Sudoku Cube [SEP] based on
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Sudoku Cube


The Sudoku Cube or Sudokube is a variation on a Rubik's Cube in which the faces have numbers one to nine on the sides instead of colours. The aim is to solve Sudoku puzzles on one or more of the sides. The toy was created in 2006 by Jay Horowitz in Sebring, Ohio. The Sudoku Cube was invented by veteran toy maker Jay Horowitz after he had the idea to combine Sudoku and a Rubik's Cube. Horowitz already owned molds to produce Rubik's Cubes and was able to use them to produce
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Sudoku Cube


repetition. This is achieved by rotating the sides of the cube. Variations of the Sudoku Cube are the Sudokube and Roxdoku, as well as cubes with 4×4×4 squares instead of the normal 3×3×3. This cube is very difficult compared to other cubes because as well as requiring basic knowledge of a Rubik's cube, the player must also know basic sudoku concepts. Any wrong move could put the puzzle in jeopardy. 3-D programming languages such as VPython can be used to create simulations of a Sudoku Cube. Such simulations can offer features
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Sudoku Cube


his new design. Mass production is completed in China by American Classic Toy Inc, a company belonging to Horowitz. The product is sold in the United States in retailers such as Barnes & Noble and FAO Schwarz. There are 12 types of Sudoku Cube, which differ in difficulty and are aimed at different age ranges. In a standard Rubik's Cube, the player must match up colours on each side of the cube. In the Sudoku Cube, the player must place the numbers one to nine on each side with no
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Sudoku


specific locations in grids needing to be transferred to others. A tabletop version of Sudoku can be played with a standard 81-card Set deck (see Set game). A three-dimensional Sudoku puzzle was published in "The Daily Telegraph" in May 2005. "The Times" also publishes a three-dimensional version under the name Tredoku. Also, a Sudoku version of the Rubik's Cube is named Sudoku Cube. Many other variants have been developed. Some are different shapes in the arrangement of overlapping 9×9 grids, such
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Nine-Colour Cube


and moves the four edge and four corner pieces that surround it. However, the difference between the two puzzles is their purpose: on a standard Rubik's Cube, the aim is to arrange the puzzle in such a way that every face has only "one colour"; on the Nine-Colour Cube, the goal is opposite: to arrange it so that every face contains "all nine colours exactly once". The Sudoku Cube is similar to the Nine-Colour Cube in that the objective of the Sudoku Cube
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36 Cube


The 36 Cube is a three-dimensional sudoku puzzle created by ThinkFun. The puzzle consists of a gray base that resembles a city skyline, plus 36 colored towers. The towers come in six different colors and six different heights. The goal of the puzzle is to place all the towers onto the base so as to form a level cube with each of the six colors appearing once, and only once, in each row and column. The 36 cube was invented by Dr. Derrick Niederman, a PhD. at MIT. He
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Nine-Colour Cube


gave it the name "Nine-Colour Scramble Cube", which reflected the key feature and the "de facto" objective of the puzzle. This name was later shortened by some to Nine-Colour Cube. When Meffert's started mass-producing the puzzle, the company changed the shape of the cubies into spheres and thus adopted the name Ball Sudoku Cube (since the aim of the puzzle is similar to that of the Sudoku Cube). However, when Recent Toys started selling the puzzle with Meffert's branding,
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FUN Technologies


license to Pop Cap's Bejeweled for cash and prizes, sudoku, chess, Zuma, Big Money!" and "Dynomite, as well as partnerships with service providers like DirecTV offering its game tournaments via DirecTV's set top boxes. In 2006 FUN acquired its Newton, Massachusetts-based competitor WorldWinner, an established tournament games platform with a large portfolio of games, including "Scrabble Cubes", solitaire and "Luxor," founded by Alex Bloom (Saidakovsky), Alex Ganelis, and Daniil Utin in 1999. It
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Sudoku solving algorithms


may also be modelled as a constraint satisfaction problem. In his paper "Sudoku as a Constraint Problem", Helmut Simonis describes many "reasoning algorithms" based on constraints which can be applied to model and solve problems. Some constraint solvers include a method to model and solve Sudokus, and a program may require less than 100 lines of code to solve a simple Sudoku. If the code employs a strong reasoning algorithm, incorporating backtracking is only needed for the most difficult Sudokus. An algorithm combining a constraint-model-based
10978989
Uwe Mèffert


number print puzzle. In addition to the standard sudoku rules, the two major diagonals must also contain the numerals from 1 to 9. Additionally, a Chinese magic square is hidden somewhere in the solution. He named this puzzle "Kokonotsu", Japanese for "nine". Mèffert has also produced puzzle designs by Tony Fisher, including the "Golden Cube", and Oskar van Deventer, including the "Gear Cube". Mèffert was born in Wernigerode in the Harz Mountains of Germany on the 28 November 1939. Mèffert
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Sudoku Codes


Sudoku codes are non-linear forward error correcting codes following rules of sudoku puzzles designed for an erasure channel. Based on this model, the transmitter sends a sequence of all symbols of a solved sudoku. The receiver either receives a symbol correctly or an erasure symbol to indicate that the symbol was not received. The decoder gets a matrix with missing entries and uses the constraints of sudoku puzzles to reconstruct a limited amount of erased symbols. Sudoku codes are not suitable for practical usage but are subject of research. Questions like the
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Buku Sudoku


Buku Sudoku (titled Buku Números in Mexico and Buku数字パズル in Japan) is a downloadable puzzle game developed by Ukrainian studio Absolutist Ltd and published by Merscom based on Sudoku for the Windows PC's. The game was also released for the Xbox 360 via Xbox Live Arcade, on May 28, 2008. Buku Sudoku 360 offers variations on the traditional Sudoku puzzle including 4x4, 6x6, 8x8, 9x9, 12x12 and 16x16 grids. There are also three difficulty levels featured, as well as a "Create Your Own Sudoku" feature
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Go! Sudoku


