### Instruction: On a Tuesday, a magician said, ``I made my wife disappear 31 days ago.'' What day of the week did he make her disappear?### Response: To find the day of the week when the magician made his wife disappear, I need to subtract 31 days from Tuesday and see what day I get.
I can use modular arithmetic to do this, since the days of the week repeat in a cycle of 7.
That means I can reduce 31 mod 7 and get the same answer as subtracting 31 days from Tuesday.
31 mod 7 is 3, since 31 = 7 x 4 + 3.
So I need to subtract 3 days from Tuesday.
Going back 3 days from Tuesday, I get Monday, then Sunday, then Saturday.
So the magician made his wife disappear on a Saturday.