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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 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.
Some of the techniques from Sudoku and Killer Sudoku can be used here, but much of the process involves the listing of all the possible options and eliminating the options one by one as other information requires. In the example here: (sets of numbers such as "5,6" and "4,5" could appear in any order) "11+" in the leftmost column can only be "5,6"
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 ...
Box-Number: Each box must contain each number exactly once. While the first constraint might seem trivial, it is nevertheless needed to ensure there is only one number per cell. Naturally, placing a number into a cell prohibits placing any other number into the now occupied cell. Solving Sudoku is an exact cover problem.
The name stemmed from a Nipponised 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, or a quarter or half turn about the centre.
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Sudoku puzzles also constrain square blocks of cells to contain each number once, making a restricted type of Latin square called a gerechte design. [ 1 ] Chapters four and five concern the combinatorial enumeration of completed Sudoku puzzles, before and after factoring out the symmetries and equivalence classes of these puzzles using Burnside ...