Go! Sudoku is a sudoku puzzle game for the PlayStation Portable, released in Europe on December 2, 2005 and North America on March 21, 2006. It was later released in Japan on April 27, 2006 under the name of "Kazuo" (カズオ), as Nikoli holds the trademark for Sudoku. The game was mildly received by gamers and professional critics. The base game features 1000 Sudoku puzzles grouped by difficulty, as well as various modes, customizable grids and multiplayer. 200 more puzzles are available for download
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Sudoku Codes


(e.g. integers formula_4) have to be mapped onto base 2. The binary erasure channel model however is not applicable because it erases only individual bits with some probability and not Sudoku symbols. If the symbols of the Sudoku are sent in packets the channel can be described as a packet erasure channel model. A sudoku is a formula_5 number-placement puzzle. It is filled in a way, that in each column, row and sub-grid N distinct symbols occur exactly once. Typical alphabet is the set of the integers
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Sudoku solving algorithms


Sudoku can be solved nowadays in less than 30 seconds using an exhaustive search routine and faster processors. Sudoku can be solved using stochastic (random-based) algorithms. An example of this method is to: A solution to the puzzle is then found. Approaches for shuffling the numbers include simulated annealing, genetic algorithm and tabu search. Stochastic-based algorithms are known to be fast, though perhaps not as fast as deductive techniques. Unlike the latter however, optimisation algorithms do not necessarily require problems to be logic-solvable
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Sudoku Codes


sudoku has the advantage, that its size can be chosen more freely. Due to the sub-grid structure normal sudokus can only be of size n², diagonal sudokus have valid solutions for all odd formula_9. Sudoku codes are non-linear. In a linear code any linear combination of codewords give a new valid codeword, this does not hold for sudoku codes. The symbols of a sudoku are from a finite alphabet (e.g. integers formula_4). The constraints of Sudoku codes are non-linear: all symbols within a
12292650
Edward W. Veitch


the front corners. For four, five, or six variables the problem becomes more complicated. How do we depict the multi-dimensional cube on a flat diagram that makes it easy to see these relationships? In a last minute change before his presentation Veitch removed the spacing between the 2x2 cell groups. This was a poor decision because it made it more difficult for the user to grasp the overall structure of the function, as well as the rules Veitch used in recognizing simplifications. Veitch learned recently from solving Sudoku puzzles that
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Entertainment


levels. Physical games can develop agility and competence in motor skills. Number games such as Sudoku and puzzle games like the Rubik's cube can develop mental prowess. Video games are played using a controller to create results on a screen. They can also be played online with participants joining in remotely. In the second half of the 20th century and in the 21st century the number of such games increased enormously, providing a wide variety of entertainment to players around the world. Video games are popular across the world. Reading has
9276591
Sudoku graph


In the mathematics of Sudoku, the Sudoku graph is an undirected graph whose vertices represent the cells of a (blank) Sudoku puzzle and whose edges represent pairs of cells that belong to the same row, column, or block of the puzzle. The problem of solving a Sudoku puzzle can be represented as precoloring extension on this graph. It is an integral Cayley graph. On a Sudoku board of size formula_1, the Sudoku graph has formula_2 vertices, each with exactly formula_3 neighbors. Therefore, it is a regular graph.
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Sudoku solving algorithms


49,000 Sudokus with 17 clues have been found, but discovering new distinct ones (not transformations of existing known Sudokus) is becoming more difficult as undiscovered ones become more rare. One common method of searching for Sudokus with a particular characteristic is called "neighbor searching". Using this strategy, one or more known Sudokus which satisfy or nearly satisfy the characteristic being searched for is used as a starting point, and these Sudokus are then altered to look for other Sudokus with the property being sought. The alteration can be relocating one
10978991
Verbal arithmetic


, giving 1,814,400 possibilities. They also provide good examples for backtracking paradigm of algorithm design. When generalized to arbitrary bases, the problem of determining if a cryptarithm has a solution is NP-complete. (The generalization is necessary for the hardness result because in base 10, there are only 10! possible assignments of digits to letters, and these can be checked against the puzzle in linear time.) Alphametics can be combined with other number puzzles such as Sudoku and Kakuro to create cryptic Sudoku and Kakuro. Anton Pavlis constructed
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SUDO-Q


SUDO-Q is a British game show that was broadcast between 5 December 2005 and 23 March 2007. It was hosted by Eamonn Holmes. The format was based on a mix of the number puzzle Sudoku and general knowledge questions. Three teams of two (originally three) compete. There are four rounds in the game. The first round is based on general knowledge questions and a 4×4 Sudoku grid. Teams are shown the grid, with four numbers already placed. Then a square gets highlighted and the teams lock in what
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Rishi Puri


Rishi Puri is an Indian Sudoku Solver. He is a two time Indian National Sudoku Champion. He was part of the top three from India along with Rohan Rao and Prasanna Seshadri at the National championships and the World Sudoku Championships. Rishi won the Indian Sudoku Championships in 2014 and 2015. He also won the Times Sudoku Championship in 2013. Rishi has also won various international Sudoku competitions. He was twice runners up at the Brand's international Sudoku Competition held at Bangkok, Thailand in 2011 and 2012. Rishi also won the
7038619
Mathematics of Sudoku


automorphic Sudokus, and an automorphic grid are shown below. In the first two examples, notice that if the Sudoku is rotated 180 degrees, and the clues relabeled with the permutation (123456789) - (987654321), it returns to the same Sudoku. Expressed another way, these Sudokus have the property that every 180 degree rotational pair of clues (a, b) follows the rule (a) + (b) = 10. Since these Sudokus are automorphic, so too their solutions grids are automorphic. Furthermore,
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Uwe Mèffert


anyone else would be interested in them, and put them away and forgot about them until Ernő Rubik's Rubik's Cube became a worldwide sensation in the 1980s. In 1981 Mèffert took his puzzles to a Japanese toymaker who agreed to market them. One of them, Pyraminx, sold more than 10 million pieces that year, and 90 million within three years. Since that time, Mèffert and his associates have created more than 100 3D rotating mechanical puzzles. Mèffert also created his own version of sudoku, the popular nine-
1506581
Mathematics of Sudoku


of Sudoku falls into two main areas: analyzing the properties of (1) completed grids and (2) puzzles. Also studied are computer algorithms to solve Sudokus, and to develop (or search for) new Sudokus. Analysis has largely focused on enumerating solutions, with results first appearing in 2004. There are many Sudoku variants, partially characterized by size ("N"), and the shape of their "regions". Unless noted, discussion in this article assumes classic Sudoku, i.e. "N"=9 (a 9×9
7981531
Mathematics of Sudoku


