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A Sudoku starts with some cells containing numbers (clues), and the goal is to solve the remaining cells. Proper Sudokus have one solution. [1] Players and investigators 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.
A Sudoku whose regions are not (necessarily) square or rectangular is known as a Jigsaw Sudoku. In particular, an N × N square where N is prime can only be tiled with irregular N -ominoes . For small values of N the number of ways to tile the square (excluding symmetries) has been computed (sequence A172477 in the OEIS ). [ 10 ]
Tanner graph of a Sudoku. denotes the entries of the Sudoku in row-scan order. denotes the constraint functions: =, …, associated with rows, =, …, associated with columns and =, …, associated with the sub-grids of the Sudoku.. There are several possible decoding methods for sudoku codes. Some algorithms are very specific developments for Sudoku codes. Several methods are described in ...
Download as PDF; Printable version; ... Articles relating to Sudoku, the logic-based placement puzzle ... Sudoku graph; Sudoku solving algorithms; T.
Many Sudoku solving algorithms, such as brute force-backtracking and dancing links can solve most 9×9 puzzles efficiently, but combinatorial explosion occurs as n increases, creating practical limits to the properties of Sudokus that can be constructed, analyzed, and solved as n increases.
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.
Backtracking is an important tool for solving constraint satisfaction problems, [2] such as crosswords, verbal arithmetic, Sudoku, and many other puzzles. It is often the most convenient technique for parsing , [ 3 ] for the knapsack problem and other combinatorial optimization problems.
After an introductory chapter on Sudoku and its deductive puzzle-solving techniques [1] (also touching on Euler tours and Hamiltonian cycles), [5] the book has eight more chapters and an epilogue. Chapters two and three discuss Latin squares , the thirty-six officers problem , Leonhard Euler 's incorrect conjecture on Graeco-Latin squares , and ...