", "Ava", "Elizabeth", "James", "Mia", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Lily is a knave, Ava is a knight, Elizabeth is a knight, James is a knight, Mia is a knight, and Noah is a knight.", "solution_text_format": "(1) Lily is a knave\n(2) Ava is a knight\n(3) Elizabeth is a knight\n(4) James is a knight\n(5) Mia is a knight\n(6) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Noah is a knight and James is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Ava is a knave then Mia is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Lily is a knight or James is a knight.", "James cannot be a knight, because this would contradict the claim of Lily that Noah is a knight and James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that Ava is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the false claim of their own that Lily is a knight or James is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Noah.", "Noah cannot be a knave, because this would contradict the claim of Lily that Noah is a knight and James is a knave.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Noah is a knight and James is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Ava is a knave then Mia is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Lily is a knight or James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Ava is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Ava is a knight and James is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that James is a knave or Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 3)), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('lying', 3), ('lying', 0)), ('telling-truth', 1), ('and', ('telling-truth', 1), ('telling-truth', 3)), ('->', ('lying', 1), ('lying', 4)))", "index": 915}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Sebastian, Ella, Matthew, Logan, and Oliver. Mason said, \"If Logan is a knight then Mason is a knight.\" Sebastian said, \"If Mason is a knave then Ella is a knave.\" Ella was heard saying, \"If Mason is a knave then Logan is a knight\". Matthew expressed that Sebastian is a knave or Oliver is a knave. In Logan's words: \"Matthew is a knave\". Oliver was heard saying, \"Mason is a knave and Sebastian is a knave\". So who is a knight and who is a knave?", "names": ["Mason", "Sebastian", "Ella", "Matthew", "Logan", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Mason is a knight, Sebastian is a knight, Ella is a knight, Matthew is a knight, Logan is a knave, and Oliver is a knave.", "solution_text_format": "(1) Mason is a knight\n(2) Sebastian is a knight\n(3) Ella is a knight\n(4) Matthew is a knight\n(5) Logan is a knave\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that If Logan is a knight then Mason is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Matthew is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Logan that Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Sebastian is a knave or Oliver is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Mason is a knave then Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Mason is a knave then Logan is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Sebastian is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of Matthew that Sebastian is a knave or Oliver is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Mason is a knave then Logan is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that If Mason is a knave then Ella is a knave.", "We have exhausted all possibilities for Sebastian and Matthew, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Matthew is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Sebastian is a knave or Oliver is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Mason is a knave then Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Mason is a knave then Logan is a knight.", "Oliver cannot be a knight, because this would contradict the claim of Matthew that Sebastian is a knave or Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Mason is a knave and Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('telling-truth', 0)), ('->', ('lying', 0), ('lying', 2)), ('->', ('lying', 0), ('telling-truth', 4)), ('or', ('lying', 1), ('lying', 5)), ('lying', 3), ('and', ('lying', 0), ('lying', 1)))", "index": 916}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Jackson, Avery, Chloe, Lucas, and Scarlett. \"Avery is a knight and Scarlett is a knight,\" Alexander claimed. Jackson was heard saying, \"Alexander is a knight or Scarlett is a knave\". Avery commented, \"Scarlett is not a knave\". Chloe was heard saying, \"Avery is a knave\". As Lucas put it, \"Avery is not a knave\". Scarlett said, \"If Chloe is a knave then Scarlett is a knight.\" So who is a knight and who is a knave?", "names": ["Alexander", "Jackson", "Avery", "Chloe", "Lucas", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Alexander is a knight, Jackson is a knight, Avery is a knight, Chloe is a knave, Lucas is a knight, and Scarlett is a knight.", "solution_text_format": "(1) Alexander is a knight\n(2) Jackson is a knight\n(3) Avery is a knight\n(4) Chloe is a knave\n(5) Lucas is a knight\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Avery is a knight and Scarlett is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Scarlett is not a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Chloe is a knave then Scarlett is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Avery is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Avery is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Alexander is a knight or Scarlett is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that Avery is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('telling-truth', 0), ('lying', 5)), ('not', ('lying', 5)), ('lying', 2), ('not', ('lying', 2)), ('->', ('lying', 3), ('telling-truth', 5)))", "index": 917}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Elizabeth, Aurora, Grace, Harper, and Oliver. \"Elizabeth is a knight,\" Abigail mentioned. Elizabeth told you that Oliver is a knight or Harper is a knave. As Aurora put it, \"Abigail is a knight or Elizabeth is a knave\". Grace was heard saying, \"Elizabeth is a knight and Abigail is a knave\". Harper stated, \"Grace is a knave if and only if Aurora is a knight\". \"If Harper is a knave then Abigail is a knight,\" Oliver claimed. So who is a knight and who is a knave?", "names": ["Abigail", "Elizabeth", "Aurora", "Grace", "Harper", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Abigail is a knight, Elizabeth is a knight, Aurora is a knight, Grace is a knave, Harper is a knight, and Oliver is a knight.", "solution_text_format": "(1) Abigail is a knight\n(2) Elizabeth is a knight\n(3) Aurora is a knight\n(4) Grace is a knave\n(5) Harper is a knight\n(6) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Oliver is a knight or Harper is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Harper is a knave then Abigail is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Grace is a knave if and only if Aurora is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Abigail is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Abigail is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Abigail is a knight or Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('or', ('telling-truth', 5), ('lying', 4)), ('or', ('telling-truth', 0), ('lying', 1)), ('and', ('telling-truth', 1), ('lying', 0)), ('<=>', ('lying', 3), ('telling-truth', 2)), ('->', ('lying', 4), ('telling-truth', 0)))", "index": 918}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Olivia, Isabella, Aiden, Alexander, and Elizabeth. Sebastian stated, \"Sebastian is a knight\". \"Sebastian is a knave and Aiden is a knight,\" Olivia declared. Isabella said, \"If Sebastian is a knave then Alexander is a knave.\" As Aiden put it, \"Olivia is a knight if and only if Sebastian is a knight\". In a statement by Alexander: \"Isabella is a knight and Olivia is a knight\". Elizabeth expressed that Alexander is a knight and Olivia is a knave. So who is a knight and who is a knave?", "names": ["Sebastian", "Olivia", "Isabella", "Aiden", "Alexander", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Sebastian is a knight, Olivia is a knave, Isabella is a knight, Aiden is a knave, Alexander is a knave, and Elizabeth is a knave.", "solution_text_format": "(1) Sebastian is a knight\n(2) Olivia is a knave\n(3) Isabella is a knight\n(4) Aiden is a knave\n(5) Alexander is a knave\n(6) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Olivia cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave and Aiden is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Sebastian is a knave and Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Olivia is a knight if and only if Sebastian is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Sebastian is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Sebastian is a knave then Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Isabella is a knight and Olivia is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Isabella is a knight and Olivia is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Alexander is a knight and Olivia is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Alexander is a knight and Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 0), ('and', ('lying', 0), ('telling-truth', 3)), ('->', ('lying', 0), ('lying', 4)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('and', ('telling-truth', 4), ('lying', 1)))", "index": 919}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Daniel, Logan, Jackson, Isabella, and Alexander. In a statement by Sebastian: \"Isabella is a knave and Isabella is a knight\". Daniel said that Isabella is not a knave. As Logan put it, \"Sebastian is a knight or Daniel is a knight\". \"Logan is a knave or Sebastian is a knight,\" Jackson claimed. Isabella noted, \"Isabella is a knight or Alexander is a knight\". Alexander stated, \"Daniel is a knave if and only if Isabella is a knave\". So who is a knight and who is a knave?", "names": ["Sebastian", "Daniel", "Logan", "Jackson", "Isabella", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Sebastian is a knave, Daniel is a knight, Logan is a knight, Jackson is a knave, Isabella is a knight, and Alexander is a knight.", "solution_text_format": "(1) Sebastian is a knave\n(2) Daniel is a knight\n(3) Logan is a knight\n(4) Jackson is a knave\n(5) Isabella is a knight\n(6) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Sebastian cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Isabella is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Isabella is a knave and Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Isabella is a knight or Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Isabella is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Isabella is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Sebastian is a knight or Daniel is a knight.", "Jackson cannot be a knight, because this would contradict the claim of their own that Logan is a knave or Sebastian is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Logan is a knave or Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 4)), ('not', ('lying', 4)), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('lying', 2), ('telling-truth', 0)), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('<=>', ('lying', 1), ('lying', 4)))", "index": 920}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, William, Mia, Chloe, Owen, and Isabella. \"Mia is not a knight\" - David. \"Mia is a knave if and only if Isabella is a knight\" - William. \"David is a knight or Owen is a knave\" - Mia. Chloe was heard saying, \"David is not a knave\". Owen noted, \"Isabella is a knave or William is a knight\". \"David is a knave,\" Isabella declared. So who is a knight and who is a knave?", "names": ["David", "William", "Mia", "Chloe", "Owen", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true], "solution_text": "David is a knave, William is a knave, Mia is a knight, Chloe is a knave, Owen is a knave, and Isabella is a knight.", "solution_text_format": "(1) David is a knave\n(2) William is a knave\n(3) Mia is a knight\n(4) Chloe is a knave\n(5) Owen is a knave\n(6) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Mia is not a knight.", "Mia cannot be a knight, because this would contradict the claim of David that Mia is not a knight.", "Mia cannot be a knave, because this would contradict the false claim of their own that David is a knight or Owen is a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Mia is not a knight.", "Assume Mia is a knight. No contradiction is found in their claim that David is a knight or Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Mia that David is a knight or Owen is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Isabella is a knave or William is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that David is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Mia is a knave if and only if Isabella is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Isabella is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that David is not a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that David is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('<=>', ('lying', 2), ('telling-truth', 5)), ('or', ('telling-truth', 0), ('lying', 4)), ('not', ('lying', 0)), ('or', ('lying', 5), ('telling-truth', 1)), ('lying', 0))", "index": 921}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Sebastian, Harper, Jacob, Ava, and Aiden. Olivia said that Aiden is not a knave. Sebastian said, \"Olivia is a knave.\" According to Harper, \"If Olivia is a knave then Sebastian is a knave\". As Jacob put it, \"Olivia is a knight if and only if Sebastian is a knave\". Ava expressed that Sebastian is a knight and Sebastian is a knave. As Aiden put it, \"Jacob is a knave\". So who is a knight and who is a knave?", "names": ["Olivia", "Sebastian", "Harper", "Jacob", "Ava", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false], "solution_text": "Olivia is a knave, Sebastian is a knight, Harper is a knave, Jacob is a knight, Ava is a knave, and Aiden is a knave.", "solution_text_format": "(1) Olivia is a knave\n(2) Sebastian is a knight\n(3) Harper is a knave\n(4) Jacob is a knight\n(5) Ava is a knave\n(6) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Aiden is not a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Jacob is a knave.", "Jacob cannot be a knight, because this would contradict the claim of Aiden that Jacob is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Sebastian is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Sebastian cannot be a knave, because this would contradict the false claim of Jacob that Olivia is a knight if and only if Sebastian is a knave.", "We have exhausted all possibilities for Sebastian and Jacob, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Olivia that Aiden is not a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aiden is not a knave.", "Aiden cannot be a knight, because this would contradict the false claim of Olivia that Aiden is not a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Sebastian is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Olivia is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that If Olivia is a knave then Sebastian is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that If Olivia is a knave then Sebastian is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Sebastian is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Sebastian is a knight and Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('lying', 0), ('->', ('lying', 0), ('lying', 1)), ('<=>', ('telling-truth', 0), ('lying', 1)), ('and', ('telling-truth', 1), ('lying', 1)), ('lying', 3))", "index": 922}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Matthew, Harper, Riley, Zoey, and Sebastian. As Logan put it, \"Zoey is not a knight\". According to Matthew, \"Sebastian is a knight and Harper is a knight\". \"Matthew is a knight and Sebastian is a knave\" - Harper. As Riley put it, \"Sebastian is not a knave\". According to Zoey, \"Harper is a knave\". As Sebastian put it, \"Logan is not a knave\". So who is a knight and who is a knave?", "names": ["Logan", "Matthew", "Harper", "Riley", "Zoey", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false], "solution_text": "Logan is a knave, Matthew is a knave, Harper is a knave, Riley is a knave, Zoey is a knight, and Sebastian is a knave.", "solution_text_format": "(1) Logan is a knave\n(2) Matthew is a knave\n(3) Harper is a knave\n(4) Riley is a knave\n(5) Zoey is a knight\n(6) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Logan is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Logan that Zoey is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Matthew is a knight and Sebastian is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Sebastian is a knight and Harper is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Harper that Matthew is a knight and Sebastian is a knave.", "Sebastian cannot be a knave, because this would contradict the claim of Matthew that Sebastian is a knight and Harper is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the claim of Harper that Matthew is a knight and Sebastian is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the false claim of Zoey that Harper is a knave.", "We have exhausted all possibilities for Harper and Zoey, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of Zoey that Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Matthew is a knight and Sebastian is a knave.", "Matthew cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Harper is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Sebastian is a knight and Harper is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Logan is not a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Logan is not a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Sebastian is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('and', ('telling-truth', 5), ('telling-truth', 2)), ('and', ('telling-truth', 1), ('lying', 5)), ('not', ('lying', 5)), ('lying', 2), ('not', ('lying', 0)))", "index": 923}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Harper, Riley, Charlotte, Jack, and Amelia. In Benjamin's words: \"Harper is a knight and Jack is a knight\". Harper was heard saying, \"Amelia is a knave\". Riley stated, \"Harper is not a knight\". In a statement by Charlotte: \"Harper is a knave if and only if Benjamin is a knight\". As Jack put it, \"Amelia is a knave if and only if Benjamin is a knight\". Amelia asserted: \"Charlotte is a knight or Jack is a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Harper", "Riley", "Charlotte", "Jack", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true], "solution_text": "Benjamin is a knave, Harper is a knave, Riley is a knight, Charlotte is a knave, Jack is a knight, and Amelia is a knight.", "solution_text_format": "(1) Benjamin is a knave\n(2) Harper is a knave\n(3) Riley is a knight\n(4) Charlotte is a knave\n(5) Jack is a knight\n(6) Amelia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Harper is a knight and Jack is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Harper that Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Charlotte is a knight or Jack is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Harper is a knave if and only if Benjamin is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Benjamin is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Amelia that Charlotte is a knight or Jack is a knight.", "Jack cannot be a knave, because this would contradict the claim of Benjamin that Harper is a knight and Jack is a knight.", "We have exhausted all possibilities for Jack, Charlotte, and Amelia, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Benjamin that Harper is a knight and Jack is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Harper is a knight and Jack is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Harper that Amelia is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that Charlotte is a knight or Jack is a knight.", "Charlotte cannot be a knight, because this would contradict the false claim of Amelia that Charlotte is a knight or Jack is a knight.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Harper is a knave if and only if Benjamin is a knight.", "We have exhausted all possibilities for Charlotte and Amelia, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Charlotte is a knight or Jack is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Harper is a knave if and only if Benjamin is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Harper is a knave if and only if Benjamin is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Benjamin is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Harper is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 4)), ('lying', 5), ('not', ('telling-truth', 1)), ('<=>', ('lying', 1), ('telling-truth', 0)), ('<=>', ('lying', 5), ('telling-truth', 0)), ('or', ('telling-truth', 3), ('telling-truth', 4)))", "index": 924}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Sebastian, Harper, Benjamin, Alexander, and Sophia. Charlotte told you that Benjamin is not a knave. Sebastian noted, \"Benjamin is a knight\". Harper noted, \"If Charlotte is a knave then Benjamin is a knight\". Benjamin said, \"Sophia is a knight and Alexander is a knight.\" Alexander told you that Alexander is a knight if and only if Sebastian is a knight. Sophia expressed that Sebastian is a knave or Sophia is a knight. So who is a knight and who is a knave?", "names": ["Charlotte", "Sebastian", "Harper", "Benjamin", "Alexander", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Charlotte is a knight, Sebastian is a knight, Harper is a knight, Benjamin is a knight, Alexander is a knight, and Sophia is a knight.", "solution_text_format": "(1) Charlotte is a knight\n(2) Sebastian is a knight\n(3) Harper is a knight\n(4) Benjamin is a knight\n(5) Alexander is a knight\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Sophia is a knight and Alexander is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Sebastian is a knave or Sophia is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Sebastian is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Charlotte is a knave then Benjamin is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('telling-truth', 3), ('->', ('lying', 0), ('telling-truth', 3)), ('and', ('telling-truth', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('or', ('lying', 1), ('telling-truth', 5)))", "index": 925}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Aria, Jack, Sebastian, Alexander, and Sofia. Samuel remarked, \"Sebastian is a knight or Alexander is a knight\". Aria told you that Jack is a knave. Jack asserted: \"Alexander is a knave\". \"Sebastian is a knight or Sofia is a knave,\" Sebastian mentioned. In a statement by Alexander: \"Samuel is a knave if and only if Sofia is a knight\". Sofia commented, \"Alexander is a knave if and only if Alexander is a knight\". So who is a knight and who is a knave?", "names": ["Samuel", "Aria", "Jack", "Sebastian", "Alexander", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "Samuel is a knight, Aria is a knight, Jack is a knave, Sebastian is a knight, Alexander is a knight, and Sofia is a knave.", "solution_text_format": "(1) Samuel is a knight\n(2) Aria is a knight\n(3) Jack is a knave\n(4) Sebastian is a knight\n(5) Alexander is a knight\n(6) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Sebastian is a knight or Alexander is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sebastian is a knight or Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Alexander is a knave if and only if Alexander is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Alexander is a knave if and only if Alexander is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Sofia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of Aria that Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('telling-truth', 4)), ('lying', 2), ('lying', 4), ('or', ('telling-truth', 3), ('lying', 5)), ('<=>', ('lying', 0), ('telling-truth', 5)), ('<=>', ('lying', 4), ('telling-truth', 4)))", "index": 926}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, David, Penelope, Charlotte, Sebastian, and Logan. Luke stated, \"David is a knight if and only if Luke is a knight\". David noted, \"David is a knight and Charlotte is a knight\". Penelope asserted: \"David is not a knight\". \"Luke is not a knight,\" Charlotte claimed. \"David is a knave if and only if Penelope is a knight,\" Sebastian claimed. Logan expressed that Luke is a knight or Sebastian is a knave. So who is a knight and who is a knave?", "names": ["Luke", "David", "Penelope", "Charlotte", "Sebastian", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Luke is a knave, David is a knight, Penelope is a knave, Charlotte is a knight, Sebastian is a knight, and Logan is a knave.", "solution_text_format": "(1) Luke is a knave\n(2) David is a knight\n(3) Penelope is a knave\n(4) Charlotte is a knight\n(5) Sebastian is a knight\n(6) Logan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that David is a knight if and only if Luke is a knight.", "Assume David is a knight. No contradiction is found in their claim that David is a knight and Charlotte is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Luke is not a knight.", "Charlotte cannot be a knave, because this would contradict the claim of David that David is a knight and Charlotte is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Luke that David is a knight if and only if Luke is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that David is a knight if and only if Luke is a knight.", "Assume David is a knight. No contradiction is found in their claim that David is a knight and Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Luke is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that David is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that David is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that David is a knave if and only if Penelope is a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Luke is a knight or Sebastian is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Luke is a knight or Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('telling-truth', 3)), ('not', ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('<=>', ('lying', 1), ('telling-truth', 2)), ('or', ('telling-truth', 0), ('lying', 4)))", "index": 927}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Avery, Lily, Henry, Benjamin, and Mason. \"Benjamin is a knave,\" Jackson claimed. Avery expressed that If Henry is a knave then Benjamin is a knight. Lily said, \"If Jackson is a knave then Henry is a knight.\" Henry stated, \"Lily is a knight if and only if Jackson is a knight\". Benjamin said, \"Mason is a knave if and only if Avery is a knave.\" In Mason's words: \"Jackson is a knave and Jackson is a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Avery", "Lily", "Henry", "Benjamin", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Jackson is a knight, Avery is a knight, Lily is a knight, Henry is a knight, Benjamin is a knave, and Mason is a knave.", "solution_text_format": "(1) Jackson is a knight\n(2) Avery is a knight\n(3) Lily is a knight\n(4) Henry is a knight\n(5) Benjamin is a knave\n(6) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Jackson that Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Avery is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Jackson is a knave and Jackson is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Jackson is a knave and Jackson is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that If Henry is a knave then Benjamin is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Lily is a knight if and only if Jackson is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Jackson is a knave then Henry is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('->', ('lying', 3), ('telling-truth', 4)), ('->', ('lying', 0), ('telling-truth', 3)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('<=>', ('lying', 5), ('lying', 1)), ('and', ('lying', 0), ('telling-truth', 0)))", "index": 928}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Owen, Emily, Ethan, Sebastian, and Charlotte. Victoria said, \"Ethan is not a knight.\" \"Sebastian is a knave or Victoria is a knave,\" Owen declared. Emily said that Ethan is a knight if and only if Sebastian is a knave. As Ethan put it, \"Sebastian is not a knight\". Sebastian stated, \"Charlotte is a knave and Ethan is a knave\". In Charlotte's words: \"If Sebastian is a knight then Victoria is a knight\". So who is a knight and who is a knave?", "names": ["Victoria", "Owen", "Emily", "Ethan", "Sebastian", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Victoria is a knave, Owen is a knight, Emily is a knight, Ethan is a knight, Sebastian is a knave, and Charlotte is a knight.", "solution_text_format": "(1) Victoria is a knave\n(2) Owen is a knight\n(3) Emily is a knight\n(4) Ethan is a knight\n(5) Sebastian is a knave\n(6) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Ethan is not a knight.", "Ethan cannot be a knight, because this would contradict the claim of Victoria that Ethan is not a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Charlotte is a knave and Ethan is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Sebastian that Charlotte is a knave and Ethan is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Sebastian is a knight then Victoria is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of Ethan that Sebastian is not a knight.", "We have exhausted all possibilities for Sebastian and Ethan, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Sebastian is not a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Ethan that Sebastian is not a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Charlotte is a knave and Ethan is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Sebastian is a knight then Victoria is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Sebastian is a knave or Victoria is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('or', ('lying', 4), ('lying', 0)), ('<=>', ('telling-truth', 3), ('lying', 4)), ('not', ('telling-truth', 4)), ('and', ('lying', 5), ('lying', 3)), ('->', ('telling-truth', 4), ('telling-truth', 0)))", "index": 929}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Penelope, Mia, David, Riley, and Harper. \"Harper is not a knave,\" Grace mentioned. \"Harper is a knight and David is a knave,\" Penelope declared. Mia asserted: \"Penelope is a knave or Riley is a knave\". David commented, \"If Riley is a knight then Mia is a knight\". Riley asserted: \"Mia is not a knave\". In Harper's words: \"Penelope is a knight if and only if Penelope is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Penelope", "Mia", "David", "Riley", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Grace is a knave, Penelope is a knave, Mia is a knight, David is a knight, Riley is a knight, and Harper is a knave.", "solution_text_format": "(1) Grace is a knave\n(2) Penelope is a knave\n(3) Mia is a knight\n(4) David is a knight\n(5) Riley is a knight\n(6) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Harper is not a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that Penelope is a knight if and only if Penelope is a knave.", "Harper cannot be a knave, because this would contradict the claim of Grace that Harper is not a knave.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Harper is not a knave.", "Harper cannot be a knight, because this would contradict the false claim of Grace that Harper is not a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Penelope is a knave.", "Penelope cannot be a knight, because this would contradict the claim of their own that Harper is a knight and David is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Harper is a knight and David is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Riley is a knight then Mia is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Mia is not a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Penelope is a knave or Riley is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('and', ('telling-truth', 5), ('lying', 3)), ('or', ('lying', 1), ('lying', 4)), ('->', ('telling-truth', 4), ('telling-truth', 2)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 1), ('lying', 1)))", "index": 930}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Michael, Luke, Evelyn, Victoria, and Jackson. \"Luke is not a knave\" - David. Michael expressed that Jackson is a knight. As Luke put it, \"Evelyn is a knave if and only if Evelyn is a knight\". As Evelyn put it, \"Victoria is a knave if and only if Jackson is a knave\". Victoria expressed that Jackson is not a knight. According to Jackson, \"If David is a knight then Luke is a knave\". So who is a knight and who is a knave?", "names": ["David", "Michael", "Luke", "Evelyn", "Victoria", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, true], "solution_text": "David is a knave, Michael is a knight, Luke is a knave, Evelyn is a knave, Victoria is a knave, and Jackson is a knight.", "solution_text_format": "(1) David is a knave\n(2) Michael is a knight\n(3) Luke is a knave\n(4) Evelyn is a knave\n(5) Victoria is a knave\n(6) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave if and only if Evelyn is a knight.", "Luke cannot be a knave, because this would contradict the claim of David that Luke is not a knave.", "We have exhausted all possibilities for Luke, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Luke is not a knave.", "Luke cannot be a knight, because this would contradict the false claim of David that Luke is not a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Jackson is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Victoria that Jackson is not a knight.", "Jackson cannot be a knave, because this would contradict the claim of Evelyn that Victoria is a knave if and only if Jackson is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Evelyn that Victoria is a knave if and only if Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of Victoria that Jackson is not a knight.", "We have exhausted all possibilities for Jackson and Victoria, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Jackson is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Evelyn that Victoria is a knave if and only if Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that If David is a knight then Luke is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If David is a knight then Luke is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Jackson is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('telling-truth', 5), ('<=>', ('lying', 3), ('telling-truth', 3)), ('<=>', ('lying', 4), ('lying', 5)), ('not', ('telling-truth', 5)), ('->', ('telling-truth', 0), ('lying', 2)))", "index": 931}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Ethan, Daniel, Liam, Amelia, and Ava. Owen noted, \"Ava is a knight if and only if Owen is a knight\". Ethan asserted: \"If Liam is a knight then Daniel is a knight\". Daniel noted, \"Ava is a knight\". \"If Ava is a knight then Amelia is a knave\" - Liam. As Amelia put it, \"Ava is a knave if and only if Owen is a knight\". Ava asserted: \"Ava is a knight if and only if Amelia is a knave\". So who is a knight and who is a knave?", "names": ["Owen", "Ethan", "Daniel", "Liam", "Amelia", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Owen is a knight, Ethan is a knight, Daniel is a knight, Liam is a knight, Amelia is a knave, and Ava is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Ethan is a knight\n(3) Daniel is a knight\n(4) Liam is a knight\n(5) Amelia is a knave\n(6) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Ava is a knight if and only if Owen is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Ava is a knight if and only if Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Owen is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Owen is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Liam is a knight then Daniel is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Ava is a knight then Amelia is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('telling-truth', 0)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('telling-truth', 5), ('->', ('telling-truth', 5), ('lying', 4)), ('<=>', ('lying', 5), ('telling-truth', 0)), ('<=>', ('telling-truth', 5), ('lying', 4)))", "index": 932}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Jacob, Olivia, Samuel, Evelyn, and Scarlett. In Aurora's words: \"Evelyn is a knight if and only if Olivia is a knight\". \"Olivia is a knave if and only if Aurora is a knight\" - Jacob. \"Aurora is a knight and Olivia is a knight,\" Olivia declared. \"Evelyn is a knave\" - Samuel. In a statement by Evelyn: \"Aurora is a knave if and only if Evelyn is a knight\". Scarlett said that Evelyn is not a knave. So who is a knight and who is a knave?", "names": ["Aurora", "Jacob", "Olivia", "Samuel", "Evelyn", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Aurora is a knave, Jacob is a knave, Olivia is a knave, Samuel is a knave, Evelyn is a knight, and Scarlett is a knight.", "solution_text_format": "(1) Aurora is a knave\n(2) Jacob is a knave\n(3) Olivia is a knave\n(4) Samuel is a knave\n(5) Evelyn is a knight\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Olivia is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Aurora is a knave if and only if Evelyn is a knight.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Aurora is a knave if and only if Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Olivia is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Evelyn is a knight.", "Olivia cannot be a knight, because this would contradict the false claim of Aurora that Evelyn is a knight if and only if Olivia is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Aurora is a knight and Olivia is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Olivia is a knave if and only if Aurora is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Aurora is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Evelyn is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('telling-truth', 2)), ('<=>', ('lying', 2), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('telling-truth', 2)), ('lying', 4), ('<=>', ('lying', 0), ('telling-truth', 4)), ('not', ('lying', 4)))", "index": 933}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Aurora, Mason, Liam, Amelia, and Benjamin. \"Amelia is a knight and Aurora is a knave,\" Elizabeth declared. \"Mason is a knight\" - Aurora. Mason commented, \"Elizabeth is a knight if and only if Benjamin is a knave\". Liam remarked, \"If Mason is a knight then Elizabeth is a knave\". Amelia asserted: \"Benjamin is a knight if and only if Liam is a knave\". \"Liam is a knave if and only if Elizabeth is a knight,\" Benjamin declared. So who is a knight and who is a knave?", "names": ["Elizabeth", "Aurora", "Mason", "Liam", "Amelia", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Elizabeth is a knave, Aurora is a knight, Mason is a knight, Liam is a knight, Amelia is a knave, and Benjamin is a knight.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Aurora is a knight\n(3) Mason is a knight\n(4) Liam is a knight\n(5) Amelia is a knave\n(6) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Amelia is a knight and Aurora is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Liam is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Liam is a knave if and only if Elizabeth is a knight.", "Liam cannot be a knight, because this would contradict the claim of Amelia that Benjamin is a knight if and only if Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that If Mason is a knight then Elizabeth is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight if and only if Benjamin is a knave.", "Mason cannot be a knave, because this would contradict the false claim of Liam that If Mason is a knight then Elizabeth is a knave.", "We have exhausted all possibilities for Mason and Liam, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Elizabeth is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Mason is a knight then Elizabeth is a knave.", "Mason cannot be a knight, because this would contradict the claim of Liam that If Mason is a knight then Elizabeth is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knight if and only if Benjamin is a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Amelia that Benjamin is a knight if and only if Liam is a knave.", "We have exhausted all possibilities for Liam and Benjamin, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Elizabeth that Amelia is a knight and Aurora is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Amelia is a knight and Aurora is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Liam is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Liam is a knave if and only if Elizabeth is a knight.", "Liam cannot be a knight, because this would contradict the claim of Amelia that Benjamin is a knight if and only if Liam is a knave.", "Liam cannot be a knave, because this would contradict the false claim of their own that If Mason is a knight then Elizabeth is a knave.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Elizabeth is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Benjamin that Liam is a knave if and only if Elizabeth is a knight.", "Liam cannot be a knave, because this would contradict the false claim of their own that If Mason is a knight then Elizabeth is a knave.", "We have exhausted all possibilities for Liam and Benjamin, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Liam is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Liam is a knave if and only if Elizabeth is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Mason is a knight then Elizabeth is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if Benjamin is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 4), ('lying', 1)), ('telling-truth', 2), ('<=>', ('telling-truth', 0), ('lying', 5)), ('->', ('telling-truth', 2), ('lying', 0)), ('<=>', ('telling-truth', 5), ('lying', 3)), ('<=>', ('lying', 3), ('telling-truth', 0)))", "index": 934}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Mason, Emma, Victoria, Jack, and James. According to Jackson, \"James is not a knight\". \"Emma is a knave,\" Mason declared. In Emma's words: \"If James is a knave then Victoria is a knight\". \"Mason is a knave or Mason is a knight,\" Victoria claimed. Jack stated, \"James is not a knave\". In James's words: \"If Jack is a knight then James is a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Mason", "Emma", "Victoria", "Jack", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Jackson is a knave, Mason is a knave, Emma is a knight, Victoria is a knight, Jack is a knight, and James is a knight.", "solution_text_format": "(1) Jackson is a knave\n(2) Mason is a knave\n(3) Emma is a knight\n(4) Victoria is a knight\n(5) Jack is a knight\n(6) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that James is not a knight.", "James cannot be a knight, because this would contradict the claim of Jackson that James is not a knight.", "Assume James is a knave. No contradiction is found in their false claim that If Jack is a knight then James is a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that James is not a knave.", "Jack cannot be a knave, because this would contradict the false claim of James that If Jack is a knight then James is a knight.", "We have exhausted all possibilities for Jack and James, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that James is not a knight.", "Assume James is a knight. No contradiction is found in their claim that If Jack is a knight then James is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that James is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Mason that Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that If James is a knave then Victoria is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If James is a knave then Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Mason is a knave or Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('lying', 2), ('->', ('lying', 5), ('telling-truth', 3)), ('or', ('lying', 1), ('telling-truth', 1)), ('not', ('lying', 5)), ('->', ('telling-truth', 4), ('telling-truth', 5)))", "index": 935}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Benjamin, Aurora, Abigail, James, and William. Liam said, \"Aurora is not a knight.\" In Benjamin's words: \"Liam is a knight\". Aurora told you that William is a knight or Liam is a knight. Abigail said that Aurora is a knave if and only if Liam is a knave. James said, \"Liam is a knave and Aurora is a knight.\" According to William, \"If William is a knight then Liam is a knave\". So who is a knight and who is a knave?", "names": ["Liam", "Benjamin", "Aurora", "Abigail", "James", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true], "solution_text": "Liam is a knave, Benjamin is a knave, Aurora is a knight, Abigail is a knave, James is a knight, and William is a knight.", "solution_text_format": "(1) Liam is a knave\n(2) Benjamin is a knave\n(3) Aurora is a knight\n(4) Abigail is a knave\n(5) James is a knight\n(6) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Aurora is not a knight.", "Aurora cannot be a knight, because this would contradict the claim of Liam that Aurora is not a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that William is a knight or Liam is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that William is a knight or Liam is a knight.", "Assume William is a knight. No contradiction is found in their claim that If William is a knight then Liam is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Liam is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Liam is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Aurora is a knave if and only if Liam is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Liam is a knave.", "Assume James is a knight. No contradiction is found in their claim that Liam is a knave and Aurora is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('telling-truth', 0), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('<=>', ('lying', 2), ('lying', 0)), ('and', ('lying', 0), ('telling-truth', 2)), ('->', ('telling-truth', 5), ('lying', 0)))", "index": 936}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Emily, Jacob, Michael, Emma, and Owen. Riley commented, \"Jacob is a knave and Jacob is a knight\". Emily told you that Jacob is not a knight. In Jacob's words: \"If Michael is a knave then Riley is a knave\". \"If Jacob is a knave then Owen is a knave,\" Michael claimed. In Emma's words: \"Jacob is a knight\". Owen remarked, \"If Emma is a knave then Riley is a knight\". So who is a knight and who is a knave?", "names": ["Riley", "Emily", "Jacob", "Michael", "Emma", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Riley is a knave, Emily is a knave, Jacob is a knight, Michael is a knight, Emma is a knight, and Owen is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Emily is a knave\n(3) Jacob is a knight\n(4) Michael is a knight\n(5) Emma is a knight\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Riley cannot be a knight, because this would contradict the claim of their own that Jacob is a knave and Jacob is a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Jacob is a knave and Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Michael is a knave then Riley is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that If Jacob is a knave then Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Emma is a knave then Riley is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Jacob is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Jacob is not a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Jacob is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('telling-truth', 2)), ('not', ('telling-truth', 2)), ('->', ('lying', 3), ('lying', 0)), ('->', ('lying', 2), ('lying', 5)), ('telling-truth', 2), ('->', ('lying', 4), ('telling-truth', 0)))", "index": 937}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Evelyn, Ella, William, Avery, and Harper. According to Michael, \"Ella is a knave or Harper is a knight\". Evelyn stated, \"William is a knight and Harper is a knight\". \"Harper is a knight\" - Ella. As William put it, \"Ella is a knave\". Avery expressed that If Michael is a knight then Michael is a knave. In a statement by Harper: \"William is a knave and Ella is a knave\". So who is a knight and who is a knave?", "names": ["Michael", "Evelyn", "Ella", "William", "Avery", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false], "solution_text": "Michael is a knight, Evelyn is a knave, Ella is a knave, William is a knight, Avery is a knave, and Harper is a knave.", "solution_text_format": "(1) Michael is a knight\n(2) Evelyn is a knave\n(3) Ella is a knave\n(4) William is a knight\n(5) Avery is a knave\n(6) Harper is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Ella is a knave or Harper is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that William is a knave and Ella is a knave.", "Harper cannot be a knave, because this would contradict the claim of Michael that Ella is a knave or Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Harper is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Ella that Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that William is a knave and Ella is a knave.", "Assume William is a knight. No contradiction is found in their claim that Ella is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that William is a knight and Harper is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that William is a knight and Harper is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that If Michael is a knight then Michael is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that If Michael is a knight then Michael is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 5)), ('and', ('telling-truth', 3), ('telling-truth', 5)), ('telling-truth', 5), ('lying', 2), ('->', ('telling-truth', 0), ('lying', 0)), ('and', ('lying', 3), ('lying', 2)))", "index": 938}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, Owen, Luke, Penelope, Abigail, and Scarlett. David asserted: \"Penelope is not a knave\". \"Abigail is a knight and David is a knave\" - Owen. \"Abigail is a knight or Owen is a knave\" - Luke. Penelope remarked, \"Luke is a knave and Owen is a knave\". Abigail said, \"Penelope is a knave or Abigail is a knight.\" Scarlett said, \"David is not a knight.\" So who is a knight and who is a knave?", "names": ["David", "Owen", "Luke", "Penelope", "Abigail", "Scarlett"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "David is a knave, Owen is a knight, Luke is a knight, Penelope is a knave, Abigail is a knight, and Scarlett is a knight.", "solution_text_format": "(1) David is a knave\n(2) Owen is a knight\n(3) Luke is a knight\n(4) Penelope is a knave\n(5) Abigail is a knight\n(6) Scarlett is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume David is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Luke is a knave and Owen is a knave.", "Luke cannot be a knight, because this would contradict the claim of Penelope that Luke is a knave and Owen is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Abigail is a knight or Owen is a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Luke that Abigail is a knight or Owen is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Penelope is a knave or Abigail is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Abigail is a knight and David is a knave.", "Owen cannot be a knave, because this would contradict the false claim of Luke that Abigail is a knight or Owen is a knave.", "We have exhausted all possibilities for Owen, Abigail, and Luke, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of David that Penelope is not a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Penelope cannot be a knight, because this would contradict the false claim of David that Penelope is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Luke is a knave and Owen is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Abigail is a knight or Owen is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Penelope is a knave or Abigail is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Abigail is a knight and David is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that David is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('and', ('telling-truth', 4), ('lying', 0)), ('or', ('telling-truth', 4), ('lying', 1)), ('and', ('lying', 2), ('lying', 1)), ('or', ('lying', 3), ('telling-truth', 4)), ('not', ('telling-truth', 0)))", "index": 939}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Joseph, Ella, Jacob, Abigail, and Avery. \"If Abigail is a knight then Abigail is a knave\" - Scarlett. \"Avery is a knave or Ella is a knight,\" Joseph mentioned. Ella asserted: \"If Joseph is a knave then Ella is a knight\". \"If Joseph is a knight then Ella is a knight,\" Jacob mentioned. Abigail said that If Jacob is a knave then Jacob is a knight. In a statement by Avery: \"Scarlett is a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Joseph", "Ella", "Jacob", "Abigail", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Scarlett is a knave, Joseph is a knight, Ella is a knight, Jacob is a knight, Abigail is a knight, and Avery is a knave.", "solution_text_format": "(1) Scarlett is a knave\n(2) Joseph is a knight\n(3) Ella is a knight\n(4) Jacob is a knight\n(5) Abigail is a knight\n(6) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that If Abigail is a knight then Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Scarlett that If Abigail is a knight then Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Jacob is a knave then Jacob is a knight.", "Jacob cannot be a knight, because this would contradict the false claim of Abigail that If Jacob is a knave then Jacob is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Joseph is a knight then Ella is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Avery is a knave or Ella is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Jacob that If Joseph is a knight then Ella is a knight.", "Ella cannot be a knave, because this would contradict the claim of Joseph that Avery is a knave or Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Avery.", "Avery cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the false claim of Jacob that If Joseph is a knight then Ella is a knight.", "We have exhausted all possibilities for Joseph, Jacob, and Abigail, so let us go back and reconsider Scarlett.", "Assume Scarlett is a knave. No contradiction is found in their false claim that If Abigail is a knight then Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that If Jacob is a knave then Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Joseph is a knight then Ella is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Avery is a knave or Ella is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Scarlett is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Joseph is a knave then Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 4)), ('or', ('lying', 5), ('telling-truth', 2)), ('->', ('lying', 1), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('->', ('lying', 3), ('telling-truth', 3)), ('telling-truth', 0))", "index": 940}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Harper, Chloe, Oliver, Lucas, and William. \"Mason is a knight and William is a knight\" - Mason. Harper asserted: \"Harper is a knight and William is a knight\". Chloe stated, \"Lucas is a knave or William is a knight\". Oliver told you that William is a knave or William is a knight. In a statement by Lucas: \"If Harper is a knave then Oliver is a knight\". William asserted: \"Mason is a knave and Harper is a knave\". So who is a knight and who is a knave?", "names": ["Mason", "Harper", "Chloe", "Oliver", "Lucas", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Mason is a knave, Harper is a knave, Chloe is a knight, Oliver is a knight, Lucas is a knight, and William is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Harper is a knave\n(3) Chloe is a knight\n(4) Oliver is a knight\n(5) Lucas is a knight\n(6) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Mason is a knight and William is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Mason is a knave and Harper is a knave.", "William cannot be a knave, because this would contradict the claim of Mason that Mason is a knight and William is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Mason is a knight and William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Mason is a knave and Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of William that Mason is a knave and Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Harper is a knight and William is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Lucas is a knave or William is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that If Harper is a knave then Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that William is a knave or William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('telling-truth', 1), ('telling-truth', 5)), ('or', ('lying', 4), ('telling-truth', 5)), ('or', ('lying', 5), ('telling-truth', 5)), ('->', ('lying', 1), ('telling-truth', 3)), ('and', ('lying', 0), ('lying', 1)))", "index": 941}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Grace, Alexander, Lucas, Samuel, and Aiden. Ava said, \"Grace is a knave or Alexander is a knight.