" are a "stack". A "proper" puzzle has a unique solution. See Glossary of Sudoku for other terminology. Solving Sudokus from the viewpoint of a player has been explored in Denis Berthier's book "The Hidden Logic of Sudoku" (2007) which considers strategies such as "hidden xy-chains". The general problem of solving Sudoku puzzles on "n"×"n" grids of "n"×"n" blocks is known to be NP-complete. For "n"=3 (classical Sudoku), however, this result
7981533
Mathematics of Sudoku


Sudoku can have clues limited to the range of positions in the pattern above (first image). The largest rectangular orthogonal "hole" (region with no clues) in a proper Sudoku is believed to be a rectangle of 30 cells (a 5 x 6 rectangular area). One example is a Sudoku with 22 clues (second image). The largest total number of empty groups (rows, columns, and boxes) in a Sudoku is believed to be nine. One example is a Sudoku with 3 empty rows
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Sudoku solving algorithms


, giving them the potential to solve a wider range of problems. Algorithms designed for graph colouring are also known to perform well with Sudokus. It is also possible to express a Sudoku as an integer linear programming problem. Such approaches get close to a solution quickly, and can then use branching towards the end. The simplex algorithm is able to solve non-proper Sudokus, indicating if the Sudoku is not valid (no solution), or providing the set of answers when there is more than one solution. A Sudoku
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Sudoku solving algorithms


algorithm with backtracking would have the advantage of fast solving time, and the ability to solve all sudokus. Sudoku puzzles may be described as an exact cover problem. This allows for an elegant description of the problem and an efficient solution. Modelling Sudoku as an exact cover problem and using an algorithm such as dancing links will typically solve a Sudoku in a few milliseconds. Computer programs are often used to "search" for Sudokus with certain properties, such as a small number of clues, or certain types of symmetry. Over
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Sudoku graph


For instance, the graph shown in the figure, for a formula_4 board, has 16 vertices and is 7-regular. For the most common form of Sudoku, on a formula_5 board, the Sudoku graph is a 20-regular graph with 81 vertices. Each row, column, or block of the Sudoku puzzle forms a clique in the Sudoku graph, whose size equals the number of symbols used to solve the puzzle. A graph coloring of the Sudoku graph using this number of colors (the minimum possible number of colors for this graph
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Indian Sudoku Championship


The Indian Sudoku Championship (commonly abbreviated as 'ISC') is an annual national contest held in India to crown the Indian Sudoku Champion and to select the national team for the Asian Sudoku Championship and World Sudoku Championship. It usually consists of multiple rounds of solving various classic sudoku and its variants, and the scores of players are aggregated for the final rankings. It is conducted by Logic Masters India (commonly abbreviated as 'LMI'), which is the Indian affiliate of the World Puzzle Federation. Of the 13 national
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Indian Sudoku Championship


across the years and attracts the top solvers of India. It is a platform for sudoku authors to create their own sudokus for the event, as well as for sudoku enthusiasts to participate and solve them in a national championship involving various sudoku variants. Since 2016, several online rounds were held across the year followed by an offline finals. In 2015, 2014, 2013 and 2009, the championship was held as an online contest. In 2012, the championship was held in collaboration with Times Sudoku Championship (TSC), sponsored
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Sudoku solving algorithms


be solved and has a single solution). Methods can also be employed to prevent essentially equivalent Sudokus from being redundantly tested. As a specific example, a search for a 17-clue Sudoku could start with a known 18-clue Sudoku, and then altering it by removing "three clues", and replacing them with only "two clues", in different positions (see last two images). This may discover new Sudokus, but there would be no immediate guarantee that they are essentially different from already known Sudokus. If searching for
10978993
Sudoku Codes


constraint (row, line, sub-grid) must be different from any other symbol within this constraint. Hence there is no all-zero codeword in Sudoku codes. Sudoku codes can be represented by probabilistic graphical model in which they take the form of a low-density parity-check code. There are several possible decoding methods for sudoku codes. Some algorithms are very specific developments for Sudoku codes. Several methods are described in sudoku solving algorithms. Another efficient method is with dancing links. Decoding methods like belief propagation
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Sudoku


Sudoku" with 12 regions of 4×3 squares. Dell Magazines regularly publishes 16×16 "Number Place Challenger" puzzles (using the numbers 1–16 or the letters A-P). Nikoli offers 25×25 "Sudoku the Giant" behemoths. A 100×100-grid puzzle dubbed Sudoku-zilla was published in 2010. Under the name "Mini Sudoku", a 6×6 variant with 3×2 regions appears in the American newspaper "USA Today" and elsewhere. The object is the same as that of standard Sudoku, but the puzzle only uses the numbers 1
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Sudoku Challenge!


