Tool/Solver to resolve sudoku/wordoku grids (directly or step by step). The aim of the sudoku game is to fill the rows and columns of a 9x9 grid with each digit only once.

Sudoku Solver - dCode

Tag(s) : Number Games

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Sudoku is a puzzle game whose goal is to fill a grid with the numbers from 1 to 9 (there are variants with letters or symbols) so that they appear only once per row, column or block.

Make a copy/paste or type directly in cells. Letters (Wordoku/alphadoku) and digits are accepted.

__Example:__ Copy the Sudoku content in the first cell (top left) `97 1 5 5 9 2 18 4 8 7 26 92 3 6 2 9 19 4572`

to get:

9 | 7 | ␣ | 1 | ␣ | ␣ | ␣ | ␣ | 5 |

␣ | ␣ | 5 | ␣ | 9 | ␣ | 2 | ␣ | 1 |

8 | ␣ | ␣ | ␣ | 4 | ␣ | ␣ | ␣ | ␣ |

␣ | ␣ | ␣ | ␣ | 8 | ␣ | ␣ | ␣ | ␣ |

␣ | ␣ | ␣ | 7 | ␣ | ␣ | ␣ | ␣ | ␣ |

␣ | ␣ | ␣ | ␣ | 2 | 6 | ␣ | ␣ | 9 |

2 | ␣ | ␣ | 3 | ␣ | ␣ | ␣ | ␣ | 6 |

␣ | ␣ | ␣ | 2 | ␣ | ␣ | 9 | ␣ | ␣ |

␣ | ␣ | 1 | 9 | ␣ | 4 | 5 | 7 | 2 |

Software solves the 9x9 sudoku almost like a human and displays each step of its progress to understand. If a box or a number has only one possibility then it is validated and the solver displays each of the stages of its progress to understand.

Sometimes the reasoning arrives at a stage where *no quick logical deduction* allows to deduce the value of a box (several possible values). The solver then analyzes the boxes where there are the fewest possibilities and selects a value that it considers the most probable and continues, if an inconsistency occurs (that the sudoku has no more solution) then it returns to step selection and takes another value. To optimize the chances, the selection is not random, the choice is made on a number which, if it is positioned in the box, will allow the maximum deduction for the next sudoku steps. This method is the fastest for the solver, it may be that sometimes a *slower and complex deduction* could achieve the same result.

NB: If the program indicates that there is only one possible value, it means that no other value is acceptable in the box (the dCode solver is always right).

In a sudoku, the 9x9 grid presents 9 squares of 3x3 which are called *blocks* (or regions, or groups, or sectors or sub-grids).

dCode calculates all the solutions for the sudoku, not only the first one. To check a homemade sudoku, the solver can confirm that there is only one solution.

The first Sudoku versions are from 1979

A single row can consist of $ 9! $ (Factorial of 9) different ways, same for the columns, but the whole sudoku has a number of possibilities much less than $ 9!^9 $, because some permutations can lead to identical grids. The total number of grids would be $ 9! \times 72^2 \times 2^7 \times 27704267971 = 6670903752021072936960 $ combinations.

By keeping the sudoku NxN rules that require the N characters to be used on each row and column, then it is impossible to respect them if the sudoku is not square.

Some variants of the square sudoku, however, use non-square inner blocks (see sudoku 6x6, sudoku 7x7 or sudoku 8x8)

dCode retains ownership of the "Sudoku Solver" source code. Except explicit open source licence (indicated Creative Commons / free), the "Sudoku Solver" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Sudoku Solver" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Sudoku Solver" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!

Reminder : dCode is free to use.

The copy-paste of the page "Sudoku Solver" or any of its results, is allowed as long as you cite dCode!

Cite as source (bibliography):

*Sudoku Solver* on dCode.fr [online website], retrieved on 2022-10-05,

sudoku,grid,9x9,row,column,block

https://www.dcode.fr/sudoku-solver

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