\" Grace commented, \"Alexander is a knave\". Alexander said, \"Ava is a knight and Grace is a knight.\" In Lucas's words: \"Aiden is a knight\". \"If Grace is a knave then Aiden is a knight\" - Samuel. \"Samuel is a knight and Ava is a knave,\" Aiden claimed. So who is a knight and who is a knave?", "names": ["Ava", "Grace", "Alexander", "Lucas", "Samuel", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Ava is a knave, Grace is a knight, Alexander is a knave, Lucas is a knight, Samuel is a knight, and Aiden is a knight.", "solution_text_format": "(1) Ava is a knave\n(2) Grace is a knight\n(3) Alexander is a knave\n(4) Lucas is a knight\n(5) Samuel is a knight\n(6) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Grace is a knave or Alexander is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Grace that Alexander is a knave.", "Alexander cannot be a knave, because this would contradict the claim of Ava that Grace is a knave or Alexander is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Ava is a knight and Grace is a knight.", "Alexander cannot be a knave, because this would contradict the false claim of Grace that Alexander is a knave.", "We have exhausted all possibilities for Alexander and Grace, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Grace is a knave or Alexander is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the false claim of Ava that Grace is a knave or Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ava is a knight and Grace is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Samuel is a knight and Ava is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Grace is a knave then Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 2)), ('lying', 2), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 5), ('->', ('lying', 1), ('telling-truth', 5)), ('and', ('telling-truth', 4), ('lying', 0)))", "index": 942}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Logan, Isabella, Liam, Aria, and Victoria. James said that If Isabella is a knave then Logan is a knave. \"Liam is a knave or Isabella is a knave,\" Logan claimed. Isabella said that Liam is a knight if and only if James is a knight. As Liam put it, \"James is a knight if and only if Aria is a knave\". \"Liam is not a knight\" - Aria. In a statement by Victoria: \"Aria is a knave and Liam is a knight\". So who is a knight and who is a knave?", "names": ["James", "Logan", "Isabella", "Liam", "Aria", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "James is a knight, Logan is a knave, Isabella is a knight, Liam is a knight, Aria is a knave, and Victoria is a knight.", "solution_text_format": "(1) James is a knight\n(2) Logan is a knave\n(3) Isabella is a knight\n(4) Liam is a knight\n(5) Aria is a knave\n(6) Victoria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that If Isabella is a knave then Logan is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Liam is a knight if and only if James is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that James is a knight if and only if Aria is a knave.", "Aria cannot be a knight, because this would contradict the claim of Liam that James is a knight if and only if Aria is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Liam is not a knight.", "Logan cannot be a knight, because this would contradict the claim of their own that Liam is a knave or Isabella is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Liam is a knave or Isabella is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Aria is a knave and Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('lying', 1)), ('or', ('lying', 3), ('lying', 2)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('<=>', ('telling-truth', 0), ('lying', 4)), ('not', ('telling-truth', 3)), ('and', ('lying', 4), ('telling-truth', 3)))", "index": 943}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Daniel, Logan, James, Sofia, and Ethan. Isabella said, \"Sofia is a knight.\" Daniel said, \"Isabella is a knight.\" \"Logan is a knight if and only if Daniel is a knave,\" Logan claimed. James said, \"Sofia is not a knave.\" Sofia told you that Logan is a knave. Ethan noted, \"If Isabella is a knight then Ethan is a knight\". So who is a knight and who is a knave?", "names": ["Isabella", "Daniel", "Logan", "James", "Sofia", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true], "solution_text": "Isabella is a knave, Daniel is a knave, Logan is a knight, James is a knave, Sofia is a knave, and Ethan is a knight.", "solution_text_format": "(1) Isabella is a knave\n(2) Daniel is a knave\n(3) Logan is a knight\n(4) James is a knave\n(5) Sofia is a knave\n(6) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Logan is a knave.", "Logan cannot be a knight, because this would contradict the claim of Sofia that Logan is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the false claim of Logan that Logan is a knight if and only if Daniel is a knave.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Isabella is a knight.", "We have exhausted all possibilities for Daniel and Logan, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of Isabella that Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Sofia is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of Isabella that Sofia is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight if and only if Daniel is a knave.", "Daniel cannot be a knight, because this would contradict the claim of their own that Isabella is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Isabella is a knight.", "James cannot be a knight, because this would contradict the claim of their own that Sofia is not a knave.", "Assume James is a knave. No contradiction is found in their false claim that Sofia is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Isabella is a knight then Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('telling-truth', 0), ('<=>', ('telling-truth', 2), ('lying', 1)), ('not', ('lying', 4)), ('lying', 2), ('->', ('telling-truth', 0), ('telling-truth', 5)))", "index": 944}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Aurora, Olivia, Ella, Chloe, and Penelope. According to Ava, \"If Ella is a knave then Penelope is a knight\". Aurora asserted: \"If Ava is a knave then Chloe is a knave\". \"Penelope is not a knave,\" Olivia mentioned. Ella was heard saying, \"Aurora is not a knight\". Chloe expressed that Penelope is a knave or Olivia is a knight. Penelope asserted: \"Ella is not a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Aurora", "Olivia", "Ella", "Chloe", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Ava is a knight, Aurora is a knight, Olivia is a knight, Ella is a knave, Chloe is a knight, and Penelope is a knight.", "solution_text_format": "(1) Ava is a knight\n(2) Aurora is a knight\n(3) Olivia is a knight\n(4) Ella is a knave\n(5) Chloe is a knight\n(6) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that If Ella is a knave then Penelope is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Aurora is not a knight.", "Aurora cannot be a knight, because this would contradict the claim of Ella that Aurora is not a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Ava is a knave then Chloe is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that If Ava is a knave then Chloe is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Penelope is a knave or Olivia is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Ella is not a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Penelope is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 5)), ('->', ('lying', 0), ('lying', 4)), ('not', ('lying', 5)), ('not', ('telling-truth', 1)), ('or', ('lying', 5), ('telling-truth', 2)), ('not', ('telling-truth', 3)))", "index": 945}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Avery, Mia, Victoria, James, and Lily. Emily said that If Mia is a knave then Avery is a knight. Avery noted, \"Lily is a knight and Mia is a knave\". Mia was heard saying, \"Victoria is a knight\". Victoria said that If Avery is a knight then Avery is a knave. \"If Mia is a knave then Emily is a knight,\" James claimed. Lily asserted: \"Avery is a knave and James is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Avery", "Mia", "Victoria", "James", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Emily is a knight, Avery is a knave, Mia is a knight, Victoria is a knight, James is a knight, and Lily is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Avery is a knave\n(3) Mia is a knight\n(4) Victoria is a knight\n(5) James is a knight\n(6) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that If Mia is a knave then Avery is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that If Avery is a knight then Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Mia is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Lily is a knight and Mia is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Avery is a knave and James is a knave.", "James cannot be a knight, because this would contradict the claim of Lily that Avery is a knave and James is a knave.", "James cannot be a knave, because this would contradict the false claim of their own that If Mia is a knave then Emily is a knight.", "We have exhausted all possibilities for James, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Avery is a knave and James is a knave.", "Assume James is a knight. No contradiction is found in their claim that If Mia is a knave then Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 1)), ('and', ('telling-truth', 5), ('lying', 2)), ('telling-truth', 3), ('->', ('telling-truth', 1), ('lying', 1)), ('->', ('lying', 2), ('telling-truth', 0)), ('and', ('lying', 1), ('lying', 4)))", "index": 946}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Avery, Penelope, Henry, Grace, and William. Samuel stated, \"Henry is a knight and Grace is a knight\". Avery expressed that Penelope is a knave and William is a knave. Penelope told you that Samuel is a knight. \"Samuel is a knave and Grace is a knight\" - Henry. Grace remarked, \"Grace is a knight or William is a knight\". In a statement by William: \"Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Samuel", "Avery", "Penelope", "Henry", "Grace", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false], "solution_text": "Samuel is a knave, Avery is a knight, Penelope is a knave, Henry is a knave, Grace is a knave, and William is a knave.", "solution_text_format": "(1) Samuel is a knave\n(2) Avery is a knight\n(3) Penelope is a knave\n(4) Henry is a knave\n(5) Grace is a knave\n(6) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Henry is a knight and Grace is a knight.", "Henry cannot be a knight, because this would contradict the claim of their own that Samuel is a knave and Grace is a knight.", "Henry cannot be a knave, because this would contradict the claim of Samuel that Henry is a knight and Grace is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Henry is a knight and Grace is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Samuel is a knave and Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Samuel that Henry is a knight and Grace is a knight.", "Grace cannot be a knave, because this would contradict the claim of Henry that Samuel is a knave and Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Samuel is a knave and Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Henry that Samuel is a knave and Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Grace is a knight or William is a knight.", "William cannot be a knight, because this would contradict the false claim of Grace that Grace is a knight or William is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Samuel is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Samuel is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Penelope is a knave and William is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 3), ('telling-truth', 4)), ('and', ('lying', 2), ('lying', 5)), ('telling-truth', 0), ('and', ('lying', 0), ('telling-truth', 4)), ('or', ('telling-truth', 4), ('telling-truth', 5)), ('telling-truth', 2))", "index": 947}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, Chloe, Ella, Grace, Emily, and Aiden. Penelope was heard saying, \"Grace is a knave and Penelope is a knight\". \"Ella is a knave,\" Chloe declared. Ella commented, \"If Aiden is a knight then Grace is a knight\". Grace remarked, \"If Ella is a knave then Chloe is a knight\". Emily commented, \"Penelope is not a knight\". \"Emily is not a knave,\" Aiden mentioned. So who is a knight and who is a knave?", "names": ["Penelope", "Chloe", "Ella", "Grace", "Emily", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Penelope is a knave, Chloe is a knave, Ella is a knight, Grace is a knight, Emily is a knight, and Aiden is a knight.", "solution_text_format": "(1) Penelope is a knave\n(2) Chloe is a knave\n(3) Ella is a knight\n(4) Grace is a knight\n(5) Emily is a knight\n(6) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Grace is a knave and Penelope is a knight.", "Grace cannot be a knight, because this would contradict the claim of Penelope that Grace is a knave and Penelope is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that If Ella is a knave then Chloe is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Grace that If Ella is a knave then Chloe is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that If Aiden is a knight then Grace is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Penelope is not a knight.", "Emily cannot be a knave, because this would contradict the claim of Aiden that Emily is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of Ella that If Aiden is a knight then Grace is a knight.", "We have exhausted all possibilities for Aiden, Ella, and Grace, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Grace is a knave and Penelope is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Ella is a knave then Chloe is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Aiden is a knight then Grace is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Ella is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 0)), ('lying', 2), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('lying', 2), ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('not', ('lying', 4)))", "index": 948}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Michael, Logan, James, Matthew, and Mason. Sophia noted, \"James is a knave if and only if Michael is a knave\". Michael was heard saying, \"Mason is a knight if and only if Matthew is a knight\". Logan expressed that Michael is a knave and Mason is a knight. As James put it, \"Michael is a knave\". Matthew said, \"Michael is a knave and Sophia is a knave.\" Mason noted, \"Matthew is a knight and James is a knight\". So who is a knight and who is a knave?", "names": ["Sophia", "Michael", "Logan", "James", "Matthew", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false], "solution_text": "Sophia is a knave, Michael is a knight, Logan is a knave, James is a knave, Matthew is a knave, and Mason is a knave.", "solution_text_format": "(1) Sophia is a knave\n(2) Michael is a knight\n(3) Logan is a knave\n(4) James is a knave\n(5) Matthew is a knave\n(6) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that James is a knave if and only if Michael is a knave.", "Assume James is a knight. No contradiction is found in their claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of James that Michael is a knave.", "Michael cannot be a knave, because this would contradict the claim of Sophia that James is a knave if and only if Michael is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Sophia that James is a knave if and only if Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of James that Michael is a knave.", "We have exhausted all possibilities for Michael and James, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that James is a knave if and only if Michael is a knave.", "Assume James is a knight. No contradiction is found in their claim that Michael is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Sophia that James is a knave if and only if Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Matthew is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Matthew is a knight and James is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Michael that Mason is a knight if and only if Matthew is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Michael is a knave and Sophia is a knave.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Matthew is a knight and James is a knight.", "Matthew cannot be a knight, because this would contradict the false claim of Mason that Matthew is a knight and James is a knight.", "Matthew cannot be a knave, because this would contradict the false claim of Michael that Mason is a knight if and only if Matthew is a knight.", "We have exhausted all possibilities for Matthew, Mason, and Michael, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Mason is a knight if and only if Matthew is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Matthew is a knight and James is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Matthew is a knight and James is a knight.", "Matthew cannot be a knight, because this would contradict the claim of Michael that Mason is a knight if and only if Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Michael is a knave and Sophia is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Mason is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Michael is a knave and Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 1)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('and', ('lying', 1), ('telling-truth', 5)), ('lying', 1), ('and', ('lying', 1), ('lying', 0)), ('and', ('telling-truth', 4), ('telling-truth', 3)))", "index": 949}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Matthew, Luke, Charlotte, Owen, and Lucas. Joseph remarked, \"If Lucas is a knight then Luke is a knight\". Matthew told you that Luke is a knave if and only if Owen is a knave. Luke noted, \"Joseph is not a knight\". Charlotte said that If Lucas is a knave then Joseph is a knave. Owen was heard saying, \"If Joseph is a knave then Matthew is a knight\". Lucas noted, \"Luke is a knight\". So who is a knight and who is a knave?", "names": ["Joseph", "Matthew", "Luke", "Charlotte", "Owen", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false], "solution_text": "Joseph is a knight, Matthew is a knave, Luke is a knave, Charlotte is a knave, Owen is a knight, and Lucas is a knave.", "solution_text_format": "(1) Joseph is a knight\n(2) Matthew is a knave\n(3) Luke is a knave\n(4) Charlotte is a knave\n(5) Owen is a knight\n(6) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that If Lucas is a knight then Luke is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Joseph is not a knight.", "Luke cannot be a knave, because this would contradict the claim of Joseph that If Lucas is a knight then Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Joseph is not a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Joseph is not a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Luke is a knave if and only if Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Matthew that Luke is a knave if and only if Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knave then Matthew is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Joseph is a knave then Matthew is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that If Lucas is a knave then Joseph is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that If Lucas is a knave then Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('telling-truth', 2)), ('<=>', ('lying', 2), ('lying', 4)), ('not', ('telling-truth', 0)), ('->', ('lying', 5), ('lying', 0)), ('->', ('lying', 0), ('telling-truth', 1)), ('telling-truth', 2))", "index": 950}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Matthew, Olivia, Ella, Sebastian, and Owen. Chloe stated, \"Sebastian is a knight\". \"Ella is a knave or Olivia is a knave,\" Matthew claimed. Olivia asserted: \"Chloe is a knave if and only if Matthew is a knight\". As Ella put it, \"Chloe is a knave if and only if Sebastian is a knight\". Sebastian expressed that Olivia is a knight and Chloe is a knight. In Owen's words: \"Olivia is a knight or Chloe is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Matthew", "Olivia", "Ella", "Sebastian", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Chloe is a knave, Matthew is a knight, Olivia is a knight, Ella is a knave, Sebastian is a knave, and Owen is a knight.", "solution_text_format": "(1) Chloe is a knave\n(2) Matthew is a knight\n(3) Olivia is a knight\n(4) Ella is a knave\n(5) Sebastian is a knave\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Olivia is a knight and Chloe is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of Olivia that Chloe is a knave if and only if Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Ella is a knave or Olivia is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Chloe is a knave if and only if Sebastian is a knight.", "Ella cannot be a knave, because this would contradict the false claim of Matthew that Ella is a knave or Olivia is a knave.", "We have exhausted all possibilities for Ella and Matthew, so let us go back and reconsider Olivia.", "Olivia cannot be a knave, because this would contradict the claim of Sebastian that Olivia is a knight and Chloe is a knight.", "We have exhausted all possibilities for Olivia, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the claim of Chloe that Sebastian is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Sebastian is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Chloe that Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Olivia is a knight and Chloe is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Ella is a knave or Olivia is a knave.", "Ella cannot be a knight, because this would contradict the claim of Matthew that Ella is a knave or Olivia is a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Chloe is a knave if and only if Sebastian is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Olivia is a knight or Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('or', ('lying', 3), ('lying', 2)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('<=>', ('lying', 0), ('telling-truth', 4)), ('and', ('telling-truth', 2), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('lying', 0)))", "index": 951}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Lucas, Ella, Jackson, Avery, and Evelyn. In a statement by Henry: \"Lucas is a knave if and only if Avery is a knight\". Lucas said, \"Evelyn is a knave and Jackson is a knave.\" Ella told you that If Lucas is a knave then Avery is a knight. In a statement by Jackson: \"Avery is not a knave\". \"If Evelyn is a knave then Henry is a knight,\" Avery claimed. Evelyn asserted: \"Henry is a knight\". So who is a knight and who is a knave?", "names": ["Henry", "Lucas", "Ella", "Jackson", "Avery", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Henry is a knight, Lucas is a knave, Ella is a knight, Jackson is a knight, Avery is a knight, and Evelyn is a knight.", "solution_text_format": "(1) Henry is a knight\n(2) Lucas is a knave\n(3) Ella is a knight\n(4) Jackson is a knight\n(5) Avery is a knight\n(6) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Avery is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Evelyn is a knave and Jackson is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Lucas that Evelyn is a knave and Jackson is a knave.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Henry is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Evelyn is a knave and Jackson is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Henry is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Avery is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Evelyn is a knave then Henry is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Lucas is a knave then Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 4)), ('and', ('lying', 5), ('lying', 3)), ('->', ('lying', 1), ('telling-truth', 4)), ('not', ('lying', 4)), ('->', ('lying', 5), ('telling-truth', 0)), ('telling-truth', 0))", "index": 952}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Mia, Henry, Zoey, Matthew, and Jacob. \"Matthew is a knight\" - Sophia. In a statement by Mia: \"Jacob is a knave and Matthew is a knight\". Henry said that Jacob is a knight or Matthew is a knight. Zoey expressed that Mia is a knave if and only if Matthew is a knight. Matthew said, \"Zoey is a knight if and only if Sophia is a knave.\" Jacob remarked, \"Matthew is a knave and Henry is a knave\". So who is a knight and who is a knave?", "names": ["Sophia", "Mia", "Henry", "Zoey", "Matthew", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, false], "solution_text": "Sophia is a knight, Mia is a knight, Henry is a knight, Zoey is a knave, Matthew is a knight, and Jacob is a knave.", "solution_text_format": "(1) Sophia is a knight\n(2) Mia is a knight\n(3) Henry is a knight\n(4) Zoey is a knave\n(5) Matthew is a knight\n(6) Jacob is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Sophia is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Matthew that Zoey is a knight if and only if Sophia is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Matthew is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Jacob is a knave and Matthew is a knight.", "Jacob cannot be a knight, because this would contradict the claim of Mia that Jacob is a knave and Matthew is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Matthew is a knave and Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Jacob is a knight or Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 4), ('and', ('lying', 5), ('telling-truth', 4)), ('or', ('telling-truth', 5), ('telling-truth', 4)), ('<=>', ('lying', 1), ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('lying', 0)), ('and', ('lying', 4), ('lying', 2)))", "index": 953}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Sophia, Charlotte, Alexander, Aiden, and Aurora. \"Sophia is a knave if and only if Alexander is a knight,\" Jackson mentioned. According to Sophia, \"If Aurora is a knave then Alexander is a knave\". Charlotte stated, \"Alexander is a knave and Jackson is a knave\". \"If Charlotte is a knave then Aiden is a knight,\" Alexander claimed. \"Aurora is a knave if and only if Charlotte is a knave,\" Aiden declared. Aurora was heard saying, \"Jackson is a knight if and only if Charlotte is a knave\". So who is a knight and who is a knave?", "names": ["Jackson", "Sophia", "Charlotte", "Alexander", "Aiden", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, true], "solution_text": "Jackson is a knight, Sophia is a knight, Charlotte is a knave, Alexander is a knave, Aiden is a knave, and Aurora is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Sophia is a knight\n(3) Charlotte is a knave\n(4) Alexander is a knave\n(5) Aiden is a knave\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Alexander is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Aurora is a knave then Alexander is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Alexander is a knave and Jackson is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Alexander is a knave and Jackson is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Jackson that Sophia is a knave if and only if Alexander is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Charlotte is a knave then Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Alexander that If Charlotte is a knave then Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 3)), ('->', ('lying', 5), ('lying', 3)), ('and', ('lying', 3), ('lying', 0)), ('->', ('lying', 2), ('telling-truth', 4)), ('<=>', ('lying', 5), ('lying', 2)), ('<=>', ('telling-truth', 0), ('lying', 2)))", "index": 954}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Liam, Ethan, Alexander, Charlotte, and Henry. Jacob remarked, \"Alexander is a knave\". Liam asserted: \"If Charlotte is a knave then Henry is a knave\". \"If Jacob is a knight then Alexander is a knave\" - Ethan. Alexander stated, \"Ethan is not a knight\". In a statement by Charlotte: \"Alexander is a knight if and only if Jacob is a knight\". Henry told you that Alexander is a knave if and only if Jacob is a knight. So who is a knight and who is a knave?", "names": ["Jacob", "Liam", "Ethan", "Alexander", "Charlotte", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Jacob is a knight, Liam is a knave, Ethan is a knight, Alexander is a knave, Charlotte is a knave, and Henry is a knight.", "solution_text_format": "(1) Jacob is a knight\n(2) Liam is a knave\n(3) Ethan is a knight\n(4) Alexander is a knave\n(5) Charlotte is a knave\n(6) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Jacob that Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ethan is not a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Jacob is a knight then Alexander is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that If Charlotte is a knave then Henry is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Alexander is a knight if and only if Jacob is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Jacob is a knight.", "Henry cannot be a knight, because this would contradict the claim of Liam that If Charlotte is a knave then Henry is a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that Alexander is a knave if and only if Jacob is a knight.", "We have exhausted all possibilities for Henry and Charlotte, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that If Charlotte is a knave then Henry is a knave.", "Charlotte cannot be a knight, because this would contradict the false claim of Liam that If Charlotte is a knave then Henry is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Alexander is a knight if and only if Jacob is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('->', ('lying', 4), ('lying', 5)), ('->', ('telling-truth', 0), ('lying', 3)), ('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('<=>', ('lying', 3), ('telling-truth', 0)))", "index": 955}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Zoey, Ethan, Charlotte, Evelyn, and Sofia. Mason commented, \"Ethan is a knave and Charlotte is a knave\". Zoey said that Ethan is not a knave. In Ethan's words: \"Zoey is a knight if and only if Ethan is a knight\". Charlotte commented, \"Zoey is a knight or Ethan is a knave\". In a statement by Evelyn: \"Sofia is a knave\". Sofia commented, \"Mason is a knave or Ethan is a knight\". So who is a knight and who is a knave?", "names": ["Mason", "Zoey", "Ethan", "Charlotte", "Evelyn", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, false, true], "solution_text": "Mason is a knave, Zoey is a knight, Ethan is a knight, Charlotte is a knight, Evelyn is a knave, and Sofia is a knight.", "solution_text_format": "(1) Mason is a knave\n(2) Zoey is a knight\n(3) Ethan is a knight\n(4) Charlotte is a knight\n(5) Evelyn is a knave\n(6) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Ethan is a knave and Charlotte is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Mason that Ethan is a knave and Charlotte is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Ethan is a knight.", "Zoey cannot be a knight, because this would contradict the claim of their own that Ethan is not a knave.", "Zoey cannot be a knave, because this would contradict the false claim of Ethan that Zoey is a knight if and only if Ethan is a knight.", "We have exhausted all possibilities for Zoey and Ethan, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that Ethan is a knave and Charlotte is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Ethan is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Zoey is a knight or Ethan is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Evelyn that Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Mason is a knave or Ethan is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Mason is a knave or Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 3)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('telling-truth', 1), ('lying', 2)), ('lying', 5), ('or', ('lying', 0), ('telling-truth', 2)))", "index": 956}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Amelia, Harper, Charlotte, Victoria, and Benjamin. \"Benjamin is a knave and Harper is a knave,\" Lucas declared. According to Amelia, \"Harper is a knave or Victoria is a knight\". Harper said, \"Victoria is a knave.\" Charlotte stated, \"If Lucas is a knave then Victoria is a knave\". Victoria noted, \"Charlotte is a knave and Harper is a knave\". \"Harper is a knight,\" Benjamin mentioned. So who is a knight and who is a knave?", "names": ["Lucas", "Amelia", "Harper", "Charlotte", "Victoria", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Lucas is a knave, Amelia is a knave, Harper is a knight, Charlotte is a knight, Victoria is a knave, and Benjamin is a knight.", "solution_text_format": "(1) Lucas is a knave\n(2) Amelia is a knave\n(3) Harper is a knight\n(4) Charlotte is a knight\n(5) Victoria is a knave\n(6) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Benjamin is a knave and Harper is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Lucas that Benjamin is a knave and Harper is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of Lucas that Benjamin is a knave and Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Charlotte is a knave and Harper is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Victoria that Charlotte is a knave and Harper is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that If Lucas is a knave then Victoria is a knave.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the false claim of Harper that Victoria is a knave.", "We have exhausted all possibilities for Victoria, Harper, and Benjamin, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Benjamin is a knave and Harper is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Victoria is a knave.", "Victoria cannot be a knight, because this would contradict the claim of Harper that Victoria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that Charlotte is a knave and Harper is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Lucas is a knave then Victoria is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Harper is a knave or Victoria is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Harper is a knave or Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('lying', 2)), ('or', ('lying', 2), ('telling-truth', 4)), ('lying', 4), ('->', ('lying', 0), ('lying', 4)), ('and', ('lying', 3), ('lying', 2)), ('telling-truth', 2))", "index": 957}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, James, Penelope, Avery, Liam, and Zoey. Sebastian stated, \"James is a knave if and only if James is a knight\". James said, \"Avery is a knave if and only if Sebastian is a knave.\" Penelope stated, \"Zoey is not a knight\". Avery remarked, \"Liam is a knight\". In a statement by Liam: \"Zoey is not a knight\". In a statement by Zoey: \"James is a knight if and only if Penelope is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "James", "Penelope", "Avery", "Liam", "Zoey"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Sebastian is a knave, James is a knave, Penelope is a knight, Avery is a knight, Liam is a knight, and Zoey is a knave.", "solution_text_format": "(1) Sebastian is a knave\n(2) James is a knave\n(3) Penelope is a knight\n(4) Avery is a knight\n(5) Liam is a knight\n(6) Zoey is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Sebastian cannot be a knight, because this would contradict the claim of their own that James is a knave if and only if James is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that James is a knave if and only if James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Avery is a knave if and only if Sebastian is a knave.", "Avery cannot be a knight, because this would contradict the claim of James that Avery is a knave if and only if Sebastian is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Liam is a knight.", "Liam cannot be a knight, because this would contradict the false claim of Avery that Liam is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Zoey is not a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that James is a knight if and only if Penelope is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Zoey is not a knight.", "Penelope cannot be a knave, because this would contradict the claim of Zoey that James is a knight if and only if Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the false claim of Liam that Zoey is not a knight.", "We have exhausted all possibilities for Zoey, Liam, and Avery, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Avery is a knave if and only if Sebastian is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Zoey cannot be a knight, because this would contradict the claim of Liam that Zoey is not a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that James is a knight if and only if Penelope is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Zoey is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 1)), ('<=>', ('lying', 3), ('lying', 0)), ('not', ('telling-truth', 5)), ('telling-truth', 4), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)))", "index": 958}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Elizabeth, Zoey, Ella, Michael, Matthew, and Penelope. \"Michael is a knave if and only if Zoey is a knave,\" Elizabeth declared. \"Ella is a knight,\" Zoey mentioned. Ella noted, \"Matthew is a knight or Elizabeth is a knave\". \"Zoey is a knave and Zoey is a knight,\" Michael mentioned. \"Michael is not a knight,\" Matthew declared. Penelope expressed that Ella is a knight or Michael is a knight. So who is a knight and who is a knave?", "names": ["Elizabeth", "Zoey", "Ella", "Michael", "Matthew", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Elizabeth is a knave, Zoey is a knight, Ella is a knight, Michael is a knave, Matthew is a knight, and Penelope is a knight.", "solution_text_format": "(1) Elizabeth is a knave\n(2) Zoey is a knight\n(3) Ella is a knight\n(4) Michael is a knave\n(5) Matthew is a knight\n(6) Penelope is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Elizabeth is a knight. No contradiction is found in their claim that Michael is a knave if and only if Zoey is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Zoey is a knave and Zoey is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Zoey is a knave and Zoey is a knight.", "Zoey cannot be a knight, because this would contradict the claim of Elizabeth that Michael is a knave if and only if Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Zoey that Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Matthew is a knight or Elizabeth is a knave.", "Matthew cannot be a knight, because this would contradict the false claim of Ella that Matthew is a knight or Elizabeth is a knave.", "Matthew cannot be a knave, because this would contradict the false claim of their own that Michael is not a knight.", "We have exhausted all possibilities for Matthew, Ella, Zoey, and Michael, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Zoey is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Zoey is a knave and Zoey is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Zoey is a knave and Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Matthew is a knight or Elizabeth is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Michael is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Ella is a knight or Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 1)), ('telling-truth', 2), ('or', ('telling-truth', 4), ('lying', 0)), ('and', ('lying', 1), ('telling-truth', 1)), ('not', ('telling-truth', 3)), ('or', ('telling-truth', 2), ('telling-truth', 3)))", "index": 959}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Aria, Lily, Abigail, Noah, and Emily. Aurora expressed that Emily is a knave. According to Aria, \"Aurora is a knave if and only if Abigail is a knight\". Lily said that Aurora is a knave and Aria is a knave. As Abigail put it, \"If Emily is a knight then Aria is a knight\". Noah said that Aurora is a knight or Emily is a knight. As Emily put it, \"If Emily is a knight then Abigail is a knight\". So who is a knight and who is a knave?", "names": ["Aurora", "Aria", "Lily", "Abigail", "Noah", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Aurora is a knave, Aria is a knight, Lily is a knave, Abigail is a knight, Noah is a knight, and Emily is a knight.", "solution_text_format": "(1) Aurora is a knave\n(2) Aria is a knight\n(3) Lily is a knave\n(4) Abigail is a knight\n(5) Noah is a knight\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aurora is a knight. No contradiction is found in their claim that Emily is a knave.", "Emily cannot be a knight, because this would contradict the claim of Aurora that Emily is a knave.", "Emily cannot be a knave, because this would contradict the false claim of their own that If Emily is a knight then Abigail is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that If Emily is a knight then Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Emily is a knight then Aria is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Abigail is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Aria is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Aurora is a knave and Aria is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that Aurora is a knight or Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('<=>', ('lying', 0), ('telling-truth', 3)), ('and', ('lying', 0), ('lying', 1)), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('->', ('telling-truth', 5), ('telling-truth', 3)))", "index": 960}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Joseph, Jackson, Zoey, Ethan, and Ella. Samuel remarked, \"Joseph is a knight\". Joseph commented, \"Jackson is a knave and Ethan is a knight\". Jackson noted, \"Zoey is a knave if and only if Joseph is a knave\". \"Joseph is a knave and Ella is a knight,\" Zoey declared. Ethan asserted: \"Samuel is a knight and Joseph is a knave\". \"Samuel is a knave and Ethan is a knight,\" Ella mentioned. So who is a knight and who is a knave?", "names": ["Samuel", "Joseph", "Jackson", "Zoey", "Ethan", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false], "solution_text": "Samuel is a knave, Joseph is a knave, Jackson is a knight, Zoey is a knave, Ethan is a knave, and Ella is a knave.", "solution_text_format": "(1) Samuel is a knave\n(2) Joseph is a knave\n(3) Jackson is a knight\n(4) Zoey is a knave\n(5) Ethan is a knave\n(6) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Jackson is a knave and Ethan is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Joseph that Jackson is a knave and Ethan is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Zoey is a knave if and only if Joseph is a knave.", "Zoey cannot be a knight, because this would contradict the false claim of Jackson that Zoey is a knave if and only if Joseph is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Joseph is a knave and Ella is a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Samuel is a knave and Ethan is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Samuel is a knave and Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Samuel is a knight and Joseph is a knave.", "Ethan cannot be a knave, because this would contradict the claim of Joseph that Jackson is a knave and Ethan is a knight.", "We have exhausted all possibilities for Ethan, Ella, Zoey, and Jackson, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Samuel that Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Samuel that Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Jackson is a knave and Ethan is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Joseph is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Jackson that Zoey is a knave if and only if Joseph is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Joseph is a knave and Ella is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Zoey that Joseph is a knave and Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that Samuel is a knave and Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Samuel is a knight and Joseph is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Samuel is a knight and Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('and', ('lying', 2), ('telling-truth', 4)), ('<=>', ('lying', 3), ('lying', 1)), ('and', ('lying', 1), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('lying', 1)), ('and', ('lying', 0), ('telling-truth', 4)))", "index": 961}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Aiden, Ethan, Isabella, Owen, and Joseph. In a statement by Sofia: \"Joseph is a knight and Joseph is a knave\". Aiden said that Ethan is a knight if and only if Isabella is a knave. Ethan expressed that If Ethan is a knight then Sofia is a knave. Isabella said, \"Sofia is not a knight.\" Owen said, \"Sofia is a knave if and only if Joseph is a knight.\" Joseph expressed that Sofia is not a knight. So who is a knight and who is a knave?", "names": ["Sofia", "Aiden", "Ethan", "Isabella", "Owen", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Sofia is a knave, Aiden is a knave, Ethan is a knight, Isabella is a knight, Owen is a knight, and Joseph is a knight.", "solution_text_format": "(1) Sofia is a knave\n(2) Aiden is a knave\n(3) Ethan is a knight\n(4) Isabella is a knight\n(5) Owen is a knight\n(6) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Sofia cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Joseph is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Joseph is a knight and Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Isabella is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Ethan is a knight then Sofia is a knave.", "Isabella cannot be a knight, because this would contradict the claim of Aiden that Ethan is a knight if and only if Isabella is a knave.", "Isabella cannot be a knave, because this would contradict the false claim of their own that Sofia is not a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the false claim of their own that If Ethan is a knight then Sofia is a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Isabella is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Ethan is a knight then Sofia is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Sofia is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Joseph is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 5)), ('<=>', ('telling-truth', 2), ('lying', 3)), ('->', ('telling-truth', 2), ('lying', 0)), ('not', ('telling-truth', 0)), ('<=>', ('lying', 0), ('telling-truth', 5)), ('not', ('telling-truth', 0)))", "index": 962}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Isabella, Logan, Aiden, Michael, and James. In Jackson's words: \"Logan is a knight if and only if Isabella is a knave\". Isabella told you that Logan is a knight and Aiden is a knave. \"Isabella is a knave or Aiden is a knight,\" Logan claimed. Aiden remarked, \"If Aiden is a knight then Michael is a knight\". Michael expressed that James is a knave if and only if Logan is a knight. \"Isabella is not a knave\" - James. So who is a knight and who is a knave?", "names": ["Jackson", "Isabella", "Logan", "Aiden", "Michael", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Jackson is a knight, Isabella is a knave, Logan is a knight, Aiden is a knight, Michael is a knight, and James is a knave.", "solution_text_format": "(1) Jackson is a knight\n(2) Isabella is a knave\n(3) Logan is a knight\n(4) Aiden is a knight\n(5) Michael is a knight\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Logan is a knight if and only if Isabella is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Isabella is a knave or Aiden is a knight.", "Isabella cannot be a knight, because this would contradict the claim of Jackson that Logan is a knight if and only if Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Logan is a knight and Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that If Aiden is a knight then Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that James is a knave if and only if Logan is a knight.", "James cannot be a knight, because this would contradict the claim of Michael that James is a knave if and only if Logan is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Isabella is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 1)), ('and', ('telling-truth', 2), ('lying', 3)), ('or', ('lying', 1), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('telling-truth', 4)), ('<=>', ('lying', 5), ('telling-truth', 2)), ('not', ('lying', 1)))", "index": 963}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Aurora, Ava, Lily, Benjamin, and Lucas. According to Amelia, \"Lily is a knave or Aurora is a knave\". \"Ava is a knight if and only if Amelia is a knave,\" Aurora mentioned. Ava was heard saying, \"Lily is a knave if and only if Lucas is a knave\". \"Ava is not a knight,\" Lily declared. Benjamin told you that Lucas is not a knave. Lucas commented, \"Amelia is a knave and Lily is a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "Aurora", "Ava", "Lily", "Benjamin", "Lucas"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Amelia is a knight, Aurora is a knave, Ava is a knight, Lily is a knave, Benjamin is a knave, and Lucas is a knave.", "solution_text_format": "(1) Amelia is a knight\n(2) Aurora is a knave\n(3) Ava is a knight\n(4) Lily is a knave\n(5) Benjamin is a knave\n(6) Lucas is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Lily is a knave or Aurora is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Lily that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the false claim of Ava that Lily is a knave if and only if Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Amelia is a knave and Lily is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Amelia that Lily is a knave or Aurora is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Ava is a knight if and only if Amelia is a knave.", "We have exhausted all possibilities for Aurora, Lucas, and Ava, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Lily is a knave if and only if Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Ava that Lily is a knave if and only if Lucas is a knave.", "Assume Lucas is a knave. No contradiction is found in their false claim that Amelia is a knave and Lily is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Ava is a knight if and only if Amelia is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Amelia is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Lucas is not a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Lucas is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('lying', 1)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('<=>', ('lying', 3), ('lying', 5)), ('not', ('telling-truth', 2)), ('not', ('lying', 5)), ('and', ('lying', 0), ('lying', 3)))", "index": 964}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Benjamin, Oliver, Logan, Chloe, and Aurora. William noted, \"Oliver is a knight\". Benjamin told you that William is a knave. Oliver asserted: \"Oliver is a knight if and only if Logan is a knight\". Logan told you that Oliver is a knight if and only if Logan is a knight. Chloe told you that William is not a knave. Aurora remarked, \"Oliver is a knight if and only if Oliver is a knave\". So who is a knight and who is a knave?", "names": ["William", "Benjamin", "Oliver", "Logan", "Chloe", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "William is a knight, Benjamin is a knave, Oliver is a knight, Logan is a knight, Chloe is a knight, and Aurora is a knave.", "solution_text_format": "(1) William is a knight\n(2) Benjamin is a knave\n(3) Oliver is a knight\n(4) Logan is a knight\n(5) Chloe is a knight\n(6) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Logan is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that William is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that William is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that William is not a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Oliver is a knight if and only if Oliver is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('lying', 0), ('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('lying', 0)), ('<=>', ('telling-truth', 2), ('lying', 2)))", "index": 965}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Luke, Mia, Scarlett, Oliver, and Liam. Amelia stated, \"Liam is a knight and Oliver is a knight\". Luke remarked, \"Oliver is a knave and Mia is a knave\". As Mia put it, \"If Liam is a knave then Oliver is a knave\". According to Scarlett, \"Liam is a knight if and only if Amelia is a knave\". Oliver told you that Liam is a knight and Luke is a knight. In Liam's words: \"Mia is a knight or Mia is a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "Luke", "Mia", "Scarlett", "Oliver", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Amelia is a knave, Luke is a knave, Mia is a knight, Scarlett is a knight, Oliver is a knave, and Liam is a knight.", "solution_text_format": "(1) Amelia is a knave\n(2) Luke is a knave\n(3) Mia is a knight\n(4) Scarlett is a knight\n(5) Oliver is a knave\n(6) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Liam is a knight and Oliver is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Mia is a knight or Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Liam is a knave then Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Liam is a knight and Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Oliver is a knave and Mia is a knave.", "Luke cannot be a knave, because this would contradict the claim of Oliver that Liam is a knight and Luke is a knight.", "We have exhausted all possibilities for Luke, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of Amelia that Liam is a knight and Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of their own that If Liam is a knave then Oliver is a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the claim of Amelia that Liam is a knight and Oliver is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Liam is a knight and Oliver is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Mia is a knight or Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that If Liam is a knave then Oliver is a knave.", "Oliver cannot be a knight, because this would contradict the false claim of Amelia that Liam is a knight and Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Liam is a knight and Luke is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Oliver is a knave and Mia is a knave.", "Assume Luke is a knave. No contradiction is found in their false claim that Oliver is a knave and Mia is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Liam is a knight if and only if Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 4)), ('and', ('lying', 4), ('lying', 2)), ('->', ('lying', 5), ('lying', 4)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('and', ('telling-truth', 5), ('telling-truth', 1)), ('or', ('telling-truth', 2), ('lying', 2)))", "index": 966}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Grace, Chloe, Samuel, Sophia, and Jack. Ethan noted, \"Samuel is a knave and Ethan is a knight\". \"Chloe is a knave or Ethan is a knave,\" Grace mentioned. Chloe told you that Grace is a knight and Ethan is a knight. Samuel said, \"Ethan is a knave and Jack is a knight.