Sudoku Challenge! is a WiiWare sudoku game developed by Digital Leisure. The game was released in North America on November 24, 2008 and in the PAL region on December 19, 2008 and costs 500 Wii Points. The DSiWare version has been released in North America on November 30, 2009 and in the PAL region on May 14, 2010. The game includes three difficulty levels, Original and Grand Sudoku game modes (where the player has to complete five intersecting Sudoku boards at the same time), and over 100,000,000 sudoku
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Rohan Rao


the Director of the World Sudoku Championship 2017 and core organizer of World Sudoku and Puzzle Championship (WSPC) 2017 held in October, 2017 in Bengaluru, India. 15 Titles, 6 Runners-up, 6 Third-places Ranks in the Indian Puzzle Championship (IPC), Indian Sudoku Championship (ISC) and Times Sudoku Championship (TSC) 2 ASC Appearances Ranks in the Asian Sudoku Championship (ASC) 10 WSC Appearances, 10 WPC Appearances Ranks in the World Sudoku Championship (WSC), World Puzzle Championship (WPC
4076229
Mathematics of Sudoku


, 90° rotational symmetry, 180° rotational symmetry, and diagonal symmetry) is known to exist, and is also automorphic. Again here, it is not known if this number of clues is minimal for this class of Sudoku. The fewest clues in a Sudoku with two-way diagonal symmetry is believed to be 18, and in at least one case such a Sudoku also exhibits automorphism. Additional constraints (here, on 3×3 Sudokus) lead to a smaller minimum number of clues. "Du-sum-oh
7981553
Sudoku Codes


has formula_27 bits of information. One Sudoku code can be seen as 72.5 bits of information and 184.3 bits redundancy. Theoretically a string of 72 bits can be mapped to one sudoku that is sent over the channel as a string of 81 symbols. However, there is no linear function that maps a string to a sudoku code. A suggested encoding approach by Sayir is as follows: For a formula_28 sudoku the first entry can be filled with a source of cardinality 4. In this example this a 1. For the rest
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Sudoku


as butterfly, windmill, or flower. Others vary the logic for solving the grid. One of these is "Greater Than Sudoku". In this, a 3×3 grid of the Sudoku is given with 12 symbols of Greater Than () or Less Than (<) on the common line of the two adjacent numbers. Another variant on the logic of solution is "Clueless Sudoku", in which nine 9×9 Sudoku grids are each placed in a 3×3 array. The center cell in each 3×3 grid of all nine puzzles
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Sudoku


is left blank and form a tenth Sudoku puzzle without any cell completed; hence, "clueless". Examples and other variants can be found in the Glossary of Sudoku. This section refers to classic Sudoku, disregarding jigsaw, hyper, and other variants. A completed Sudoku grid is a special type of Latin square with the additional property of no repeated values in any of the nine blocks (or "boxes" of 3×3 cells). The relationship between the two theories is known, after it was proven that a first
17887178
Mathematics of Sudoku


Sudoku is not known. The number of minimal Sudokus (Sudokus in which no clue can be deleted without losing uniqueness of the solution) is not precisely known. However, statistical techniques combined with a generator (), show that there are approximately (with 0.065% relative error): Other authors used faster methods and calculated additional precise distribution statistics. As in the case of Latin squares the (addition- or) multiplication tables (Cayley tables) of finite groups can be used to construct Sudokus and related tables of numbers.
7981537
Mathematics of Sudoku


Jarvis / Russell showed that there are 49 essentially different grids (see also the article by Bailey, Cameron and Connelly), to the 2x4 case, where Russell showed that there are 1,673,187 essentially different grids (verified by Pettersen), and to the 2x5 case where Pettersen showed that there are 4,743,933,602,050,718 essentially different grids (not verified). Ordinary Sudokus ("proper" puzzles) have a unique solution. A "minimal" Sudoku is a Sudoku from which no clue can be removed leaving it a proper Sudoku. Different
7981550
Mathematics of Sudoku


relative values of (some but not all) adjacent region sums. She demonstrates an example with only eight relations. It is not known whether this is the best possible. The most clues for a "minimal" Sudoku is believed to be 40, of which only two are known. If any clue is removed from either of these Sudokus, the puzzle would have more than one solution (and thus not be a proper Sudoku). In the work to find these Sudokus, other high-clue puzzles were catalogued,
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Sudoku solving algorithms


not fulfil the constraints of the Sudoku. Advantages of this method are: The disadvantage of this method is that the solving time may be slow compared to algorithms modeled after deductive methods. One programmer reported that such an algorithm may typically require as few as 15,000 cycles, or as many as 900,000 cycles to solve a Sudoku, each cycle being the change in position of a "pointer" as it moves through the cells of a Sudoku. A Sudoku can be constructed to work against backtracking. Assuming the solver works from top
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Killer sudoku


Killer sudoku (also killer su doku, sumdoku, sum doku, sumoku, addoku, or samunamupure) is a puzzle that combines elements of sudoku and kakuro. Despite the name, the simpler killer sudokus can be easier to solve than regular sudokus, depending on the solver's skill at mental arithmetic; the hardest ones, however, can take hours to crack. A typical problem is shown on the right, using colors to define the groups of cells. More often, puzzles are printed in black and white, with
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Killer sudoku


thin dotted lines used to outline the "cages" (see below for terminology). Killer sudokus were already an established variant of sudoku in Japan by the mid 1990s, where they were known as "samunamupure." The name stemmed from a Japanized form of the English words "sum number place." Killer sudokus were introduced to most of the English-speaking world by "The Times" in 2005. Traditionally, as with regular sudoku puzzles, the grid layout is symmetrical around a diagonal, horizontal or vertical axis
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Sudoku Codes


not only with the classical formula_11 Sudoku but with a variety of those. LDPC decoding is a common use-case for belief propagation, with slight modifications this approach can be used for solving Sudoku codes. The constraint satisfaction using a tanner graph is shown in the figure on the right. formula_12 denotes the entries of the sudoku in row-scan order. formula_13 denotes the constraint functions: formula_14 associated with rows, formula_15 associated with columns and formula_16 associated with the formula_3 sub-grids of the Sudoku. formula_13 is defined as
12292653
Sudoku


-order formula that does not mention blocks is valid for Sudoku if and only if it is valid for Latin squares. The general problem of solving Sudoku puzzles on "n"×"n" grids of "n"×"n" blocks is known to be NP-complete. Many computer algorithms, such as backtracking and dancing links can solve most 9×9 puzzles efficiently, but combinatorial explosion occurs as "n" increases, creating limits to the properties of Sudokus that can be constructed, analyzed, and solved as "n" increases. A Sudoku puzzle
17887179
Mathematics of Sudoku


not been standardised: click on the attribution links to see the definitions. A Sudoku will remain valid under the actions of the Sudoku preserving symmetries (see also Jarvis). Some Sudokus are special in that some operations merely have the effect of relabelling the digits; several of these are listed below. Further calculations of this ilk combine to show that the number of essentially different Sudoku grids is 5,472,730,538, for example as demonstrated by Jarvis / Russell and verified by Pettersen. Similar methods have been applied to the 2x3 case, where
7981549
Sudoku Gridmaster


