Considering Sudoku 1

Using the rules and goals of a Sudoku puzzle, there are many thousands of possible arrangements of digits that would satisfy the conditions for a proper Sudoku solution.

Given a proper Sudoku solution, how many distinct (unique) arrangements of the digits in the grid could be presented by simply swapping the digits in individual cells?

For example, changing all the 9s to 1s and 1s to 9s would produce a different arrangement in the grid, but would still be a legitimate correct solution.


The answer is 362880.

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2 solutions

Darryl Dennis
Jan 11, 2016

There are 9 possible digits to select from and 9 none repeating locations to place the digits

9! = 362,880 possible different arrangements.

Ramesh Jayaraman
Jan 11, 2016

Problem is same as rearranging 9 items in all possible orders. Hence 9! = 362880 is the answer.

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