\" Sophia commented, \"Jack is a knave\". Jack asserted: \"Chloe is a knave or Grace is a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Grace", "Chloe", "Samuel", "Sophia", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true], "solution_text": "Ethan is a knave, Grace is a knight, Chloe is a knave, Samuel is a knight, Sophia is a knave, and Jack is a knight.", "solution_text_format": "(1) Ethan is a knave\n(2) Grace is a knight\n(3) Chloe is a knave\n(4) Samuel is a knight\n(5) Sophia is a knave\n(6) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Samuel is a knave and Ethan is a knight.", "Samuel cannot be a knight, because this would contradict the claim of Ethan that Samuel is a knave and Ethan is a knight.", "Assume Samuel is a knave. No contradiction is found in their false claim that Ethan is a knave and Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Chloe is a knave or Grace is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Grace is a knight and Ethan is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Chloe is a knave or Ethan is a knave.", "Grace cannot be a knave, because this would contradict the claim of Chloe that Grace is a knight and Ethan is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Grace is a knight and Ethan is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Chloe that Grace is a knight and Ethan is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave or Ethan is a knave.", "We have exhausted all possibilities for Grace and Chloe, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that Chloe is a knave or Grace is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Grace is a knight and Ethan is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Chloe is a knave or Ethan is a knave.", "Grace cannot be a knave, because this would contradict the claim of Chloe that Grace is a knight and Ethan is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of Jack that Chloe is a knave or Grace is a knight.", "We have exhausted all possibilities for Chloe, Jack, and Samuel, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Samuel is a knave and Ethan is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Ethan is a knave and Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Chloe is a knave or Grace is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Grace is a knight and Ethan is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Grace is a knight and Ethan is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Chloe is a knave or Ethan is a knave.", "Sophia cannot be a knight, because this would contradict the claim of their own that Jack is a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 0)), ('or', ('lying', 2), ('lying', 0)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('lying', 0), ('telling-truth', 5)), ('lying', 5), ('or', ('lying', 2), ('telling-truth', 1)))", "index": 967}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Mason, Jack, William, Amelia, and Emily. In a statement by Chloe: \"Emily is a knave if and only if Jack is a knave\". Mason asserted: \"If Chloe is a knight then Jack is a knight\". Jack stated, \"Chloe is a knave\". William stated, \"Chloe is not a knave\". Amelia said, \"Jack is a knight if and only if Mason is a knight.\" Emily expressed that Jack is not a knight. So who is a knight and who is a knave?", "names": ["Chloe", "Mason", "Jack", "William", "Amelia", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, false], "solution_text": "Chloe is a knave, Mason is a knight, Jack is a knight, William is a knave, Amelia is a knight, and Emily is a knave.", "solution_text_format": "(1) Chloe is a knave\n(2) Mason is a knight\n(3) Jack is a knight\n(4) William is a knave\n(5) Amelia is a knight\n(6) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Emily is a knave if and only if Jack is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Jack is not a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Chloe is a knave.", "Jack cannot be a knave, because this would contradict the claim of Chloe that Emily is a knave if and only if Jack is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Jack cannot be a knight, because this would contradict the claim of Chloe that Emily is a knave if and only if Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of Emily that Jack is not a knight.", "We have exhausted all possibilities for Jack and Emily, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Jack is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Jack is not a knight.", "Jack cannot be a knight, because this would contradict the false claim of Chloe that Emily is a knave if and only if Jack is a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Chloe is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Chloe is a knight then Jack is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Chloe is not a knave.", "Assume William is a knave. No contradiction is found in their false claim that Chloe is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Jack is a knight if and only if Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('lying', 2)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('lying', 0), ('not', ('lying', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('not', ('telling-truth', 2)))", "index": 968}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Daniel, Ethan, Liam, Amelia, and Harper. As Isabella put it, \"If Harper is a knave then Harper is a knight\". Daniel told you that Liam is a knave. Ethan expressed that If Isabella is a knight then Daniel is a knave. In Liam's words: \"Amelia is not a knight\". As Amelia put it, \"Isabella is a knave and Daniel is a knight\". Harper remarked, \"Daniel is a knave if and only if Amelia is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Daniel", "Ethan", "Liam", "Amelia", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "Isabella is a knight, Daniel is a knave, Ethan is a knight, Liam is a knight, Amelia is a knave, and Harper is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Daniel is a knave\n(3) Ethan is a knight\n(4) Liam is a knight\n(5) Amelia is a knave\n(6) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that If Harper is a knave then Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Amelia is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Daniel that Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Isabella is a knave and Daniel is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of Liam that Amelia is not a knight.", "We have exhausted all possibilities for Amelia and Liam, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Amelia is not a knight.", "Amelia cannot be a knight, because this would contradict the claim of Liam that Amelia is not a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Isabella is a knave and Daniel is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Isabella is a knight then Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 5)), ('lying', 3), ('->', ('telling-truth', 0), ('lying', 1)), ('not', ('telling-truth', 4)), ('and', ('lying', 0), ('telling-truth', 1)), ('<=>', ('lying', 1), ('lying', 4)))", "index": 969}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Sofia, Owen, Oliver, James, and Ava. Lily remarked, \"Owen is not a knave\". Sofia was heard saying, \"Owen is a knight and Oliver is a knave\". Owen stated, \"James is a knave if and only if James is a knight\". Oliver asserted: \"Sofia is a knave or Ava is a knave\". James was heard saying, \"Lily is a knave and Ava is a knight\". \"Lily is not a knave\" - Ava. So who is a knight and who is a knave?", "names": ["Lily", "Sofia", "Owen", "Oliver", "James", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, false], "solution_text": "Lily is a knave, Sofia is a knave, Owen is a knave, Oliver is a knight, James is a knave, and Ava is a knave.", "solution_text_format": "(1) Lily is a knave\n(2) Sofia is a knave\n(3) Owen is a knave\n(4) Oliver is a knight\n(5) James is a knave\n(6) Ava is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Owen is not a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that James is a knave if and only if James is a knight.", "Owen cannot be a knave, because this would contradict the claim of Lily that Owen is not a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Owen is not a knave.", "Owen cannot be a knight, because this would contradict the false claim of Lily that Owen is not a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that James is a knave if and only if James is a knight.", "Assume James is a knight. No contradiction is found in their claim that Lily is a knave and Ava is a knight.", "Ava cannot be a knight, because this would contradict the claim of their own that Lily is not a knave.", "Ava cannot be a knave, because this would contradict the claim of James that Lily is a knave and Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Lily is a knave and Ava is a knight.", "Ava cannot be a knight, because this would contradict the false claim of James that Lily is a knave and Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Lily is not a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Oliver is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Owen is a knight and Oliver is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Sofia is a knave or Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('and', ('telling-truth', 2), ('lying', 3)), ('<=>', ('lying', 4), ('telling-truth', 4)), ('or', ('lying', 1), ('lying', 5)), ('and', ('lying', 0), ('telling-truth', 5)), ('not', ('lying', 0)))", "index": 970}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Grace, Matthew, Elizabeth, Michael, and Chloe. \"Elizabeth is a knave or Riley is a knight,\" Riley mentioned. Grace told you that Riley is a knight. Matthew expressed that Elizabeth is a knave and Michael is a knave. Elizabeth told you that Riley is a knave if and only if Grace is a knight. \"Riley is a knight,\" Michael claimed. Chloe said, \"Grace is a knight and Michael is a knight.\" So who is a knight and who is a knave?", "names": ["Riley", "Grace", "Matthew", "Elizabeth", "Michael", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, true], "solution_text": "Riley is a knight, Grace is a knight, Matthew is a knave, Elizabeth is a knave, Michael is a knight, and Chloe is a knight.", "solution_text_format": "(1) Riley is a knight\n(2) Grace is a knight\n(3) Matthew is a knave\n(4) Elizabeth is a knave\n(5) Michael is a knight\n(6) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Elizabeth is a knave or Riley is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Riley is a knave if and only if Grace is a knight.", "Grace cannot be a knight, because this would contradict the claim of Elizabeth that Riley is a knave if and only if Grace is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that Riley is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Riley is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Elizabeth is a knave and Michael is a knave.", "Michael cannot be a knight, because this would contradict the claim of Matthew that Elizabeth is a knave and Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that Riley is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Michael is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Riley is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Grace is a knight and Michael is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 0)), ('telling-truth', 0), ('and', ('lying', 3), ('lying', 4)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('telling-truth', 0), ('and', ('telling-truth', 1), ('telling-truth', 4)))", "index": 971}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, Liam, Sebastian, Victoria, Jackson, and Aria. Penelope remarked, \"Sebastian is a knight or Victoria is a knave\". Liam expressed that Sebastian is a knight or Aria is a knight. Sebastian commented, \"Aria is a knave if and only if Liam is a knave\". Victoria noted, \"If Penelope is a knight then Aria is a knave\". Jackson said that Jackson is a knight or Victoria is a knight. Aria remarked, \"Sebastian is a knave or Jackson is a knave\". So who is a knight and who is a knave?", "names": ["Penelope", "Liam", "Sebastian", "Victoria", "Jackson", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Penelope is a knight, Liam is a knight, Sebastian is a knight, Victoria is a knave, Jackson is a knave, and Aria is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) Liam is a knight\n(3) Sebastian is a knight\n(4) Victoria is a knave\n(5) Jackson is a knave\n(6) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Sebastian is a knight or Victoria is a knave.", "Assume Sebastian is a knight. No contradiction is found in their claim that Aria is a knave if and only if Liam is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Sebastian is a knave or Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Aria that Sebastian is a knave or Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Jackson is a knight or Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that If Penelope is a knight then Aria is a knave.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Penelope is a knight then Aria is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Sebastian is a knight or Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 3)), ('or', ('telling-truth', 2), ('telling-truth', 5)), ('<=>', ('lying', 5), ('lying', 1)), ('->', ('telling-truth', 0), ('lying', 5)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('or', ('lying', 2), ('lying', 4)))", "index": 972}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Charlotte, Sebastian, Elizabeth, Scarlett, and Oliver. \"Charlotte is a knave,\" Ella declared. In a statement by Charlotte: \"Ella is not a knight\". Sebastian told you that If Scarlett is a knight then Charlotte is a knave. Elizabeth said that Sebastian is a knight if and only if Ella is a knave. Scarlett noted, \"If Sebastian is a knight then Ella is a knave\". Oliver remarked, \"If Oliver is a knight then Charlotte is a knight\". So who is a knight and who is a knave?", "names": ["Ella", "Charlotte", "Sebastian", "Elizabeth", "Scarlett", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, true], "solution_text": "Ella is a knave, Charlotte is a knight, Sebastian is a knave, Elizabeth is a knave, Scarlett is a knight, and Oliver is a knight.", "solution_text_format": "(1) Ella is a knave\n(2) Charlotte is a knight\n(3) Sebastian is a knave\n(4) Elizabeth is a knave\n(5) Scarlett is a knight\n(6) Oliver is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Ella that Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Scarlett is a knight then Charlotte is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that If Sebastian is a knight then Ella is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Ella is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight if and only if Ella is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Ella is a knave.", "Oliver cannot be a knight, because this would contradict the claim of their own that If Oliver is a knight then Charlotte is a knight.", "Oliver cannot be a knave, because this would contradict the false claim of their own that If Oliver is a knight then Charlotte is a knight.", "We have exhausted all possibilities for Oliver, Elizabeth, and Scarlett, so let us go back and reconsider Sebastian.", "Sebastian cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knight then Charlotte is a knave.", "We have exhausted all possibilities for Sebastian and Charlotte, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Ella is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Scarlett is a knight then Charlotte is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Sebastian that If Scarlett is a knight then Charlotte is a knave.", "Scarlett cannot be a knave, because this would contradict the false claim of their own that If Sebastian is a knight then Ella is a knave.", "We have exhausted all possibilities for Scarlett, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that If Scarlett is a knight then Charlotte is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that If Sebastian is a knight then Ella is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight if and only if Ella is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Ella is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that If Oliver is a knight then Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('not', ('telling-truth', 0)), ('->', ('telling-truth', 4), ('lying', 1)), ('<=>', ('telling-truth', 2), ('lying', 0)), ('->', ('telling-truth', 2), ('lying', 0)), ('->', ('telling-truth', 5), ('telling-truth', 1)))", "index": 973}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Charlotte, Victoria, Sophia, Daniel, and Avery. Harper was heard saying, \"Victoria is a knight or Daniel is a knave\". Charlotte noted, \"Sophia is a knight or Daniel is a knight\". Victoria commented, \"Daniel is a knave or Sophia is a knave\". \"Harper is a knight,\" Sophia claimed. Daniel noted, \"Victoria is a knight if and only if Charlotte is a knave\". As Avery put it, \"Sophia is a knight if and only if Victoria is a knave\". So who is a knight and who is a knave?", "names": ["Harper", "Charlotte", "Victoria", "Sophia", "Daniel", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Harper is a knight, Charlotte is a knight, Victoria is a knight, Sophia is a knight, Daniel is a knave, and Avery is a knave.", "solution_text_format": "(1) Harper is a knight\n(2) Charlotte is a knight\n(3) Victoria is a knight\n(4) Sophia is a knight\n(5) Daniel is a knave\n(6) Avery is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Harper is a knight. No contradiction is found in their claim that Victoria is a knight or Daniel is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Daniel is a knave or Sophia is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of Daniel that Victoria is a knight if and only if Charlotte is a knave.", "Charlotte cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight or Daniel is a knight.", "We have exhausted all possibilities for Charlotte, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Sophia is a knight or Daniel is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Harper is a knight.", "Avery cannot be a knight, because this would contradict the claim of their own that Sophia is a knight if and only if Victoria is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Victoria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('lying', 4)), ('or', ('telling-truth', 3), ('telling-truth', 4)), ('or', ('lying', 4), ('lying', 3)), ('telling-truth', 0), ('<=>', ('telling-truth', 2), ('lying', 1)), ('<=>', ('telling-truth', 3), ('lying', 2)))", "index": 974}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, James, Jackson, Aurora, Ava, and Amelia. \"Amelia is a knave if and only if Olivia is a knight\" - Olivia. James remarked, \"Jackson is a knave\". \"Ava is a knight and James is a knight\" - Jackson. Aurora stated, \"Ava is a knave\". \"If Olivia is a knight then Aurora is a knave,\" Ava mentioned. Amelia expressed that Olivia is a knave if and only if Olivia is a knight. So who is a knight and who is a knave?", "names": ["Olivia", "James", "Jackson", "Aurora", "Ava", "Amelia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Olivia is a knight, James is a knight, Jackson is a knave, Aurora is a knight, Ava is a knave, and Amelia is a knave.", "solution_text_format": "(1) Olivia is a knight\n(2) James is a knight\n(3) Jackson is a knave\n(4) Aurora is a knight\n(5) Ava is a knave\n(6) Amelia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Olivia is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Olivia that Amelia is a knave if and only if Olivia is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Olivia is a knight.", "Assume James is a knight. No contradiction is found in their claim that Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of James that Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Ava is a knight and James is a knight.", "Ava cannot be a knight, because this would contradict the false claim of Jackson that Ava is a knight and James is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that If Olivia is a knight then Aurora is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('telling-truth', 0)), ('lying', 2), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('lying', 4), ('->', ('telling-truth', 0), ('lying', 3)), ('<=>', ('lying', 0), ('telling-truth', 0)))", "index": 975}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Aurora, Owen, Chloe, Isabella, and Mia. Alexander noted, \"Mia is not a knave\". \"Isabella is a knight if and only if Aurora is a knight,\" Aurora declared. Owen noted, \"Mia is a knave if and only if Owen is a knight\". Chloe commented, \"If Isabella is a knave then Alexander is a knave\". Isabella was heard saying, \"Aurora is a knave and Chloe is a knight\". Mia stated, \"Owen is a knave\". So who is a knight and who is a knave?", "names": ["Alexander", "Aurora", "Owen", "Chloe", "Isabella", "Mia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, false], "solution_text": "Alexander is a knave, Aurora is a knave, Owen is a knight, Chloe is a knight, Isabella is a knight, and Mia is a knave.", "solution_text_format": "(1) Alexander is a knave\n(2) Aurora is a knave\n(3) Owen is a knight\n(4) Chloe is a knight\n(5) Isabella is a knight\n(6) Mia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Mia is not a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Mia is a knave if and only if Owen is a knight.", "Owen cannot be a knave, because this would contradict the false claim of their own that Mia is a knave if and only if Owen is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Alexander that Mia is not a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Mia is not a knave.", "Mia cannot be a knight, because this would contradict the false claim of Alexander that Mia is not a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Mia is a knave if and only if Owen is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Aurora is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Chloe is a knight.", "Isabella cannot be a knave, because this would contradict the claim of Aurora that Isabella is a knight if and only if Aurora is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Aurora is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Aurora is a knave and Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that If Isabella is a knave then Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('<=>', ('lying', 5), ('telling-truth', 2)), ('->', ('lying', 4), ('lying', 0)), ('and', ('lying', 1), ('telling-truth', 3)), ('lying', 2))", "index": 976}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Noah, Jackson, Logan, Grace, and Emma. Chloe remarked, \"Chloe is a knight or Jackson is a knave\". \"If Grace is a knight then Emma is a knight,\" Noah declared. Jackson said that If Chloe is a knave then Grace is a knight. Logan noted, \"Grace is a knight if and only if Emma is a knave\". Grace expressed that Chloe is a knight and Jackson is a knave. Emma remarked, \"Jackson is a knave\". So who is a knight and who is a knave?", "names": ["Chloe", "Noah", "Jackson", "Logan", "Grace", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Chloe is a knight, Noah is a knight, Jackson is a knight, Logan is a knave, Grace is a knave, and Emma is a knave.", "solution_text_format": "(1) Chloe is a knight\n(2) Noah is a knight\n(3) Jackson is a knight\n(4) Logan is a knave\n(5) Grace is a knave\n(6) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that Chloe is a knight or Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that If Chloe is a knave then Grace is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Chloe is a knight and Jackson is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Chloe is a knight and Jackson is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Grace is a knight then Emma is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Jackson is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Jackson is a knave.", "Logan cannot be a knight, because this would contradict the claim of their own that Grace is a knight if and only if Emma is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('lying', 2)), ('->', ('telling-truth', 4), ('telling-truth', 5)), ('->', ('lying', 0), ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('lying', 5)), ('and', ('telling-truth', 0), ('lying', 2)), ('lying', 2))", "index": 977}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Emma, Evelyn, Daniel, Noah, and Ella. In a statement by Victoria: \"Ella is not a knight\". Emma said that Victoria is a knave and Daniel is a knight. \"Victoria is a knight if and only if Emma is a knave,\" Evelyn mentioned. \"Noah is a knight if and only if Victoria is a knave,\" Daniel declared. Noah was heard saying, \"If Emma is a knave then Evelyn is a knight\". Ella said that If Noah is a knave then Noah is a knight. So who is a knight and who is a knave?", "names": ["Victoria", "Emma", "Evelyn", "Daniel", "Noah", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Victoria is a knave, Emma is a knight, Evelyn is a knight, Daniel is a knight, Noah is a knight, and Ella is a knight.", "solution_text_format": "(1) Victoria is a knave\n(2) Emma is a knight\n(3) Evelyn is a knight\n(4) Daniel is a knight\n(5) Noah is a knight\n(6) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that Ella is not a knight.", "Ella cannot be a knight, because this would contradict the claim of Victoria that Ella is not a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that If Noah is a knave then Noah is a knight.", "Noah cannot be a knight, because this would contradict the false claim of Ella that If Noah is a knave then Noah is a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that If Emma is a knave then Evelyn is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Victoria is a knave and Daniel is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Victoria is a knave and Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Noah is a knight if and only if Victoria is a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of Noah that If Emma is a knave then Evelyn is a knight.", "Evelyn cannot be a knave, because this would contradict the false claim of their own that Victoria is a knight if and only if Emma is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the false claim of their own that Noah is a knight if and only if Victoria is a knave.", "We have exhausted all possibilities for Daniel, Emma, Noah, and Ella, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Noah is a knave then Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Emma is a knave then Evelyn is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Victoria is a knave and Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Noah is a knight if and only if Victoria is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('and', ('lying', 0), ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('lying', 1)), ('<=>', ('telling-truth', 4), ('lying', 0)), ('->', ('lying', 1), ('telling-truth', 2)), ('->', ('lying', 4), ('telling-truth', 4)))", "index": 978}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Jack, Alexander, Riley, Aria, and Emily. Emma told you that Jack is a knight and Aria is a knight. As Jack put it, \"Emma is a knave if and only if Emily is a knight\". In a statement by Alexander: \"Emily is a knave if and only if Jack is a knave\". Riley noted, \"Aria is not a knight\". In Aria's words: \"Emily is a knave if and only if Alexander is a knave\". \"Jack is not a knight,\" Emily mentioned. So who is a knight and who is a knave?", "names": ["Emma", "Jack", "Alexander", "Riley", "Aria", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false], "solution_text": "Emma is a knight, Jack is a knight, Alexander is a knave, Riley is a knave, Aria is a knight, and Emily is a knave.", "solution_text_format": "(1) Emma is a knight\n(2) Jack is a knight\n(3) Alexander is a knave\n(4) Riley is a knave\n(5) Aria is a knight\n(6) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Jack is a knight and Aria is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Emma is a knave if and only if Emily is a knight.", "Emily cannot be a knight, because this would contradict the claim of Jack that Emma is a knave if and only if Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Jack is not a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Emily is a knave if and only if Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Emily is a knave if and only if Jack is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Emily is a knave if and only if Jack is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Aria is not a knight.", "Assume Riley is a knave. No contradiction is found in their false claim that Aria is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 4)), ('<=>', ('lying', 0), ('telling-truth', 5)), ('<=>', ('lying', 5), ('lying', 1)), ('not', ('telling-truth', 4)), ('<=>', ('lying', 5), ('lying', 2)), ('not', ('telling-truth', 1)))", "index": 979}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Joseph, Benjamin, Lucas, Isabella, and Ethan. Ava told you that Joseph is a knave if and only if Ava is a knight. Joseph told you that Ava is a knight if and only if Isabella is a knave. Benjamin remarked, \"Ava is a knight\". Lucas said, \"Isabella is a knave and Ava is a knave.\" In Isabella's words: \"Isabella is a knight and Benjamin is a knave\". Ethan noted, \"Ava is a knave\". So who is a knight and who is a knave?", "names": ["Ava", "Joseph", "Benjamin", "Lucas", "Isabella", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "Ava is a knave, Joseph is a knave, Benjamin is a knave, Lucas is a knight, Isabella is a knave, and Ethan is a knight.", "solution_text_format": "(1) Ava is a knave\n(2) Joseph is a knave\n(3) Benjamin is a knave\n(4) Lucas is a knight\n(5) Isabella is a knave\n(6) Ethan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Ava is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Ava that Joseph is a knave if and only if Ava is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Isabella is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Isabella is a knight and Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Isabella that Isabella is a knight and Benjamin is a knave.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that Ava is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Isabella.", "Isabella cannot be a knave, because this would contradict the false claim of Joseph that Ava is a knight if and only if Isabella is a knave.", "We have exhausted all possibilities for Isabella and Joseph, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Ava is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Ava that Joseph is a knave if and only if Ava is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the false claim of Joseph that Ava is a knight if and only if Isabella is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Isabella is a knight and Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Ava is a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Ava is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Isabella is a knave and Ava is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 0)), ('<=>', ('telling-truth', 0), ('lying', 4)), ('telling-truth', 0), ('and', ('lying', 4), ('lying', 0)), ('and', ('telling-truth', 4), ('lying', 2)), ('lying', 0))", "index": 980}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Aria, Aiden, Grace, Ava, and Lily. \"Lily is a knight if and only if Ava is a knight\" - Lucas. In Aria's words: \"Lily is a knave or Aiden is a knight\". \"Lucas is not a knight,\" Aiden claimed. Grace remarked, \"Aiden is a knave or Grace is a knight\". Ava commented, \"Lily is a knight or Aria is a knave\". Lily was heard saying, \"Lucas is a knave if and only if Grace is a knight\". So who is a knight and who is a knave?", "names": ["Lucas", "Aria", "Aiden", "Grace", "Ava", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Lucas is a knight, Aria is a knight, Aiden is a knave, Grace is a knight, Ava is a knave, and Lily is a knave.", "solution_text_format": "(1) Lucas is a knight\n(2) Aria is a knight\n(3) Aiden is a knave\n(4) Grace is a knight\n(5) Ava is a knave\n(6) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Lily is a knight if and only if Ava is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Grace is a knight.", "Grace cannot be a knight, because this would contradict the claim of Lily that Lucas is a knave if and only if Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Aiden is a knave or Grace is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Lucas is not a knight.", "Aiden cannot be a knave, because this would contradict the false claim of Grace that Aiden is a knave or Grace is a knight.", "We have exhausted all possibilities for Aiden and Grace, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Aiden is a knave or Grace is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that Lucas is not a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Lucas is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Lucas that Lily is a knight if and only if Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Lily is a knight or Aria is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Lily is a knave or Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('or', ('lying', 5), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('or', ('lying', 2), ('telling-truth', 3)), ('or', ('telling-truth', 5), ('lying', 1)), ('<=>', ('lying', 0), ('telling-truth', 3)))", "index": 981}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Michael, Lily, Riley, Avery, and Chloe. James commented, \"Lily is a knave\". Michael told you that Avery is not a knight. \"Chloe is a knight or James is a knight,\" Lily claimed. In a statement by Riley: \"James is a knight or Avery is a knight\". Avery said, \"James is a knave.\" \"Lily is a knave if and only if Avery is a knave,\" Chloe mentioned. So who is a knight and who is a knave?", "names": ["James", "Michael", "Lily", "Riley", "Avery", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "James is a knave, Michael is a knave, Lily is a knight, Riley is a knight, Avery is a knight, and Chloe is a knight.", "solution_text_format": "(1) James is a knave\n(2) Michael is a knave\n(3) Lily is a knight\n(4) Riley is a knight\n(5) Avery is a knight\n(6) Chloe is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of James that Lily is a knave.", "Lily cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight or James is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Chloe is a knight or James is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Lily is a knave if and only if Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that James is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Avery is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Assume Riley is a knight. No contradiction is found in their claim that James is a knight or Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('not', ('telling-truth', 4)), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 4)), ('lying', 0), ('<=>', ('lying', 2), ('lying', 4)))", "index": 982}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Avery, Ethan, Alexander, Penelope, and Abigail. Benjamin expressed that Benjamin is a knight if and only if Avery is a knave. Avery told you that Ethan is a knave or Benjamin is a knight. As Ethan put it, \"Benjamin is not a knight\". Alexander told you that If Abigail is a knave then Benjamin is a knight. In Penelope's words: \"Avery is a knave if and only if Alexander is a knight\". According to Abigail, \"Avery is not a knight\". So who is a knight and who is a knave?", "names": ["Benjamin", "Avery", "Ethan", "Alexander", "Penelope", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Benjamin is a knave, Avery is a knave, Ethan is a knight, Alexander is a knight, Penelope is a knight, and Abigail is a knight.", "solution_text_format": "(1) Benjamin is a knave\n(2) Avery is a knave\n(3) Ethan is a knight\n(4) Alexander is a knight\n(5) Penelope is a knight\n(6) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Benjamin that Benjamin is a knight if and only if Avery is a knave.", "Avery cannot be a knave, because this would contradict the false claim of their own that Ethan is a knave or Benjamin is a knight.", "We have exhausted all possibilities for Avery, so let us go back and reconsider Benjamin.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Avery is a knave.", "Avery cannot be a knight, because this would contradict the false claim of Benjamin that Benjamin is a knight if and only if Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that Ethan is a knave or Benjamin is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Abigail is a knave then Benjamin is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Avery is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Avery is a knave if and only if Alexander is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 0), ('lying', 1)), ('or', ('lying', 2), ('telling-truth', 0)), ('not', ('telling-truth', 0)), ('->', ('lying', 5), ('telling-truth', 0)), ('<=>', ('lying', 1), ('telling-truth', 3)), ('not', ('telling-truth', 1)))", "index": 983}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Victoria, Evelyn, Benjamin, Liam, and James. As Aiden put it, \"Benjamin is not a knight\". Victoria expressed that Aiden is a knight and Benjamin is a knight. \"Evelyn is a knight or Liam is a knight,\" Evelyn claimed. In a statement by Benjamin: \"Evelyn is not a knight\". Liam noted, \"Victoria is not a knight\". \"If James is a knight then Benjamin is a knave,\" James claimed. So who is a knight and who is a knave?", "names": ["Aiden", "Victoria", "Evelyn", "Benjamin", "Liam", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Aiden is a knight, Victoria is a knave, Evelyn is a knight, Benjamin is a knave, Liam is a knight, and James is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Victoria is a knave\n(3) Evelyn is a knight\n(4) Benjamin is a knave\n(5) Liam is a knight\n(6) James is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Aiden that Benjamin is not a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Evelyn is a knight or Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Benjamin is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Aiden is a knight and Benjamin is a knight.", "Assume James is a knight. No contradiction is found in their claim that If James is a knight then Benjamin is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 3)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('or', ('telling-truth', 2), ('telling-truth', 4)), ('not', ('telling-truth', 2)), ('not', ('telling-truth', 1)), ('->', ('telling-truth', 5), ('lying', 3)))", "index": 984}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Emma, Michael, Aurora, Scarlett, and Elizabeth. \"Michael is a knave and Aurora is a knave,\" Henry mentioned. Emma said, \"If Henry is a knight then Elizabeth is a knave.\" Michael remarked, \"Emma is a knight or Emma is a knave\". Aurora remarked, \"Emma is not a knight\". Scarlett noted, \"Aurora is a knave\". \"Scarlett is a knight and Michael is a knight,\" Elizabeth mentioned. So who is a knight and who is a knave?", "names": ["Henry", "Emma", "Michael", "Aurora", "Scarlett", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Henry is a knave, Emma is a knight, Michael is a knight, Aurora is a knave, Scarlett is a knight, and Elizabeth is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Emma is a knight\n(3) Michael is a knight\n(4) Aurora is a knave\n(5) Scarlett is a knight\n(6) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Michael is a knave and Aurora is a knave.", "Michael cannot be a knight, because this would contradict the claim of Henry that Michael is a knave and Aurora is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that Emma is a knight or Emma is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Michael is a knave and Aurora is a knave.", "Assume Michael is a knight. No contradiction is found in their claim that Emma is a knight or Emma is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that If Henry is a knight then Elizabeth is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Scarlett is a knight and Michael is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aurora is a knave.", "Aurora cannot be a knight, because this would contradict the claim of their own that Emma is not a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Emma is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 3)), ('->', ('telling-truth', 0), ('lying', 5)), ('or', ('telling-truth', 1), ('lying', 1)), ('not', ('telling-truth', 1)), ('lying', 3), ('and', ('telling-truth', 4), ('telling-truth', 2)))", "index": 985}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Sofia, Owen, Joseph, Harper, and Noah. In a statement by Grace: \"Sofia is a knight\". Sofia expressed that Owen is a knave if and only if Noah is a knave. Owen told you that Sofia is a knight and Harper is a knight. \"Noah is a knave if and only if Harper is a knight,\" Joseph mentioned. According to Harper, \"Joseph is a knight if and only if Joseph is a knave\". According to Noah, \"Grace is a knight if and only if Grace is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Sofia", "Owen", "Joseph", "Harper", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Grace is a knight, Sofia is a knight, Owen is a knave, Joseph is a knave, Harper is a knave, and Noah is a knave.", "solution_text_format": "(1) Grace is a knight\n(2) Sofia is a knight\n(3) Owen is a knave\n(4) Joseph is a knave\n(5) Harper is a knave\n(6) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Sofia is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Owen is a knave if and only if Noah is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Sofia is a knight and Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that Joseph is a knight if and only if Joseph is a knave.", "Harper cannot be a knave, because this would contradict the claim of Owen that Sofia is a knight and Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Sofia is a knight and Harper is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Owen that Sofia is a knight and Harper is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Joseph is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Noah is a knave if and only if Harper is a knight.", "Noah cannot be a knight, because this would contradict the claim of Sofia that Owen is a knave if and only if Noah is a knave.", "Noah cannot be a knave, because this would contradict the claim of Joseph that Noah is a knave if and only if Harper is a knight.", "We have exhausted all possibilities for Noah, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Harper is a knight.", "Noah cannot be a knight, because this would contradict the claim of Sofia that Owen is a knave if and only if Noah is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Grace is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('<=>', ('lying', 2), ('lying', 5)), ('and', ('telling-truth', 1), ('telling-truth', 4)), ('<=>', ('lying', 5), ('telling-truth', 4)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('<=>', ('telling-truth', 0), ('lying', 0)))", "index": 986}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Owen, Emma, Penelope, Sofia, and Victoria. Lily expressed that Emma is a knave or Lily is a knight. Owen asserted: \"Lily is a knave and Penelope is a knave\". Emma said that Victoria is a knight. Penelope told you that If Owen is a knight then Sofia is a knight. Sofia was heard saying, \"Lily is a knave\". Victoria said that Penelope is not a knight. So who is a knight and who is a knave?", "names": ["Lily", "Owen", "Emma", "Penelope", "Sofia", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false], "solution_text": "Lily is a knight, Owen is a knave, Emma is a knave, Penelope is a knight, Sofia is a knave, and Victoria is a knave.", "solution_text_format": "(1) Lily is a knight\n(2) Owen is a knave\n(3) Emma is a knave\n(4) Penelope is a knight\n(5) Sofia is a knave\n(6) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Emma is a knave or Lily is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Victoria that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that If Owen is a knight then Sofia is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Penelope is a knave.", "Owen cannot be a knave, because this would contradict the false claim of Penelope that If Owen is a knight then Sofia is a knight.", "We have exhausted all possibilities for Owen and Penelope, so let us go back and reconsider Victoria.", "Victoria cannot be a knave, because this would contradict the claim of Emma that Victoria is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Emma that Victoria is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Owen is a knight then Sofia is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Lily is a knave and Penelope is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Lily is a knave and Penelope is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Lily is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Lily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 0)), ('and', ('lying', 0), ('lying', 3)), ('telling-truth', 5), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('lying', 0), ('not', ('telling-truth', 3)))", "index": 987}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Mason, David, Benjamin, Lucas, and Samuel. \"Lucas is a knave\" - Amelia. Mason remarked, \"Lucas is a knight\". In David's words: \"If Mason is a knight then Lucas is a knight\". Benjamin told you that Mason is not a knight. Lucas was heard saying, \"If Mason is a knave then Amelia is a knight\". \"If Mason is a knight then Amelia is a knave,\" Samuel mentioned. So who is a knight and who is a knave?", "names": ["Amelia", "Mason", "David", "Benjamin", "Lucas", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Amelia is a knave, Mason is a knight, David is a knight, Benjamin is a knave, Lucas is a knight, and Samuel is a knight.", "solution_text_format": "(1) Amelia is a knave\n(2) Mason is a knight\n(3) David is a knight\n(4) Benjamin is a knave\n(5) Lucas is a knight\n(6) Samuel is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of Amelia that Lucas is a knave.", "Lucas cannot be a knave, because this would contradict the false claim of their own that If Mason is a knave then Amelia is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Mason is a knave then Amelia is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Lucas is a knight.", "Assume David is a knight. No contradiction is found in their claim that If Mason is a knight then Lucas is a knight.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Mason is not a knight.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Mason is not a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that If Mason is a knight then Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('telling-truth', 4), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('not', ('telling-truth', 1)), ('->', ('lying', 1), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('lying', 0)))", "index": 988}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Mia, Michael, Jack, Joseph, and Victoria. Ella said, \"Joseph is a knave if and only if Michael is a knave.\" In a statement by Mia: \"Jack is a knight\". Michael remarked, \"Joseph is not a knight\". In a statement by Jack: \"Mia is a knight or Joseph is a knave\". Joseph expressed that Mia is a knave if and only if Ella is a knight. As Victoria put it, \"Mia is not a knave\". So who is a knight and who is a knave?", "names": ["Ella", "Mia", "Michael", "Jack", "Joseph", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Ella is a knave, Mia is a knight, Michael is a knave, Jack is a knight, Joseph is a knight, and Victoria is a knight.", "solution_text_format": "(1) Ella is a knave\n(2) Mia is a knight\n(3) Michael is a knave\n(4) Jack is a knight\n(5) Joseph is a knight\n(6) Victoria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Michael is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Mia is a knave if and only if Ella is a knight.", "Mia cannot be a knight, because this would contradict the claim of Joseph that Mia is a knave if and only if Ella is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Mia that Jack is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Mia is a knight or Joseph is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Joseph is not a knight.", "Michael cannot be a knave, because this would contradict the claim of Ella that Joseph is a knave if and only if Michael is a knave.", "We have exhausted all possibilities for Michael, Jack, and Mia, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Ella is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Mia is a knight or Joseph is a knave.", "Michael cannot be a knight, because this would contradict the claim of Ella that Joseph is a knave if and only if Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that Joseph is not a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Mia that Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of Joseph that Mia is a knave if and only if Ella is a knight.", "We have exhausted all possibilities for Mia and Joseph, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Michael is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Mia is a knave if and only if Ella is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Mia is a knight or Joseph is a knave.", "Michael cannot be a knight, because this would contradict the false claim of Ella that Joseph is a knave if and only if Michael is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Joseph is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Mia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 4), ('lying', 2)), ('telling-truth', 3), ('not', ('telling-truth', 4)), ('or', ('telling-truth', 1), ('lying', 4)), ('<=>', ('lying', 1), ('telling-truth', 0)), ('not', ('lying', 1)))", "index": 989}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Victoria, Emma, Samuel, Sophia, and Jacob. Scarlett asserted: \"Sophia is a knave or Emma is a knight\". \"Sophia is a knave or Jacob is a knight,\" Victoria claimed. Emma said, \"Scarlett is a knave.