Sudoku Gridmaster (known as Puzzle Series Vol. 3: Sudoku in Japan and Sudoku Master in Europe) is a Touch generations puzzle game for the Nintendo DS, released on March 23, 2006 in Japan, June 26, 2006 in the United States and October 27, 2006 in Europe. It was developed and published by Hudson Soft in Japan, and published by Nintendo in the rest of the world. The game features four hundred sudoku puzzles, four different tutorials as well as four difficulty settings (practice, easy,
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Sudoku solving algorithms


. Players and investigators may use a wide range of computer algorithms to solve Sudokus, study their properties, and make new puzzles, including Sudokus with interesting symmetries and other properties. There are several computer algorithms that will solve most 9×9 puzzles (=9) in fractions of a second, but combinatorial explosion occurs as increases, creating limits to the properties of Sudokus that can be constructed, analyzed, and solved as increases. Some hobbyists have developed computer programs that will solve Sudoku puzzles using a backtracking algorithm, which is a
10978981
Sudoku Codes


information up one gets formula_40 bits. The rate in this example is formula_41. The exact number of possible Sudoku grids according to Mathematics of Sudoku is formula_42. With the total information of formula_43 the average rate of a standard Sudoku is formula_44. The average number of possible entries for a cell is formula_45 or formula_46 of information per Sudoku cell. Note that the rate may vary between codewords. The minimum number of given entries that render a unique solution was proven to be 17. In the worst case only four missing entries can
12292660
Sudoku


can be expressed as a graph coloring problem. The aim is to construct a 9-coloring of a particular graph, given a partial 9-coloring. The fewest clues possible for a proper Sudoku is 17 (proven January 2012, and confirmed September 2013). Over 49,000 Sudokus with 17 clues have been found, many by Japanese enthusiasts. Sudokus with 18 clues and rotational symmetry have been found, and there is at least one Sudoku that has 18 clues, exhibits two-way diagonal symmetry and is automorphic. The maximum number of clues
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Rohan Rao


Rohan Rao is an Indian sudoku and puzzle solver, widely considered as the best sudoku solver of India. He is a 15-time national champion and has been one of the best Indians at the World Sudoku Championship (WSC), World Puzzle Championship (WPC) and Asian Sudoku Championship (ASC). He won the Indian Sudoku Championship seven times, in 2010, 2011, 2012, 2016, 2017, 2018, 2019 and the Indian Puzzle Championship five times, in 2010, 2011, 2012, 2015, 2017. He
4076227
Mathematics of Sudoku


the number of solutions to a Sudoku grid of size "N"x"N", it is necessary to determine how many "N"-omino tilings exist for a given size (including the standard square tilings, as well as the rectangular tilings). The size ordering of Sudoku puzzle can be used to define an integer series, e.g. for square Sudoku, the integer series of possible solutions . Sudoku with square "N"×"N" regions are more symmetrical than immediately obvious from the "One Rule". Each row and column intersects "N" regions
7981579
Sudoku Codes


are also used for low-density parity-check codes are of special interest. Performance analysis of these methods on sudoku codes can help to understand decoding problems for low-density parity-check codes better. By modeling sudoku codes as a probabilistic graphical model belief propagation can be used for Sudoku codes. Belief propagation on the tanner graph or factor graph to decode Sudoku codes is discussed in by Sayir. and Moon This method is originally designed for low-density parity-check codes. Due to its generality belief propagation works
12292652
Sudoku


Sudoku is "". Critically and commercially well-received, it generated particular praise for its Sudoku implementation and sold more than 8 million copies worldwide. Due to its popularity, Nintendo made a second "Brain Age" game titled "Brain Age", which has over 100 new Sudoku puzzles and other activities. In June 2008, an Australian drugs-related jury trial costing over A$ 1 million was aborted when it was discovered that five of the twelve jurors had been playing Sudoku instead of listening to evidence. Although the
17887167
Rohan Rao


also won the Times National Sudoku Championship three times, in 2012, 2015, 2016. Rao was ranked 17th after WSC 2018 and 44th after WPC 2018. He stood 8th in the World Sudoku Championship 2012 to became the first Indian to be ranked in the top-10 in the World in Sudoku. He stood 3rd at the Asian Sudoku Championship 2018 to become the first and only Indian to finish on the podium at an international WPF Sudoku Championship. In 2019, he equalled his 3rd place again at the Asian Championships. He was
4076228
Sudoku Codes


rate and error performance are still unknown for general dimensions. In a sudoku one can find missing information by using different techniques to reproduce the full puzzle. This method can be seen as decoding a sudoku coded message that is sent over an erasure channel where some symbols got erased. By using the sudoku rules the decoder can recover the missing information. Sudokus can be modeled as a probabilistic graphical model and thus methods from decoding low-density parity-check codes like belief propagation can be used. In the erasure channel model a
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Colin Murray


also fronted the Sudoku-based game show "Street-Cred Sudoku" broadcast on UKTV G2 in 2005 and the Channel Five quiz show "Payday" in 2007. Other TV work has included presenting shows on BBC Three such as "EastEnders Revealed", a companion show to the popular soap series. As a narrator, Murray has appeared on the BBC television series "Can't Take It With You", and "Boys Will Be Girls" on E4. He has also provided the narration for the gameshow "Scream
21303802
Mathematics of Sudoku


by factor of 1/648 compared to any non-automorphic grid. In these examples the automorphisms are easy to identify, but in general automorphism is not always obvious. The table at right shows the number of the essentially different Sudoku solution grids for all existing automorphisms. An enumeration technique based on "band generation" was developed that is significantly less computationally intensive. The strategy begins by analyzing the permutations of the top band used in valid solutions. Once the Band1 symmetries and equivalence class for the partial solutions are identified, the completions
7981563
Sudoku Codes


