Each of the 81 cells is a vertex of the graph. Another approach considers the Sudoku puzzle as a graph coloring problem (Delahaye 2006). The first one refers to the result that to complete a partial Latin square is NP-complete (Colbourn 1984).
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How to grade the difficulty of a Sudoku puzzle? What is the minimal number of clues in the starting configuration and guarantee a unique solution? How easy is it to solve Sudoku puzzles by employing a set of rules or strategies?įrom what starting configurations is the puzzle uniquely solvable? What is the computational complexity of the Sudoku puzzle? But it soon attracted mathematicians who analysed questions such as The Sudoku puzzle is a logic game that needs just strategic reasoning to get it solved. Soon after, newspapers and magazines all over the world started to publish the Sudoku puzzle. He started to write computer programs for generating Sudoku puzzles, and he tried to get the puzzles published in English newspapers, which finally happened in 2004 in The Times, and in 2005 in the Daily Telegraph. Then, at the end of the 1990’s, the puzzle was discovered by Wayne Gould.
The Sudoku became popular in Japan and puzzles were published in newspaper, magazines, and puzzle booklets. Garns’ puzzle remains unknown until it was introduced in Japan in 1984 under the name Sudoku. A Sudoku is clearly a special kind of Latin square, namely by the extra condition of the blocks being permutations as well. When the symbols are the numbers 1 to n, all rows and columns of a Latin square are permutations of these numbers. The name Latin square was tossed by the famous 18-th century Swiss mathematician Leonard Euler who analysed some general properties and theorems. A Latin square is a n × n grid filled with n symbols such that the same symbol never appears twice in the same row or column. Probably, Garns was inspired by the concept of Latin squares. It was published under the name of Number Place. The Sudoku puzzle became immense popular during the last fifteen years, though the first version appeared in 1979 as a puzzle in Dell Pencil Puzzles and Word Games, created by a retired architect named Howard Garns. Here is an example of a starting configuration (the Sudoku puzzle), and the (unique) solution of it (the solved Sudoku).įigure 1.Sudoku puzzle and solution.
The puzzle is well-formed if there is a unique solution from the starting configuration to a complete Sudoku grid. The starting configuration of the grid has some digits already filled in, and then the puzzle is to complete the grid. The objective is to fill the grid with the numbers 1 to 9 by placing a single number in each cell, in such a way that no digit appears twice in the same row, column, or block. It is a logic puzzle or game consisting of a square grid of 81 cells (nine rows by nine columns) that is divided in nine 3 × 3 subgrids called blocks. Everyone is familiar with the Sudoku puzzle.
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