\" \"Emma is a knave if and only if Samuel is a knight\" - Samuel. \"Samuel is a knave,\" Sophia mentioned. Jacob told you that Emma is a knave or Samuel is a knave. So who is a knight and who is a knave?", "names": ["Scarlett", "Victoria", "Emma", "Samuel", "Sophia", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Scarlett is a knight, Victoria is a knight, Emma is a knave, Samuel is a knight, Sophia is a knave, and Jacob is a knight.", "solution_text_format": "(1) Scarlett is a knight\n(2) Victoria is a knight\n(3) Emma is a knave\n(4) Samuel is a knight\n(5) Sophia is a knave\n(6) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that Sophia is a knave or Emma is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Samuel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Sophia that Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Samuel is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave.", "Emma cannot be a knave, because this would contradict the claim of Scarlett that Sophia is a knave or Emma is a knight.", "We have exhausted all possibilities for Emma and Samuel, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Samuel is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Emma is a knave if and only if Samuel is a knight.", "Emma cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Scarlett is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Sophia is a knave or Jacob is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Emma is a knave or Samuel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 2)), ('or', ('lying', 4), ('telling-truth', 5)), ('lying', 0), ('<=>', ('lying', 2), ('telling-truth', 3)), ('lying', 3), ('or', ('lying', 2), ('lying', 3)))", "index": 990}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Penelope, Oliver, Chloe, Noah, and Sofia. James asserted: \"Chloe is a knave if and only if Penelope is a knave\". As Penelope put it, \"If James is a knight then Noah is a knight\". Oliver expressed that Chloe is a knave. \"Penelope is not a knight\" - Chloe. Noah was heard saying, \"If Chloe is a knight then James is a knight\". As Sofia put it, \"James is a knight or Noah is a knight\". So who is a knight and who is a knave?", "names": ["James", "Penelope", "Oliver", "Chloe", "Noah", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "James is a knave, Penelope is a knight, Oliver is a knight, Chloe is a knave, Noah is a knight, and Sofia is a knight.", "solution_text_format": "(1) James is a knave\n(2) Penelope is a knight\n(3) Oliver is a knight\n(4) Chloe is a knave\n(5) Noah is a knight\n(6) Sofia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Penelope is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Chloe that Penelope is not a knight.", "Penelope cannot be a knave, because this would contradict the claim of James that Chloe is a knave if and only if Penelope is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of James that Chloe is a knave if and only if Penelope is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of Chloe that Penelope is not a knight.", "We have exhausted all possibilities for Penelope and Chloe, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Chloe is a knave if and only if Penelope is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the false claim of James that Chloe is a knave if and only if Penelope is a knave.", "Penelope cannot be a knave, because this would contradict the false claim of their own that If James is a knight then Noah is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If James is a knight then Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If Chloe is a knight then James is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Chloe is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that James is a knight or Noah is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 1)), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('lying', 3), ('not', ('telling-truth', 1)), ('->', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('telling-truth', 4)))", "index": 991}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Aiden, Daniel, Ethan, Abigail, and Victoria. \"If Daniel is a knight then Scarlett is a knight,\" Scarlett mentioned. Aiden said that If Aiden is a knight then Abigail is a knave. \"Victoria is a knight or Scarlett is a knight,\" Daniel mentioned. Ethan noted, \"If Daniel is a knave then Abigail is a knight\". According to Abigail, \"Scarlett is a knave and Abigail is a knight\". According to Victoria, \"Abigail is a knight if and only if Aiden is a knight\". So who is a knight and who is a knave?", "names": ["Scarlett", "Aiden", "Daniel", "Ethan", "Abigail", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Scarlett is a knight, Aiden is a knight, Daniel is a knight, Ethan is a knight, Abigail is a knave, and Victoria is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Aiden is a knight\n(3) Daniel is a knight\n(4) Ethan is a knight\n(5) Abigail is a knave\n(6) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that If Daniel is a knight then Scarlett is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Victoria is a knight or Scarlett is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Aiden is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave and Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Scarlett is a knave and Abigail is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Victoria that Abigail is a knight if and only if Aiden is a knight.", "Aiden cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knight then Abigail is a knave.", "We have exhausted all possibilities for Aiden and Abigail, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Aiden is a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Scarlett is a knave and Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Scarlett is a knave and Abigail is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Aiden is a knight then Abigail is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Daniel is a knave then Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('lying', 4)), ('or', ('telling-truth', 5), ('telling-truth', 0)), ('->', ('lying', 2), ('telling-truth', 4)), ('and', ('lying', 0), ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)))", "index": 992}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Lily, Emma, Ella, Aiden, and Jackson. In Sofia's words: \"Aiden is a knight if and only if Jackson is a knave\". \"If Aiden is a knave then Ella is a knave,\" Lily mentioned. Emma told you that Jackson is a knight or Ella is a knight. \"Lily is a knight,\" Ella claimed. \"Lily is a knight if and only if Ella is a knight,\" Aiden declared. Jackson noted, \"If Emma is a knave then Emma is a knight\". So who is a knight and who is a knave?", "names": ["Sofia", "Lily", "Emma", "Ella", "Aiden", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Sofia is a knave, Lily is a knight, Emma is a knight, Ella is a knight, Aiden is a knight, and Jackson is a knight.", "solution_text_format": "(1) Sofia is a knave\n(2) Lily is a knight\n(3) Emma is a knight\n(4) Ella is a knight\n(5) Aiden is a knight\n(6) Jackson is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sofia is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Jackson is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Lily is a knight if and only if Ella is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Aiden is a knave then Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Lily is a knight.", "Jackson cannot be a knight, because this would contradict the claim of Sofia that Aiden is a knight if and only if Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that If Emma is a knave then Emma is a knight.", "Emma cannot be a knight, because this would contradict the false claim of Jackson that If Emma is a knave then Emma is a knight.", "Emma cannot be a knave, because this would contradict the false claim of their own that Jackson is a knight or Ella is a knight.", "We have exhausted all possibilities for Emma and Jackson, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that Lily is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knave then Ella is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Ella is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Aiden is a knave then Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of Lily that If Aiden is a knave then Ella is a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that Lily is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that If Aiden is a knave then Ella is a knave.", "Ella cannot be a knight, because this would contradict the claim of their own that Lily is a knight.", "Ella cannot be a knave, because this would contradict the false claim of Lily that If Aiden is a knave then Ella is a knave.", "We have exhausted all possibilities for Ella, Lily, and Aiden, so let us go back and reconsider Sofia.", "Assume Sofia is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Jackson is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Lily is a knight if and only if Ella is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Aiden is a knave then Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Lily is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that If Emma is a knave then Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Jackson is a knight or Ella is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('lying', 5)), ('->', ('lying', 4), ('lying', 3)), ('or', ('telling-truth', 5), ('telling-truth', 3)), ('telling-truth', 1), ('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('->', ('lying', 2), ('telling-truth', 2)))", "index": 993}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Joseph, Aiden, Emily, Jack, and Owen. Evelyn asserted: \"Owen is a knight and Emily is a knight\". Joseph said that Owen is a knight. \"Owen is a knight or Evelyn is a knave,\" Aiden claimed. Emily told you that Jack is a knight and Jack is a knave. In a statement by Jack: \"Owen is a knight and Owen is a knave\". As Owen put it, \"Aiden is a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "Joseph", "Aiden", "Emily", "Jack", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Evelyn is a knave, Joseph is a knight, Aiden is a knight, Emily is a knave, Jack is a knave, and Owen is a knight.", "solution_text_format": "(1) Evelyn is a knave\n(2) Joseph is a knight\n(3) Aiden is a knight\n(4) Emily is a knave\n(5) Jack is a knave\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Owen is a knight and Emily is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Owen is a knight or Evelyn is a knave.", "Emily cannot be a knight, because this would contradict the claim of their own that Jack is a knight and Jack is a knave.", "Emily cannot be a knave, because this would contradict the claim of Evelyn that Owen is a knight and Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the false claim of their own that Owen is a knight or Evelyn is a knave.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the claim of Evelyn that Owen is a knight and Emily is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Owen is a knight and Emily is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Owen is a knight or Evelyn is a knave.", "Emily cannot be a knight, because this would contradict the false claim of Evelyn that Owen is a knight and Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Jack is a knight and Jack is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Owen is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Owen is a knight and Owen is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 3)), ('telling-truth', 5), ('or', ('telling-truth', 5), ('lying', 0)), ('and', ('telling-truth', 4), ('lying', 4)), ('and', ('telling-truth', 5), ('lying', 5)), ('telling-truth', 2))", "index": 994}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Avery, Emma, Noah, Sofia, and Aiden. Henry expressed that Sofia is a knight if and only if Emma is a knave. As Avery put it, \"Aiden is not a knight\". In a statement by Emma: \"Sofia is a knight\". Noah remarked, \"Emma is a knave or Aiden is a knave\". Sofia expressed that Henry is not a knave. Aiden said that If Emma is a knight then Aiden is a knight. So who is a knight and who is a knave?", "names": ["Henry", "Avery", "Emma", "Noah", "Sofia", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "Henry is a knave, Avery is a knave, Emma is a knave, Noah is a knight, Sofia is a knave, and Aiden is a knight.", "solution_text_format": "(1) Henry is a knave\n(2) Avery is a knave\n(3) Emma is a knave\n(4) Noah is a knight\n(5) Sofia is a knave\n(6) Aiden is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Emma is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Henry is not a knave.", "Emma cannot be a knight, because this would contradict the claim of Henry that Sofia is a knight if and only if Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight.", "We have exhausted all possibilities for Emma, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Henry is not a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Henry.", "Assume Henry is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Emma is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Henry is not a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Henry is not a knave.", "Emma cannot be a knight, because this would contradict the false claim of Henry that Sofia is a knight if and only if Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Sofia is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Aiden is not a knight.", "Aiden cannot be a knight, because this would contradict the claim of Avery that Aiden is not a knight.", "Aiden cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Aiden is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Aiden is not a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that If Emma is a knight then Aiden is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Emma is a knave or Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('lying', 2)), ('not', ('telling-truth', 5)), ('telling-truth', 4), ('or', ('lying', 2), ('lying', 5)), ('not', ('lying', 0)), ('->', ('telling-truth', 2), ('telling-truth', 5)))", "index": 995}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Lily, Ava, Penelope, Jackson, and Benjamin. Samuel stated, \"Lily is a knave or Penelope is a knight\". Lily stated, \"Penelope is not a knave\". Ava asserted: \"If Lily is a knight then Jackson is a knave\". Penelope said that Ava is not a knight. Jackson commented, \"Benjamin is not a knight\". Benjamin said that If Jackson is a knight then Samuel is a knight. So who is a knight and who is a knave?", "names": ["Samuel", "Lily", "Ava", "Penelope", "Jackson", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Samuel is a knight, Lily is a knave, Ava is a knight, Penelope is a knave, Jackson is a knave, and Benjamin is a knight.", "solution_text_format": "(1) Samuel is a knight\n(2) Lily is a knave\n(3) Ava is a knight\n(4) Penelope is a knave\n(5) Jackson is a knave\n(6) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Samuel is a knight. No contradiction is found in their claim that Lily is a knave or Penelope is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Ava is not a knight.", "Ava cannot be a knight, because this would contradict the claim of Penelope that Ava is not a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that If Lily is a knight then Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Jackson that Benjamin is not a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knight then Samuel is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Jackson.", "Jackson cannot be a knave, because this would contradict the false claim of Ava that If Lily is a knight then Jackson is a knave.", "We have exhausted all possibilities for Jackson and Ava, so let us go back and reconsider Penelope.", "Penelope cannot be a knave, because this would contradict the claim of Samuel that Lily is a knave or Penelope is a knight.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider Lily.", "Assume Lily is a knave. No contradiction is found in their false claim that Penelope is not a knave.", "Penelope cannot be a knight, because this would contradict the false claim of Lily that Penelope is not a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Ava is a knight. No contradiction is found in their claim that If Lily is a knight then Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Benjamin is not a knight.", "Benjamin cannot be a knight, because this would contradict the claim of Jackson that Benjamin is not a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knight then Samuel is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Benjamin is not a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Jackson is a knight then Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 3)), ('not', ('lying', 3)), ('->', ('telling-truth', 1), ('lying', 4)), ('not', ('telling-truth', 2)), ('not', ('telling-truth', 5)), ('->', ('telling-truth', 4), ('telling-truth', 0)))", "index": 996}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Matthew, Emily, David, Zoey, and Lily. \"Matthew is not a knave\" - Avery. Matthew said that David is a knight or Zoey is a knave. Emily commented, \"If Emily is a knight then Avery is a knight\". David said, \"Avery is a knave and Matthew is a knave.\" Zoey asserted: \"Lily is not a knight\". According to Lily, \"If David is a knight then Zoey is a knight\". So who is a knight and who is a knave?", "names": ["Avery", "Matthew", "Emily", "David", "Zoey", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Avery is a knight, Matthew is a knight, Emily is a knight, David is a knave, Zoey is a knave, and Lily is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Matthew is a knight\n(3) Emily is a knight\n(4) David is a knave\n(5) Zoey is a knave\n(6) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that David is a knight or Zoey is a knave.", "David cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Matthew is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Avery is a knave and Matthew is a knave.", "Zoey cannot be a knight, because this would contradict the claim of Matthew that David is a knight or Zoey is a knave.", "Assume Zoey is a knave. No contradiction is found in their false claim that Lily is not a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If David is a knight then Zoey is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Emily is a knight then Avery is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('or', ('telling-truth', 3), ('lying', 4)), ('->', ('telling-truth', 2), ('telling-truth', 0)), ('and', ('lying', 0), ('lying', 1)), ('not', ('telling-truth', 5)), ('->', ('telling-truth', 3), ('telling-truth', 4)))", "index": 997}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Jack, Aiden, Joseph, Owen, and Mason. According to Liam, \"Mason is a knight\". Jack was heard saying, \"Aiden is a knight and Mason is a knight\". \"Owen is a knight if and only if Joseph is a knight,\" Aiden claimed. Joseph stated, \"Owen is not a knight\". According to Owen, \"If Liam is a knave then Liam is a knight\". Mason noted, \"Aiden is a knave if and only if Jack is a knave\". So who is a knight and who is a knave?", "names": ["Liam", "Jack", "Aiden", "Joseph", "Owen", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true], "solution_text": "Liam is a knight, Jack is a knave, Aiden is a knave, Joseph is a knave, Owen is a knight, and Mason is a knight.", "solution_text_format": "(1) Liam is a knight\n(2) Jack is a knave\n(3) Aiden is a knave\n(4) Joseph is a knave\n(5) Owen is a knight\n(6) Mason is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Mason is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Jack is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Owen is a knight if and only if Joseph is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Liam is a knave then Liam is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Owen is not a knight.", "Joseph cannot be a knave, because this would contradict the claim of Aiden that Owen is a knight if and only if Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Owen.", "Owen cannot be a knave, because this would contradict the false claim of their own that If Liam is a knave then Liam is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Joseph is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that If Liam is a knave then Liam is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Aiden that Owen is a knight if and only if Joseph is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Jack cannot be a knight, because this would contradict the claim of their own that Aiden is a knight and Mason is a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Aiden is a knight and Mason is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 5), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('<=>', ('telling-truth', 4), ('telling-truth', 3)), ('not', ('telling-truth', 4)), ('->', ('lying', 0), ('telling-truth', 0)), ('<=>', ('lying', 2), ('lying', 1)))", "index": 998}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Amelia, Emily, Lucas, Abigail, and Aurora. \"Lucas is a knight,\" Ethan declared. Amelia expressed that Emily is a knight or Emily is a knave. Emily noted, \"Ethan is a knave if and only if Abigail is a knight\". Lucas asserted: \"Abigail is a knave and Amelia is a knave\". Abigail told you that Aurora is not a knave. \"If Ethan is a knave then Lucas is a knave\" - Aurora. So who is a knight and who is a knave?", "names": ["Ethan", "Amelia", "Emily", "Lucas", "Abigail", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Ethan is a knave, Amelia is a knight, Emily is a knight, Lucas is a knave, Abigail is a knight, and Aurora is a knight.", "solution_text_format": "(1) Ethan is a knave\n(2) Amelia is a knight\n(3) Emily is a knight\n(4) Lucas is a knave\n(5) Abigail is a knight\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Lucas is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Abigail is a knave and Amelia is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Lucas that Abigail is a knave and Amelia is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aurora is not a knave.", "Aurora cannot be a knight, because this would contradict the false claim of Abigail that Aurora is not a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Ethan is a knave then Lucas is a knave.", "We have exhausted all possibilities for Aurora and Abigail, so let us go back and reconsider Lucas.", "Lucas cannot be a knave, because this would contradict the claim of Ethan that Lucas is a knight.", "We have exhausted all possibilities for Lucas, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Lucas is a knight.", "Lucas cannot be a knight, because this would contradict the false claim of Ethan that Lucas is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Abigail is a knave and Amelia is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Ethan is a knave then Lucas is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Emily is a knight or Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('or', ('telling-truth', 2), ('lying', 2)), ('<=>', ('lying', 0), ('telling-truth', 4)), ('and', ('lying', 4), ('lying', 1)), ('not', ('lying', 5)), ('->', ('lying', 0), ('lying', 3)))", "index": 999}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Jackson, Henry, Scarlett, Olivia, and David. Benjamin commented, \"Scarlett is a knave and Henry is a knight\". \"Olivia is a knight if and only if Benjamin is a knave,\" Jackson declared. According to Henry, \"Olivia is not a knight\". Scarlett asserted: \"Jackson is a knight if and only if Henry is a knave\". Olivia commented, \"Scarlett is a knave if and only if Henry is a knave\". David stated, \"Henry is a knave if and only if Jackson is a knave\". So who is a knight and who is a knave?", "names": ["Benjamin", "Jackson", "Henry", "Scarlett", "Olivia", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Benjamin is a knight, Jackson is a knight, Henry is a knight, Scarlett is a knave, Olivia is a knave, and David is a knight.", "solution_text_format": "(1) Benjamin is a knight\n(2) Jackson is a knight\n(3) Henry is a knight\n(4) Scarlett is a knave\n(5) Olivia is a knave\n(6) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Benjamin is a knight. No contradiction is found in their claim that Scarlett is a knave and Henry is a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Benjamin that Scarlett is a knave and Henry is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Henry is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Benjamin is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Jackson that Olivia is a knight if and only if Benjamin is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Henry is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Olivia is not a knight.", "Assume David is a knight. No contradiction is found in their claim that Henry is a knave if and only if Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 3), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('lying', 0)), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 1), ('lying', 2)), ('<=>', ('lying', 3), ('lying', 2)), ('<=>', ('lying', 2), ('lying', 1)))", "index": 1000}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Abigail, Aiden, Jack, Harper, and Oliver. Ava asserted: \"Abigail is a knave or Jack is a knight\". \"If Harper is a knight then Aiden is a knave,\" Abigail claimed. Aiden stated, \"If Harper is a knight then Ava is a knave\". Jack noted, \"Harper is a knave if and only if Aiden is a knight\". Harper asserted: \"Oliver is not a knight\". Oliver expressed that Oliver is a knight and Harper is a knight. So who is a knight and who is a knave?", "names": ["Ava", "Abigail", "Aiden", "Jack", "Harper", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "Ava is a knight, Abigail is a knight, Aiden is a knave, Jack is a knight, Harper is a knight, and Oliver is a knave.", "solution_text_format": "(1) Ava is a knight\n(2) Abigail is a knight\n(3) Aiden is a knave\n(4) Jack is a knight\n(5) Harper is a knight\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Abigail is a knave or Jack is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Harper is a knight then Aiden is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Oliver is not a knight.", "Oliver cannot be a knight, because this would contradict the claim of Harper that Oliver is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Oliver is a knight and Harper is a knight.", "Aiden cannot be a knight, because this would contradict the claim of Abigail that If Harper is a knight then Aiden is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Harper is a knight then Ava is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Harper is a knave if and only if Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 3)), ('->', ('telling-truth', 4), ('lying', 2)), ('->', ('telling-truth', 4), ('lying', 0)), ('<=>', ('lying', 4), ('telling-truth', 2)), ('not', ('telling-truth', 5)), ('and', ('telling-truth', 5), ('telling-truth', 4)))", "index": 1001}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Avery, Grace, Ava, Scarlett, and Evelyn. As Isabella put it, \"Ava is a knight or Ava is a knave\". Avery commented, \"Grace is a knight\". According to Grace, \"If Ava is a knave then Evelyn is a knight\". Ava was heard saying, \"Avery is not a knight\". Scarlett noted, \"Isabella is a knave or Evelyn is a knave\". \"If Ava is a knight then Scarlett is a knave\" - Evelyn. So who is a knight and who is a knave?", "names": ["Isabella", "Avery", "Grace", "Ava", "Scarlett", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Isabella is a knight, Avery is a knight, Grace is a knight, Ava is a knave, Scarlett is a knave, and Evelyn is a knight.", "solution_text_format": "(1) Isabella is a knight\n(2) Avery is a knight\n(3) Grace is a knight\n(4) Ava is a knave\n(5) Scarlett is a knave\n(6) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Ava is a knight or Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Avery is not a knight.", "Avery cannot be a knight, because this would contradict the claim of Ava that Avery is not a knight.", "Assume Avery is a knave. No contradiction is found in their false claim that Grace is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Avery that Grace is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that If Ava is a knave then Evelyn is a knight.", "We have exhausted all possibilities for Grace and Avery, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Ava is a knave then Evelyn is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Ava is a knight then Scarlett is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Isabella is a knave or Evelyn is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Isabella is a knave or Evelyn is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 3), ('lying', 3)), ('telling-truth', 2), ('->', ('lying', 3), ('telling-truth', 5)), ('not', ('telling-truth', 1)), ('or', ('lying', 0), ('lying', 5)), ('->', ('telling-truth', 3), ('lying', 4)))", "index": 1002}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Avery, Matthew, Jack, Chloe, and Sofia. \"Sofia is a knave and Matthew is a knight\" - Emily. In Avery's words: \"Jack is a knight\". Matthew asserted: \"If Emily is a knight then Matthew is a knight\". Jack asserted: \"Matthew is a knight\". Chloe expressed that Avery is a knight and Jack is a knave. Sofia noted, \"Matthew is a knave or Jack is a knave\". So who is a knight and who is a knave?", "names": ["Emily", "Avery", "Matthew", "Jack", "Chloe", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Emily is a knight, Avery is a knight, Matthew is a knight, Jack is a knight, Chloe is a knave, and Sofia is a knave.", "solution_text_format": "(1) Emily is a knight\n(2) Avery is a knight\n(3) Matthew is a knight\n(4) Jack is a knight\n(5) Chloe is a knave\n(6) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Sofia is a knave and Matthew is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Emily that Sofia is a knave and Matthew is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Matthew is a knave or Jack is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that If Emily is a knight then Matthew is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Matthew is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Jack is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Jack is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Avery is a knight and Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 2)), ('telling-truth', 3), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 2), ('and', ('telling-truth', 1), ('lying', 3)), ('or', ('lying', 2), ('lying', 3)))", "index": 1003}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Alexander, Sofia, Mia, Sebastian, and Henry. According to Emily, \"Alexander is a knight or Mia is a knave\". Alexander remarked, \"Sofia is not a knave\". Sofia said, \"Emily is a knight if and only if Alexander is a knight.\" In Mia's words: \"Sofia is a knave or Alexander is a knight\". In a statement by Sebastian: \"Sofia is a knight\". Henry noted, \"Alexander is a knight if and only if Mia is a knight\". So who is a knight and who is a knave?", "names": ["Emily", "Alexander", "Sofia", "Mia", "Sebastian", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Emily is a knight, Alexander is a knight, Sofia is a knight, Mia is a knight, Sebastian is a knight, and Henry is a knight.", "solution_text_format": "(1) Emily is a knight\n(2) Alexander is a knight\n(3) Sofia is a knight\n(4) Mia is a knight\n(5) Sebastian is a knight\n(6) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emily is a knight. No contradiction is found in their claim that Alexander is a knight or Mia is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Emily is a knight if and only if Alexander is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that Sofia is a knave or Alexander is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sofia is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Alexander is a knight if and only if Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 1), ('lying', 3)), ('not', ('lying', 2)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('lying', 2), ('telling-truth', 1)), ('telling-truth', 2), ('<=>', ('telling-truth', 1), ('telling-truth', 3)))", "index": 1004}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Scarlett, Aurora, Mia, Owen, Aiden, and Victoria. \"If Owen is a knave then Aurora is a knave,\" Scarlett mentioned. Aurora said that Victoria is a knight and Victoria is a knave. Mia commented, \"Victoria is a knight\". In Owen's words: \"Mia is a knave\". Aiden stated, \"Mia is a knave if and only if Aiden is a knight\". Victoria said, \"If Aiden is a knave then Aiden is a knight.\" So who is a knight and who is a knave?", "names": ["Scarlett", "Aurora", "Mia", "Owen", "Aiden", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false], "solution_text": "Scarlett is a knight, Aurora is a knave, Mia is a knave, Owen is a knight, Aiden is a knave, and Victoria is a knave.", "solution_text_format": "(1) Scarlett is a knight\n(2) Aurora is a knave\n(3) Mia is a knave\n(4) Owen is a knight\n(5) Aiden is a knave\n(6) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Scarlett is a knight. No contradiction is found in their claim that If Owen is a knave then Aurora is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of Owen that Mia is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Victoria is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Mia that Victoria is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that If Aiden is a knave then Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Victoria that If Aiden is a knave then Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Aiden is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Victoria is a knight and Victoria is a knave.", "Assume Aurora is a knave. No contradiction is found in their false claim that Victoria is a knight and Victoria is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('lying', 1)), ('and', ('telling-truth', 5), ('lying', 5)), ('telling-truth', 5), ('lying', 2), ('<=>', ('lying', 2), ('telling-truth', 4)), ('->', ('lying', 4), ('telling-truth', 4)))", "index": 1005}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Chloe, Luke, Owen, Michael, and Abigail. In a statement by Liam: \"Michael is not a knight\". As Chloe put it, \"Owen is a knave or Owen is a knight\". Luke told you that Michael is a knave and Michael is a knight. Owen said, \"Abigail is not a knave.\" \"Owen is a knight or Chloe is a knave,\" Michael claimed. As Abigail put it, \"Luke is a knight and Owen is a knight\". So who is a knight and who is a knave?", "names": ["Liam", "Chloe", "Luke", "Owen", "Michael", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Liam is a knight, Chloe is a knight, Luke is a knave, Owen is a knave, Michael is a knave, and Abigail is a knave.", "solution_text_format": "(1) Liam is a knight\n(2) Chloe is a knight\n(3) Luke is a knave\n(4) Owen is a knave\n(5) Michael is a knave\n(6) Abigail is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Liam that Michael is not a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Owen is a knight or Chloe is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Michael that Owen is a knight or Chloe is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Abigail is not a knave.", "Abigail cannot be a knight, because this would contradict the false claim of Owen that Abigail is not a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Luke is a knight and Owen is a knight.", "Luke cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Michael is a knight.", "Assume Luke is a knave. No contradiction is found in their false claim that Michael is a knave and Michael is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Owen is a knave or Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 4)), ('or', ('lying', 3), ('telling-truth', 3)), ('and', ('lying', 4), ('telling-truth', 4)), ('not', ('lying', 5)), ('or', ('telling-truth', 3), ('lying', 1)), ('and', ('telling-truth', 2), ('telling-truth', 3)))", "index": 1006}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Sofia, David, Mason, Grace, and Aurora. Victoria expressed that David is a knight. \"If Mason is a knave then Aurora is a knight\" - Sofia. David said that Mason is a knight if and only if Sofia is a knave. \"If Victoria is a knight then Sofia is a knave,\" Mason declared. Grace asserted: \"David is a knave or Mason is a knave\". Aurora expressed that Grace is a knave. So who is a knight and who is a knave?", "names": ["Victoria", "Sofia", "David", "Mason", "Grace", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Victoria is a knave, Sofia is a knight, David is a knave, Mason is a knight, Grace is a knight, and Aurora is a knave.", "solution_text_format": "(1) Victoria is a knave\n(2) Sofia is a knight\n(3) David is a knave\n(4) Mason is a knight\n(5) Grace is a knight\n(6) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that David is a knight.", "Assume David is a knight. No contradiction is found in their claim that Mason is a knight if and only if Sofia is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Victoria is a knight then Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of David that Mason is a knight if and only if Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that If Mason is a knave then Aurora is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Mason.", "Assume Mason is a knave. No contradiction is found in their false claim that If Victoria is a knight then Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Mason is a knave then Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Aurora that Grace is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that David is a knave or Mason is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Aurora.", "Aurora cannot be a knave, because this would contradict the claim of Sofia that If Mason is a knave then Aurora is a knight.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Sofia.", "Sofia cannot be a knave, because this would contradict the claim of David that Mason is a knight if and only if Sofia is a knave.", "We have exhausted all possibilities for Sofia and Mason, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Victoria that David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Victoria.", "Assume Victoria is a knave. No contradiction is found in their false claim that David is a knight.", "David cannot be a knight, because this would contradict the false claim of Victoria that David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Sofia is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that If Victoria is a knight then Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that If Mason is a knave then Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Grace is a knave.", "Grace cannot be a knight, because this would contradict the claim of Aurora that Grace is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that David is a knave or Mason is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Grace is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that David is a knave or Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 2), ('->', ('lying', 3), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 1)), ('->', ('telling-truth', 0), ('lying', 1)), ('or', ('lying', 2), ('lying', 3)), ('lying', 4))", "index": 1007}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Owen, Matthew, Ava, Samuel, and Lily. Sebastian stated, \"Ava is a knave\". \"Lily is a knight if and only if Matthew is a knave,\" Owen declared. As Matthew put it, \"Lily is a knave\". \"If Owen is a knave then Lily is a knight\" - Ava. Samuel said, \"If Matthew is a knave then Ava is a knight.\" Lily noted, \"Sebastian is a knight if and only if Owen is a knave\". So who is a knight and who is a knave?", "names": ["Sebastian", "Owen", "Matthew", "Ava", "Samuel", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Sebastian is a knave, Owen is a knight, Matthew is a knave, Ava is a knight, Samuel is a knight, and Lily is a knight.", "solution_text_format": "(1) Sebastian is a knave\n(2) Owen is a knight\n(3) Matthew is a knave\n(4) Ava is a knight\n(5) Samuel is a knight\n(6) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Ava is a knave.", "Ava cannot be a knight, because this would contradict the claim of Sebastian that Ava is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that If Owen is a knave then Lily is a knight.", "Owen cannot be a knight, because this would contradict the false claim of Ava that If Owen is a knave then Lily is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Matthew is a knave.", "Lily cannot be a knight, because this would contradict the false claim of Ava that If Owen is a knave then Lily is a knight.", "Lily cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knight if and only if Owen is a knave.", "We have exhausted all possibilities for Lily, Owen, and Ava, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that If Owen is a knave then Lily is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Lily is a knight if and only if Matthew is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Owen is a knave.", "Matthew cannot be a knight, because this would contradict the claim of Owen that Lily is a knight if and only if Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Lily is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that If Matthew is a knave then Ava is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('<=>', ('telling-truth', 5), ('lying', 2)), ('lying', 5), ('->', ('lying', 1), ('telling-truth', 5)), ('->', ('lying', 2), ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('lying', 1)))", "index": 1008}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Evelyn, David, Ella, Sebastian, and Henry. According to Abigail, \"Ella is a knave if and only if Henry is a knave\". According to Evelyn, \"If Abigail is a knave then Ella is a knave\". David asserted: \"If Ella is a knight then Evelyn is a knave\". Ella said, \"Henry is not a knight.\" Sebastian expressed that Ella is not a knight. As Henry put it, \"Sebastian is a knight and Ella is a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Evelyn", "David", "Ella", "Sebastian", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Abigail is a knave, Evelyn is a knave, David is a knight, Ella is a knight, Sebastian is a knave, and Henry is a knave.", "solution_text_format": "(1) Abigail is a knave\n(2) Evelyn is a knave\n(3) David is a knight\n(4) Ella is a knight\n(5) Sebastian is a knave\n(6) Henry is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Ella is a knave if and only if Henry is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of Ella that Henry is not a knight.", "Henry cannot be a knave, because this would contradict the claim of Abigail that Ella is a knave if and only if Henry is a knave.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the claim of Abigail that Ella is a knave if and only if Henry is a knave.", "Henry cannot be a knave, because this would contradict the false claim of Ella that Henry is not a knight.", "We have exhausted all possibilities for Henry and Ella, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Henry is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Henry is not a knight.", "Henry cannot be a knight, because this would contradict the false claim of Abigail that Ella is a knave if and only if Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Sebastian is a knight and Ella is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Ella is not a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that If Abigail is a knave then Ella is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that If Abigail is a knave then Ella is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Ella is a knight then Evelyn is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 3), ('lying', 5)), ('->', ('lying', 0), ('lying', 3)), ('->', ('telling-truth', 3), ('lying', 1)), ('not', ('telling-truth', 5)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 4), ('telling-truth', 3)))", "index": 1009}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Aurora, Harper, Charlotte, Jacob, and Joseph. Amelia told you that Charlotte is a knave or Charlotte is a knight. In a statement by Aurora: \"If Jacob is a knave then Amelia is a knave\". In a statement by Harper: \"If Joseph is a knight then Charlotte is a knight\". In Charlotte's words: \"Aurora is a knight or Aurora is a knave\". Jacob remarked, \"Joseph is a knave if and only if Amelia is a knight\". Joseph expressed that If Harper is a knave then Joseph is a knight. So who is a knight and who is a knave?", "names": ["Amelia", "Aurora", "Harper", "Charlotte", "Jacob", "Joseph"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "Amelia is a knight, Aurora is a knave, Harper is a knight, Charlotte is a knight, Jacob is a knave, and Joseph is a knight.", "solution_text_format": "(1) Amelia is a knight\n(2) Aurora is a knave\n(3) Harper is a knight\n(4) Charlotte is a knight\n(5) Jacob is a knave\n(6) Joseph is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that Charlotte is a knave or Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Aurora is a knight or Aurora is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Jacob is a knave then Amelia is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Amelia is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Jacob that Joseph is a knave if and only if Amelia is a knight.", "Assume Joseph is a knave. No contradiction is found in their false claim that If Harper is a knave then Joseph is a knight.", "Harper cannot be a knight, because this would contradict the false claim of Joseph that If Harper is a knave then Joseph is a knight.", "Harper cannot be a knave, because this would contradict the false claim of their own that If Joseph is a knight then Charlotte is a knight.", "We have exhausted all possibilities for Harper and Joseph, so let us go back and reconsider Jacob.", "Jacob cannot be a knave, because this would contradict the claim of Aurora that If Jacob is a knave then Amelia is a knave.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that If Jacob is a knave then Amelia is a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Aurora that If Jacob is a knave then Amelia is a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Amelia is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that If Harper is a knave then Joseph is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Joseph is a knight then Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 3)), ('->', ('lying', 4), ('lying', 0)), ('->', ('telling-truth', 5), ('telling-truth', 3)), ('or', ('telling-truth', 1), ('lying', 1)), ('<=>', ('lying', 5), ('telling-truth', 0)), ('->', ('lying', 2), ('telling-truth', 5)))", "index": 1010}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Lily, Ella, David, Oliver, and Sebastian. Michael expressed that David is a knave. As Lily put it, \"Ella is not a knight\". According to Ella, \"Lily is a knight if and only if Sebastian is a knave\". As David put it, \"If Ella is a knight then Oliver is a knave\". \"If Michael is a knave then Lily is a knight\" - Oliver. Sebastian was heard saying, \"Ella is a knave if and only if Michael is a knight\". So who is a knight and who is a knave?", "names": ["Michael", "Lily", "Ella", "David", "Oliver", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Michael is a knave, Lily is a knave, Ella is a knight, David is a knight, Oliver is a knave, and Sebastian is a knight.", "solution_text_format": "(1) Michael is a knave\n(2) Lily is a knave\n(3) Ella is a knight\n(4) David is a knight\n(5) Oliver is a knave\n(6) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Michael that David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that If Ella is a knight then Oliver is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Lily is a knight if and only if Sebastian is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Ella is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Ella is a knave if and only if Michael is a knight.", "Sebastian cannot be a knave, because this would contradict the claim of Ella that Lily is a knight if and only if Sebastian is a knave.", "We have exhausted all possibilities for Sebastian and Lily, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of David that If Ella is a knight then Oliver is a knave.", "We have exhausted all possibilities for Ella and David, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that David is a knave.", "Assume David is a knight. No contradiction is found in their claim that If Ella is a knight then Oliver is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Lily is a knight if and only if Sebastian is a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Ella is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Ella is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Ella is a knave if and only if Michael is a knight.", "Oliver cannot be a knight, because this would contradict the claim of David that If Ella is a knight then Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Michael is a knave then Lily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('lying', 5)), ('->', ('telling-truth', 2), ('lying', 4)), ('->', ('lying', 0), ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 0)))", "index": 1011}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Abigail, Zoey, Aurora, Ethan, and Harper. According to Emma, \"Harper is a knight or Abigail is a knave\". Abigail was heard saying, \"Ethan is a knight and Abigail is a knight\". As Zoey put it, \"Emma is a knight\". In Aurora's words: \"If Abigail is a knight then Ethan is a knave\". Ethan said that Aurora is a knave and Abigail is a knave. Harper said, \"If Emma is a knave then Zoey is a knight.