following example based on a formula_30 standard Sudoku. Inputs to the constraint nodes are the possible symbols of the connected entry nodes. Cardinality 1 means that the symbol of the source node is already determined. Again a non-decreasing analysis is sufficient. Lets assume the true output value is 4 and the inputs have cardinalities formula_60 with the true symbols 1-2-3. The messages with cardinality 1 are formula_61 and formula_62. The message of cardinality 2 might be formula_63, formula_64 or formula_65 as the true symbol 3 must be
12292665
Christopher Hobbs


in strict permutations, while maintaining a friendly, melodic soundworld. This combination of strict rigour and audience-friendly surface is typical of most of Hobbs' work since 1970, as is his use of cheap (toy or amateur) electronics. Hobbs has recently begun using Apple Computer's basic GarageBand software to write a series of pieces based on sudoku puzzles (which provide permutations of numbers and letters in a grid). This has led to a double album released in November 2006, called "Sudoku Music" (Experimental Music
16730807
Nimrod Kamer


Nimrod Kamer is a satirist, comedy writer/performer and journalist based in London. Kamer claims to hold both Romanian and Israeli passports. Kamers' public career started in Israel in 2005, as the Sudoku tutor known as "Captain Sudoku". In 2006, he started writing for the Hebrew-language financial newspaper "Globes" under editor Roy Arad. He contributed to the first edition of "Maayan", an Israeli arts magazine edited by Roy Arad and Joshua Simon. In 2009, Kamer became social media manager of
22010661
Unknown Worlds Entertainment


commercial sequel to the game: "Natural Selection 2". Soon after Cleveland founded Unknown Worlds Entertainment as a commercial computer games studio. Although the casual games market is not the intended direction of Unknown Worlds, "Zen of Sudoku", a casual puzzle computer game based on the popular logic puzzle "Sudoku", was created in November 2006 in order to generate revenue towards funding the development of Natural Selection 2. Charlie Cleveland, one of the developers of Unknown Worlds Entertainment, cited casual games development as a "last
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Go! Sudoku


no way to close the dialog box, though it will vanish on its own usually after about 15 seconds. The problem is exacerbated due to "Go! Sudoku" being a single-player game that is played against the clock. Since the object of the game is to complete each puzzle in as little time as possible, with points being awarded based on how quickly the player finishes, the frequent appearance of the message dialog hinders any attempts at beating one's previous high scores, largely negating the competitive element of the
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Mathematics of Sudoku


by class size, gives the total number of solutions as 6,670,903,752,021,072,936,960, confirming the value obtained by QSCGZ. The value was subsequently confirmed numerous times independently. A second enumeration technique based on band generation was later developed that is significantly less computationally intensive. Two valid grids are "essentially" the same if one can be derived from the other. The following operations are Sudoku preserving symmetries and always translate a valid grid into another valid grid: These operations define a symmetry relation between equivalent grids. Excluding relabeling, and with respect to
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Signal Transfer Point


A Signal Transfer Point (STP) is a router that relays SS7 messages between "signaling end-points" (SEPs) and other signaling transfer points (STPs). Typical SEPs include "service switching points" (SSPs) and "service control points" (SCPs). The STP is connected to adjacent SEPs and STPs via signaling links. Based on the address fields of the SS7 messages, the STP routes the messages to the appropriate outgoing signaling link. Edge STPs can also route based upon message body content using
21819466
Mathematics of Sudoku


9. In this case, two distinct vertices labeled by ("x", "y") and ("x"′, "y"′) are joined by an edge if and only if: The puzzle is then completed by assigning an integer between 1 and 9 to each vertex, in such a way that vertices that are joined by an edge do not have the same integer assigned to them. A Sudoku solution grid is also a Latin square. There are significantly fewer Sudoku grids than Latin squares because Sudoku imposes the
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Sudoku graph


) can be interpreted as a solution to the puzzle. The usual form of a Sudoku puzzle, in which some cells are filled in with symbols and the rest must be filled in by the person solving the puzzle, corresponds to the precoloring extension problem on this graph. For any formula_6, the Sudoku graph of an formula_1 Sudoku board is an integral graph, meaning that the spectrum of its adjacency matrix consists only of integers. More precisely, its spectrum consists of the eigenvalues It can be represented as a Cayley graph of
2600837
Shaper of Worlds


The Shaper of Worlds is a fictional character appearing in American comic books published by Marvel Comics. The Shaper of Worlds was created by Archie Goodwin and Herb Trimpe, and first appeared in "Incredible Hulk" #155 (Sep 1972). Its origin was first revealed in "Captain America Annual" #7 (1983). The Shaper of Worlds' existence began thousands of years ago as a Cosmic Cube created by Skrull scientists on an unnamed planet in the Andromeda Galaxy that was part of the Skrull Empire. It was
14526488
David J. Bodycombe


modern puzzles. In 2005 he became a leading author of sudoku puzzles, and he was the first person to have sudokus published in several major territories, including India and Scandinavia. As well as the classic 9x9 puzzle, he pioneered a number of alternative designs which have proved popular with readers all over the world. His games, puzzles and questions also appear in many magazines, and on websites, advertising campaigns, board games and interactive television. He edits UKGameshows.com, a wiki-based web site cataloguing UK television and radio
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Glossary of Sudoku


