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Although it has been established that approximately 5.96 x 10 26 final grids exist, a brute force algorithm can be a practical method to solve Sudoku puzzles. A brute force algorithm visits the empty cells in some order, filling in digits sequentially, or backtracking when the number is found to be not valid.
The general problem of solving Sudoku puzzles on n 2 ×n 2 grids of n×n blocks is known to be NP-complete. [8] A puzzle can be expressed as a graph coloring problem. [9] The aim is to construct a 9-coloring of a particular graph, given a partial 9-coloring. The Sudoku graph has 81 vertices, one vertex for each cell.
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). [25] The general problem of solving Sudoku puzzles on n 2 ×n 2 grids of n×n blocks is known to be NP-complete. [26]
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. [1] Three horizontally adjacent blocks are a band, and three vertically adjacent blocks are a stack. [2] The initially defined values are clues or givens. An ordinary ...
Diagonal regions instead of square sub-grids can be used for performance investigations. [2] The diagonal 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 . [2] Sudoku codes are non-linear.
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) can be interpreted as a solution to the puzzle.
Killer sudoku (also killer su doku, sumdoku, sum doku, sumoku, addoku, or samunanpure サムナンプレ sum-num(ber) pla(ce)) 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 ...
Free Software implementation of an Exact Cover solver in C - uses Algorithm X and Dancing Links. Includes examples for sudoku and logic grid puzzles. DlxLib NuGet package - a C# class library that implements DLX; dlxlib npm package - a JavaScript library that implements DLX; dancing-links-c++ - a C++ library that implements DLX