\" So who is a knight and who is a knave?", "names": ["Emma", "Abigail", "Zoey", "Aurora", "Ethan", "Harper"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "Emma is a knight, Abigail is a knave, Zoey is a knight, Aurora is a knight, Ethan is a knave, and Harper is a knight.", "solution_text_format": "(1) Emma is a knight\n(2) Abigail is a knave\n(3) Zoey is a knight\n(4) Aurora is a knight\n(5) Ethan is a knave\n(6) Harper is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Harper is a knight or Abigail is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that If Emma is a knave then Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Emma is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Ethan is a knight and Abigail is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Abigail is a knave.", "Ethan cannot be a knave, because this would contradict the claim of Abigail that Ethan is a knight and Abigail is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Ethan is a knight and Abigail is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Aurora is a knave and Abigail is a knave.", "Aurora cannot be a knight, because this would contradict the claim of Ethan that Aurora is a knave and Abigail is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that If Abigail is a knight then Ethan is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Aurora is a knave and Abigail is a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Abigail is a knight then Ethan is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 5), ('lying', 1)), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('telling-truth', 0), ('->', ('telling-truth', 1), ('lying', 4)), ('and', ('lying', 3), ('lying', 1)), ('->', ('lying', 0), ('telling-truth', 2)))", "index": 1012}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Owen, Olivia, Ella, Ethan, and William. Lucas expressed that Lucas is a knight or Olivia is a knave. Owen remarked, \"If Ella is a knave then Lucas is a knave\". \"Ethan is a knight\" - Olivia. Ella was heard saying, \"If Lucas is a knight then Owen is a knight\". \"If Lucas is a knight then William is a knight,\" Ethan declared. \"Ethan is a knave,\" William mentioned. So who is a knight and who is a knave?", "names": ["Lucas", "Owen", "Olivia", "Ella", "Ethan", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Lucas is a knave, Owen is a knight, Olivia is a knight, Ella is a knight, Ethan is a knight, and William is a knave.", "solution_text_format": "(1) Lucas is a knave\n(2) Owen is a knight\n(3) Olivia is a knight\n(4) Ella is a knight\n(5) Ethan is a knight\n(6) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that Lucas is a knight or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Lucas is a knight then William is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Ethan is a knave.", "William cannot be a knave, because this would contradict the claim of Ethan that If Lucas is a knight then William is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Olivia that Ethan is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Ethan is a knight.", "Ethan cannot be a knight, because this would contradict the false claim of Olivia that Ethan is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Lucas is a knight then William is a knight.", "William cannot be a knight, because this would contradict the false claim of Ethan that If Lucas is a knight then William is a knight.", "William cannot be a knave, because this would contradict the false claim of their own that Ethan is a knave.", "We have exhausted all possibilities for William, Ethan, and Olivia, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Lucas is a knight or Olivia is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that Ethan is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that If Lucas is a knight then William is a knight.", "William cannot be a knight, because this would contradict the claim of their own that Ethan is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Ethan is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that If Ella is a knave then Lucas is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that If Lucas is a knight then Owen is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 0), ('lying', 2)), ('->', ('lying', 3), ('lying', 0)), ('telling-truth', 4), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('telling-truth', 5)), ('lying', 4))", "index": 1013}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Harper, Henry, Jacob, Charlotte, and Luke. In Daniel's words: \"Harper is a knight and Henry is a knight\". \"Henry is a knave if and only if Daniel is a knight,\" Harper declared. Henry expressed that Jacob is a knave. Jacob stated, \"If Henry is a knight then Harper is a knave\". Charlotte stated, \"Harper is not a knight\". In Luke's words: \"If Jacob is a knave then Luke is a knight\". So who is a knight and who is a knave?", "names": ["Daniel", "Harper", "Henry", "Jacob", "Charlotte", "Luke"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, true], "solution_text": "Daniel is a knave, Harper is a knave, Henry is a knave, Jacob is a knight, Charlotte is a knight, and Luke is a knight.", "solution_text_format": "(1) Daniel is a knave\n(2) Harper is a knave\n(3) Henry is a knave\n(4) Jacob is a knight\n(5) Charlotte is a knight\n(6) Luke is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that Harper is a knight and Henry is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Henry is a knave if and only if Daniel is a knight.", "Henry cannot be a knight, because this would contradict the claim of Harper that Henry is a knave if and only if Daniel is a knight.", "Henry cannot be a knave, because this would contradict the claim of Daniel that Harper is a knight and Henry is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the claim of Daniel that Harper is a knight and Henry is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Daniel.", "Assume Daniel is a knave. No contradiction is found in their false claim that Harper is a knight and Henry is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Henry is a knave if and only if Daniel is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Daniel that Harper is a knight and Henry is a knight.", "Henry cannot be a knave, because this would contradict the claim of Harper that Henry is a knave if and only if Daniel is a knight.", "We have exhausted all possibilities for Henry, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Henry is a knave if and only if Daniel is a knight.", "Henry cannot be a knight, because this would contradict the false claim of Harper that Henry is a knave if and only if Daniel is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Jacob is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that If Henry is a knight then Harper is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Harper is not a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If Jacob is a knave then Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 2)), ('<=>', ('lying', 2), ('telling-truth', 0)), ('lying', 3), ('->', ('telling-truth', 2), ('lying', 1)), ('not', ('telling-truth', 1)), ('->', ('lying', 3), ('telling-truth', 5)))", "index": 1014}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Avery, Jacob, Elizabeth, Scarlett, and Jack. James remarked, \"Jack is not a knight\". \"If Scarlett is a knight then Jack is a knave,\" Avery declared. \"Elizabeth is not a knave\" - Jacob. \"Scarlett is a knight if and only if Jacob is a knave,\" Elizabeth declared. In a statement by Scarlett: \"Jacob is a knight and Jack is a knight\". Jack was heard saying, \"Elizabeth is a knight or Jacob is a knight\". So who is a knight and who is a knave?", "names": ["James", "Avery", "Jacob", "Elizabeth", "Scarlett", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "James is a knight, Avery is a knight, Jacob is a knave, Elizabeth is a knave, Scarlett is a knave, and Jack is a knave.", "solution_text_format": "(1) James is a knight\n(2) Avery is a knight\n(3) Jacob is a knave\n(4) Elizabeth is a knave\n(5) Scarlett is a knave\n(6) Jack is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Jack is not a knight.", "Jack cannot be a knight, because this would contradict the claim of James that Jack is not a knight.", "Assume Jack is a knave. No contradiction is found in their false claim that Elizabeth is a knight or Jacob is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Jack that Elizabeth is a knight or Jacob is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Jacob is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Jack is a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Jacob is a knight and Jack is a knight.", "Jacob cannot be a knight, because this would contradict the claim of their own that Elizabeth is not a knave.", "Assume Jacob is a knave. No contradiction is found in their false claim that Elizabeth is not a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Scarlett is a knight then Jack is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('->', ('telling-truth', 4), ('lying', 5)), ('not', ('lying', 3)), ('<=>', ('telling-truth', 4), ('lying', 2)), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('telling-truth', 3), ('telling-truth', 2)))", "index": 1015}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Samuel, Harper, Michael, Sofia, and Evelyn. Abigail commented, \"Sofia is a knave and Samuel is a knight\". Samuel commented, \"Abigail is a knave and Evelyn is a knave\". In a statement by Harper: \"If Evelyn is a knave then Samuel is a knight\". \"Samuel is a knave if and only if Evelyn is a knight,\" Michael declared. In Sofia's words: \"Michael is a knight and Evelyn is a knight\". Evelyn was heard saying, \"If Harper is a knave then Harper is a knight\". So who is a knight and who is a knave?", "names": ["Abigail", "Samuel", "Harper", "Michael", "Sofia", "Evelyn"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Abigail is a knave, Samuel is a knave, Harper is a knight, Michael is a knight, Sofia is a knight, and Evelyn is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Samuel is a knave\n(3) Harper is a knight\n(4) Michael is a knight\n(5) Sofia is a knight\n(6) Evelyn is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Sofia is a knave and Samuel is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Abigail that Sofia is a knave and Samuel is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Michael is a knight and Evelyn is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Evelyn is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Evelyn is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Abigail that Sofia is a knave and Samuel is a knight.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Michael.", "Assume Michael is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Evelyn is a knight.", "Samuel cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Evelyn is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Abigail that Sofia is a knave and Samuel is a knight.", "We have exhausted all possibilities for Samuel, Michael, and Sofia, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Sofia is a knave and Samuel is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Michael is a knight and Evelyn is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Evelyn is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Abigail is a knave and Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Samuel that Abigail is a knave and Evelyn is a knave.", "Evelyn cannot be a knave, because this would contradict the claim of Sofia that Michael is a knight and Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Abigail is a knave and Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Harper is a knave then Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Evelyn is a knave then Samuel is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('telling-truth', 1)), ('and', ('lying', 0), ('lying', 5)), ('->', ('lying', 5), ('telling-truth', 1)), ('<=>', ('lying', 1), ('telling-truth', 5)), ('and', ('telling-truth', 3), ('telling-truth', 5)), ('->', ('lying', 2), ('telling-truth', 2)))", "index": 1016}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Jackson, Ella, Benjamin, Henry, and Samuel. Aria asserted: \"Henry is a knave\". Jackson noted, \"Benjamin is a knight or Henry is a knave\". Ella stated, \"Jackson is not a knave\". According to Benjamin, \"Jackson is a knave\". Henry said that Samuel is a knave if and only if Aria is a knave. According to Samuel, \"Aria is a knave or Henry is a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Jackson", "Ella", "Benjamin", "Henry", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Aria is a knight, Jackson is a knight, Ella is a knight, Benjamin is a knave, Henry is a knave, and Samuel is a knave.", "solution_text_format": "(1) Aria is a knight\n(2) Jackson is a knight\n(3) Ella is a knight\n(4) Benjamin is a knave\n(5) Henry is a knave\n(6) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Henry is a knave.", "Henry cannot be a knight, because this would contradict the claim of Aria that Henry is a knave.", "Assume Henry is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Aria is a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Henry that Samuel is a knave if and only if Aria is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Aria is a knave or Henry is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Benjamin is a knight or Henry is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Jackson is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Jackson is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Jackson is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 4), ('or', ('telling-truth', 3), ('lying', 4)), ('not', ('lying', 1)), ('lying', 1), ('<=>', ('lying', 5), ('lying', 0)), ('or', ('lying', 0), ('telling-truth', 4)))", "index": 1017}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Oliver, Mia, Elizabeth, Emily, and Ava. Sebastian stated, \"Emily is not a knave\". Oliver stated, \"Sebastian is a knight and Sebastian is a knave\". Mia noted, \"Emily is not a knave\". Elizabeth said that If Ava is a knave then Oliver is a knave. In Emily's words: \"Ava is not a knave\". In a statement by Ava: \"Sebastian is a knave or Emily is a knight\". So who is a knight and who is a knave?", "names": ["Sebastian", "Oliver", "Mia", "Elizabeth", "Emily", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Sebastian is a knight, Oliver is a knave, Mia is a knight, Elizabeth is a knight, Emily is a knight, and Ava is a knight.", "solution_text_format": "(1) Sebastian is a knight\n(2) Oliver is a knave\n(3) Mia is a knight\n(4) Elizabeth is a knight\n(5) Emily is a knight\n(6) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Ava is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Sebastian is a knave or Emily is a knight.", "Oliver cannot be a knight, because this would contradict the claim of their own that Sebastian is a knight and Sebastian is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that Sebastian is a knight and Sebastian is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Ava is a knave then Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('and', ('telling-truth', 0), ('lying', 0)), ('not', ('lying', 4)), ('->', ('lying', 5), ('lying', 1)), ('not', ('lying', 5)), ('or', ('lying', 0), ('telling-truth', 4)))", "index": 1018}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Sophia, Joseph, Daniel, Chloe, and Sebastian. Isabella stated, \"Sophia is a knave or Daniel is a knight\". Sophia asserted: \"If Daniel is a knight then Joseph is a knight\". Joseph asserted: \"Sebastian is a knight if and only if Sophia is a knight\". Daniel said, \"Daniel is a knight if and only if Sophia is a knight.\" Chloe noted, \"Sophia is not a knave\". Sebastian was heard saying, \"Sophia is a knave\". So who is a knight and who is a knave?", "names": ["Isabella", "Sophia", "Joseph", "Daniel", "Chloe", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "Isabella is a knave, Sophia is a knight, Joseph is a knave, Daniel is a knave, Chloe is a knight, and Sebastian is a knave.", "solution_text_format": "(1) Isabella is a knave\n(2) Sophia is a knight\n(3) Joseph is a knave\n(4) Daniel is a knave\n(5) Chloe is a knight\n(6) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Isabella is a knight. No contradiction is found in their claim that Sophia is a knave or Daniel is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Daniel is a knight then Joseph is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Sophia is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Sophia is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Sophia is a knave.", "Sebastian cannot be a knave, because this would contradict the claim of Joseph that Sebastian is a knight if and only if Sophia is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Joseph.", "Joseph cannot be a knave, because this would contradict the claim of Sophia that If Daniel is a knight then Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Daniel.", "Daniel cannot be a knave, because this would contradict the claim of Isabella that Sophia is a knave or Daniel is a knight.", "We have exhausted all possibilities for Daniel, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Daniel is a knight then Joseph is a knight.", "Daniel cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Sophia is a knight.", "Daniel cannot be a knave, because this would contradict the false claim of Sophia that If Daniel is a knight then Joseph is a knight.", "We have exhausted all possibilities for Daniel and Sophia, so let us go back and reconsider Isabella.", "Assume Isabella is a knave. No contradiction is found in their false claim that Sophia is a knave or Daniel is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that If Daniel is a knight then Joseph is a knight.", "Daniel cannot be a knight, because this would contradict the false claim of Isabella that Sophia is a knave or Daniel is a knight.", "Assume Daniel is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Sophia is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Sophia is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Sophia is a knave.", "Sebastian cannot be a knave, because this would contradict the claim of Joseph that Sebastian is a knight if and only if Sophia is a knight.", "We have exhausted all possibilities for Sebastian, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Sophia is a knight.", "Sebastian cannot be a knight, because this would contradict the false claim of Joseph that Sebastian is a knight if and only if Sophia is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Sophia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('<=>', ('telling-truth', 3), ('telling-truth', 1)), ('not', ('lying', 1)), ('lying', 1))", "index": 1019}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Michael, Penelope, Scarlett, Joseph, and James. Olivia told you that Scarlett is a knight if and only if Joseph is a knight. \"Olivia is a knave if and only if Scarlett is a knight,\" Michael declared. In a statement by Penelope: \"Scarlett is a knave or James is a knave\". Scarlett asserted: \"Olivia is not a knave\". As Joseph put it, \"Scarlett is a knight\". \"Michael is a knave and Joseph is a knave,\" James claimed. So who is a knight and who is a knave?", "names": ["Olivia", "Michael", "Penelope", "Scarlett", "Joseph", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Olivia is a knight, Michael is a knave, Penelope is a knight, Scarlett is a knight, Joseph is a knight, and James is a knave.", "solution_text_format": "(1) Olivia is a knight\n(2) Michael is a knave\n(3) Penelope is a knight\n(4) Scarlett is a knight\n(5) Joseph is a knight\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Scarlett is a knight if and only if Joseph is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Olivia is not a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Michael cannot be a knight, because this would contradict the claim of their own that Olivia is a knave if and only if Scarlett is a knight.", "Assume Michael is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Scarlett is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Scarlett is a knave or James is a knave.", "James cannot be a knight, because this would contradict the claim of Penelope that Scarlett is a knave or James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Michael is a knave and Joseph is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('telling-truth', 4)), ('<=>', ('lying', 0), ('telling-truth', 3)), ('or', ('lying', 3), ('lying', 5)), ('not', ('lying', 0)), ('telling-truth', 3), ('and', ('lying', 1), ('lying', 4)))", "index": 1020}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Grace, Olivia, Evelyn, Elizabeth, and Ava. \"Ava is a knight and Evelyn is a knight,\" Luke claimed. Grace stated, \"Olivia is a knave and Elizabeth is a knave\". Olivia was heard saying, \"Luke is a knave if and only if Grace is a knight\". Evelyn told you that Elizabeth is not a knight. \"Olivia is a knave if and only if Elizabeth is a knight,\" Elizabeth mentioned. \"Evelyn is a knave if and only if Olivia is a knave,\" Ava declared. So who is a knight and who is a knave?", "names": ["Luke", "Grace", "Olivia", "Evelyn", "Elizabeth", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Luke is a knave, Grace is a knave, Olivia is a knave, Evelyn is a knave, Elizabeth is a knight, and Ava is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Grace is a knave\n(3) Olivia is a knave\n(4) Evelyn is a knave\n(5) Elizabeth is a knight\n(6) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Ava is a knight and Evelyn is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Olivia is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Evelyn that Elizabeth is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Elizabeth is a knight.", "Olivia cannot be a knight, because this would contradict the false claim of Elizabeth that Olivia is a knave if and only if Elizabeth is a knight.", "Olivia cannot be a knave, because this would contradict the claim of Ava that Evelyn is a knave if and only if Olivia is a knave.", "We have exhausted all possibilities for Olivia and Elizabeth, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Luke that Ava is a knight and Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Luke that Ava is a knight and Evelyn is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Ava is a knight and Evelyn is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Evelyn is a knave if and only if Olivia is a knave.", "Evelyn cannot be a knight, because this would contradict the false claim of Luke that Ava is a knight and Evelyn is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Elizabeth is not a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Elizabeth is a knight.", "Olivia cannot be a knight, because this would contradict the claim of Elizabeth that Olivia is a knave if and only if Elizabeth is a knight.", "Assume Olivia is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Grace is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Elizabeth is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Olivia is a knave and Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('telling-truth', 3)), ('and', ('lying', 2), ('lying', 4)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('not', ('telling-truth', 4)), ('<=>', ('lying', 2), ('telling-truth', 4)), ('<=>', ('lying', 3), ('lying', 2)))", "index": 1021}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Oliver, Aurora, Riley, Ethan, Sebastian, and Alexander. In a statement by Oliver: \"Riley is a knave and Aurora is a knave\". In a statement by Aurora: \"Alexander is not a knave\". Riley told you that If Aurora is a knave then Oliver is a knight. Ethan asserted: \"Sebastian is a knave\". Sebastian commented, \"If Ethan is a knave then Sebastian is a knight\". In Alexander's words: \"Sebastian is a knave if and only if Oliver is a knight\". So who is a knight and who is a knave?", "names": ["Oliver", "Aurora", "Riley", "Ethan", "Sebastian", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, true, true], "solution_text": "Oliver is a knave, Aurora is a knight, Riley is a knight, Ethan is a knave, Sebastian is a knight, and Alexander is a knight.", "solution_text_format": "(1) Oliver is a knave\n(2) Aurora is a knight\n(3) Riley is a knight\n(4) Ethan is a knave\n(5) Sebastian is a knight\n(6) Alexander is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Oliver is a knight. No contradiction is found in their claim that Riley is a knave and Aurora is a knave.", "Riley cannot be a knight, because this would contradict the claim of Oliver that Riley is a knave and Aurora is a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knave then Oliver is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Riley is a knave and Aurora is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Aurora is a knave then Oliver is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Oliver is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that If Ethan is a knave then Sebastian is a knight.", "Ethan cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Sebastian is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 1)), ('not', ('lying', 5)), ('->', ('lying', 1), ('telling-truth', 0)), ('lying', 4), ('->', ('lying', 3), ('telling-truth', 4)), ('<=>', ('lying', 4), ('telling-truth', 0)))", "index": 1022}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Oliver, Amelia, Chloe, Benjamin, and Abigail. Avery commented, \"Abigail is a knave\". As Oliver put it, \"Chloe is a knight or Amelia is a knave\". Amelia stated, \"Chloe is a knight\". \"Amelia is a knight if and only if Abigail is a knight,\" Chloe declared. In Benjamin's words: \"Amelia is a knight or Avery is a knave\". In Abigail's words: \"Chloe is a knave if and only if Benjamin is a knave\". So who is a knight and who is a knave?", "names": ["Avery", "Oliver", "Amelia", "Chloe", "Benjamin", "Abigail"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Avery is a knave, Oliver is a knight, Amelia is a knight, Chloe is a knight, Benjamin is a knight, and Abigail is a knight.", "solution_text_format": "(1) Avery is a knave\n(2) Oliver is a knight\n(3) Amelia is a knight\n(4) Chloe is a knight\n(5) Benjamin is a knight\n(6) Abigail is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Avery that Abigail is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Chloe is a knave if and only if Benjamin is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Abigail is a knight.", "Amelia cannot be a knight, because this would contradict the claim of Chloe that Amelia is a knight if and only if Abigail is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Chloe.", "Assume Chloe is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Abigail is a knight.", "Amelia cannot be a knight, because this would contradict the claim of their own that Chloe is a knight.", "Amelia cannot be a knave, because this would contradict the false claim of Chloe that Amelia is a knight if and only if Abigail is a knight.", "We have exhausted all possibilities for Amelia, Chloe, and Abigail, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Benjamin is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Abigail is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Chloe is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Amelia is a knight or Avery is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Chloe is a knight or Amelia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('or', ('telling-truth', 3), ('lying', 2)), ('telling-truth', 3), ('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('telling-truth', 2), ('lying', 0)), ('<=>', ('lying', 3), ('lying', 4)))", "index": 1023}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Evelyn, Sebastian, James, Oliver, and Sophia. Grace said, \"Sebastian is not a knight.\" Evelyn remarked, \"Oliver is not a knight\". Sebastian expressed that Evelyn is not a knight. James stated, \"Sophia is a knave if and only if Sophia is a knight\". Oliver stated, \"James is a knave or Sebastian is a knave\". \"James is a knave if and only if Sebastian is a knight,\" Sophia declared. So who is a knight and who is a knave?", "names": ["Grace", "Evelyn", "Sebastian", "James", "Oliver", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, true], "solution_text": "Grace is a knave, Evelyn is a knave, Sebastian is a knight, James is a knave, Oliver is a knight, and Sophia is a knight.", "solution_text_format": "(1) Grace is a knave\n(2) Evelyn is a knave\n(3) Sebastian is a knight\n(4) James is a knave\n(5) Oliver is a knight\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Sebastian is not a knight.", "Sebastian cannot be a knight, because this would contradict the claim of Grace that Sebastian is not a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Oliver is not a knight.", "Oliver cannot be a knight, because this would contradict the claim of Evelyn that Oliver is not a knight.", "Oliver cannot be a knave, because this would contradict the false claim of their own that James is a knave or Sebastian is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the false claim of Sebastian that Evelyn is not a knight.", "We have exhausted all possibilities for Evelyn and Sebastian, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Sebastian is not a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Evelyn is not a knight.", "Evelyn cannot be a knight, because this would contradict the claim of Sebastian that Evelyn is not a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Oliver is not a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that James is a knave or Sebastian is a knave.", "James cannot be a knight, because this would contradict the claim of their own that Sophia is a knave if and only if Sophia is a knight.", "Assume James is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Sophia is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that James is a knave if and only if Sebastian is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('not', ('telling-truth', 4)), ('not', ('telling-truth', 1)), ('<=>', ('lying', 5), ('telling-truth', 5)), ('or', ('lying', 3), ('lying', 2)), ('<=>', ('lying', 3), ('telling-truth', 2)))", "index": 1024}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Avery, Owen, Scarlett, Charlotte, and Ava. As Ella put it, \"Avery is a knave\". Avery noted, \"If Ava is a knave then Scarlett is a knave\". Owen remarked, \"Scarlett is not a knight\". Scarlett told you that Ava is a knight and Scarlett is a knight. \"Avery is a knight if and only if Scarlett is a knight\" - Charlotte. Ava said, \"Owen is a knight or Charlotte is a knave.\" So who is a knight and who is a knave?", "names": ["Ella", "Avery", "Owen", "Scarlett", "Charlotte", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, true], "solution_text": "Ella is a knave, Avery is a knight, Owen is a knight, Scarlett is a knave, Charlotte is a knave, and Ava is a knight.", "solution_text_format": "(1) Ella is a knave\n(2) Avery is a knight\n(3) Owen is a knight\n(4) Scarlett is a knave\n(5) Charlotte is a knave\n(6) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Avery is a knave.", "Avery cannot be a knight, because this would contradict the claim of Ella that Avery is a knave.", "Assume Avery is a knave. No contradiction is found in their false claim that If Ava is a knave then Scarlett is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Avery that If Ava is a knave then Scarlett is a knave.", "Assume Ava is a knave. No contradiction is found in their false claim that Owen is a knight or Charlotte is a knave.", "Owen cannot be a knight, because this would contradict the false claim of Ava that Owen is a knight or Charlotte is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Scarlett is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of their own that Ava is a knight and Scarlett is a knight.", "Scarlett cannot be a knave, because this would contradict the false claim of Avery that If Ava is a knave then Scarlett is a knave.", "We have exhausted all possibilities for Scarlett, Owen, Ava, and Avery, so let us go back and reconsider Ella.", "Assume Ella is a knave. No contradiction is found in their false claim that Avery is a knave.", "Assume Avery is a knight. No contradiction is found in their claim that If Ava is a knave then Scarlett is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Owen is a knight or Charlotte is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Scarlett is not a knight.", "Scarlett cannot be a knight, because this would contradict the claim of Owen that Scarlett is not a knight.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Ava is a knight and Scarlett is a knight.", "Charlotte cannot be a knight, because this would contradict the claim of their own that Avery is a knight if and only if Scarlett is a knight.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Scarlett is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('->', ('lying', 5), ('lying', 3)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('or', ('telling-truth', 2), ('lying', 4)))", "index": 1025}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Riley, Olivia, Evelyn, Matthew, and Emma. In Owen's words: \"Olivia is a knave and Emma is a knave\". As Riley put it, \"Olivia is a knave\". In Olivia's words: \"If Emma is a knave then Matthew is a knave\". Evelyn noted, \"If Evelyn is a knight then Owen is a knave\". In Matthew's words: \"Evelyn is a knave\". Emma expressed that Olivia is a knave and Owen is a knight. So who is a knight and who is a knave?", "names": ["Owen", "Riley", "Olivia", "Evelyn", "Matthew", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Owen is a knave, Riley is a knave, Olivia is a knight, Evelyn is a knight, Matthew is a knave, and Emma is a knave.", "solution_text_format": "(1) Owen is a knave\n(2) Riley is a knave\n(3) Olivia is a knight\n(4) Evelyn is a knight\n(5) Matthew is a knave\n(6) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Olivia is a knave and Emma is a knave.", "Olivia cannot be a knight, because this would contradict the claim of Owen that Olivia is a knave and Emma is a knave.", "Assume Olivia is a knave. No contradiction is found in their false claim that If Emma is a knave then Matthew is a knave.", "Emma cannot be a knight, because this would contradict the claim of Owen that Olivia is a knave and Emma is a knave.", "Emma cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave and Owen is a knight.", "We have exhausted all possibilities for Emma and Olivia, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Olivia is a knave and Emma is a knave.", "Assume Olivia is a knight. No contradiction is found in their claim that If Emma is a knave then Matthew is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Olivia is a knave and Owen is a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Olivia is a knave and Owen is a knight.", "Matthew cannot be a knight, because this would contradict the claim of Olivia that If Emma is a knave then Matthew is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Evelyn is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that If Evelyn is a knight then Owen is a knave.", "Riley cannot be a knight, because this would contradict the claim of their own that Olivia is a knave.", "Assume Riley is a knave. No contradiction is found in their false claim that Olivia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 5)), ('lying', 2), ('->', ('lying', 5), ('lying', 4)), ('->', ('telling-truth', 3), ('lying', 0)), ('lying', 3), ('and', ('lying', 2), ('telling-truth', 0)))", "index": 1026}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, Sebastian, Harper, Jack, Lily, and Ella. Penelope commented, \"Harper is a knave or Lily is a knight\". Sebastian commented, \"Ella is a knave\". Harper said that Jack is not a knave. Jack said, \"Ella is a knight or Ella is a knave.\" Lily was heard saying, \"Penelope is a knave if and only if Penelope is a knight\". Ella said that Harper is not a knave. So who is a knight and who is a knave?", "names": ["Penelope", "Sebastian", "Harper", "Jack", "Lily", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, true], "solution_text": "Penelope is a knave, Sebastian is a knave, Harper is a knight, Jack is a knight, Lily is a knave, and Ella is a knight.", "solution_text_format": "(1) Penelope is a knave\n(2) Sebastian is a knave\n(3) Harper is a knight\n(4) Jack is a knight\n(5) Lily is a knave\n(6) Ella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Harper is a knave or Lily is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Ella is a knight or Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Harper is not a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Penelope is a knave if and only if Penelope is a knight.", "Lily cannot be a knave, because this would contradict the claim of Penelope that Harper is a knave or Lily is a knight.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Ella.", "Ella cannot be a knave, because this would contradict the false claim of their own that Harper is not a knave.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Harper that Jack is not a knave.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Jack is not a knave.", "Jack cannot be a knight, because this would contradict the false claim of Harper that Jack is not a knave.", "Jack cannot be a knave, because this would contradict the false claim of their own that Ella is a knight or Ella is a knave.", "We have exhausted all possibilities for Jack and Harper, so let us go back and reconsider Penelope.", "Assume Penelope is a knave. No contradiction is found in their false claim that Harper is a knave or Lily is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Jack is not a knave.", "Assume Jack is a knight. No contradiction is found in their claim that Ella is a knight or Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Harper is not a knave.", "Lily cannot be a knight, because this would contradict the false claim of Penelope that Harper is a knave or Lily is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Penelope is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Ella is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Ella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 2), ('telling-truth', 4)), ('lying', 5), ('not', ('lying', 3)), ('or', ('telling-truth', 5), ('lying', 5)), ('<=>', ('lying', 0), ('telling-truth', 0)), ('not', ('lying', 2)))", "index": 1027}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Emma, Aiden, Alexander, Daniel, and Penelope. Victoria said that If Daniel is a knight then Victoria is a knight. In a statement by Emma: \"Daniel is not a knight\". Aiden said, \"Victoria is a knight.\" \"Emma is a knave,\" Alexander mentioned. \"If Emma is a knave then Penelope is a knave,\" Daniel declared. Penelope told you that Aiden is a knave and Emma is a knave. So who is a knight and who is a knave?", "names": ["Victoria", "Emma", "Aiden", "Alexander", "Daniel", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Victoria is a knight, Emma is a knave, Aiden is a knight, Alexander is a knight, Daniel is a knight, and Penelope is a knave.", "solution_text_format": "(1) Victoria is a knight\n(2) Emma is a knave\n(3) Aiden is a knight\n(4) Alexander is a knight\n(5) Daniel is a knight\n(6) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Victoria is a knight. No contradiction is found in their claim that If Daniel is a knight then Victoria is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Emma is a knave then Penelope is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Daniel is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Daniel is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Daniel that If Emma is a knave then Penelope is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Aiden is a knave and Emma is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Victoria is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('telling-truth', 0)), ('not', ('telling-truth', 4)), ('telling-truth', 0), ('lying', 1), ('->', ('lying', 1), ('lying', 5)), ('and', ('lying', 2), ('lying', 1)))", "index": 1028}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Riley, Abigail, Aria, Owen, and Lily. Luke told you that If Riley is a knight then Abigail is a knave. \"Aria is not a knight,\" Riley claimed. Abigail stated, \"If Lily is a knave then Abigail is a knight\". Aria was heard saying, \"Abigail is a knave or Owen is a knight\". \"Luke is a knave,\" Owen declared. Lily told you that Abigail is a knight and Abigail is a knave. So who is a knight and who is a knave?", "names": ["Luke", "Riley", "Abigail", "Aria", "Owen", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, false], "solution_text": "Luke is a knight, Riley is a knave, Abigail is a knave, Aria is a knight, Owen is a knave, and Lily is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Riley is a knave\n(3) Abigail is a knave\n(4) Aria is a knight\n(5) Owen is a knave\n(6) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that If Riley is a knight then Abigail is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Aria is not a knight.", "Aria cannot be a knight, because this would contradict the claim of Riley that Aria is not a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Abigail is a knave or Owen is a knight.", "Abigail cannot be a knight, because this would contradict the claim of Luke that If Riley is a knight then Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of Aria that Abigail is a knave or Owen is a knight.", "We have exhausted all possibilities for Abigail and Aria, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Aria is not a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Abigail is a knave or Owen is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that If Lily is a knave then Abigail is a knight.", "Lily cannot be a knight, because this would contradict the claim of their own that Abigail is a knight and Abigail is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that Abigail is a knight and Abigail is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Luke is a knave.", "Owen cannot be a knave, because this would contradict the claim of Aria that Abigail is a knave or Owen is a knight.", "We have exhausted all possibilities for Owen and Lily, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that If Lily is a knave then Abigail is a knight.", "Lily cannot be a knight, because this would contradict the false claim of Abigail that If Lily is a knave then Abigail is a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Abigail is a knight and Abigail is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Luke is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Luke is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 1), ('lying', 2)), ('not', ('telling-truth', 3)), ('->', ('lying', 5), ('telling-truth', 2)), ('or', ('lying', 2), ('telling-truth', 4)), ('lying', 0), ('and', ('telling-truth', 2), ('lying', 2)))", "index": 1029}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Henry, Amelia, Logan, Chloe, and Penelope. Luke expressed that Penelope is a knight if and only if Henry is a knight. \"Amelia is not a knight,\" Henry declared. In Amelia's words: \"Henry is a knave\". \"If Logan is a knight then Luke is a knight\" - Logan. Chloe remarked, \"Chloe is a knight or Logan is a knight\". \"Chloe is a knave if and only if Chloe is a knight,\" Penelope declared. So who is a knight and who is a knave?", "names": ["Luke", "Henry", "Amelia", "Logan", "Chloe", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Luke is a knight, Henry is a knave, Amelia is a knight, Logan is a knight, Chloe is a knight, and Penelope is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Henry is a knave\n(3) Amelia is a knight\n(4) Logan is a knight\n(5) Chloe is a knight\n(6) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Henry is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Chloe is a knave if and only if Chloe is a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Chloe is a knave if and only if Chloe is a knight.", "Assume Chloe is a knight. No contradiction is found in their claim that Chloe is a knight or Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Logan is a knight then Luke is a knight.", "Henry cannot be a knight, because this would contradict the claim of Luke that Penelope is a knight if and only if Henry is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Amelia is not a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('not', ('telling-truth', 2)), ('lying', 1), ('->', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('<=>', ('lying', 4), ('telling-truth', 4)))", "index": 1030}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Mia, Evelyn, Jack, Logan, and Lily. Ava told you that Jack is a knight if and only if Evelyn is a knave. Mia commented, \"Ava is not a knight\". Evelyn remarked, \"Ava is a knight if and only if Mia is a knave\". Jack stated, \"Mia is a knave and Ava is a knave\". Logan said, \"If Lily is a knight then Evelyn is a knave.\" Lily stated, \"Mia is a knave\". So who is a knight and who is a knave?", "names": ["Ava", "Mia", "Evelyn", "Jack", "Logan", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, true], "solution_text": "Ava is a knight, Mia is a knave, Evelyn is a knight, Jack is a knave, Logan is a knave, and Lily is a knight.", "solution_text_format": "(1) Ava is a knight\n(2) Mia is a knave\n(3) Evelyn is a knight\n(4) Jack is a knave\n(5) Logan is a knave\n(6) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Jack is a knight if and only if Evelyn is a knave.", "Jack cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Ava is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Mia is a knave and Ava is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Ava is not a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that Ava is not a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Ava is a knight if and only if Mia is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that If Lily is a knight then Evelyn is a knave.", "Lily cannot be a knight, because this would contradict the claim of Logan that If Lily is a knight then Evelyn is a knave.", "Lily cannot be a knave, because this would contradict the false claim of their own that Mia is a knave.", "We have exhausted all possibilities for Lily, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that If Lily is a knight then Evelyn is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that Mia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 2)), ('not', ('telling-truth', 0)), ('<=>', ('telling-truth', 0), ('lying', 1)), ('and', ('lying', 1), ('lying', 0)), ('->', ('telling-truth', 5), ('lying', 2)), ('lying', 1))", "index": 1031}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Daniel, Evelyn, Samuel, Charlotte, and Victoria. Mason commented, \"Daniel is a knave or Daniel is a knight\". \"If Evelyn is a knave then Samuel is a knave,\" Daniel mentioned. Evelyn said that Mason is a knight if and only if Daniel is a knave. Samuel stated, \"Charlotte is a knave if and only if Charlotte is a knight\". Charlotte was heard saying, \"Victoria is a knave if and only if Evelyn is a knight\". Victoria commented, \"Daniel is a knave\". So who is a knight and who is a knave?", "names": ["Mason", "Daniel", "Evelyn", "Samuel", "Charlotte", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Mason is a knight, Daniel is a knight, Evelyn is a knave, Samuel is a knave, Charlotte is a knave, and Victoria is a knave.", "solution_text_format": "(1) Mason is a knight\n(2) Daniel is a knight\n(3) Evelyn is a knave\n(4) Samuel is a knave\n(5) Charlotte is a knave\n(6) Victoria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mason is a knight. No contradiction is found in their claim that Daniel is a knave or Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that If Evelyn is a knave then Samuel is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Mason is a knight if and only if Daniel is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Daniel is a knave.", "Samuel cannot be a knight, because this would contradict the claim of Daniel that If Evelyn is a knave then Samuel is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Charlotte is a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that Victoria is a knave if and only if Evelyn is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Daniel is a knave.", "Victoria cannot be a knave, because this would contradict the claim of Charlotte that Victoria is a knave if and only if Evelyn is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Charlotte.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Evelyn is a knight.", "Victoria cannot be a knight, because this would contradict the false claim of Charlotte that Victoria is a knave if and only if Evelyn is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Daniel is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 1)), ('->', ('lying', 2), ('lying', 3)), ('<=>', ('telling-truth', 0), ('lying', 1)), ('<=>', ('lying', 4), ('telling-truth', 4)), ('<=>', ('lying', 5), ('telling-truth', 2)), ('lying', 1))", "index": 1032}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Benjamin, Jackson, Abigail, Penelope, and Ava. According to Sophia, \"Jackson is not a knight\". In Benjamin's words: \"Penelope is a knight\". Jackson asserted: \"Penelope is a knight if and only if Benjamin is a knight\". Abigail said, \"Jackson is not a knave.\" Penelope remarked, \"Sophia is a knave\". Ava was heard saying, \"Sophia is not a knight\". So who is a knight and who is a knave?", "names": ["Sophia", "Benjamin", "Jackson", "Abigail", "Penelope", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Sophia is a knave, Benjamin is a knight, Jackson is a knight, Abigail is a knight, Penelope is a knight, and Ava is a knight.", "solution_text_format": "(1) Sophia is a knave\n(2) Benjamin is a knight\n(3) Jackson is a knight\n(4) Abigail is a knight\n(5) Penelope is a knight\n(6) Ava is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Jackson is not a knight.", "Jackson cannot be a knight, because this would contradict the claim of Sophia that Jackson is not a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Penelope is a knight if and only if Benjamin is a knight.", "Penelope cannot be a knight, because this would contradict the claim of their own that Sophia is a knave.", "Assume Penelope is a knave. No contradiction is found in their false claim that Sophia is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Penelope is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of Jackson that Penelope is a knight if and only if Benjamin is a knight.", "We have exhausted all possibilities for Benjamin, Penelope, and Jackson, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Jackson is not a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Penelope is a knight if and only if Benjamin is a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Sophia is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Penelope is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Jackson is not a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Sophia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('telling-truth', 4), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('lying', 2)), ('lying', 0), ('not', ('telling-truth', 0)))", "index": 1033}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, William, Jacob, Harper, Grace, and Sebastian. \"Jacob is a knight or Grace is a knight,\" Aiden declared. William told you that Grace is a knight or Jacob is a knave. \"If Sebastian is a knave then Harper is a knight,\" Jacob claimed. Harper remarked, \"Aiden is a knave if and only if William is a knight\". Grace noted, \"Jacob is a knight\". Sebastian asserted: \"Sebastian is a knight\". So who is a knight and who is a knave?", "names": ["Aiden", "William", "Jacob", "Harper", "Grace", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Aiden is a knight, William is a knight, Jacob is a knight, Harper is a knave, Grace is a knight, and Sebastian is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) William is a knight\n(3) Jacob is a knight\n(4) Harper is a knave\n(5) Grace is a knight\n(6) Sebastian is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Jacob is a knight or Grace is a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Sebastian is a knave then Harper is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Aiden is a knave if and only if William is a knight.", "William cannot be a knight, because this would contradict the claim of Harper that Aiden is a knave if and only if William is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Grace is a knight or Jacob is a knave.", "Grace cannot be a knight, because this would contradict the false claim of William that Grace is a knight or Jacob is a knave.", "Grace cannot be a knave, because this would contradict the false claim of their own that Jacob is a knight.", "We have exhausted all possibilities for Grace and William, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Grace is a knight or Jacob is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Jacob is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 4)), ('or', ('telling-truth', 4), ('lying', 2)), ('->', ('lying', 5), ('telling-truth', 3)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('telling-truth', 2), ('telling-truth', 5))", "index": 1034}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, Henry, Mia, Victoria, Sebastian, and William. \"If Sebastian is a knave then William is a knight,\" Penelope claimed. As Henry put it, \"If William is a knave then Victoria is a knight\". Mia said that Henry is a knight if and only if Penelope is a knight. As Victoria put it, \"Sebastian is a knight\". \"Penelope is a knight or Victoria is a knave,\" Sebastian declared. In William's words: \"If Sebastian is a knave then Mia is a knave\". So who is a knight and who is a knave?", "names": ["Penelope", "Henry", "Mia", "Victoria", "Sebastian", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Penelope is a knight, Henry is a knight, Mia is a knight, Victoria is a knight, Sebastian is a knight, and William is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) Henry is a knight\n(3) Mia is a knight\n(4) Victoria is a knight\n(5) Sebastian is a knight\n(6) William is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that If Sebastian is a knave then William is a knight.", "Assume Sebastian is a knight. No contradiction is found in their claim that Penelope is a knight or Victoria is a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Sebastian is a knight.", "Assume William is a knight. No contradiction is found in their claim that If Sebastian is a knave then Mia is a knave.", "Assume Mia is a knight. No contradiction is found in their claim that Henry is a knight if and only if Penelope is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that If William is a knave then Victoria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('telling-truth', 5)), ('->', ('lying', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('telling-truth', 4), ('or', ('telling-truth', 0), ('lying', 3)), ('->', ('lying', 4), ('lying', 2)))", "index": 1035}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Victoria, Elizabeth, Jack, Liam, and David. In Jackson's words: \"Liam is a knight if and only if Jack is a knave\". Victoria expressed that Elizabeth is not a knight. \"David is a knight or Liam is a knight,\" Elizabeth declared. Jack expressed that Victoria is a knave and David is a knight. \"Jackson is a knight and Jack is a knight,\" Liam claimed. David expressed that Jack is a knave if and only if Elizabeth is a knight. So who is a knight and who is a knave?", "names": ["Jackson", "Victoria", "Elizabeth", "Jack", "Liam", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false], "solution_text": "Jackson is a knave, Victoria is a knight, Elizabeth is a knave, Jack is a knave, Liam is a knave, and David is a knave.", "solution_text_format": "(1) Jackson is a knave\n(2) Victoria is a knight\n(3) Elizabeth is a knave\n(4) Jack is a knave\n(5) Liam is a knave\n(6) David is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Liam is a knight if and only if Jack is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Jackson is a knight and Jack is a knight.", "Jack cannot be a knight, because this would contradict the claim of Jackson that Liam is a knight if and only if Jack is a knave.", "Jack cannot be a knave, because this would contradict the claim of Liam that Jackson is a knight and Jack is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Jackson is a knight and Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Liam that Jackson is a knight and Jack is a knight.", "Jack cannot be a knave, because this would contradict the claim of Jackson that Liam is a knight if and only if Jack is a knave.", "We have exhausted all possibilities for Jack and Liam, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Jack is a knave.", "Liam cannot be a knight, because this would contradict the claim of their own that Jackson is a knight and Jack is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Jackson is a knight and Jack is a knight.", "Jack cannot be a knight, because this would contradict the false claim of Jackson that Liam is a knight if and only if Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that Victoria is a knave and David is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Victoria that Elizabeth is not a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that David is a knight or Liam is a knight.", "David cannot be a knight, because this would contradict the false claim of Elizabeth that David is a knight or Liam is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 4), ('lying', 3)), ('not', ('telling-truth', 2)), ('or', ('telling-truth', 5), ('telling-truth', 4)), ('and', ('lying', 1), ('telling-truth', 5)), ('and', ('telling-truth', 0), ('telling-truth', 3)), ('<=>', ('lying', 3), ('telling-truth', 2)))", "index": 1036}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Joseph, Ava, Mason, Sofia, and Aurora. In Ella's words: \"Mason is a knight if and only if Sofia is a knave\". \"Mason is not a knave,\" Joseph declared. Ava told you that Joseph is a knight and Sofia is a knight. \"Aurora is not a knave\" - Mason. \"Ella is a knave and Aurora is a knave,\" Sofia claimed. Aurora told you that If Aurora is a knight then Ella is a knight. So who is a knight and who is a knave?", "names": ["Ella", "Joseph", "Ava", "Mason", "Sofia", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Ella is a knight, Joseph is a knight, Ava is a knave, Mason is a knight, Sofia is a knave, and Aurora is a knight.", "solution_text_format": "(1) Ella is a knight\n(2) Joseph is a knight\n(3) Ava is a knave\n(4) Mason is a knight\n(5) Sofia is a knave\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Mason is a knight if and only if Sofia is a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Aurora is not a knave.", "Assume Aurora is a knight. No contradiction is found in their claim that If Aurora is a knight then Ella is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Ella that Mason is a knight if and only if Sofia is a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Ella is a knave and Aurora is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Mason is not a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Sofia is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Joseph is a knight and Sofia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('lying', 4)), ('not', ('lying', 3)), ('and', ('telling-truth', 1), ('telling-truth', 4)), ('not', ('lying', 5)), ('and', ('lying', 0), ('lying', 5)), ('->', ('telling-truth', 5), ('telling-truth', 0)))", "index": 1037}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Grace, Charlotte, Ella, Luke, and Noah. Aiden said, \"If Noah is a knave then Noah is a knight.