This is a glossary of Sudoku terms and jargon. It is organized thematically, with links to references and example usage provided as ([1]). Sudoku with a 9×9 grid is assumed, unless otherwise noted. A Sudoku (i.e. the "puzzle") is a partially completed grid. A grid has 9 rows, 9 columns and 9 boxes, each having 9 cells (81 total). Boxes can also be called blocks or regions. Horizontally adjacent rows are a band, and vertically adjacent columns are a
645088
Mathematics of Sudoku


the number of ways of completing a Sudoku band of "R" horizontally adjacent "R"×"C" boxes. Petersen's algorithm, as implemented by Silver, is currently the fastest known technique for exact evaluation of these "b". The band counts for problems whose full Sudoku grid-count is unknown are listed below. As in the previous section, "Dimensions" are those of the regions. The expression for the 4×C case is: formula_16 where: The following are all restrictions of 3x3 Sudokus. The type names have
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Sudoku Codes


symbols narrow down to a subset of the alphabet as symbols get excluded due to constraints. All values that are used by another cell in the constraint, and pairs that are shared among two other cells and so on are eliminated. Sudoku players use this method of logic excluding to solve most sudoku puzzles. The aim of error-correcting codes is to encode data in a way such that it is more resilient to errors in the transmission process. The encoder has to map data formula_21 to a valid sudoku grid from which the
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Sudoku


such as when "The Guardian" "G2" section advertised itself as the first newspaper supplement with a Sudoku grid on every page). Recognizing the different psychological appeals of easy and difficult puzzles, "The Times" introduced both, side by side, on June 20, 2005. From July 2005, Channel 4 included a daily Sudoku game in their teletext service. On August 2, the BBC's program guide "Radio Times" featured a weekly Super Sudoku with a 16×16 grid. In the United States, the
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Sudoku


first newspaper to publish a Sudoku puzzle by Wayne Gould was "The Conway Daily Sun" (New Hampshire), in 2004. The world's first live TV Sudoku show, "Sudoku Live", was a puzzle contest first broadcast on July 1, 2005, on Sky One. It was presented by Carol Vorderman. Nine teams of nine players (with one celebrity in each team) representing geographical regions competed to solve a puzzle. Each player had a hand-held device for entering numbers corresponding to answers for four
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Sudoku


" puzzles are all of this variant, as are the Sudoku X puzzles in "The Daily Mail", which use 6×6 grids. The Killer Sudoku variant combines elements of Sudoku and Kakuro. Alphabetical variations have emerged, sometimes called Wordoku; no functional difference exists in the puzzle unless the letters spell something. Some variants, such as in the "TV Guide", include a word reading along a main diagonal, row, or column once solved; determining the word in advance can be viewed as a solving aid.
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Exact cover


and 72 columns corresponding to constraints. Each row contains a single 1 in the column identifying the pentomino and five 1s in the columns identifying the squares covered by the pentomino. Using the matrix, a computer can find all solutions relatively quickly, for example, using Dancing Links. "Main articles: Sudoku, Sudoku solving algorithms" The problem in Sudoku is to assign numbers (or digits, values, symbols) to cells (or squares) in a grid so as to satisfy certain constraints. In the standard 9×9 Sudoku
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Sudoku solving algorithms


A standard Sudoku contains 81 cells, in a 9×9 grid, and has 9 boxes, each box being the intersection of the first, middle, or last 3 rows, and the first, middle, or last 3 columns. Each cell may contain a number from one to nine, and each number can only occur once in each row, column, and box. A Sudoku starts with some cells containing numbers ("clues"), and the goal is to solve the remaining cells. Proper Sudokus have one solution
10978980
Sudoku Codes


formula_6. The size of the sub-grids limit the size of SUDOKUs to formula_7 with formula_8. Every solved sudoku and every sub-grid of it is a Latin square, meaning every symbol occurs exactly once in each row and column. At the starting point (in this case after the erasure channel) the puzzle is only partially complete but has only one unique solution. For channel codes also other varieties of sudokus are conceivable. Diagonal regions instead of square sub-grids can be used for performance investigations. The diagonal
12292649
Sudoku


Levy's Sudoku tribute song, but quickly had to take down the MP3 file due to heavy traffic. British and Australian radio picked up the song, which is to feature in a British-made Sudoku documentary. The Japanese Embassy also nominated the song for an award, with Levy doing talks with Sony in Japan to release the song as a single. Sudoku software is very popular on PCs, websites, and mobile phones. It comes with many distributions of Linux. Software has also been released on video game consoles,
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Sudoku


A Wordoku might contain words other than the main word. ""Quadratum latinum"" is a Sudoku variation with Roman numerals (I, II, III, IV, ..., IX) proposed by "Hebdomada aenigmatum", a monthly magazine of Latin puzzles and crosswords. Like the Wordoku, it presents no functional difference from a normal Sudoku, but adds the visual difficulty of using Roman numerals. Hyper Sudoku uses the classic 9×9 grid with 3×3 regions, but defines four additional interior 3×3 regions in which the numbers 1–9
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Glossary of Sudoku


stack. The initially defined values are clues or givens. An ordinary Sudoku (i.e. a proper Sudoku) has one solution. Rows, columns and regions can be collectively referred to as groups, of which the grid has 27. The One Rule encapsulates the three prime rules, i.e. each digit (or number) can occur only once in each row, column, and box; and can be compactly stated as: "Each digit appears once in each group." The classic 9×9 Sudoku format can be generalized to an
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Mathematics of Sudoku


by Ed Russell, after a search through equivalence transformations of Gordon Royle's database of 17-clue puzzles. Sudoku puzzles with 18 clues have been found with 180° rotational symmetry, and others with orthogonal symmetry, although it is not known if this number of clues is minimal in either case. Sudoku puzzles with 19 clues have been found with two-way orthogonal symmetry, and again it is unknown if this number of clues is minimal for this case. A Sudoku with 24 clues, dihedral symmetry (symmetry on both orthogonal axis
7981552
Mathematics of Sudoku


, 3 empty columns, and 3 empty boxes (third image). A Sudoku grid is automorphic if it can be transformed in a way that leads back to the original grid, when that same transformation would not otherwise lead back to the original grid. One example of a grid which is automorphic would be a grid which can be rotated 180 degrees resulting in a new grid where the new cell values are a permutation of the original grid. Automorphic Sudokus are Sudoku puzzles which solve to an automorphic grid. Two examples of
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Killer sudoku


in Japan, killer sudoku cages do not include duplicate numbers. However, when "The Times" first introduced the killer sudoku on 31 August 2005, the newspaper did not make this rule explicit. Even though the vast majority of killer sudoku puzzles followed the rule anyway, English-speaking solvers were confused about appropriate solving strategies given the ambiguity. On September 16, 2005 The Times added a new ruling that “Within each dotted-line shape, a digit CAN be repeated if the normal row, column and 3x3 box
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Glossary of Sudoku


