Function Repository Resource:

SudokuSolve

Solve Sudoku puzzles

Contributed by: Jon McLoone

ResourceFunction["SudokuSolve"][data]

treats a 9×9 matrix of data as a partially solved Sudoku puzzle and replaces all elements that are not integers from 1 to 9 with the correct elements to fully solve the puzzle.

Details and Options

Sudoku is a popular number puzzle. Its rules are easily stated:

A 9×9 grid is presented, containing some predefined numbers.

The player’s task is to fill in the grid so that every row, every column and the nine 3×3 subgrids contain the digits 1 through 9.

Examples

Basic Examples (1)

Solve a puzzle:

In[1]:=

ResourceFunction["SudokuSolve"][ {
{ , , 8, 1, 7, 6, , 2, },
{ , 4, , , , 9, 7, , },
{ , , , , , , , , },
{ , 7, 1, 8, , , , , },
{ , , , , , , 6, 7, 9},
{ , , , 5, 9, 7, , 8, 1},
{ , , , , 2, , , , },
{ , 5, 9, , , , , 1, },
{ , 1, 4, 6, 5, , 3, , }
} ]

Out[1]=

Scope (1)

If a puzzle cannot be solved, a "Contradiction" Failure will be returned:

In[2]:=

{
{4, , 3, 7, 6, 2, 8, , },
{, 6, 8, 4, 3, 1, , 7, },
{, , , , 8, 5, , 3, 6},
{3, 2, 6, 8, , 9, , 4, },
{, , 7, , 2, , 9, 6, },
{, 5, , 1, , 6, 3, 2, },
{, 4, , 6, 1, , , , },
{, 3, , 2, , 7, 6, 9, },
{6, , , , 9, , , , }
} // ResourceFunction["SudokuSolve"]

Out[2]=

Options (1)

The option "ShowSteps" shows when it was necessary to guess values rather than use pure logic:

In[3]:=

ResourceFunction["SudokuSolve"][{
{5, 3, 8, 1, 7, 6, , 2, },
{ , , , , , 9, 7, , },
{ , , , , , , , , },
{ , 7, 1, 8, , , , , },
{ , , , , , , 6, 7, 9},
{ , , , 5, 9, 7, , 8, 1},
{ , , , , 2, , , , },
{ , 5, 9, , , , , 1, },
{ , 1, 4, 6, 5, , 3, , }
} , "ShowSteps" -> True]

Out[3]=

Publisher

Jon McLoone

Requirements

Wolfram Language 11.3 (March 2018) or above

Version History

1.0.0 – 10 December 2018

License Information

This work is licensed under a Creative Commons Attribution 4.0 International License