\" \"Charlotte is a knave and Noah is a knave,\" Grace declared. As Charlotte put it, \"If Charlotte is a knight then Noah is a knight\". Ella remarked, \"Aiden is a knight or Aiden is a knave\". \"Ella is a knave or Aiden is a knight,\" Luke declared. Noah told you that Noah is a knight. So who is a knight and who is a knave?", "names": ["Aiden", "Grace", "Charlotte", "Ella", "Luke", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Aiden is a knight, Grace is a knave, Charlotte is a knight, Ella is a knight, Luke is a knight, and Noah is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Grace is a knave\n(3) Charlotte is a knight\n(4) Ella is a knight\n(5) Luke is a knight\n(6) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that If Noah is a knave then Noah is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Noah is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave and Noah is a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Charlotte is a knave and Noah is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Charlotte is a knight then Noah is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that Aiden is a knight or Aiden is a knave.", "Assume Luke is a knight. No contradiction is found in their claim that Ella is a knave or Aiden is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 5)), ('and', ('lying', 2), ('lying', 5)), ('->', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('telling-truth', 0), ('lying', 0)), ('or', ('lying', 3), ('telling-truth', 0)), ('telling-truth', 5))", "index": 1038}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Olivia, Isabella, Evelyn, Abigail, Ethan, and Lily. In Olivia's words: \"Evelyn is a knave\". Isabella said, \"Evelyn is not a knave.\" \"Abigail is a knave,\" Evelyn claimed. \"Ethan is a knave or Isabella is a knave\" - Abigail. Ethan said that Abigail is not a knave. Lily asserted: \"Ethan is not a knight\". So who is a knight and who is a knave?", "names": ["Olivia", "Isabella", "Evelyn", "Abigail", "Ethan", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, false], "solution_text": "Olivia is a knight, Isabella is a knave, Evelyn is a knave, Abigail is a knight, Ethan is a knight, and Lily is a knave.", "solution_text_format": "(1) Olivia is a knight\n(2) Isabella is a knave\n(3) Evelyn is a knave\n(4) Abigail is a knight\n(5) Ethan is a knight\n(6) Lily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Olivia is a knight. No contradiction is found in their claim that Evelyn is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of Olivia that Evelyn is a knave.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Abigail is a knave.", "Assume Abigail is a knight. No contradiction is found in their claim that Ethan is a knave or Isabella is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Abigail is not a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Evelyn is not a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Evelyn is not a knave.", "Lily cannot be a knight, because this would contradict the claim of their own that Ethan is not a knight.", "Assume Lily is a knave. No contradiction is found in their false claim that Ethan is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 2), ('not', ('lying', 2)), ('lying', 3), ('or', ('lying', 4), ('lying', 1)), ('not', ('lying', 3)), ('not', ('telling-truth', 4)))", "index": 1039}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Benjamin, Grace, Lucas, Jack, and William. Owen said that If Grace is a knight then Benjamin is a knave. Benjamin was heard saying, \"William is a knight or Lucas is a knave\". Grace noted, \"Owen is not a knave\". Lucas said that If Benjamin is a knight then Owen is a knight. Jack stated, \"Lucas is a knight\". William said that Grace is a knave if and only if Benjamin is a knave. So who is a knight and who is a knave?", "names": ["Owen", "Benjamin", "Grace", "Lucas", "Jack", "William"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Owen is a knight, Benjamin is a knave, Grace is a knight, Lucas is a knight, Jack is a knight, and William is a knave.", "solution_text_format": "(1) Owen is a knight\n(2) Benjamin is a knave\n(3) Grace is a knight\n(4) Lucas is a knight\n(5) Jack is a knight\n(6) William is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that If Grace is a knight then Benjamin is a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Owen is not a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Owen that If Grace is a knight then Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that William is a knight or Lucas is a knave.", "William cannot be a knight, because this would contradict the false claim of Benjamin that William is a knight or Lucas is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Benjamin is a knave.", "Assume Lucas is a knight. No contradiction is found in their claim that If Benjamin is a knight then Owen is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Lucas is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('lying', 1)), ('or', ('telling-truth', 5), ('lying', 3)), ('not', ('lying', 0)), ('->', ('telling-truth', 1), ('telling-truth', 0)), ('telling-truth', 3), ('<=>', ('lying', 2), ('lying', 1)))", "index": 1040}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Liam, Emma, Ella, Aria, and Owen. Avery said, \"Liam is not a knave.\" In Liam's words: \"Emma is a knight or Aria is a knave\". According to Emma, \"Avery is a knight\". Ella commented, \"Aria is a knave\". Aria said that Ella is a knight and Ella is a knave. \"Aria is not a knight,\" Owen declared. So who is a knight and who is a knave?", "names": ["Avery", "Liam", "Emma", "Ella", "Aria", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Avery is a knight, Liam is a knight, Emma is a knight, Ella is a knight, Aria is a knave, and Owen is a knight.", "solution_text_format": "(1) Avery is a knight\n(2) Liam is a knight\n(3) Emma is a knight\n(4) Ella is a knight\n(5) Aria is a knave\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Avery is a knight. No contradiction is found in their claim that Liam is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Emma is a knight or Aria is a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Avery is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Ella is a knave.", "Assume Aria is a knave. No contradiction is found in their false claim that Ella is a knight and Ella is a knave.", "Assume Ella is a knight. No contradiction is found in their claim that Aria is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Aria is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('or', ('telling-truth', 2), ('lying', 4)), ('telling-truth', 0), ('lying', 4), ('and', ('telling-truth', 3), ('lying', 3)), ('not', ('telling-truth', 4)))", "index": 1041}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Evelyn, Elizabeth, Aria, Lucas, Jackson, and Sofia. Evelyn asserted: \"Aria is not a knave\". Elizabeth said that If Jackson is a knight then Jackson is a knave. Aria was heard saying, \"Elizabeth is a knight or Lucas is a knight\". Lucas expressed that Jackson is a knave if and only if Aria is a knight. Jackson commented, \"Evelyn is not a knight\". In Sofia's words: \"Aria is not a knight\". So who is a knight and who is a knave?", "names": ["Evelyn", "Elizabeth", "Aria", "Lucas", "Jackson", "Sofia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, false], "solution_text": "Evelyn is a knight, Elizabeth is a knight, Aria is a knight, Lucas is a knight, Jackson is a knave, and Sofia is a knave.", "solution_text_format": "(1) Evelyn is a knight\n(2) Elizabeth is a knight\n(3) Aria is a knight\n(4) Lucas is a knight\n(5) Jackson is a knave\n(6) Sofia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Evelyn is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Elizabeth is a knight or Lucas is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Jackson is a knight then Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Elizabeth that If Jackson is a knight then Jackson is a knave.", "Assume Jackson is a knave. No contradiction is found in their false claim that Evelyn is not a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Aria is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Aria is not a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Aria is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 2)), ('->', ('telling-truth', 4), ('lying', 4)), ('or', ('telling-truth', 1), ('telling-truth', 3)), ('<=>', ('lying', 4), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('not', ('telling-truth', 2)))", "index": 1042}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Alexander, Liam, Mason, Sophia, and Ava. Luke commented, \"If Ava is a knight then Mason is a knave\". Alexander remarked, \"Ava is a knight if and only if Luke is a knight\". In Liam's words: \"Liam is a knight if and only if Ava is a knave\". Mason stated, \"Ava is not a knave\". Sophia noted, \"If Mason is a knave then Liam is a knave\". According to Ava, \"Sophia is not a knave\". So who is a knight and who is a knave?", "names": ["Luke", "Alexander", "Liam", "Mason", "Sophia", "Ava"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Luke is a knight, Alexander is a knave, Liam is a knight, Mason is a knave, Sophia is a knave, and Ava is a knave.", "solution_text_format": "(1) Luke is a knight\n(2) Alexander is a knave\n(3) Liam is a knight\n(4) Mason is a knave\n(5) Sophia is a knave\n(6) Ava is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that If Ava is a knight then Mason is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Sophia is not a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that If Mason is a knave then Liam is a knave.", "Mason cannot be a knight, because this would contradict the claim of Luke that If Ava is a knight then Mason is a knave.", "Mason cannot be a knave, because this would contradict the false claim of their own that Ava is not a knave.", "We have exhausted all possibilities for Mason, so let us go back and reconsider Sophia.", "Sophia cannot be a knave, because this would contradict the claim of Ava that Sophia is not a knave.", "We have exhausted all possibilities for Sophia, so let us go back and reconsider Ava.", "Assume Ava is a knave. No contradiction is found in their false claim that Sophia is not a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Ava that Sophia is not a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that If Mason is a knave then Liam is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Ava is not a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Ava is not a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight if and only if Ava is a knave.", "Alexander cannot be a knight, because this would contradict the claim of their own that Ava is a knight if and only if Luke is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Luke is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 5), ('lying', 3)), ('<=>', ('telling-truth', 5), ('telling-truth', 0)), ('<=>', ('telling-truth', 2), ('lying', 5)), ('not', ('lying', 5)), ('->', ('lying', 3), ('lying', 2)), ('not', ('lying', 4)))", "index": 1043}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Isabella, Aiden, Sofia, Matthew, and Aurora. James was heard saying, \"Aiden is a knave if and only if Matthew is a knight\". Isabella remarked, \"Aurora is a knave and James is a knave\". As Aiden put it, \"Aurora is a knight or Aiden is a knight\". Sofia said, \"Matthew is a knave or James is a knave.\" Matthew stated, \"James is a knave and Sofia is a knave\". \"Aurora is a knight if and only if James is a knave\" - Aurora. So who is a knight and who is a knave?", "names": ["James", "Isabella", "Aiden", "Sofia", "Matthew", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, false], "solution_text": "James is a knave, Isabella is a knight, Aiden is a knave, Sofia is a knight, Matthew is a knave, and Aurora is a knave.", "solution_text_format": "(1) James is a knave\n(2) Isabella is a knight\n(3) Aiden is a knave\n(4) Sofia is a knight\n(5) Matthew is a knave\n(6) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Aiden is a knave if and only if Matthew is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Aurora is a knight or Aiden is a knight.", "Aurora cannot be a knight, because this would contradict the claim of their own that Aurora is a knight if and only if James is a knave.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight if and only if James is a knave.", "We have exhausted all possibilities for Aurora, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aurora is a knight or Aiden is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Aiden that Aurora is a knight or Aiden is a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight if and only if James is a knave.", "We have exhausted all possibilities for Aurora and Aiden, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Matthew is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Aurora is a knight or Aiden is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Aurora is a knight if and only if James is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that James is a knave and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Matthew that James is a knave and Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave or James is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of James that Aiden is a knave if and only if Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if James is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that James is a knave and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Matthew that James is a knave and Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave or James is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Matthew.", "Matthew cannot be a knave, because this would contradict the false claim of James that Aiden is a knave if and only if Matthew is a knight.", "We have exhausted all possibilities for Matthew and Aurora, so let us go back and reconsider Aiden.", "Assume Aiden is a knave. No contradiction is found in their false claim that Aurora is a knight or Aiden is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Aiden that Aurora is a knight or Aiden is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if James is a knave.", "Matthew cannot be a knight, because this would contradict the false claim of James that Aiden is a knave if and only if Matthew is a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that James is a knave and Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Matthew is a knave or James is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that Aurora is a knave and James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('telling-truth', 4)), ('and', ('lying', 5), ('lying', 0)), ('or', ('telling-truth', 5), ('telling-truth', 2)), ('or', ('lying', 4), ('lying', 0)), ('and', ('lying', 0), ('lying', 3)), ('<=>', ('telling-truth', 5), ('lying', 0)))", "index": 1044}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Avery, Samuel, Emily, Aria, and Owen. As Ella put it, \"Samuel is a knight if and only if Ella is a knight\". Avery stated, \"Samuel is a knave if and only if Emily is a knave\". Samuel stated, \"Avery is a knave or Ella is a knight\". Emily expressed that Ella is a knave or Owen is a knave. As Aria put it, \"Samuel is a knave if and only if Emily is a knight\". Owen stated, \"Owen is a knight or Samuel is a knight\". So who is a knight and who is a knave?", "names": ["Ella", "Avery", "Samuel", "Emily", "Aria", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Ella is a knight, Avery is a knave, Samuel is a knight, Emily is a knave, Aria is a knight, and Owen is a knight.", "solution_text_format": "(1) Ella is a knight\n(2) Avery is a knave\n(3) Samuel is a knight\n(4) Emily is a knave\n(5) Aria is a knight\n(6) Owen is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ella is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Ella is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Avery is a knave or Ella is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Emily is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Ella is a knave or Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of Emily that Ella is a knave or Owen is a knave.", "Owen cannot be a knave, because this would contradict the false claim of their own that Owen is a knight or Samuel is a knight.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Avery that Samuel is a knave if and only if Emily is a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Avery.", "Assume Avery is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Emily is a knave.", "Emily cannot be a knight, because this would contradict the false claim of Avery that Samuel is a knave if and only if Emily is a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Ella is a knave or Owen is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Owen is a knight or Samuel is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('<=>', ('lying', 2), ('lying', 3)), ('or', ('lying', 1), ('telling-truth', 0)), ('or', ('lying', 0), ('lying', 5)), ('<=>', ('lying', 2), ('telling-truth', 3)), ('or', ('telling-truth', 5), ('telling-truth', 2)))", "index": 1045}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Harper, Mason, Riley, Samuel, Victoria, and Sebastian. According to Harper, \"Riley is a knight if and only if Riley is a knave\". In a statement by Mason: \"Samuel is a knave if and only if Sebastian is a knight\". In a statement by Riley: \"Harper is a knave or Harper is a knight\". \"Sebastian is a knave or Mason is a knave,\" Samuel declared. In Victoria's words: \"Riley is not a knave\". Sebastian stated, \"Riley is not a knight\". So who is a knight and who is a knave?", "names": ["Harper", "Mason", "Riley", "Samuel", "Victoria", "Sebastian"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, false], "solution_text": "Harper is a knave, Mason is a knight, Riley is a knight, Samuel is a knight, Victoria is a knight, and Sebastian is a knave.", "solution_text_format": "(1) Harper is a knave\n(2) Mason is a knight\n(3) Riley is a knight\n(4) Samuel is a knight\n(5) Victoria is a knight\n(6) Sebastian is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Harper cannot be a knight, because this would contradict the claim of their own that Riley is a knight if and only if Riley is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Harper is a knave or Harper is a knight.", "Assume Mason is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Sebastian is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Sebastian is a knave or Mason is a knave.", "Sebastian cannot be a knight, because this would contradict the claim of Mason that Samuel is a knave if and only if Sebastian is a knight.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Riley is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Riley is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 2), ('lying', 2)), ('<=>', ('lying', 3), ('telling-truth', 5)), ('or', ('lying', 0), ('telling-truth', 0)), ('or', ('lying', 5), ('lying', 1)), ('not', ('lying', 2)), ('not', ('telling-truth', 2)))", "index": 1046}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Aria, Sofia, Amelia, James, and Jack. \"Aria is a knight if and only if Sofia is a knight,\" William mentioned. Aria noted, \"Sofia is a knave and Jack is a knight\". \"William is a knight or William is a knave,\" Sofia mentioned. Amelia commented, \"James is a knave and James is a knight\". In James's words: \"William is a knight\". Jack said, \"William is a knave.\" So who is a knight and who is a knave?", "names": ["William", "Aria", "Sofia", "Amelia", "James", "Jack"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, true], "solution_text": "William is a knave, Aria is a knave, Sofia is a knight, Amelia is a knave, James is a knave, and Jack is a knight.", "solution_text_format": "(1) William is a knave\n(2) Aria is a knave\n(3) Sofia is a knight\n(4) Amelia is a knave\n(5) James is a knave\n(6) Jack is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume William is a knight. No contradiction is found in their claim that Aria is a knight if and only if Sofia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Sofia is a knave and Jack is a knight.", "Sofia cannot be a knight, because this would contradict the claim of Aria that Sofia is a knave and Jack is a knight.", "Sofia cannot be a knave, because this would contradict the claim of William that Aria is a knight if and only if Sofia is a knight.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Sofia is a knave and Jack is a knight.", "Sofia cannot be a knight, because this would contradict the claim of William that Aria is a knight if and only if Sofia is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of their own that William is a knight or William is a knave.", "We have exhausted all possibilities for Sofia and Aria, so let us go back and reconsider William.", "Assume William is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Sofia is a knight.", "Assume Aria is a knight. No contradiction is found in their claim that Sofia is a knave and Jack is a knight.", "Sofia cannot be a knight, because this would contradict the false claim of William that Aria is a knight if and only if Sofia is a knight.", "Sofia cannot be a knave, because this would contradict the false claim of their own that William is a knight or William is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Aria.", "Assume Aria is a knave. No contradiction is found in their false claim that Sofia is a knave and Jack is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that William is a knight or William is a knave.", "Assume Jack is a knight. No contradiction is found in their claim that William is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that James is a knave and James is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that James is a knave and James is a knight.", "James cannot be a knight, because this would contradict the claim of their own that William is a knight.", "Assume James is a knave. No contradiction is found in their false claim that William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('lying', 2), ('telling-truth', 5)), ('or', ('telling-truth', 0), ('lying', 0)), ('and', ('lying', 4), ('telling-truth', 4)), ('telling-truth', 0), ('lying', 0))", "index": 1047}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Sebastian, Evelyn, Isabella, Penelope, and Samuel. Michael was heard saying, \"Penelope is not a knave\". In Sebastian's words: \"Isabella is a knight if and only if Isabella is a knave\". In a statement by Evelyn: \"Samuel is not a knave\". \"Penelope is a knave,\" Isabella declared. In Penelope's words: \"Sebastian is a knave if and only if Penelope is a knight\". Samuel noted, \"Evelyn is a knave and Michael is a knave\". So who is a knight and who is a knave?", "names": ["Michael", "Sebastian", "Evelyn", "Isabella", "Penelope", "Samuel"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, false], "solution_text": "Michael is a knight, Sebastian is a knave, Evelyn is a knave, Isabella is a knave, Penelope is a knight, and Samuel is a knave.", "solution_text_format": "(1) Michael is a knight\n(2) Sebastian is a knave\n(3) Evelyn is a knave\n(4) Isabella is a knave\n(5) Penelope is a knight\n(6) Samuel is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Michael is a knight. No contradiction is found in their claim that Penelope is not a knave.", "Assume Penelope is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Penelope is a knight.", "Sebastian cannot be a knight, because this would contradict the claim of their own that Isabella is a knight if and only if Isabella is a knave.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Isabella is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Penelope is a knave.", "Assume Isabella is a knave. No contradiction is found in their false claim that Penelope is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Samuel is not a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave and Michael is a knave.", "Samuel cannot be a knave, because this would contradict the claim of Evelyn that Samuel is not a knave.", "We have exhausted all possibilities for Samuel, so let us go back and reconsider Evelyn.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Samuel is not a knave.", "Samuel cannot be a knight, because this would contradict the false claim of Evelyn that Samuel is not a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Evelyn is a knave and Michael is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('<=>', ('telling-truth', 3), ('lying', 3)), ('not', ('lying', 5)), ('lying', 4), ('<=>', ('lying', 1), ('telling-truth', 4)), ('and', ('lying', 2), ('lying', 0)))", "index": 1048}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Riley, Sofia, Michael, Grace, and Avery. Owen stated, \"Michael is a knight if and only if Sofia is a knight\". Riley commented, \"Sofia is a knight and Avery is a knight\". Sofia noted, \"Riley is a knave or Michael is a knight\". Michael remarked, \"If Avery is a knight then Riley is a knight\". \"If Sofia is a knave then Riley is a knave\" - Grace. According to Avery, \"Michael is a knave if and only if Sofia is a knave\". So who is a knight and who is a knave?", "names": ["Owen", "Riley", "Sofia", "Michael", "Grace", "Avery"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Owen is a knight, Riley is a knight, Sofia is a knight, Michael is a knight, Grace is a knight, and Avery is a knight.", "solution_text_format": "(1) Owen is a knight\n(2) Riley is a knight\n(3) Sofia is a knight\n(4) Michael is a knight\n(5) Grace is a knight\n(6) Avery is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Owen is a knight. No contradiction is found in their claim that Michael is a knight if and only if Sofia is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that If Avery is a knight then Riley is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Michael is a knave if and only if Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Riley is a knave or Michael is a knight.", "Assume Riley is a knight. No contradiction is found in their claim that Sofia is a knight and Avery is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Sofia is a knave then Riley is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('telling-truth', 2)), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('lying', 1), ('telling-truth', 3)), ('->', ('telling-truth', 5), ('telling-truth', 1)), ('->', ('lying', 2), ('lying', 1)), ('<=>', ('lying', 3), ('lying', 2)))", "index": 1049}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Samuel, Matthew, Benjamin, Emily, and David. In a statement by Jacob: \"Emily is not a knave\". Samuel stated, \"Matthew is a knave if and only if David is a knave\". As Matthew put it, \"David is a knave\". Benjamin commented, \"David is a knight or Matthew is a knight\". As Emily put it, \"Samuel is a knight if and only if Benjamin is a knight\". David commented, \"Samuel is a knave\". So who is a knight and who is a knave?", "names": ["Jacob", "Samuel", "Matthew", "Benjamin", "Emily", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "Jacob is a knave, Samuel is a knave, Matthew is a knave, Benjamin is a knight, Emily is a knave, and David is a knight.", "solution_text_format": "(1) Jacob is a knave\n(2) Samuel is a knave\n(3) Matthew is a knave\n(4) Benjamin is a knight\n(5) Emily is a knave\n(6) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that Emily is not a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Samuel is a knight if and only if Benjamin is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Matthew is a knave if and only if David is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Matthew that David is a knave.", "David cannot be a knave, because this would contradict the claim of Samuel that Matthew is a knave if and only if David is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Samuel that Matthew is a knave if and only if David is a knave.", "David cannot be a knave, because this would contradict the false claim of Matthew that David is a knave.", "We have exhausted all possibilities for David and Matthew, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if David is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the false claim of Samuel that Matthew is a knave if and only if David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that Samuel is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Samuel is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Emily that Samuel is a knight if and only if Benjamin is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that David is a knight or Matthew is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of Samuel that Matthew is a knave if and only if David is a knave.", "We have exhausted all possibilities for David, Matthew, and Samuel, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Jacob that Emily is not a knave.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Emily is not a knave.", "Emily cannot be a knight, because this would contradict the false claim of Jacob that Emily is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Samuel is a knight if and only if Benjamin is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Matthew is a knave if and only if David is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Matthew that David is a knave.", "David cannot be a knave, because this would contradict the claim of Samuel that Matthew is a knave if and only if David is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Samuel that Matthew is a knave if and only if David is a knave.", "David cannot be a knave, because this would contradict the false claim of Matthew that David is a knave.", "We have exhausted all possibilities for David and Matthew, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if David is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the false claim of Samuel that Matthew is a knave if and only if David is a knave.", "David cannot be a knave, because this would contradict the false claim of their own that Samuel is a knave.", "We have exhausted all possibilities for David, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Samuel is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that David is a knight or Matthew is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('<=>', ('lying', 2), ('lying', 5)), ('lying', 5), ('or', ('telling-truth', 5), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('lying', 1))", "index": 1050}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, Zoey, Ella, James, Liam, and Benjamin. Jacob told you that If James is a knight then Ella is a knight. In Zoey's words: \"If Liam is a knight then Liam is a knave\". Ella told you that If Liam is a knave then Ella is a knight. As James put it, \"If Zoey is a knave then Zoey is a knight\". Liam expressed that Ella is a knight if and only if James is a knight. \"Jacob is a knight or Liam is a knave,\" Benjamin claimed. So who is a knight and who is a knave?", "names": ["Jacob", "Zoey", "Ella", "James", "Liam", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true], "solution_text": "Jacob is a knave, Zoey is a knight, Ella is a knave, James is a knight, Liam is a knave, and Benjamin is a knight.", "solution_text_format": "(1) Jacob is a knave\n(2) Zoey is a knight\n(3) Ella is a knave\n(4) James is a knight\n(5) Liam is a knave\n(6) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jacob is a knight. No contradiction is found in their claim that If James is a knight then Ella is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Zoey is a knave then Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Liam is a knight then Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Zoey that If Liam is a knight then Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Ella is a knight if and only if James is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Liam that Ella is a knight if and only if James is a knight.", "Ella cannot be a knave, because this would contradict the claim of Jacob that If James is a knight then Ella is a knight.", "We have exhausted all possibilities for Ella and Liam, so let us go back and reconsider Zoey.", "Zoey cannot be a knave, because this would contradict the claim of James that If Zoey is a knave then Zoey is a knight.", "We have exhausted all possibilities for Zoey, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that If Zoey is a knave then Zoey is a knight.", "Zoey cannot be a knight, because this would contradict the false claim of James that If Zoey is a knave then Zoey is a knight.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Liam is a knight then Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Ella is a knight if and only if James is a knight.", "Ella cannot be a knight, because this would contradict the claim of Liam that Ella is a knight if and only if James is a knight.", "Ella cannot be a knave, because this would contradict the false claim of their own that If Liam is a knave then Ella is a knight.", "We have exhausted all possibilities for Ella, so let us go back and reconsider Liam.", "Liam cannot be a knave, because this would contradict the false claim of Zoey that If Liam is a knight then Liam is a knave.", "We have exhausted all possibilities for Liam, Zoey, and James, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that If James is a knight then Ella is a knight.", "Assume James is a knight. No contradiction is found in their claim that If Zoey is a knave then Zoey is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that If Liam is a knight then Liam is a knave.", "Liam cannot be a knight, because this would contradict the claim of Zoey that If Liam is a knight then Liam is a knave.", "Assume Liam is a knave. No contradiction is found in their false claim that Ella is a knight if and only if James is a knight.", "Ella cannot be a knight, because this would contradict the false claim of Jacob that If James is a knight then Ella is a knight.", "Assume Ella is a knave. No contradiction is found in their false claim that If Liam is a knave then Ella is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Jacob is a knight or Liam is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 3), ('telling-truth', 2)), ('->', ('telling-truth', 4), ('lying', 4)), ('->', ('lying', 4), ('telling-truth', 2)), ('->', ('lying', 1), ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('lying', 4)))", "index": 1051}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Elizabeth, Logan, Ethan, Michael, and Owen. \"Logan is a knave and Michael is a knave,\" Sophia claimed. Elizabeth remarked, \"Logan is not a knight\". Logan asserted: \"Ethan is a knight and Michael is a knight\". As Ethan put it, \"Michael is not a knight\". According to Michael, \"Michael is a knight if and only if Sophia is a knave\". \"Elizabeth is a knave if and only if Sophia is a knave,\" Owen claimed. So who is a knight and who is a knave?", "names": ["Sophia", "Elizabeth", "Logan", "Ethan", "Michael", "Owen"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, true, false], "solution_text": "Sophia is a knave, Elizabeth is a knight, Logan is a knave, Ethan is a knave, Michael is a knight, and Owen is a knave.", "solution_text_format": "(1) Sophia is a knave\n(2) Elizabeth is a knight\n(3) Logan is a knave\n(4) Ethan is a knave\n(5) Michael is a knight\n(6) Owen is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sophia is a knight. No contradiction is found in their claim that Logan is a knave and Michael is a knave.", "Logan cannot be a knight, because this would contradict the claim of Sophia that Logan is a knave and Michael is a knave.", "Assume Logan is a knave. No contradiction is found in their false claim that Ethan is a knight and Michael is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Sophia that Logan is a knave and Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of their own that Michael is a knight if and only if Sophia is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Sophia that Logan is a knave and Michael is a knave.", "Michael cannot be a knave, because this would contradict the false claim of Ethan that Michael is not a knight.", "We have exhausted all possibilities for Michael, Ethan, and Logan, so let us go back and reconsider Sophia.", "Assume Sophia is a knave. No contradiction is found in their false claim that Logan is a knave and Michael is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Ethan is a knight and Michael is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the claim of Ethan that Michael is not a knight.", "Michael cannot be a knave, because this would contradict the claim of Logan that Ethan is a knight and Michael is a knight.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Ethan.", "Ethan cannot be a knave, because this would contradict the claim of Logan that Ethan is a knight and Michael is a knight.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Ethan is a knight and Michael is a knight.", "Assume Ethan is a knight. No contradiction is found in their claim that Michael is not a knight.", "Michael cannot be a knight, because this would contradict the false claim of Logan that Ethan is a knight and Michael is a knight.", "Michael cannot be a knave, because this would contradict the false claim of Sophia that Logan is a knave and Michael is a knave.", "We have exhausted all possibilities for Michael, so let us go back and reconsider Ethan.", "Assume Ethan is a knave. No contradiction is found in their false claim that Michael is not a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Michael is a knight if and only if Sophia is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Logan is not a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave if and only if Sophia is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Sophia is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 2), ('lying', 4)), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 3), ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('lying', 0)), ('<=>', ('lying', 1), ('lying', 0)))", "index": 1052}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Chloe, Sofia, Logan, Zoey, and Ella. Emma said, \"Chloe is a knight.\" Chloe commented, \"Logan is a knight if and only if Logan is a knave\". \"Chloe is not a knave,\" Sofia declared. Logan stated, \"If Sofia is a knight then Emma is a knave\". \"Emma is not a knight\" - Zoey. Ella told you that Emma is not a knave. So who is a knight and who is a knave?", "names": ["Emma", "Chloe", "Sofia", "Logan", "Zoey", "Ella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false], "solution_text": "Emma is a knave, Chloe is a knave, Sofia is a knave, Logan is a knight, Zoey is a knight, and Ella is a knave.", "solution_text_format": "(1) Emma is a knave\n(2) Chloe is a knave\n(3) Sofia is a knave\n(4) Logan is a knight\n(5) Zoey is a knight\n(6) Ella is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the claim of their own that Logan is a knight if and only if Logan is a knave.", "Chloe cannot be a knave, because this would contradict the claim of Emma that Chloe is a knight.", "We have exhausted all possibilities for Chloe, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Chloe cannot be a knight, because this would contradict the false claim of Emma that Chloe is a knight.", "Assume Chloe is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Logan is a knave.", "Assume Logan is a knight. No contradiction is found in their claim that If Sofia is a knight then Emma is a knave.", "Sofia cannot be a knight, because this would contradict the claim of their own that Chloe is not a knave.", "Assume Sofia is a knave. No contradiction is found in their false claim that Chloe is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Emma is not a knight.", "Ella cannot be a knight, because this would contradict the claim of their own that Emma is not a knave.", "Assume Ella is a knave. No contradiction is found in their false claim that Emma is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 1), ('<=>', ('telling-truth', 3), ('lying', 3)), ('not', ('lying', 1)), ('->', ('telling-truth', 2), ('lying', 0)), ('not', ('telling-truth', 0)), ('not', ('lying', 0)))", "index": 1053}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Owen, Daniel, Henry, Matthew, and Alexander. Mia remarked, \"Alexander is a knave\". Owen told you that Daniel is not a knave. \"Alexander is not a knight,\" Daniel mentioned. Henry said that Owen is not a knave. In a statement by Matthew: \"If Matthew is a knight then Alexander is a knave\". Alexander stated, \"Owen is a knave or Matthew is a knave\". So who is a knight and who is a knave?", "names": ["Mia", "Owen", "Daniel", "Henry", "Matthew", "Alexander"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Mia is a knight, Owen is a knight, Daniel is a knight, Henry is a knight, Matthew is a knight, and Alexander is a knave.", "solution_text_format": "(1) Mia is a knight\n(2) Owen is a knight\n(3) Daniel is a knight\n(4) Henry is a knight\n(5) Matthew is a knight\n(6) Alexander is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Mia is a knight. No contradiction is found in their claim that Alexander is a knave.", "Alexander cannot be a knight, because this would contradict the claim of Mia that Alexander is a knave.", "Assume Alexander is a knave. No contradiction is found in their false claim that Owen is a knave or Matthew is a knave.", "Assume Owen is a knight. No contradiction is found in their claim that Daniel is not a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Alexander is not a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Matthew is a knight then Alexander is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Owen is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 5), ('not', ('lying', 2)), ('not', ('telling-truth', 5)), ('not', ('lying', 1)), ('->', ('telling-truth', 4), ('lying', 5)), ('or', ('lying', 1), ('lying', 4)))", "index": 1054}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Grace, Ella, Jack, Sofia, and Emma. Aiden told you that Grace is a knight and Emma is a knight. \"Jack is a knight if and only if Sofia is a knight,\" Grace mentioned. In Ella's words: \"If Aiden is a knight then Grace is a knight\". Jack said that Ella is a knight. Sofia was heard saying, \"Aiden is a knave or Sofia is a knight\". According to Emma, \"Sofia is not a knave\". So who is a knight and who is a knave?", "names": ["Aiden", "Grace", "Ella", "Jack", "Sofia", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Aiden is a knight, Grace is a knight, Ella is a knight, Jack is a knight, Sofia is a knight, and Emma is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Grace is a knight\n(3) Ella is a knight\n(4) Jack is a knight\n(5) Sofia is a knight\n(6) Emma is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Grace is a knight and Emma is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Jack is a knight if and only if Sofia is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Ella is a knight.", "Assume Ella is a knight. No contradiction is found in their claim that If Aiden is a knight then Grace is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Aiden is a knave or Sofia is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Sofia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 2), ('or', ('lying', 0), ('telling-truth', 4)), ('not', ('lying', 4)))", "index": 1055}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, William, Noah, Grace, Jacob, and Liam. Abigail noted, \"Noah is not a knight\". William asserted: \"Liam is a knight if and only if Liam is a knave\". Noah told you that If William is a knight then Abigail is a knave. Grace was heard saying, \"Noah is a knight if and only if Abigail is a knight\". Jacob told you that If William is a knight then Grace is a knight. \"Jacob is not a knight,\" Liam claimed. So who is a knight and who is a knave?", "names": ["Abigail", "William", "Noah", "Grace", "Jacob", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, true, false], "solution_text": "Abigail is a knave, William is a knave, Noah is a knight, Grace is a knave, Jacob is a knight, and Liam is a knave.", "solution_text_format": "(1) Abigail is a knave\n(2) William is a knave\n(3) Noah is a knight\n(4) Grace is a knave\n(5) Jacob is a knight\n(6) Liam is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Abigail is a knight. No contradiction is found in their claim that Noah is not a knight.", "Noah cannot be a knight, because this would contradict the claim of Abigail that Noah is not a knight.", "Assume Noah is a knave. No contradiction is found in their false claim that If William is a knight then Abigail is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Liam is a knight if and only if Liam is a knave.", "William cannot be a knave, because this would contradict the false claim of Noah that If William is a knight then Abigail is a knave.", "We have exhausted all possibilities for William and Noah, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Noah is not a knight.", "Assume Noah is a knight. No contradiction is found in their claim that If William is a knight then Abigail is a knave.", "William cannot be a knight, because this would contradict the claim of their own that Liam is a knight if and only if Liam is a knave.", "Assume William is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Jacob is not a knight.", "Jacob cannot be a knight, because this would contradict the claim of Liam that Jacob is not a knight.", "Jacob cannot be a knave, because this would contradict the false claim of their own that If William is a knight then Grace is a knight.", "We have exhausted all possibilities for Jacob, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If William is a knight then Grace is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Noah is a knight if and only if Abigail is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Noah is a knight if and only if Abigail is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 5), ('lying', 5)), ('->', ('telling-truth', 1), ('lying', 0)), ('<=>', ('telling-truth', 2), ('telling-truth', 0)), ('->', ('telling-truth', 1), ('telling-truth', 3)), ('not', ('telling-truth', 4)))", "index": 1056}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, David, Mason, Ava, Jackson, and Sophia. Aiden said, \"If Sophia is a knave then Ava is a knight.\" David asserted: \"Jackson is a knave or Sophia is a knave\". Mason remarked, \"If Sophia is a knight then Aiden is a knave\". Ava said, \"Aiden is a knight and Sophia is a knight.\" In a statement by Jackson: \"Sophia is a knight or Aiden is a knave\". \"Aiden is a knave or Aiden is a knight\" - Sophia. So who is a knight and who is a knave?", "names": ["Aiden", "David", "Mason", "Ava", "Jackson", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, true, true], "solution_text": "Aiden is a knight, David is a knave, Mason is a knave, Ava is a knight, Jackson is a knight, and Sophia is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) David is a knave\n(3) Mason is a knave\n(4) Ava is a knight\n(5) Jackson is a knight\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that If Sophia is a knave then Ava is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Aiden is a knave or Aiden is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Aiden is a knight and Sophia is a knight.", "Assume David is a knight. No contradiction is found in their claim that Jackson is a knave or Sophia is a knave.", "Jackson cannot be a knight, because this would contradict the claim of David that Jackson is a knave or Sophia is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight or Aiden is a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider David.", "Assume David is a knave. No contradiction is found in their false claim that Jackson is a knave or Sophia is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Sophia is a knight or Aiden is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that If Sophia is a knight then Aiden is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that If Sophia is a knight then Aiden is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 3)), ('or', ('lying', 4), ('lying', 5)), ('->', ('telling-truth', 5), ('lying', 0)), ('and', ('telling-truth', 0), ('telling-truth', 5)), ('or', ('telling-truth', 5), ('lying', 0)), ('or', ('lying', 0), ('telling-truth', 0)))", "index": 1057}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, David, Jack, Logan, Amelia, and Emily. In Joseph's words: \"Emily is a knave or Jack is a knave\". \"Joseph is a knight or Jack is a knave,\" David declared. \"If Logan is a knight then Joseph is a knave,\" Jack declared. According to Logan, \"If Emily is a knight then Joseph is a knight\". Amelia said, \"David is a knight if and only if Emily is a knave.\" \"Joseph is a knight or Logan is a knight,\" Emily claimed. So who is a knight and who is a knave?", "names": ["Joseph", "David", "Jack", "Logan", "Amelia", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, true], "solution_text": "Joseph is a knight, David is a knight, Jack is a knave, Logan is a knight, Amelia is a knave, and Emily is a knight.", "solution_text_format": "(1) Joseph is a knight\n(2) David is a knight\n(3) Jack is a knave\n(4) Logan is a knight\n(5) Amelia is a knave\n(6) Emily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Emily is a knave or Jack is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Joseph is a knight or Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that If Emily is a knight then Joseph is a knight.", "Jack cannot be a knight, because this would contradict the claim of Joseph that Emily is a knave or Jack is a knave.", "Assume Jack is a knave. No contradiction is found in their false claim that If Logan is a knight then Joseph is a knave.", "Assume David is a knight. No contradiction is found in their claim that Joseph is a knight or Jack is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that David is a knight if and only if Emily is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that David is a knight if and only if Emily is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('lying', 2)), ('or', ('telling-truth', 0), ('lying', 2)), ('->', ('telling-truth', 3), ('lying', 0)), ('->', ('telling-truth', 5), ('telling-truth', 0)), ('<=>', ('telling-truth', 1), ('lying', 5)), ('or', ('telling-truth', 0), ('telling-truth', 3)))", "index": 1058}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, William, Amelia, Zoey, Ella, and James. \"Amelia is a knight or James is a knight,\" Charlotte declared. William said that Amelia is not a knave. \"James is a knave,\" Amelia claimed. Zoey said that Amelia is not a knave. \"James is not a knight\" - Ella. \"William is a knight if and only if James is a knight,\" James claimed. So who is a knight and who is a knave?", "names": ["Charlotte", "William", "Amelia", "Zoey", "Ella", "James"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, false], "solution_text": "Charlotte is a knight, William is a knight, Amelia is a knight, Zoey is a knight, Ella is a knight, and James is a knave.", "solution_text_format": "(1) Charlotte is a knight\n(2) William is a knight\n(3) Amelia is a knight\n(4) Zoey is a knight\n(5) Ella is a knight\n(6) James is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Amelia is a knight or James is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that James is a knave.", "James cannot be a knight, because this would contradict the claim of Amelia that James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that William is a knight if and only if James is a knight.", "Assume William is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume Zoey is a knight. No contradiction is found in their claim that Amelia is not a knave.", "Assume Ella is a knight. No contradiction is found in their claim that James is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('lying', 2)), ('lying', 5), ('not', ('lying', 2)), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 1), ('telling-truth', 5)))", "index": 1059}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Owen, Isabella, Victoria, Liam, and Penelope. \"Penelope is not a knight\" - Charlotte. Owen said that Isabella is not a knight. Isabella commented, \"If Victoria is a knight then Charlotte is a knight\". \"Penelope is not a knight,\" Victoria mentioned. Liam expressed that Liam is a knight if and only if Victoria is a knight. \"Charlotte is a knight if and only if Liam is a knave,\" Penelope mentioned. So who is a knight and who is a knave?", "names": ["Charlotte", "Owen", "Isabella", "Victoria", "Liam", "Penelope"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, false], "solution_text": "Charlotte is a knight, Owen is a knave, Isabella is a knight, Victoria is a knight, Liam is a knight, and Penelope is a knave.", "solution_text_format": "(1) Charlotte is a knight\n(2) Owen is a knave\n(3) Isabella is a knight\n(4) Victoria is a knight\n(5) Liam is a knight\n(6) Penelope is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of Charlotte that Penelope is not a knight.", "Assume Penelope is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Liam is a knave.", "Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight if and only if Victoria is a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Isabella is not a knight.", "Isabella cannot be a knight, because this would contradict the claim of Owen that Isabella is not a knight.", "Isabella cannot be a knave, because this would contradict the false claim of their own that If Victoria is a knight then Charlotte is a knight.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Isabella is not a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that If Victoria is a knight then Charlotte is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('not', ('telling-truth', 2)), ('->', ('telling-truth', 3), ('telling-truth', 0)), ('not', ('telling-truth', 5)), ('<=>', ('telling-truth', 4), ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('lying', 4)))", "index": 1060}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Victoria, Mia, Elizabeth, Emily, and Aurora. Alexander expressed that Victoria is a knight and Mia is a knight. Victoria noted, \"Aurora is a knave and Aurora is a knight\". Mia asserted: \"If Emily is a knave then Elizabeth is a knight\". Elizabeth said, \"If Mia is a knave then Aurora is a knight.