Sudoku solver

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Question

How to describe a sudoku and the sudoku rules in Opasnet so that it can be solved automatically?

Answer

You need the following tables.

Hypotheses

Cell	Result	Description
Row: All; Column: All	1,2,3,4,5,6,7,8,9	For all row and column locations it applies that the plausible hypotheses are a single integer between 1 and 9 (unless more information is available).

Area descriptions

Row	Column	Area
1	1	A
1	2	A
1	3	A
1	4	B
…
2	1	A
…
4	1	D
…
9	9	I

Rules of exclusion when comparing two cells.

Property1	Condition1	Property2	Condition2	Rule	Description
Row	Same	Column	Different	Same integer not allowed	Two cells with the same row and different column are not allowed to have the same integer.
Row	Different	Column	Same	Same integer not allowed	Two cells with the different row and same column are not allowed to have the same integer.
Area	Same	Column	Different	Same integer not allowed	Two cells with the same area and different column are not allowed to have the same integer.
Area	Same	Row	Different	Same integer not allowed	Two cells with the same area and different row are not allowed to have the same integer.

The sudoku data (this example is "the most difficult sudoku in the world")

Row	Column
	1	2	3	4	5	6	7	8	9
1	8
2			3	6
3		7			9		2
4		5				7
5					4	5	7
6				1				3
7			1					6	8
8			8	5				1
9		9					4

Procedure

1. Go through all pairs of cells (using two for loops).
   1. Test for the rules with this pair.
      1. If the other cell is known for sure, remove all inconsistent hypotheses from the other cell.
2. Go back to the beginning.

See also

• file:Sudoku solver.ANA (a draft solver using Analytica)

Related files

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