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Sudoku solving algorithms. A typical Sudoku puzzle. 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.
The general problem of solving Sudoku puzzles on n 2 ×n 2 grids of n×n blocks is known to be NP-complete. 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 ...
Mathematical context. The general problem of solving Sudoku puzzles on n2 × n2 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 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]
Backtracking is an important tool for solving constraint satisfaction problems, 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.
The World Sudoku Championship (WSC) is an annual international puzzle competition organised by a member of the World Puzzle Federation. The first event was held in Lucca in 2006. National teams are determined by local affiliates of the World Puzzle Federation. The competition typically consists of 100 or more puzzles solved by all competitors ...
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.
One Sudoku contains therewith about the same information as 72 coin tosses or a sequence of 72 bits. A sequence of 81 random symbols has 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 ...
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