\" Emily was heard saying, \"Victoria is not a knave\". Aurora was heard saying, \"Elizabeth is not a knight\". So who is a knight and who is a knave?", "names": ["Alexander", "Victoria", "Mia", "Elizabeth", "Emily", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, false, false], "solution_text": "Alexander is a knave, Victoria is a knave, Mia is a knight, Elizabeth is a knight, Emily is a knave, and Aurora is a knave.", "solution_text_format": "(1) Alexander is a knave\n(2) Victoria is a knave\n(3) Mia is a knight\n(4) Elizabeth is a knight\n(5) Emily is a knave\n(6) Aurora is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Alexander is a knight. No contradiction is found in their claim that Victoria is a knight and Mia is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Aurora is a knight.", "Victoria cannot be a knave, because this would contradict the claim of Alexander that Victoria is a knight and Mia is a knight.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Victoria is a knight and Mia is a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Aurora is a knight.", "Assume Victoria is a knave. No contradiction is found in their false claim that Aurora is a knave and Aurora is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Elizabeth is not a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Aurora that Elizabeth is not a knight.", "Elizabeth cannot be a knave, because this would contradict the false claim of their own that If Mia is a knave then Aurora is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that Elizabeth is not a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Mia is a knave then Aurora is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Emily is a knave then Elizabeth is a knight.", "Emily cannot be a knight, because this would contradict the claim of their own that Victoria is not a knave.", "Assume Emily is a knave. No contradiction is found in their false claim that Victoria is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 1), ('telling-truth', 2)), ('and', ('lying', 5), ('telling-truth', 5)), ('->', ('lying', 4), ('telling-truth', 3)), ('->', ('lying', 2), ('telling-truth', 5)), ('not', ('lying', 1)), ('not', ('telling-truth', 3)))", "index": 1061}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Joseph, Ava, Alexander, Mia, and Victoria. \"Alexander is not a knave\" - Emma. In Joseph's words: \"Emma is a knight\". Ava noted, \"Victoria is not a knave\". As Alexander put it, \"If Ava is a knave then Alexander is a knight\". Mia noted, \"If Ava is a knight then Alexander is a knave\". \"Ava is a knight or Ava is a knave\" - Victoria. So who is a knight and who is a knave?", "names": ["Emma", "Joseph", "Ava", "Alexander", "Mia", "Victoria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Emma is a knight, Joseph is a knight, Ava is a knight, Alexander is a knight, Mia is a knave, and Victoria is a knight.", "solution_text_format": "(1) Emma is a knight\n(2) Joseph is a knight\n(3) Ava is a knight\n(4) Alexander is a knight\n(5) Mia is a knave\n(6) Victoria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that Alexander is not a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that If Ava is a knave then Alexander is a knight.", "Assume Ava is a knight. No contradiction is found in their claim that Victoria is not a knave.", "Assume Victoria is a knight. No contradiction is found in their claim that Ava is a knight or Ava is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Emma is a knight.", "Mia cannot be a knight, because this would contradict the claim of their own that If Ava is a knight then Alexander is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that If Ava is a knight then Alexander is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('telling-truth', 0), ('not', ('lying', 5)), ('->', ('lying', 2), ('telling-truth', 3)), ('->', ('telling-truth', 2), ('lying', 3)), ('or', ('telling-truth', 2), ('lying', 2)))", "index": 1062}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Benjamin, Amelia, Logan, Alexander, and Sophia. Matthew commented, \"If Alexander is a knight then Logan is a knave\". Benjamin noted, \"If Matthew is a knave then Logan is a knight\". In Amelia's words: \"Amelia is a knight or Benjamin is a knight\". Logan was heard saying, \"Benjamin is not a knave\". Alexander was heard saying, \"Alexander is a knight or Benjamin is a knight\". Sophia commented, \"Amelia is not a knave\". So who is a knight and who is a knave?", "names": ["Matthew", "Benjamin", "Amelia", "Logan", "Alexander", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, true, true, true], "solution_text": "Matthew is a knave, Benjamin is a knight, Amelia is a knight, Logan is a knight, Alexander is a knight, and Sophia is a knight.", "solution_text_format": "(1) Matthew is a knave\n(2) Benjamin is a knight\n(3) Amelia is a knight\n(4) Logan is a knight\n(5) Alexander is a knight\n(6) Sophia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that If Alexander is a knight then Logan is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Alexander is a knight or Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Matthew is a knave then Logan is a knight.", "Logan cannot be a knight, because this would contradict the claim of Matthew that If Alexander is a knight then Logan is a knave.", "Logan cannot be a knave, because this would contradict the false claim of their own that Benjamin is not a knave.", "We have exhausted all possibilities for Logan, so let us go back and reconsider Benjamin.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knave then Logan is a knight.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that Alexander is a knight or Benjamin is a knight.", "Benjamin cannot be a knight, because this would contradict the false claim of Alexander that Alexander is a knight or Benjamin is a knight.", "Benjamin cannot be a knave, because this would contradict the false claim of their own that If Matthew is a knave then Logan is a knight.", "We have exhausted all possibilities for Benjamin and Alexander, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that If Alexander is a knight then Logan is a knave.", "Assume Alexander is a knight. No contradiction is found in their claim that Alexander is a knight or Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that If Matthew is a knave then Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Benjamin is not a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight or Benjamin is a knight.", "Assume Sophia is a knight. No contradiction is found in their claim that Amelia is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('lying', 3)), ('->', ('lying', 0), ('telling-truth', 3)), ('or', ('telling-truth', 2), ('telling-truth', 1)), ('not', ('lying', 1)), ('or', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('lying', 2)))", "index": 1063}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Charlotte, Amelia, Ethan, Sofia, Grace, and Noah. \"Sofia is a knight if and only if Charlotte is a knight,\" Charlotte claimed. Amelia told you that Sofia is not a knave. Ethan said that Noah is a knight or Charlotte is a knave. \"Noah is a knight if and only if Amelia is a knight,\" Sofia declared. \"If Amelia is a knight then Amelia is a knave\" - Grace. \"Charlotte is a knight or Grace is a knight,\" Noah declared. So who is a knight and who is a knave?", "names": ["Charlotte", "Amelia", "Ethan", "Sofia", "Grace", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Charlotte is a knight, Amelia is a knight, Ethan is a knight, Sofia is a knight, Grace is a knave, and Noah is a knight.", "solution_text_format": "(1) Charlotte is a knight\n(2) Amelia is a knight\n(3) Ethan is a knight\n(4) Sofia is a knight\n(5) Grace is a knave\n(6) Noah is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Charlotte is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Charlotte is a knight.", "Assume Sofia is a knight. No contradiction is found in their claim that Noah is a knight if and only if Amelia is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Charlotte is a knight or Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Amelia is a knight then Amelia is a knave.", "Amelia cannot be a knight, because this would contradict the claim of Grace that If Amelia is a knight then Amelia is a knave.", "Amelia cannot be a knave, because this would contradict the false claim of their own that Sofia is not a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that If Amelia is a knight then Amelia is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Sofia is not a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that Noah is a knight or Charlotte is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('not', ('lying', 3)), ('or', ('telling-truth', 5), ('lying', 0)), ('<=>', ('telling-truth', 5), ('telling-truth', 1)), ('->', ('telling-truth', 1), ('lying', 1)), ('or', ('telling-truth', 0), ('telling-truth', 4)))", "index": 1064}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Grace, Owen, Matthew, Ethan, Emily, and Oliver. Grace remarked, \"Ethan is a knave\". Owen expressed that Matthew is a knight and Oliver is a knight. As Matthew put it, \"Oliver is a knave and Grace is a knave\". Ethan commented, \"Emily is a knight and Matthew is a knight\". \"If Grace is a knight then Matthew is a knight\" - Emily. Oliver remarked, \"Emily is a knight if and only if Owen is a knave\". So who is a knight and who is a knave?", "names": ["Grace", "Owen", "Matthew", "Ethan", "Emily", "Oliver"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, false], "solution_text": "Grace is a knight, Owen is a knave, Matthew is a knave, Ethan is a knave, Emily is a knave, and Oliver is a knave.", "solution_text_format": "(1) Grace is a knight\n(2) Owen is a knave\n(3) Matthew is a knave\n(4) Ethan is a knave\n(5) Emily is a knave\n(6) Oliver is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Grace is a knight. No contradiction is found in their claim that Ethan is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Grace that Ethan is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Emily is a knight and Matthew is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that If Grace is a knight then Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Oliver is a knave and Grace is a knave.", "Matthew cannot be a knave, because this would contradict the claim of Emily that If Grace is a knight then Matthew is a knight.", "We have exhausted all possibilities for Matthew, so let us go back and reconsider Emily.", "Assume Emily is a knave. No contradiction is found in their false claim that If Grace is a knight then Matthew is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Oliver is a knave and Grace is a knave.", "Assume Matthew is a knave. No contradiction is found in their false claim that Oliver is a knave and Grace is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Emily is a knight if and only if Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Matthew is a knight and Oliver is a knight.", "Owen cannot be a knave, because this would contradict the claim of Oliver that Emily is a knight if and only if Owen is a knave.", "We have exhausted all possibilities for Owen, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Owen is a knave.", "Owen cannot be a knight, because this would contradict the claim of their own that Matthew is a knight and Oliver is a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Matthew is a knight and Oliver is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 3), ('and', ('telling-truth', 2), ('telling-truth', 5)), ('and', ('lying', 5), ('lying', 0)), ('and', ('telling-truth', 4), ('telling-truth', 2)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 4), ('lying', 1)))", "index": 1065}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, David, Abigail, Lily, Penelope, and Jackson. Emma remarked, \"If Jackson is a knave then David is a knight\". David said, \"Penelope is not a knight.\" Abigail told you that Lily is not a knight. \"David is a knave or Abigail is a knave,\" Lily declared. Penelope commented, \"If Penelope is a knight then David is a knave\". Jackson stated, \"Lily is a knave\". So who is a knight and who is a knave?", "names": ["Emma", "David", "Abigail", "Lily", "Penelope", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, true, false], "solution_text": "Emma is a knave, David is a knave, Abigail is a knave, Lily is a knight, Penelope is a knight, and Jackson is a knave.", "solution_text_format": "(1) Emma is a knave\n(2) David is a knave\n(3) Abigail is a knave\n(4) Lily is a knight\n(5) Penelope is a knight\n(6) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Emma is a knight. No contradiction is found in their claim that If Jackson is a knave then David is a knight.", "Assume Jackson is a knight. No contradiction is found in their claim that Lily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Jackson that Lily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that David is a knave or Abigail is a knave.", "Assume David is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of David that Penelope is not a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that If Penelope is a knight then David is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the false claim of Lily that David is a knave or Abigail is a knave.", "We have exhausted all possibilities for David and Lily, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that David is a knave or Abigail is a knave.", "Assume David is a knight. No contradiction is found in their claim that Penelope is not a knight.", "Penelope cannot be a knight, because this would contradict the claim of David that Penelope is not a knight.", "Penelope cannot be a knave, because this would contradict the false claim of their own that If Penelope is a knight then David is a knave.", "We have exhausted all possibilities for Penelope, so let us go back and reconsider David.", "David cannot be a knave, because this would contradict the claim of Emma that If Jackson is a knave then David is a knight.", "We have exhausted all possibilities for David, so let us go back and reconsider Lily.", "Lily cannot be a knave, because this would contradict the false claim of Jackson that Lily is a knave.", "We have exhausted all possibilities for Lily and Jackson, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that If Jackson is a knave then David is a knight.", "Jackson cannot be a knight, because this would contradict the false claim of Emma that If Jackson is a knave then David is a knight.", "Assume Jackson is a knave. No contradiction is found in their false claim that Lily is a knave.", "Assume Lily is a knight. No contradiction is found in their claim that David is a knave or Abigail is a knave.", "David cannot be a knight, because this would contradict the false claim of Emma that If Jackson is a knave then David is a knight.", "Assume David is a knave. No contradiction is found in their false claim that Penelope is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that If Penelope is a knight then David is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Lily is not a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Lily is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 5), ('telling-truth', 1)), ('not', ('telling-truth', 4)), ('not', ('telling-truth', 3)), ('or', ('lying', 1), ('lying', 2)), ('->', ('telling-truth', 4), ('lying', 1)), ('lying', 3))", "index": 1066}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Harper, Grace, Mason, Elizabeth, and Emily. Matthew noted, \"Harper is a knave\". Harper remarked, \"Elizabeth is a knave if and only if Grace is a knight\". In a statement by Grace: \"Matthew is a knave or Elizabeth is a knave\". In a statement by Mason: \"Grace is not a knight\". Elizabeth noted, \"Grace is a knave or Emily is a knight\". Emily was heard saying, \"Matthew is a knight if and only if Matthew is a knave\". So who is a knight and who is a knave?", "names": ["Matthew", "Harper", "Grace", "Mason", "Elizabeth", "Emily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, true, false, false, false], "solution_text": "Matthew is a knave, Harper is a knight, Grace is a knight, Mason is a knave, Elizabeth is a knave, and Emily is a knave.", "solution_text_format": "(1) Matthew is a knave\n(2) Harper is a knight\n(3) Grace is a knight\n(4) Mason is a knave\n(5) Elizabeth is a knave\n(6) Emily is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Harper is a knave.", "Harper cannot be a knight, because this would contradict the claim of Matthew that Harper is a knave.", "Assume Harper is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Grace is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Grace is a knave or Emily is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Matthew is a knave or Elizabeth is a knave.", "Grace cannot be a knave, because this would contradict the false claim of Harper that Elizabeth is a knave if and only if Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Grace is a knave or Emily is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Harper that Elizabeth is a knave if and only if Grace is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave or Elizabeth is a knave.", "We have exhausted all possibilities for Grace, Elizabeth, and Harper, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Harper is a knave.", "Assume Harper is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if Grace is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Grace is a knave or Emily is a knight.", "Grace cannot be a knight, because this would contradict the claim of Harper that Elizabeth is a knave if and only if Grace is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that Matthew is a knave or Elizabeth is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Grace is a knave or Emily is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Matthew is a knave or Elizabeth is a knave.", "Emily cannot be a knight, because this would contradict the false claim of Elizabeth that Grace is a knave or Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Matthew is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Grace is not a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Grace is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('lying', 1), ('<=>', ('lying', 4), ('telling-truth', 2)), ('or', ('lying', 0), ('lying', 4)), ('not', ('telling-truth', 2)), ('or', ('lying', 2), ('telling-truth', 5)), ('<=>', ('telling-truth', 0), ('lying', 0)))", "index": 1067}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ethan, Benjamin, Abigail, Harper, Owen, and Sophia. Ethan was heard saying, \"Harper is a knight\". Benjamin asserted: \"Sophia is not a knave\". Abigail noted, \"Ethan is a knight or Sophia is a knight\". Harper told you that Harper is a knight if and only if Benjamin is a knave. As Owen put it, \"If Benjamin is a knave then Harper is a knave\". Sophia remarked, \"Benjamin is a knight if and only if Abigail is a knight\". So who is a knight and who is a knave?", "names": ["Ethan", "Benjamin", "Abigail", "Harper", "Owen", "Sophia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, false], "solution_text": "Ethan is a knight, Benjamin is a knave, Abigail is a knight, Harper is a knight, Owen is a knave, and Sophia is a knave.", "solution_text_format": "(1) Ethan is a knight\n(2) Benjamin is a knave\n(3) Abigail is a knight\n(4) Harper is a knight\n(5) Owen is a knave\n(6) Sophia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ethan is a knight. No contradiction is found in their claim that Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Harper is a knight if and only if Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of Harper that Harper is a knight if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Sophia is not a knave.", "Sophia cannot be a knight, because this would contradict the false claim of Benjamin that Sophia is not a knave.", "Assume Sophia is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Abigail is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Ethan is a knight or Sophia is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that If Benjamin is a knave then Harper is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that If Benjamin is a knave then Harper is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('telling-truth', 3), ('not', ('lying', 5)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 1)), ('->', ('lying', 1), ('lying', 3)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)))", "index": 1068}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Michael, Penelope, Charlotte, Daniel, and Isabella. \"Isabella is a knight and Penelope is a knave,\" James declared. In a statement by Michael: \"Isabella is a knave\". Penelope said that Daniel is a knave if and only if Isabella is a knave. \"Michael is a knave or Isabella is a knave,\" Charlotte declared. Daniel asserted: \"Isabella is a knight if and only if James is a knave\". Isabella said that James is not a knight. So who is a knight and who is a knave?", "names": ["James", "Michael", "Penelope", "Charlotte", "Daniel", "Isabella"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "James is a knave, Michael is a knave, Penelope is a knight, Charlotte is a knight, Daniel is a knight, and Isabella is a knight.", "solution_text_format": "(1) James is a knave\n(2) Michael is a knave\n(3) Penelope is a knight\n(4) Charlotte is a knight\n(5) Daniel is a knight\n(6) Isabella is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Isabella is a knight and Penelope is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that James is not a knight.", "Isabella cannot be a knave, because this would contradict the claim of James that Isabella is a knight and Penelope is a knave.", "We have exhausted all possibilities for Isabella, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Isabella is a knight and Penelope is a knave.", "Assume Isabella is a knight. No contradiction is found in their claim that James is not a knight.", "Assume Penelope is a knight. No contradiction is found in their claim that Daniel is a knave if and only if Isabella is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Isabella is a knight if and only if James is a knave.", "Michael cannot be a knight, because this would contradict the claim of their own that Isabella is a knave.", "Assume Michael is a knave. No contradiction is found in their false claim that Isabella is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Michael is a knave or Isabella is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('telling-truth', 5), ('lying', 2)), ('lying', 5), ('<=>', ('lying', 4), ('lying', 5)), ('or', ('lying', 1), ('lying', 5)), ('<=>', ('telling-truth', 5), ('lying', 0)), ('not', ('telling-truth', 0)))", "index": 1069}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Avery, Amelia, Elizabeth, Emma, and Liam. Joseph was heard saying, \"Amelia is a knight or Avery is a knight\". Avery expressed that Elizabeth is a knave. In a statement by Amelia: \"Joseph is a knight if and only if Avery is a knight\". Elizabeth stated, \"Emma is a knave and Joseph is a knave\". \"Avery is not a knight,\" Emma declared. Liam expressed that Avery is a knight if and only if Emma is a knave. So who is a knight and who is a knave?", "names": ["Joseph", "Avery", "Amelia", "Elizabeth", "Emma", "Liam"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, true], "solution_text": "Joseph is a knight, Avery is a knight, Amelia is a knight, Elizabeth is a knave, Emma is a knave, and Liam is a knight.", "solution_text_format": "(1) Joseph is a knight\n(2) Avery is a knight\n(3) Amelia is a knight\n(4) Elizabeth is a knave\n(5) Emma is a knave\n(6) Liam is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Amelia is a knight or Avery is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Avery is a knight.", "Assume Avery is a knight. No contradiction is found in their claim that Elizabeth is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Avery that Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Emma is a knave and Joseph is a knave.", "Emma cannot be a knight, because this would contradict the claim of their own that Avery is not a knight.", "Assume Emma is a knave. No contradiction is found in their false claim that Avery is not a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Avery is a knight if and only if Emma is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('telling-truth', 2), ('telling-truth', 1)), ('lying', 3), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('and', ('lying', 4), ('lying', 0)), ('not', ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('lying', 4)))", "index": 1070}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Sofia, Owen, Isabella, Samuel, and Mason. In a statement by Amelia: \"If Samuel is a knave then Mason is a knave\". Sofia stated, \"Amelia is a knight or Owen is a knave\". Owen expressed that Owen is a knight and Sofia is a knave. Isabella said that Sofia is not a knight. Samuel was heard saying, \"Owen is a knave if and only if Sofia is a knight\". In a statement by Mason: \"Amelia is a knave or Sofia is a knave\". So who is a knight and who is a knave?", "names": ["Amelia", "Sofia", "Owen", "Isabella", "Samuel", "Mason"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, true, false], "solution_text": "Amelia is a knight, Sofia is a knight, Owen is a knave, Isabella is a knave, Samuel is a knight, and Mason is a knave.", "solution_text_format": "(1) Amelia is a knight\n(2) Sofia is a knight\n(3) Owen is a knave\n(4) Isabella is a knave\n(5) Samuel is a knight\n(6) Mason is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Amelia is a knight. No contradiction is found in their claim that If Samuel is a knave then Mason is a knave.", "Assume Samuel is a knight. No contradiction is found in their claim that Owen is a knave if and only if Sofia is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Owen is a knight and Sofia is a knave.", "Sofia cannot be a knight, because this would contradict the claim of Owen that Owen is a knight and Sofia is a knave.", "Sofia cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight or Owen is a knave.", "We have exhausted all possibilities for Sofia, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Owen is a knight and Sofia is a knave.", "Assume Sofia is a knight. No contradiction is found in their claim that Amelia is a knight or Owen is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Amelia is a knave or Sofia is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Amelia is a knave or Sofia is a knave.", "Isabella cannot be a knight, because this would contradict the claim of their own that Sofia is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Sofia is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 4), ('lying', 5)), ('or', ('telling-truth', 0), ('lying', 2)), ('and', ('telling-truth', 2), ('lying', 1)), ('not', ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 1)), ('or', ('lying', 0), ('lying', 1)))", "index": 1071}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Oliver, William, Amelia, Ella, and Jacob. Lily remarked, \"If William is a knave then William is a knight\". \"Jacob is not a knight\" - Oliver. In a statement by William: \"If Amelia is a knight then Oliver is a knight\". Amelia told you that William is a knight if and only if Oliver is a knight. In a statement by Ella: \"William is not a knave\". Jacob stated, \"Ella is not a knave\". So who is a knight and who is a knave?", "names": ["Lily", "Oliver", "William", "Amelia", "Ella", "Jacob"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, true, true], "solution_text": "Lily is a knight, Oliver is a knave, William is a knight, Amelia is a knave, Ella is a knight, and Jacob is a knight.", "solution_text_format": "(1) Lily is a knight\n(2) Oliver is a knave\n(3) William is a knight\n(4) Amelia is a knave\n(5) Ella is a knight\n(6) Jacob is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that If William is a knave then William is a knight.", "Assume William is a knight. No contradiction is found in their claim that If Amelia is a knight then Oliver is a knight.", "Assume Amelia is a knight. No contradiction is found in their claim that William is a knight if and only if Oliver is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Jacob is not a knight.", "Jacob cannot be a knight, because this would contradict the claim of Oliver that Jacob is not a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Ella is not a knave.", "Ella cannot be a knight, because this would contradict the false claim of Jacob that Ella is not a knave.", "Ella cannot be a knave, because this would contradict the false claim of their own that William is not a knave.", "We have exhausted all possibilities for Ella and Jacob, so let us go back and reconsider Oliver.", "Oliver cannot be a knave, because this would contradict the claim of William that If Amelia is a knight then Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that William is a knight if and only if Oliver is a knight.", "Oliver cannot be a knight, because this would contradict the false claim of Amelia that William is a knight if and only if Oliver is a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Jacob is not a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that Ella is not a knave.", "Assume Ella is a knight. No contradiction is found in their claim that William is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 2)), ('not', ('telling-truth', 5)), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('not', ('lying', 2)), ('not', ('lying', 4)))", "index": 1072}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lucas, Aiden, Harper, David, Elizabeth, and Henry. Lucas noted, \"If Harper is a knight then Aiden is a knight\". Aiden said, \"If Lucas is a knight then Henry is a knave.\" As Harper put it, \"David is a knave\". David was heard saying, \"Henry is not a knave\". In a statement by Elizabeth: \"Henry is a knave and Elizabeth is a knight\". Henry remarked, \"If David is a knave then Lucas is a knight\". So who is a knight and who is a knave?", "names": ["Lucas", "Aiden", "Harper", "David", "Elizabeth", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, true, false, true], "solution_text": "Lucas is a knight, Aiden is a knave, Harper is a knave, David is a knight, Elizabeth is a knave, and Henry is a knight.", "solution_text_format": "(1) Lucas is a knight\n(2) Aiden is a knave\n(3) Harper is a knave\n(4) David is a knight\n(5) Elizabeth is a knave\n(6) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lucas is a knight. No contradiction is found in their claim that If Harper is a knight then Aiden is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that David is a knave.", "David cannot be a knight, because this would contradict the claim of Harper that David is a knave.", "Assume David is a knave. No contradiction is found in their false claim that Henry is not a knave.", "Henry cannot be a knight, because this would contradict the false claim of David that Henry is not a knave.", "Henry cannot be a knave, because this would contradict the false claim of their own that If David is a knave then Lucas is a knight.", "We have exhausted all possibilities for Henry and David, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that David is a knave.", "Assume David is a knight. No contradiction is found in their claim that Henry is not a knave.", "Assume Henry is a knight. No contradiction is found in their claim that If David is a knave then Lucas is a knight.", "Aiden cannot be a knight, because this would contradict the claim of their own that If Lucas is a knight then Henry is a knave.", "Assume Aiden is a knave. No contradiction is found in their false claim that If Lucas is a knight then Henry is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Henry is a knave and Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Henry is a knave and Elizabeth is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 1)), ('->', ('telling-truth', 0), ('lying', 5)), ('lying', 3), ('not', ('lying', 5)), ('and', ('lying', 5), ('telling-truth', 4)), ('->', ('lying', 3), ('telling-truth', 0)))", "index": 1073}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Samuel, Grace, Abigail, Harper, and Aria. Riley remarked, \"Samuel is a knave or Abigail is a knight\". As Samuel put it, \"Harper is a knave or Grace is a knight\". As Grace put it, \"Harper is a knave and Aria is a knight\". Abigail asserted: \"Riley is a knight\". As Harper put it, \"Abigail is a knight and Grace is a knight\". In a statement by Aria: \"Riley is not a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Samuel", "Grace", "Abigail", "Harper", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, false, false, false], "solution_text": "Riley is a knave, Samuel is a knight, Grace is a knave, Abigail is a knave, Harper is a knave, and Aria is a knave.", "solution_text_format": "(1) Riley is a knave\n(2) Samuel is a knight\n(3) Grace is a knave\n(4) Abigail is a knave\n(5) Harper is a knave\n(6) Aria is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Samuel is a knave or Abigail is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Harper is a knave or Grace is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Abigail is a knight and Grace is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Riley is a knight.", "Grace cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Aria is a knight.", "Grace cannot be a knave, because this would contradict the claim of Samuel that Harper is a knave or Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Riley that Samuel is a knave or Abigail is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Abigail is a knight and Grace is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Riley is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Harper that Abigail is a knight and Grace is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Harper is a knave and Aria is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Grace that Harper is a knave and Aria is a knight.", "Aria cannot be a knave, because this would contradict the false claim of their own that Riley is not a knave.", "We have exhausted all possibilities for Aria and Grace, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the claim of Riley that Samuel is a knave or Abigail is a knight.", "We have exhausted all possibilities for Abigail and Harper, so let us go back and reconsider Samuel.", "Assume Samuel is a knave. No contradiction is found in their false claim that Harper is a knave or Grace is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Abigail is a knight and Grace is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Riley is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Samuel that Harper is a knave or Grace is a knight.", "Grace cannot be a knave, because this would contradict the claim of Harper that Abigail is a knight and Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Abigail.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Riley is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the false claim of Samuel that Harper is a knave or Grace is a knight.", "We have exhausted all possibilities for Harper and Samuel, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Samuel is a knave or Abigail is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Harper is a knave or Grace is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Abigail is a knight and Grace is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Riley that Samuel is a knave or Abigail is a knight.", "Abigail cannot be a knave, because this would contradict the claim of Harper that Abigail is a knight and Grace is a knight.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Abigail is a knight and Grace is a knight.", "Abigail cannot be a knight, because this would contradict the false claim of Riley that Samuel is a knave or Abigail is a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Riley is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Harper is a knave and Aria is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Riley is not a knave.", "Aria cannot be a knave, because this would contradict the claim of Grace that Harper is a knave and Aria is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Grace.", "Assume Grace is a knave. No contradiction is found in their false claim that Harper is a knave and Aria is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Grace that Harper is a knave and Aria is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Riley is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 1), ('telling-truth', 3)), ('or', ('lying', 4), ('telling-truth', 2)), ('and', ('lying', 4), ('telling-truth', 5)), ('telling-truth', 0), ('and', ('telling-truth', 3), ('telling-truth', 2)), ('not', ('lying', 0)))", "index": 1074}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Emily, Olivia, Isabella, Grace, and Charlotte. Chloe was heard saying, \"If Chloe is a knight then Emily is a knight\". Emily remarked, \"Grace is a knight\". Olivia told you that If Chloe is a knave then Emily is a knight. Isabella asserted: \"Grace is not a knight\". Grace asserted: \"If Grace is a knight then Chloe is a knight\". \"If Charlotte is a knight then Chloe is a knight,\" Charlotte declared. So who is a knight and who is a knave?", "names": ["Chloe", "Emily", "Olivia", "Isabella", "Grace", "Charlotte"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, true, true], "solution_text": "Chloe is a knight, Emily is a knight, Olivia is a knight, Isabella is a knave, Grace is a knight, and Charlotte is a knight.", "solution_text_format": "(1) Chloe is a knight\n(2) Emily is a knight\n(3) Olivia is a knight\n(4) Isabella is a knave\n(5) Grace is a knight\n(6) Charlotte is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that If Chloe is a knight then Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Grace is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that If Grace is a knight then Chloe is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that If Chloe is a knave then Emily is a knight.", "Isabella cannot be a knight, because this would contradict the claim of their own that Grace is not a knight.", "Assume Isabella is a knave. No contradiction is found in their false claim that Grace is not a knight.", "Assume Charlotte is a knight. No contradiction is found in their claim that If Charlotte is a knight then Chloe is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 4), ('->', ('lying', 0), ('telling-truth', 1)), ('not', ('telling-truth', 4)), ('->', ('telling-truth', 4), ('telling-truth', 0)), ('->', ('telling-truth', 5), ('telling-truth', 0)))", "index": 1075}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Owen, Matthew, Amelia, Scarlett, and Olivia. Riley asserted: \"Scarlett is a knave and Matthew is a knave\". Owen commented, \"Scarlett is a knight\". Matthew remarked, \"Owen is not a knight\". Amelia stated, \"Riley is a knave and Scarlett is a knight\". Scarlett asserted: \"Amelia is a knight or Owen is a knave\". Olivia was heard saying, \"Amelia is a knave if and only if Riley is a knight\". So who is a knight and who is a knave?", "names": ["Riley", "Owen", "Matthew", "Amelia", "Scarlett", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, true], "solution_text": "Riley is a knave, Owen is a knight, Matthew is a knave, Amelia is a knight, Scarlett is a knight, and Olivia is a knight.", "solution_text_format": "(1) Riley is a knave\n(2) Owen is a knight\n(3) Matthew is a knave\n(4) Amelia is a knight\n(5) Scarlett is a knight\n(6) Olivia is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Scarlett is a knave and Matthew is a knave.", "Scarlett cannot be a knight, because this would contradict the claim of Riley that Scarlett is a knave and Matthew is a knave.", "Assume Scarlett is a knave. No contradiction is found in their false claim that Amelia is a knight or Owen is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Scarlett is a knight.", "Assume Amelia is a knave. No contradiction is found in their false claim that Riley is a knave and Scarlett is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight.", "Owen cannot be a knave, because this would contradict the false claim of Scarlett that Amelia is a knight or Owen is a knave.", "We have exhausted all possibilities for Owen, Amelia, and Scarlett, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Scarlett is a knave and Matthew is a knave.", "Assume Scarlett is a knight. No contradiction is found in their claim that Amelia is a knight or Owen is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Riley is a knave and Scarlett is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Scarlett is a knight.", "Matthew cannot be a knight, because this would contradict the claim of their own that Owen is not a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Riley is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 4), ('lying', 2)), ('telling-truth', 4), ('not', ('telling-truth', 1)), ('and', ('lying', 0), ('telling-truth', 4)), ('or', ('telling-truth', 3), ('lying', 1)), ('<=>', ('lying', 3), ('telling-truth', 0)))", "index": 1076}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Alexander, Liam, Sofia, Isabella, Henry, and Ethan. In a statement by Alexander: \"Liam is a knave if and only if Liam is a knight\". Liam remarked, \"If Ethan is a knight then Henry is a knave\". In a statement by Sofia: \"Ethan is a knight\". \"Liam is a knight\" - Isabella. In Henry's words: \"Isabella is a knight\". \"Liam is a knave if and only if Alexander is a knave\" - Ethan. So who is a knight and who is a knave?", "names": ["Alexander", "Liam", "Sofia", "Isabella", "Henry", "Ethan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, true, false], "solution_text": "Alexander is a knave, Liam is a knight, Sofia is a knave, Isabella is a knight, Henry is a knight, and Ethan is a knave.", "solution_text_format": "(1) Alexander is a knave\n(2) Liam is a knight\n(3) Sofia is a knave\n(4) Isabella is a knight\n(5) Henry is a knight\n(6) Ethan is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Alexander cannot be a knight, because this would contradict the claim of their own that Liam is a knave if and only if Liam is a knight.", "Assume Alexander is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Liam is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that If Ethan is a knight then Henry is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Liam is a knave if and only if Alexander is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Alexander is a knave.", "Assume Henry is a knight. No contradiction is found in their claim that Isabella is a knight.", "Assume Isabella is a knight. No contradiction is found in their claim that Liam is a knight.", "Sofia cannot be a knight, because this would contradict the claim of their own that Ethan is a knight.", "Assume Sofia is a knave. No contradiction is found in their false claim that Ethan is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('telling-truth', 1)), ('->', ('telling-truth', 5), ('lying', 4)), ('telling-truth', 5), ('telling-truth', 1), ('telling-truth', 3), ('<=>', ('lying', 1), ('lying', 0)))", "index": 1077}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Emily, Michael, Benjamin, Lily, and Aria. In Ava's words: \"Emily is a knave if and only if Michael is a knave\". As Emily put it, \"Aria is a knight or Michael is a knave\". Michael commented, \"Lily is a knave or Emily is a knave\". \"Lily is a knave or Emily is a knight\" - Benjamin. Lily expressed that If Emily is a knight then Emily is a knave. Aria asserted: \"If Emily is a knave then Michael is a knight\". So who is a knight and who is a knave?", "names": ["Ava", "Emily", "Michael", "Benjamin", "Lily", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, false, true], "solution_text": "Ava is a knight, Emily is a knight, Michael is a knight, Benjamin is a knight, Lily is a knave, and Aria is a knight.", "solution_text_format": "(1) Ava is a knight\n(2) Emily is a knight\n(3) Michael is a knight\n(4) Benjamin is a knight\n(5) Lily is a knave\n(6) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Emily is a knave if and only if Michael is a knave.", "Assume Emily is a knight. No contradiction is found in their claim that Aria is a knight or Michael is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that If Emily is a knave then Michael is a knight.", "Assume Michael is a knight. No contradiction is found in their claim that Lily is a knave or Emily is a knave.", "Lily cannot be a knight, because this would contradict the claim of Michael that Lily is a knave or Emily is a knave.", "Assume Lily is a knave. No contradiction is found in their false claim that If Emily is a knight then Emily is a knave.", "Assume Benjamin is a knight. No contradiction is found in their claim that Lily is a knave or Emily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 1), ('lying', 2)), ('or', ('telling-truth', 5), ('lying', 2)), ('or', ('lying', 4), ('lying', 1)), ('or', ('lying', 4), ('telling-truth', 1)), ('->', ('telling-truth', 1), ('lying', 1)), ('->', ('lying', 1), ('telling-truth', 2)))", "index": 1078}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Lucas, Noah, Elizabeth, James, and Logan. In a statement by Henry: \"Noah is a knave if and only if Elizabeth is a knave\". \"Logan is a knave and Logan is a knight,\" Lucas claimed. Noah noted, \"If Henry is a knight then James is a knave\". According to Elizabeth, \"Noah is a knight and Lucas is a knave\". James told you that Lucas is a knave. Logan said that James is a knight if and only if Lucas is a knave. So who is a knight and who is a knave?", "names": ["Henry", "Lucas", "Noah", "Elizabeth", "James", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, true, true], "solution_text": "Henry is a knight, Lucas is a knave, Noah is a knave, Elizabeth is a knave, James is a knight, and Logan is a knight.", "solution_text_format": "(1) Henry is a knight\n(2) Lucas is a knave\n(3) Noah is a knave\n(4) Elizabeth is a knave\n(5) James is a knight\n(6) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Noah is a knave if and only if Elizabeth is a knave.", "Assume Noah is a knight. No contradiction is found in their claim that If Henry is a knight then James is a knave.", "James cannot be a knight, because this would contradict the claim of Noah that If Henry is a knight then James is a knave.", "Assume James is a knave. No contradiction is found in their false claim that Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Logan is a knight.", "Lucas cannot be a knave, because this would contradict the false claim of James that Lucas is a knave.", "We have exhausted all possibilities for Lucas and James, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that If Henry is a knight then James is a knave.", "Assume James is a knight. No contradiction is found in their claim that Lucas is a knave.", "Lucas cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Logan is a knight.", "Assume Lucas is a knave. No contradiction is found in their false claim that Logan is a knave and Logan is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that James is a knight if and only if Lucas is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of Henry that Noah is a knave if and only if Elizabeth is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Noah is a knight and Lucas is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 2), ('lying', 3)), ('and', ('lying', 5), ('telling-truth', 5)), ('->', ('telling-truth', 0), ('lying', 4)), ('and', ('telling-truth', 2), ('lying', 1)), ('lying', 1), ('<=>', ('telling-truth', 4), ('lying', 1)))", "index": 1079}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Joseph, Mason, Oliver, Benjamin, Elizabeth, and Matthew. \"Matthew is not a knight\" - Joseph. In Mason's words: \"Elizabeth is a knave if and only if Matthew is a knave\". Oliver commented, \"Mason is a knight if and only if Benjamin is a knave\". Benjamin said that Mason is a knight if and only if Elizabeth is a knave. \"Matthew is a knight if and only if Joseph is a knight\" - Elizabeth. Matthew asserted: \"If Elizabeth is a knight then Matthew is a knight\". So who is a knight and who is a knave?", "names": ["Joseph", "Mason", "Oliver", "Benjamin", "Elizabeth", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, false, true], "solution_text": "Joseph is a knave, Mason is a knave, Oliver is a knave, Benjamin is a knave, Elizabeth is a knave, and Matthew is a knight.", "solution_text_format": "(1) Joseph is a knave\n(2) Mason is a knave\n(3) Oliver is a knave\n(4) Benjamin is a knave\n(5) Elizabeth is a knave\n(6) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Joseph is a knight. No contradiction is found in their claim that Matthew is not a knight.", "Matthew cannot be a knight, because this would contradict the claim of Joseph that Matthew is not a knight.", "Assume Matthew is a knave. No contradiction is found in their false claim that If Elizabeth is a knight then Matthew is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Matthew is a knight if and only if Joseph is a knight.", "Elizabeth cannot be a knave, because this would contradict the false claim of Matthew that If Elizabeth is a knight then Matthew is a knight.", "We have exhausted all possibilities for Elizabeth and Matthew, so let us go back and reconsider Joseph.", "Assume Joseph is a knave. No contradiction is found in their false claim that Matthew is not a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that If Elizabeth is a knight then Matthew is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Matthew is a knight if and only if Joseph is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Matthew is a knight if and only if Joseph is a knight.", "Mason cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave if and only if Matthew is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Matthew is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Mason is a knight if and only if Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the claim of their own that Mason is a knight if and only if Elizabeth is a knave.", "Benjamin cannot be a knave, because this would contradict the claim of Oliver that Mason is a knight if and only if Benjamin is a knave.", "We have exhausted all possibilities for Benjamin, so let us go back and reconsider Oliver.", "Assume Oliver is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Benjamin is a knave.", "Benjamin cannot be a knight, because this would contradict the false claim of Oliver that Mason is a knight if and only if Benjamin is a knave.", "Assume Benjamin is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('<=>', ('lying', 4), ('lying', 5)), ('<=>', ('telling-truth', 1), ('lying', 3)), ('<=>', ('telling-truth', 1), ('lying', 4)), ('<=>', ('telling-truth', 5), ('telling-truth', 0)), ('->', ('telling-truth', 4), ('telling-truth', 5)))", "index": 1080}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Liam, Jacob, Jackson, Owen, Zoey, and Aria. As Liam put it, \"Zoey is a knave or Jacob is a knight\". \"If Owen is a knight then Jackson is a knave\" - Jacob. Jackson was heard saying, \"Owen is not a knave\". According to Owen, \"Aria is a knave or Zoey is a knave\". In a statement by Zoey: \"Owen is not a knight\". \"Zoey is not a knight,\" Aria declared. So who is a knight and who is a knave?", "names": ["Liam", "Jacob", "Jackson", "Owen", "Zoey", "Aria"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "Liam is a knight, Jacob is a knave, Jackson is a knight, Owen is a knight, Zoey is a knave, and Aria is a knight.", "solution_text_format": "(1) Liam is a knight\n(2) Jacob is a knave\n(3) Jackson is a knight\n(4) Owen is a knight\n(5) Zoey is a knave\n(6) Aria is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Liam is a knight. No contradiction is found in their claim that Zoey is a knave or Jacob is a knight.", "Assume Zoey is a knight. No contradiction is found in their claim that Owen is not a knight.", "Owen cannot be a knight, because this would contradict the claim of Zoey that Owen is not a knight.", "Assume Owen is a knave. No contradiction is found in their false claim that Aria is a knave or Zoey is a knave.", "Aria cannot be a knight, because this would contradict the claim of their own that Zoey is not a knight.", "Aria cannot be a knave, because this would contradict the false claim of Owen that Aria is a knave or Zoey is a knave.", "We have exhausted all possibilities for Aria and Owen, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that Owen is not a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Aria is a knave or Zoey is a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Zoey is not a knight.", "Assume Jacob is a knight. No contradiction is found in their claim that If Owen is a knight then Jackson is a knave.", "Jackson cannot be a knight, because this would contradict the claim of Jacob that If Owen is a knight then Jackson is a knave.", "Jackson cannot be a knave, because this would contradict the false claim of their own that Owen is not a knave.", "We have exhausted all possibilities for Jackson, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that If Owen is a knight then Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Owen is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 1)), ('->', ('telling-truth', 3), ('lying', 2)), ('not', ('lying', 3)), ('or', ('lying', 5), ('lying', 4)), ('not', ('telling-truth', 3)), ('not', ('telling-truth', 4)))", "index": 1081}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Zoey, Mason, Jacob, Abigail, Owen, and Matthew. Zoey remarked, \"If Owen is a knight then Jacob is a knight\". Mason commented, \"Jacob is a knight or Owen is a knave\". Jacob told you that Zoey is a knight and Abigail is a knave. Abigail expressed that Jacob is not a knave. \"Zoey is a knave,\" Owen claimed. According to Matthew, \"Mason is a knave\". So who is a knight and who is a knave?", "names": ["Zoey", "Mason", "Jacob", "Abigail", "Owen", "Matthew"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, true], "solution_text": "Zoey is a knave, Mason is a knave, Jacob is a knave, Abigail is a knave, Owen is a knight, and Matthew is a knight.", "solution_text_format": "(1) Zoey is a knave\n(2) Mason is a knave\n(3) Jacob is a knave\n(4) Abigail is a knave\n(5) Owen is a knight\n(6) Matthew is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Zoey is a knight. No contradiction is found in their claim that If Owen is a knight then Jacob is a knight.", "Owen cannot be a knight, because this would contradict the claim of their own that Zoey is a knave.", "Assume Owen is a knave. No contradiction is found in their false claim that Zoey is a knave.", "Assume Jacob is a knight. No contradiction is found in their claim that Zoey is a knight and Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of Jacob that Zoey is a knight and Abigail is a knave.", "Abigail cannot be a knave, because this would contradict the false claim of their own that Jacob is not a knave.", "We have exhausted all possibilities for Abigail, so let us go back and reconsider Jacob.", "Assume Jacob is a knave. No contradiction is found in their false claim that Zoey is a knight and Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Jacob is not a knave.", "Abigail cannot be a knave, because this would contradict the false claim of Jacob that Zoey is a knight and Abigail is a knave.", "We have exhausted all possibilities for Abigail, Jacob, and Owen, so let us go back and reconsider Zoey.", "Assume Zoey is a knave. No contradiction is found in their false claim that If Owen is a knight then Jacob is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Zoey is a knave.", "Jacob cannot be a knight, because this would contradict the false claim of Zoey that If Owen is a knight then Jacob is a knight.", "Assume Jacob is a knave. No contradiction is found in their false claim that Zoey is a knight and Abigail is a knave.", "Abigail cannot be a knight, because this would contradict the claim of their own that Jacob is not a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Jacob is not a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Jacob is a knight or Owen is a knave.", "Assume Mason is a knave. No contradiction is found in their false claim that Jacob is a knight or Owen is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Mason is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('telling-truth', 2), ('lying', 4)), ('and', ('telling-truth', 0), ('lying', 3)), ('not', ('lying', 2)), ('lying', 0), ('lying', 1))", "index": 1082}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Charlotte, Aurora, Mia, William, and Elizabeth. \"If Aurora is a knight then Elizabeth is a knight\" - Riley. In Charlotte's words: \"Elizabeth is a knave or Mia is a knave\". In Aurora's words: \"William is a knight\". \"Elizabeth is a knave and Mia is a knight\" - Mia. William asserted: \"Charlotte is a knave\". In a statement by Elizabeth: \"If Mia is a knave then Riley is a knave\". So who is a knight and who is a knave?", "names": ["Riley", "Charlotte", "Aurora", "Mia", "William", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, false, false, false], "solution_text": "Riley is a knight, Charlotte is a knight, Aurora is a knave, Mia is a knave, William is a knave, and Elizabeth is a knave.", "solution_text_format": "(1) Riley is a knight\n(2) Charlotte is a knight\n(3) Aurora is a knave\n(4) Mia is a knave\n(5) William is a knave\n(6) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that If Aurora is a knight then Elizabeth is a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that William is a knight.", "Assume William is a knight. No contradiction is found in their claim that Charlotte is a knave.", "Charlotte cannot be a knight, because this would contradict the claim of William that Charlotte is a knave.", "Assume Charlotte is a knave. No contradiction is found in their false claim that Elizabeth is a knave or Mia is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Mia is a knave then Riley is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Mia is a knight.", "Mia cannot be a knave, because this would contradict the false claim of Charlotte that Elizabeth is a knave or Mia is a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Riley that If Aurora is a knight then Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth and Charlotte, so let us go back and reconsider William.", "William cannot be a knave, because this would contradict the claim of Aurora that William is a knight.", "We have exhausted all possibilities for William, so let us go back and reconsider Aurora.", "Assume Aurora is a knave. No contradiction is found in their false claim that William is a knight.", "William cannot be a knight, because this would contradict the false claim of Aurora that William is a knight.", "Assume William is a knave. No contradiction is found in their false claim that Charlotte is a knave.", "Assume Charlotte is a knight. No contradiction is found in their claim that Elizabeth is a knave or Mia is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that If Mia is a knave then Riley is a knave.", "Mia cannot be a knight, because this would contradict the claim of Charlotte that Elizabeth is a knave or Mia is a knave.", "Mia cannot be a knave, because this would contradict the claim of Elizabeth that If Mia is a knave then Riley is a knave.