This accommodates variants by region size and shape, e.g. 6-cell rectangular regions. ("N"×"N" Sudoku is square). For prime N, polyomino-shaped regions can be used and the requirement to use equal-sized regions, or have the regions entirely cover the grid can be relaxed. Other variations include additional value placement constraints, alternate symbols (e.g. letters), alternate mechanism for expressing the clues, and compositions with overlapping grids. See Sudoku – Variants for details and additional variants. Sudokus variants can also have additional
645090
Mathematics of Sudoku


minimal Sudokus can have a different number of clues. This section discusses the minimum number of givens for proper puzzles. Many Sudokus have been found with 17 clues, although finding them is not a trivial task. A paper by Gary McGuire, Bastian Tugemann, and Gilles Civario, released on 1 January 2012, explains how it was proved through an exhaustive computer search that the minimum number of clues in any proper Sudoku is 17, and this was independently confirmed in September 2013. A few 17-clue puzzles with diagonal symmetry were provided
7981551
Wayne Gould


Wayne Gould (高樂德法官) (born 3 July 1945 in Hawera, New Zealand) is a retired Hong Kong judge, most recently known for helping to popularise sudoku puzzles in the United Kingdom, and thereafter in the United States. He pioneered the global success and popularity of the Sudoku puzzle outside Japan where it had been popular for many years. Gould spent 6 years developing a computer program, known as Pappocom Sudoku that could mass-produce puzzles for the global market. His work led to the publication of sudoku puzzles in
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Australia national sudoku team


The Australian national sudoku team represents Australia in sudoku competition. In 2008 a group of former University of Western Australia Rugby Club players decided to form a team to send to the World Sudoku Championship in Goa, India despite three of the four team members not having played the game before. Dubbed the Numbats, after a small Australian marsupial, the four worked to gain corporate sponsorship for their endeavour. They eventually raised enough money to cover their trip and to provide distinctive uniforms including sporting blazers that closely resembled those worn by Australia's
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The Philadelphia Inquirer Sudoku National Championship


tournament, questions were raised by competitors including 2nd place finisher Thomas Snyder about the performance of Eugene Varshavsky in the tournament. Wearing a hooded sweatshirt during the competition, Varshavsky came nowhere close to his qualifying performance on stage which called into question his abilities as a legitimate sudoku contestant. Following a review of his performance including a retest on similar sudoku puzzles, Varshavsky was disqualified and Chris Narrikkattu, who would have qualified in the same round, was made the third place winner. The 2010 World Sudoku Championship was held in Philadelphia,
21974181
Indian Sudoku Championship


championships held so far, 7 have been won by Rohan Rao, 3 by Ritesh Gupta, 2 by Rishi Puri and 1 by Prasanna Seshadri. The latest ISC was held on 21 July, 2019 and was won by 7-time champion Rohan Rao. The national teams have been representing India at the World Sudoku Championship since 2007. The qualifications for ISC 2019 was held as a series of 6 online rounds in collaboration with Sudoku Mahabharat on LMI, followed by an offline finals. The Indian Sudoku Championship has been held online and offline
7225338
Fibonacci cube


the class of planar bipartite graphs that have Fibonacci cubes as their resonance graphs. Generalized Fibonacci cubes were presented by based on the k-th order Fibonacci numbers, which were later further extended to a larger class of networks called the Linear Recursive Networks by based on more general forms of linear recursions. modified the second order Fibonacci cubes based on different initial conditions. Another related graph is the Lucas cube, a graph with a Lucas number of vertices defined from the Fibonacci cube by forbidding a 1 bit in both the first and
15127199
United States hydrogen policy


programs. Each states energy office gets SEP funding and manages all SEP funded projects. For more information about the SEP, including project descriptions, visit the SEP website. Clean Ports USA is an incentive-based program designed to help reduce emissions by encouraging port authorities to redesign and replace older diesel engines with new technologies and cleaner fuels. The U.S. Environmental Protection Agency's National Clean Diesel Campaign offers funding to port authorities to help them overcome the obstacles that prevent the adoption of cleaner diesel technologies. Clean Construction USA promotes the reduction
8426000
World Qualification Series (2009)


18 - Aug 23" 30th Anniversary of the Lacanau Pro and good conditions this year. Surf, concerts, events scheduled. Check out the video for a summary of the event http://vimeo.com/6994555 "Aug 25 - Aug 30" "Sep 01 - Sep 06" "Sep 01 - Sep 06" "Sep 04 - Sep 06" "Sep 09 - Sep 12" "Sep 10 - Sep 13" "Sep 08 - Sep 13" "Sep 15 - Sep 20" "Sep 16 - Sep 22" "Sep
1986943
Sudoku


"quincunx" is known in Japan as "Gattai" 5 (five merged) Sudoku. In "The Times", "The Age", and "The Sydney Morning Herald", this form of puzzle is known as Samurai SuDoku. "The Baltimore Sun" and the "Toronto Star" publish a puzzle of this variant (titled High Five) in their Sunday edition. Often, no givens are placed in the overlapping regions. Sequential grids, as opposed to overlapping, are also published, with values in
17887175
List of 1982–83 NBA season transactions


1982 Oct 2, 1982 Oct 1, 1982 Sep 30, 1982 Sep 29, 1982 Sep 28, 1982 Sep 27, 1982 Sep 24, 1982 Sep 22, 1982 Sep 20, 1982 Sep 19, 1982 Sep 18, 1982 Sep 17, 1982 Sep 15, 1982 Sep 14, 1982 Sep 13, 1982 Sep 10, 1982 Sep 9, 1982 Sep 7, 1982 Sep 2, 1982 Sep 1, 1982 Aug 31, 1982 Aug 27, 1982 Aug 26, 1982 Aug 16, 1982 Aug 8,
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