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Elizabeth.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that If Mia is a knave then Riley is a knave.", "Mia cannot be a knight, because this would contradict the false claim of Elizabeth that If Mia is a knave then Riley is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Mia is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('lying', 5), ('lying', 3)), ('telling-truth', 4), ('and', ('lying', 5), ('telling-truth', 3)), ('lying', 1), ('->', ('lying', 3), ('lying', 0)))", "index": 1083}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sebastian, Liam, Grace, Daniel, Victoria, and Henry. Sebastian commented, \"Henry is a knave and Victoria is a knight\". In Liam's words: \"Victoria is not a knight\". Grace asserted: \"Liam is a knave or Henry is a knight\". Daniel expressed that Daniel is a knight or Liam is a knight. Victoria was heard saying, \"Sebastian is a knave\". \"Grace is a knave or Daniel is a knight,\" Henry mentioned. So who is a knight and who is a knave?", "names": ["Sebastian", "Liam", "Grace", "Daniel", "Victoria", "Henry"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, true, true, true], "solution_text": "Sebastian is a knave, Liam is a knave, Grace is a knight, Daniel is a knight, Victoria is a knight, and Henry is a knight.", "solution_text_format": "(1) Sebastian is a knave\n(2) Liam is a knave\n(3) Grace is a knight\n(4) Daniel is a knight\n(5) Victoria is a knight\n(6) Henry is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Sebastian is a knight. No contradiction is found in their claim that Henry is a knave and Victoria is a knight.", "Henry cannot be a knight, because this would contradict the claim of Sebastian that Henry is a knave and Victoria is a knight.", "Assume Henry is a knave. No contradiction is found in their false claim that Grace is a knave or Daniel is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Liam is a knave or Henry is a knight.", "Liam cannot be a knight, because this would contradict the claim of Grace that Liam is a knave or Henry is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave.", "Victoria cannot be a knave, because this would contradict the claim of Sebastian that Henry is a knave and Victoria is a knight.", "We have exhausted all possibilities for Victoria and Liam, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the false claim of Henry that Grace is a knave or Daniel is a knight.", "We have exhausted all possibilities for Grace and Henry, so let us go back and reconsider Sebastian.", "Assume Sebastian is a knave. No contradiction is found in their false claim that Henry is a knave and Victoria is a knight.", "Assume Henry is a knight. No contradiction is found in their claim that Grace is a knave or Daniel is a knight.", "Assume Grace is a knight. No contradiction is found in their claim that Liam is a knave or Henry is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Victoria is not a knight.", "Victoria cannot be a knight, because this would contradict the claim of Liam that Victoria is not a knight.", "Victoria cannot be a knave, because this would contradict the false claim of their own that Sebastian is a knave.", "We have exhausted all possibilities for Victoria, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Victoria is not a knight.", "Assume Victoria is a knight. No contradiction is found in their claim that Sebastian is a knave.", "Assume Daniel is a knight. No contradiction is found in their claim that Daniel is a knight or Liam is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('or', ('lying', 1), ('telling-truth', 5)), ('or', ('telling-truth', 3), ('telling-truth', 1)), ('lying', 0), ('or', ('lying', 2), ('telling-truth', 3)))", "index": 1084}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Logan, Aria, Ethan, Owen, and Riley. Lily commented, \"Owen is a knave or Owen is a knight\". Logan was heard saying, \"Aria is a knight if and only if Riley is a knight\". Aria remarked, \"Owen is a knave if and only if Riley is a knave\". \"Owen is a knight and Lily is a knight,\" Ethan declared. \"Riley is a knave,\" Owen mentioned. Riley was heard saying, \"If Owen is a knave then Lily is a knight\". So who is a knight and who is a knave?", "names": ["Lily", "Logan", "Aria", "Ethan", "Owen", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, false, false, false, true], "solution_text": "Lily is a knight, Logan is a knave, Aria is a knave, Ethan is a knave, Owen is a knave, and Riley is a knight.", "solution_text_format": "(1) Lily is a knight\n(2) Logan is a knave\n(3) Aria is a knave\n(4) Ethan is a knave\n(5) Owen is a knave\n(6) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Lily is a knight. No contradiction is found in their claim that Owen is a knave or Owen is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Riley is a knave.", "Riley cannot be a knight, because this would contradict the claim of Owen that Riley is a knave.", "Riley cannot be a knave, because this would contradict the false claim of their own that If Owen is a knave then Lily is a knight.", "We have exhausted all possibilities for Riley, so let us go back and reconsider Owen.", "Assume Owen is a knave. No contradiction is found in their false claim that Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Owen is a knave then Lily is a knight.", "Assume Logan is a knight. No contradiction is found in their claim that Aria is a knight if and only if Riley is a knight.", "Aria cannot be a knight, because this would contradict the claim of their own that Owen is a knave if and only if Riley is a knave.", "Aria cannot be a knave, because this would contradict the claim of Logan that Aria is a knight if and only if Riley is a knight.", "We have exhausted all possibilities for Aria, so let us go back and reconsider Logan.", "Assume Logan is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Riley is a knight.", "Aria cannot be a knight, because this would contradict the false claim of Logan that Aria is a knight if and only if Riley is a knight.", "Assume Aria is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Riley is a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Owen is a knight and Lily is a knight.", "Assume Ethan is a knave. No contradiction is found in their false claim that Owen is a knight and Lily is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('telling-truth', 4)), ('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('<=>', ('lying', 4), ('lying', 5)), ('and', ('telling-truth', 4), ('telling-truth', 0)), ('lying', 5), ('->', ('lying', 4), ('telling-truth', 0)))", "index": 1085}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Oliver, Owen, Emma, Aurora, and Jackson. In a statement by Daniel: \"If Owen is a knave then Jackson is a knight\". In Oliver's words: \"Jackson is a knight if and only if Aurora is a knight\". In a statement by Owen: \"Emma is a knave\". In a statement by Emma: \"Daniel is a knave and Jackson is a knave\". According to Aurora, \"Daniel is a knave if and only if Jackson is a knave\". Jackson noted, \"Oliver is not a knight\". So who is a knight and who is a knave?", "names": ["Daniel", "Oliver", "Owen", "Emma", "Aurora", "Jackson"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Daniel is a knight, Oliver is a knight, Owen is a knight, Emma is a knave, Aurora is a knave, and Jackson is a knave.", "solution_text_format": "(1) Daniel is a knight\n(2) Oliver is a knight\n(3) Owen is a knight\n(4) Emma is a knave\n(5) Aurora is a knave\n(6) Jackson is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Daniel is a knight. No contradiction is found in their claim that If Owen is a knave then Jackson is a knight.", "Assume Owen is a knight. No contradiction is found in their claim that Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Owen that Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Daniel is a knave and Jackson is a knave.", "Assume Jackson is a knight. No contradiction is found in their claim that Oliver is not a knight.", "Oliver cannot be a knight, because this would contradict the claim of Jackson that Oliver is not a knight.", "Assume Oliver is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the false claim of Oliver that Jackson is a knight if and only if Aurora is a knight.", "Aurora cannot be a knave, because this would contradict the false claim of their own that Daniel is a knave if and only if Jackson is a knave.", "We have exhausted all possibilities for Aurora and Oliver, so let us go back and reconsider Jackson.", "Assume Jackson is a knave. No contradiction is found in their false claim that Oliver is not a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Aurora is a knight.", "Aurora cannot be a knight, because this would contradict the claim of Oliver that Jackson is a knight if and only if Aurora is a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Daniel is a knave if and only if Jackson is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 2), ('telling-truth', 5)), ('<=>', ('telling-truth', 5), ('telling-truth', 4)), ('lying', 3), ('and', ('lying', 0), ('lying', 5)), ('<=>', ('lying', 0), ('lying', 5)), ('not', ('telling-truth', 1)))", "index": 1086}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Lucas, Elizabeth, Grace, Evelyn, and Emma. Logan said that Emma is a knave and Emma is a knight. Lucas noted, \"Grace is a knave if and only if Lucas is a knight\". Elizabeth told you that Lucas is a knight if and only if Grace is a knight. Grace said, \"Elizabeth is a knave.\" Evelyn expressed that Elizabeth is a knave and Emma is a knight. According to Emma, \"Evelyn is a knight if and only if Logan is a knave\". So who is a knight and who is a knave?", "names": ["Logan", "Lucas", "Elizabeth", "Grace", "Evelyn", "Emma"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, true, false, false, false], "solution_text": "Logan is a knave, Lucas is a knave, Elizabeth is a knight, Grace is a knave, Evelyn is a knave, and Emma is a knave.", "solution_text_format": "(1) Logan is a knave\n(2) Lucas is a knave\n(3) Elizabeth is a knight\n(4) Grace is a knave\n(5) Evelyn is a knave\n(6) Emma is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Logan cannot be a knight, because this would contradict the claim of their own that Emma is a knave and Emma is a knight.", "Assume Logan is a knave. No contradiction is found in their false claim that Emma is a knave and Emma is a knight.", "Assume Emma is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Logan is a knave.", "Assume Evelyn is a knight. No contradiction is found in their claim that Elizabeth is a knave and Emma is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of Evelyn that Elizabeth is a knave and Emma is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Lucas is a knight if and only if Grace is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Grace is a knave if and only if Lucas is a knight.", "Grace cannot be a knight, because this would contradict the claim of Lucas that Grace is a knave if and only if Lucas is a knight.", "Grace cannot be a knave, because this would contradict the false claim of their own that Elizabeth is a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Lucas is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Lucas that Grace is a knave if and only if Lucas is a knight.", "Grace cannot be a knave, because this would contradict the false claim of Elizabeth that Lucas is a knight if and only if Grace is a knight.", "We have exhausted all possibilities for Grace, Lucas, and Elizabeth, so let us go back and reconsider Evelyn.", "Evelyn cannot be a knave, because this would contradict the claim of Emma that Evelyn is a knight if and only if Logan is a knave.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Emma.", "Assume Emma is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Logan is a knave.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Emma is a knight.", "Assume Evelyn is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Emma is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Lucas is a knight if and only if Grace is a knight.", "Assume Lucas is a knight. No contradiction is found in their claim that Grace is a knave if and only if Lucas is a knight.", "Grace cannot be a knight, because this would contradict the claim of Lucas that Grace is a knave if and only if Lucas is a knight.", "Grace cannot be a knave, because this would contradict the claim of Elizabeth that Lucas is a knight if and only if Grace is a knight.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Lucas.", "Assume Lucas is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Lucas is a knight.", "Grace cannot be a knight, because this would contradict the false claim of Lucas that Grace is a knave if and only if Lucas is a knight.", "Assume Grace is a knave. No contradiction is found in their false claim that Elizabeth is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('and', ('lying', 5), ('telling-truth', 5)), ('<=>', ('lying', 3), ('telling-truth', 1)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('lying', 2), ('and', ('lying', 2), ('telling-truth', 5)), ('<=>', ('telling-truth', 4), ('lying', 0)))", "index": 1087}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Emily, Harper, Abigail, Grace, and Aiden. Henry said, \"Abigail is a knave or Harper is a knight.\" Emily told you that Grace is not a knave. In a statement by Harper: \"If Abigail is a knight then Henry is a knave\". \"Aiden is a knight,\" Abigail mentioned. Grace said, \"Emily is a knight and Harper is a knight.\" \"Emily is a knight,\" Aiden claimed. So who is a knight and who is a knave?", "names": ["Henry", "Emily", "Harper", "Abigail", "Grace", "Aiden"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, false, false, false], "solution_text": "Henry is a knight, Emily is a knave, Harper is a knight, Abigail is a knave, Grace is a knave, and Aiden is a knave.", "solution_text_format": "(1) Henry is a knight\n(2) Emily is a knave\n(3) Harper is a knight\n(4) Abigail is a knave\n(5) Grace is a knave\n(6) Aiden is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Henry is a knight. No contradiction is found in their claim that Abigail is a knave or Harper is a knight.", "Assume Abigail is a knight. No contradiction is found in their claim that Aiden is a knight.", "Assume Aiden is a knight. No contradiction is found in their claim that Emily is a knight.", "Assume Emily is a knight. No contradiction is found in their claim that Grace is not a knave.", "Assume Grace is a knight. No contradiction is found in their claim that Emily is a knight and Harper is a knight.", "Harper cannot be a knight, because this would contradict the claim of their own that If Abigail is a knight then Henry is a knave.", "Harper cannot be a knave, because this would contradict the claim of Henry that Abigail is a knave or Harper is a knight.", "We have exhausted all possibilities for Harper, so let us go back and reconsider Grace.", "Grace cannot be a knave, because this would contradict the claim of Emily that Grace is not a knave.", "We have exhausted all possibilities for Grace, so let us go back and reconsider Emily.", "Emily cannot be a knave, because this would contradict the claim of Aiden that Emily is a knight.", "We have exhausted all possibilities for Emily, so let us go back and reconsider Aiden.", "Aiden cannot be a knave, because this would contradict the claim of Abigail that Aiden is a knight.", "We have exhausted all possibilities for Aiden, so let us go back and reconsider Abigail.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aiden is a knight.", "Aiden cannot be a knight, because this would contradict the false claim of Abigail that Aiden is a knight.", "Assume Aiden is a knave. No contradiction is found in their false claim that Emily is a knight.", "Emily cannot be a knight, because this would contradict the false claim of Aiden that Emily is a knight.", "Assume Emily is a knave. No contradiction is found in their false claim that Grace is not a knave.", "Grace cannot be a knight, because this would contradict the false claim of Emily that Grace is not a knave.", "Assume Grace is a knave. No contradiction is found in their false claim that Emily is a knight and Harper is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that If Abigail is a knight then Henry is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 3), ('telling-truth', 2)), ('not', ('lying', 4)), ('->', ('telling-truth', 3), ('lying', 0)), ('telling-truth', 5), ('and', ('telling-truth', 1), ('telling-truth', 2)), ('telling-truth', 1))", "index": 1088}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Riley, Amelia, Mia, Ava, Joseph, and Olivia. Riley noted, \"Olivia is a knave if and only if Ava is a knight\". \"Riley is a knave if and only if Mia is a knight,\" Amelia declared. \"If Ava is a knave then Joseph is a knave\" - Mia. Ava said, \"Riley is a knight and Joseph is a knight.\" In Joseph's words: \"Mia is a knave or Ava is a knave\". Olivia said that Amelia is a knight and Ava is a knave. So who is a knight and who is a knave?", "names": ["Riley", "Amelia", "Mia", "Ava", "Joseph", "Olivia"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, false, true, false], "solution_text": "Riley is a knave, Amelia is a knave, Mia is a knave, Ava is a knave, Joseph is a knight, and Olivia is a knave.", "solution_text_format": "(1) Riley is a knave\n(2) Amelia is a knave\n(3) Mia is a knave\n(4) Ava is a knave\n(5) Joseph is a knight\n(6) Olivia is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Riley is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Ava is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Amelia is a knight and Ava is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Riley is a knave if and only if Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of Amelia that Riley is a knave if and only if Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that If Ava is a knave then Joseph is a knave.", "Ava cannot be a knight, because this would contradict the claim of Riley that Olivia is a knave if and only if Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Riley is a knight and Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the false claim of Ava that Riley is a knight and Joseph is a knight.", "Joseph cannot be a knave, because this would contradict the false claim of Mia that If Ava is a knave then Joseph is a knave.", "We have exhausted all possibilities for Joseph, Ava, and Mia, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Olivia that Amelia is a knight and Ava is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Amelia is a knight and Ava is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Riley is a knave if and only if Mia is a knight.", "Mia cannot be a knight, because this would contradict the claim of Amelia that Riley is a knave if and only if Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that If Ava is a knave then Joseph is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Mia that If Ava is a knave then Joseph is a knave.", "Ava cannot be a knave, because this would contradict the claim of Riley that Olivia is a knave if and only if Ava is a knight.", "We have exhausted all possibilities for Ava and Mia, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Ava is a knave then Joseph is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Riley is a knight and Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the claim of their own that Mia is a knave or Ava is a knave.", "Joseph cannot be a knave, because this would contradict the claim of Ava that Riley is a knight and Joseph is a knight.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Ava.", "Ava cannot be a knave, because this would contradict the claim of Riley that Olivia is a knave if and only if Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the false claim of Amelia that Riley is a knave if and only if Mia is a knight.", "We have exhausted all possibilities for Mia, Amelia, and Olivia, so let us go back and reconsider Riley.", "Assume Riley is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Ava is a knight.", "Assume Olivia is a knight. No contradiction is found in their claim that Amelia is a knight and Ava is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Riley is a knave if and only if Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Ava is a knave then Joseph is a knave.", "Ava cannot be a knight, because this would contradict the claim of their own that Riley is a knight and Joseph is a knight.", "Ava cannot be a knave, because this would contradict the false claim of Riley that Olivia is a knave if and only if Ava is a knight.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Amelia that Riley is a knave if and only if Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Amelia.", "Amelia cannot be a knave, because this would contradict the claim of Olivia that Amelia is a knight and Ava is a knave.", "We have exhausted all possibilities for Amelia, so let us go back and reconsider Olivia.", "Assume Olivia is a knave. No contradiction is found in their false claim that Amelia is a knight and Ava is a knave.", "Assume Amelia is a knight. No contradiction is found in their claim that Riley is a knave if and only if Mia is a knight.", "Assume Mia is a knight. No contradiction is found in their claim that If Ava is a knave then Joseph is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Riley that Olivia is a knave if and only if Ava is a knight.", "Ava cannot be a knave, because this would contradict the false claim of Olivia that Amelia is a knight and Ava is a knave.", "We have exhausted all possibilities for Ava, so let us go back and reconsider Mia.", "Mia cannot be a knave, because this would contradict the claim of Amelia that Riley is a knave if and only if Mia is a knight.", "We have exhausted all possibilities for Mia, so let us go back and reconsider Amelia.", "Assume Amelia is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Mia is a knight.", "Mia cannot be a knight, because this would contradict the false claim of Amelia that Riley is a knave if and only if Mia is a knight.", "Assume Mia is a knave. No contradiction is found in their false claim that If Ava is a knave then Joseph is a knave.", "Ava cannot be a knight, because this would contradict the false claim of Riley that Olivia is a knave if and only if Ava is a knight.", "Assume Ava is a knave. No contradiction is found in their false claim that Riley is a knight and Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Mia is a knave or Ava is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('lying', 5), ('telling-truth', 3)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('->', ('lying', 3), ('lying', 4)), ('and', ('telling-truth', 0), ('telling-truth', 4)), ('or', ('lying', 2), ('lying', 3)), ('and', ('telling-truth', 1), ('lying', 3)))", "index": 1089}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aria, Ethan, Chloe, Alexander, Oliver, and Noah. \"Noah is a knave or Oliver is a knight,\" Aria mentioned. Ethan said, \"If Chloe is a knight then Oliver is a knave.\" \"If Oliver is a knight then Alexander is a knave,\" Chloe declared. Alexander commented, \"If Ethan is a knight then Aria is a knave\". \"If Alexander is a knave then Chloe is a knave\" - Oliver. Noah stated, \"Alexander is a knight and Oliver is a knight\". So who is a knight and who is a knave?", "names": ["Aria", "Ethan", "Chloe", "Alexander", "Oliver", "Noah"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, false, false, false], "solution_text": "Aria is a knight, Ethan is a knight, Chloe is a knight, Alexander is a knave, Oliver is a knave, and Noah is a knave.", "solution_text_format": "(1) Aria is a knight\n(2) Ethan is a knight\n(3) Chloe is a knight\n(4) Alexander is a knave\n(5) Oliver is a knave\n(6) Noah is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aria is a knight. No contradiction is found in their claim that Noah is a knave or Oliver is a knight.", "Assume Noah is a knight. No contradiction is found in their claim that Alexander is a knight and Oliver is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Ethan is a knight then Aria is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Alexander that If Ethan is a knight then Aria is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Chloe is a knight then Oliver is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Oliver is a knight then Alexander is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Chloe that If Oliver is a knight then Alexander is a knave.", "Oliver cannot be a knave, because this would contradict the claim of Aria that Noah is a knave or Oliver is a knight.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of Ethan that If Chloe is a knight then Oliver is a knave.", "We have exhausted all possibilities for Chloe and Ethan, so let us go back and reconsider Alexander.", "Alexander cannot be a knave, because this would contradict the claim of Noah that Alexander is a knight and Oliver is a knight.", "We have exhausted all possibilities for Alexander, so let us go back and reconsider Noah.", "Assume Noah is a knave. No contradiction is found in their false claim that Alexander is a knight and Oliver is a knight.", "Assume Alexander is a knight. No contradiction is found in their claim that If Ethan is a knight then Aria is a knave.", "Ethan cannot be a knight, because this would contradict the claim of Alexander that If Ethan is a knight then Aria is a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that If Chloe is a knight then Oliver is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Oliver is a knight then Alexander is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Chloe that If Oliver is a knight then Alexander is a knave.", "Oliver cannot be a knave, because this would contradict the false claim of Ethan that If Chloe is a knight then Oliver is a knave.", "We have exhausted all possibilities for Oliver, so let us go back and reconsider Chloe.", "Chloe cannot be a knave, because this would contradict the false claim of Ethan that If Chloe is a knight then Oliver is a knave.", "We have exhausted all possibilities for Chloe and Ethan, so let us go back and reconsider Alexander.", "Assume Alexander is a knave. No contradiction is found in their false claim that If Ethan is a knight then Aria is a knave.", "Assume Ethan is a knight. No contradiction is found in their claim that If Chloe is a knight then Oliver is a knave.", "Assume Chloe is a knight. No contradiction is found in their claim that If Oliver is a knight then Alexander is a knave.", "Oliver cannot be a knight, because this would contradict the claim of Ethan that If Chloe is a knight then Oliver is a knave.", "Assume Oliver is a knave. No contradiction is found in their false claim that If Alexander is a knave then Chloe is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 5), ('telling-truth', 4)), ('->', ('telling-truth', 2), ('lying', 4)), ('->', ('telling-truth', 4), ('lying', 3)), ('->', ('telling-truth', 1), ('lying', 0)), ('->', ('lying', 3), ('lying', 2)), ('and', ('telling-truth', 3), ('telling-truth', 4)))", "index": 1090}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Sophia, Matthew, Joseph, Emma, and Riley. \"Sophia is a knight if and only if Sophia is a knave,\" Abigail claimed. Sophia noted, \"Emma is a knave\". Matthew noted, \"Sophia is a knave if and only if Joseph is a knight\". Joseph noted, \"Sophia is a knight or Riley is a knave\". \"Riley is a knight and Riley is a knave\" - Emma. \"If Abigail is a knight then Emma is a knave,\" Riley mentioned. So who is a knight and who is a knave?", "names": ["Abigail", "Sophia", "Matthew", "Joseph", "Emma", "Riley"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, true, false, true, false, true], "solution_text": "Abigail is a knave, Sophia is a knight, Matthew is a knave, Joseph is a knight, Emma is a knave, and Riley is a knight.", "solution_text_format": "(1) Abigail is a knave\n(2) Sophia is a knight\n(3) Matthew is a knave\n(4) Joseph is a knight\n(5) Emma is a knave\n(6) Riley is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Abigail cannot be a knight, because this would contradict the claim of their own that Sophia is a knight if and only if Sophia is a knave.", "Assume Abigail is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Sophia is a knave.", "Assume Sophia is a knight. No contradiction is found in their claim that Emma is a knave.", "Emma cannot be a knight, because this would contradict the claim of Sophia that Emma is a knave.", "Assume Emma is a knave. No contradiction is found in their false claim that Riley is a knight and Riley is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that If Abigail is a knight then Emma is a knave.", "Assume Matthew is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Joseph is a knight.", "Joseph cannot be a knight, because this would contradict the claim of Matthew that Sophia is a knave if and only if Joseph is a knight.", "Joseph cannot be a knave, because this would contradict the false claim of their own that Sophia is a knight or Riley is a knave.", "We have exhausted all possibilities for Joseph, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Joseph is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Sophia is a knight or Riley is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('<=>', ('telling-truth', 1), ('lying', 1)), ('lying', 4), ('<=>', ('lying', 1), ('telling-truth', 3)), ('or', ('telling-truth', 1), ('lying', 5)), ('and', ('telling-truth', 5), ('lying', 5)), ('->', ('telling-truth', 0), ('lying', 4)))", "index": 1091}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Oliver, Samuel, Joseph, Riley, and Chloe. Matthew asserted: \"Riley is a knave or Chloe is a knave\". Oliver asserted: \"If Joseph is a knave then Oliver is a knight\". \"Matthew is a knave and Oliver is a knave,\" Samuel claimed. As Joseph put it, \"Chloe is a knight or Chloe is a knave\". \"Matthew is not a knave,\" Riley claimed. Chloe noted, \"Chloe is a knight\". So who is a knight and who is a knave?", "names": ["Matthew", "Oliver", "Samuel", "Joseph", "Riley", "Chloe"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, false], "solution_text": "Matthew is a knight, Oliver is a knight, Samuel is a knave, Joseph is a knight, Riley is a knight, and Chloe is a knave.", "solution_text_format": "(1) Matthew is a knight\n(2) Oliver is a knight\n(3) Samuel is a knave\n(4) Joseph is a knight\n(5) Riley is a knight\n(6) Chloe is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Matthew is a knight. No contradiction is found in their claim that Riley is a knave or Chloe is a knave.", "Assume Riley is a knight. No contradiction is found in their claim that Matthew is not a knave.", "Chloe cannot be a knight, because this would contradict the claim of Matthew that Riley is a knave or Chloe is a knave.", "Assume Chloe is a knave. No contradiction is found in their false claim that Chloe is a knight.", "Assume Oliver is a knight. No contradiction is found in their claim that If Joseph is a knave then Oliver is a knight.", "Assume Joseph is a knight. No contradiction is found in their claim that Chloe is a knight or Chloe is a knave.", "Samuel cannot be a knight, because this would contradict the claim of their own that Matthew is a knave and Oliver is a knave.", "Assume Samuel is a knave. No contradiction is found in their false claim that Matthew is a knave and Oliver is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('or', ('lying', 4), ('lying', 5)), ('->', ('lying', 3), ('telling-truth', 1)), ('and', ('lying', 0), ('lying', 1)), ('or', ('telling-truth', 5), ('lying', 5)), ('not', ('lying', 0)), ('telling-truth', 5))", "index": 1092}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aiden, Abigail, Joseph, Jack, Mason, and David. Aiden expressed that Mason is not a knave. Abigail told you that Aiden is not a knight. Joseph said, \"Mason is a knight and David is a knight.\" According to Jack, \"Abigail is not a knight\". \"Joseph is a knave if and only if Jack is a knave,\" Mason declared. \"If David is a knight then Jack is a knight,\" David mentioned. So who is a knight and who is a knave?", "names": ["Aiden", "Abigail", "Joseph", "Jack", "Mason", "David"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, true, true], "solution_text": "Aiden is a knight, Abigail is a knave, Joseph is a knight, Jack is a knight, Mason is a knight, and David is a knight.", "solution_text_format": "(1) Aiden is a knight\n(2) Abigail is a knave\n(3) Joseph is a knight\n(4) Jack is a knight\n(5) Mason is a knight\n(6) David is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Aiden is a knight. No contradiction is found in their claim that Mason is not a knave.", "Assume Mason is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Jack is a knave.", "Assume Joseph is a knight. No contradiction is found in their claim that Mason is a knight and David is a knight.", "Assume David is a knight. No contradiction is found in their claim that If David is a knight then Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Abigail is not a knight.", "Abigail cannot be a knight, because this would contradict the claim of their own that Aiden is not a knight.", "Assume Abigail is a knave. No contradiction is found in their false claim that Aiden is not a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 4)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('telling-truth', 1)), ('<=>', ('lying', 2), ('lying', 3)), ('->', ('telling-truth', 5), ('telling-truth', 3)))", "index": 1093}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, William, Noah, Luke, Oliver, and Lily. Penelope said, \"Lily is not a knave.\" William was heard saying, \"Luke is a knight or Penelope is a knight\". Noah noted, \"William is a knave\". Luke commented, \"If William is a knight then Noah is a knave\". Oliver said that Lily is a knight and William is a knight. According to Lily, \"If Luke is a knight then William is a knight\". So who is a knight and who is a knave?", "names": ["Penelope", "William", "Noah", "Luke", "Oliver", "Lily"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, true, true], "solution_text": "Penelope is a knight, William is a knight, Noah is a knave, Luke is a knight, Oliver is a knight, and Lily is a knight.", "solution_text_format": "(1) Penelope is a knight\n(2) William is a knight\n(3) Noah is a knave\n(4) Luke is a knight\n(5) Oliver is a knight\n(6) Lily is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Penelope is a knight. No contradiction is found in their claim that Lily is not a knave.", "Assume Lily is a knight. No contradiction is found in their claim that If Luke is a knight then William is a knight.", "Assume Luke is a knight. No contradiction is found in their claim that If William is a knight then Noah is a knave.", "Assume William is a knight. No contradiction is found in their claim that Luke is a knight or Penelope is a knight.", "Noah cannot be a knight, because this would contradict the claim of their own that William is a knave.", "Assume Noah is a knave. No contradiction is found in their false claim that William is a knave.", "Assume Oliver is a knight. No contradiction is found in their claim that Lily is a knight and William is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('or', ('telling-truth', 3), ('telling-truth', 0)), ('lying', 1), ('->', ('telling-truth', 1), ('lying', 2)), ('and', ('telling-truth', 5), ('telling-truth', 1)), ('->', ('telling-truth', 3), ('telling-truth', 1)))", "index": 1094}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Ethan, Amelia, Ava, Harper, and Elizabeth. \"Ethan is not a knave,\" James mentioned. \"Ava is a knight and Ava is a knave,\" Ethan declared. According to Amelia, \"James is a knave and Ava is a knave\". Ava stated, \"Ethan is a knave\". Harper said that James is a knight. Elizabeth said, \"Ava is a knight or James is a knave.\" So who is a knight and who is a knave?", "names": ["James", "Ethan", "Amelia", "Ava", "Harper", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "James is a knave, Ethan is a knave, Amelia is a knave, Ava is a knight, Harper is a knave, and Elizabeth is a knight.", "solution_text_format": "(1) James is a knave\n(2) Ethan is a knave\n(3) Amelia is a knave\n(4) Ava is a knight\n(5) Harper is a knave\n(6) Elizabeth is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume James is a knight. No contradiction is found in their claim that Ethan is not a knave.", "Ethan cannot be a knight, because this would contradict the claim of their own that Ava is a knight and Ava is a knave.", "Ethan cannot be a knave, because this would contradict the claim of James that Ethan is not a knave.", "We have exhausted all possibilities for Ethan, so let us go back and reconsider James.", "Assume James is a knave. No contradiction is found in their false claim that Ethan is not a knave.", "Ethan cannot be a knight, because this would contradict the false claim of James that Ethan is not a knave.", "Assume Ethan is a knave. No contradiction is found in their false claim that Ava is a knight and Ava is a knave.", "Assume Ava is a knight. No contradiction is found in their claim that Ethan is a knave.", "Amelia cannot be a knight, because this would contradict the claim of their own that James is a knave and Ava is a knave.", "Assume Amelia is a knave. No contradiction is found in their false claim that James is a knave and Ava is a knave.", "Harper cannot be a knight, because this would contradict the claim of their own that James is a knight.", "Assume Harper is a knave. No contradiction is found in their false claim that James is a knight.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Ava is a knight or James is a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 1)), ('and', ('telling-truth', 3), ('lying', 3)), ('and', ('lying', 0), ('lying', 3)), ('lying', 1), ('telling-truth', 0), ('or', ('telling-truth', 3), ('lying', 0)))", "index": 1095}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jackson, Aiden, Emma, Jack, Daniel, and Logan. As Jackson put it, \"Logan is not a knave\". Aiden commented, \"Daniel is not a knave\". Emma asserted: \"Jackson is a knave if and only if Aiden is a knave\". Jack remarked, \"Emma is not a knave\". Daniel said, \"Jack is a knight.\" Logan noted, \"Daniel is a knight\". So who is a knight and who is a knave?", "names": ["Jackson", "Aiden", "Emma", "Jack", "Daniel", "Logan"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, true, true, true, true], "solution_text": "Jackson is a knight, Aiden is a knight, Emma is a knight, Jack is a knight, Daniel is a knight, and Logan is a knight.", "solution_text_format": "(1) Jackson is a knight\n(2) Aiden is a knight\n(3) Emma is a knight\n(4) Jack is a knight\n(5) Daniel is a knight\n(6) Logan is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Jackson is a knight. No contradiction is found in their claim that Logan is not a knave.", "Assume Logan is a knight. No contradiction is found in their claim that Daniel is a knight.", "Assume Daniel is a knight. No contradiction is found in their claim that Jack is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that Emma is not a knave.", "Assume Emma is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Aiden is a knave.", "Assume Aiden is a knight. No contradiction is found in their claim that Daniel is not a knave."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 5)), ('not', ('lying', 4)), ('<=>', ('lying', 0), ('lying', 1)), ('not', ('lying', 2)), ('telling-truth', 3), ('telling-truth', 4))", "index": 1096}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Evelyn, Jack, Samuel, Matthew, and Elizabeth. Chloe was heard saying, \"If Samuel is a knave then Matthew is a knight\". Evelyn noted, \"Chloe is a knave if and only if Jack is a knight\". In Jack's words: \"If Elizabeth is a knave then Chloe is a knave\". \"Matthew is a knave if and only if Evelyn is a knight\" - Samuel. \"Jack is a knight and Evelyn is a knight\" - Matthew. \"Matthew is a knave if and only if Elizabeth is a knight,\" Elizabeth declared. So who is a knight and who is a knave?", "names": ["Chloe", "Evelyn", "Jack", "Samuel", "Matthew", "Elizabeth"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, true, false, true, false, false], "solution_text": "Chloe is a knight, Evelyn is a knight, Jack is a knave, Samuel is a knight, Matthew is a knave, and Elizabeth is a knave.", "solution_text_format": "(1) Chloe is a knight\n(2) Evelyn is a knight\n(3) Jack is a knave\n(4) Samuel is a knight\n(5) Matthew is a knave\n(6) Elizabeth is a knave", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Chloe is a knight. No contradiction is found in their claim that If Samuel is a knave then Matthew is a knight.", "Assume Samuel is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Evelyn is a knight.", "Assume Matthew is a knight. No contradiction is found in their claim that Jack is a knight and Evelyn is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Chloe is a knave.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Matthew is a knave if and only if Elizabeth is a knight.", "Elizabeth cannot be a knave, because this would contradict the claim of Jack that If Elizabeth is a knave then Chloe is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Jack.", "Jack cannot be a knave, because this would contradict the claim of Matthew that Jack is a knight and Evelyn is a knight.", "We have exhausted all possibilities for Jack, so let us go back and reconsider Matthew.", "Assume Matthew is a knave. No contradiction is found in their false claim that Jack is a knight and Evelyn is a knight.", "Assume Jack is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Chloe is a knave.", "Assume Elizabeth is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Elizabeth is a knight.", "Evelyn cannot be a knight, because this would contradict the claim of their own that Chloe is a knave if and only if Jack is a knight.", "Evelyn cannot be a knave, because this would contradict the claim of Samuel that Matthew is a knave if and only if Evelyn is a knight.", "We have exhausted all possibilities for Evelyn, so let us go back and reconsider Elizabeth.", "Elizabeth cannot be a knave, because this would contradict the claim of Jack that If Elizabeth is a knave then Chloe is a knave.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Jack.", "Assume Jack is a knave. No contradiction is found in their false claim that If Elizabeth is a knave then Chloe is a knave.", "Elizabeth cannot be a knight, because this would contradict the false claim of Jack that If Elizabeth is a knave then Chloe is a knave.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Elizabeth is a knight.", "Assume Evelyn is a knight. No contradiction is found in their claim that Chloe is a knave if and only if Jack is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('->', ('lying', 3), ('telling-truth', 4)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('->', ('lying', 5), ('lying', 0)), ('<=>', ('lying', 4), ('telling-truth', 1)), ('and', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('lying', 4), ('telling-truth', 5)))", "index": 1097}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ava, Mason, Scarlett, Aria, Mia, and Benjamin. According to Ava, \"Aria is not a knave\". Mason commented, \"Ava is a knave and Ava is a knight\". Scarlett said that Aria is a knight. \"Benjamin is a knight,\" Aria declared. As Mia put it, \"Aria is a knight if and only if Aria is a knave\". In a statement by Benjamin: \"Benjamin is a knight or Mia is a knave\". So who is a knight and who is a knave?", "names": ["Ava", "Mason", "Scarlett", "Aria", "Mia", "Benjamin"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [true, false, true, true, false, true], "solution_text": "Ava is a knight, Mason is a knave, Scarlett is a knight, Aria is a knight, Mia is a knave, and Benjamin is a knight.", "solution_text_format": "(1) Ava is a knight\n(2) Mason is a knave\n(3) Scarlett is a knight\n(4) Aria is a knight\n(5) Mia is a knave\n(6) Benjamin is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Ava is a knight. No contradiction is found in their claim that Aria is not a knave.", "Assume Aria is a knight. No contradiction is found in their claim that Benjamin is a knight.", "Assume Benjamin is a knight. No contradiction is found in their claim that Benjamin is a knight or Mia is a knave.", "Mia cannot be a knight, because this would contradict the claim of their own that Aria is a knight if and only if Aria is a knave.", "Assume Mia is a knave. No contradiction is found in their false claim that Aria is a knight if and only if Aria is a knave.", "Mason cannot be a knight, because this would contradict the claim of their own that Ava is a knave and Ava is a knight.", "Assume Mason is a knave. No contradiction is found in their false claim that Ava is a knave and Ava is a knight.", "Assume Scarlett is a knight. No contradiction is found in their claim that Aria is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('lying', 3)), ('and', ('lying', 0), ('telling-truth', 0)), ('telling-truth', 3), ('telling-truth', 5), ('<=>', ('telling-truth', 3), ('lying', 3)), ('or', ('telling-truth', 5), ('lying', 4)))", "index": 1098}
{"quiz": "A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Harper, Liam, Lily, Elizabeth, and Aurora. Luke was heard saying, \"Aurora is not a knight\". \"Liam is a knave and Elizabeth is a knight,\" Harper mentioned. Liam was heard saying, \"Elizabeth is a knight\". \"If Aurora is a knave then Harper is a knight,\" Lily claimed. Elizabeth said, \"Harper is a knave and Luke is a knight.\" Aurora asserted: \"Harper is a knave or Liam is a knight\". So who is a knight and who is a knave?", "names": ["Luke", "Harper", "Liam", "Lily", "Elizabeth", "Aurora"], "knight_knave": {"knight": "knight", "knave": "knave", "a_knight": "a knight", "a_knave": "a knave", "Knight": "Knight", "Knave": "Knave"}, "solution": [false, false, false, true, false, true], "solution_text": "Luke is a knave, Harper is a knave, Liam is a knave, Lily is a knight, Elizabeth is a knave, and Aurora is a knight.", "solution_text_format": "(1) Luke is a knave\n(2) Harper is a knave\n(3) Liam is a knave\n(4) Lily is a knight\n(5) Elizabeth is a knave\n(6) Aurora is a knight", "cot_head": "Let's think step by step, by considering whether each person is lying and if that leads to contradiction.", "cot_repeat_steps": ["Assume Luke is a knight. No contradiction is found in their claim that Aurora is not a knight.", "Aurora cannot be a knight, because this would contradict the claim of Luke that Aurora is not a knight.", "Assume Aurora is a knave. No contradiction is found in their false claim that Harper is a knave or Liam is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Liam is a knave and Elizabeth is a knight.", "Liam cannot be a knight, because this would contradict the claim of Harper that Liam is a knave and Elizabeth is a knight.", "Assume Liam is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Liam that Elizabeth is a knight.", "Elizabeth cannot be a knave, because this would contradict the claim of Harper that Liam is a knave and Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth and Liam, so let us go back and reconsider Harper.", "Harper cannot be a knave, because this would contradict the false claim of Aurora that Harper is a knave or Liam is a knight.", "We have exhausted all possibilities for Harper and Aurora, so let us go back and reconsider Luke.", "Assume Luke is a knave. No contradiction is found in their false claim that Aurora is not a knight.", "Assume Aurora is a knight. No contradiction is found in their claim that Harper is a knave or Liam is a knight.", "Assume Harper is a knight. No contradiction is found in their claim that Liam is a knave and Elizabeth is a knight.", "Liam cannot be a knight, because this would contradict the claim of Harper that Liam is a knave and Elizabeth is a knight.", "Liam cannot be a knave, because this would contradict the claim of Aurora that Harper is a knave or Liam is a knight.", "We have exhausted all possibilities for Liam, so let us go back and reconsider Harper.", "Assume Harper is a knave. No contradiction is found in their false claim that Liam is a knave and Elizabeth is a knight.", "Assume Liam is a knight. No contradiction is found in their claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Luke is a knight.", "Elizabeth cannot be a knave, because this would contradict the claim of Liam that Elizabeth is a knight.", "We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Liam.", "Assume Liam is a knave. No contradiction is found in their false claim that Elizabeth is a knight.", "Elizabeth cannot be a knight, because this would contradict the false claim of Harper that Liam is a knave and Elizabeth is a knight.", "Assume Elizabeth is a knave. No contradiction is found in their false claim that Harper is a knave and Luke is a knight.", "Assume Lily is a knight. No contradiction is found in their claim that If Aurora is a knave then Harper is a knight."], "cot_foot": "This leads to a feasible solution.", "statements": "(('not', ('telling-truth', 5)), ('and', ('lying', 2), ('telling-truth', 4)), ('telling-truth', 4), ('->', ('lying', 5), ('telling-truth', 1)), ('and', ('lying', 1), ('telling-truth', 0)), ('or', ('lying', 1), ('telling-truth', 2)))", "index": 1099}