Mirrored from Sudopedia, the Free Sudoku Reference Guide


When you scramble a Sudoku puzzle, you change it to a mathematically equivalent puzzle. This scrambled version requires the same solving techniques, although some Sudoku Programs may rate it differently because the solving steps are not executed in the same order, leading to a different solving path.

The following permutations can be used to scramble a standard Sudoku:

The total number of permutations for any Sudoku is 1218998108160.

Note that reflections and rotations can be expressed as a combination of the above operations.



Because Sudoku Variations often have additional constraints, they cannot be scrambled in the same way as a standard Sudoku. Here are some scrambling considerations for popular Sudoku variants.

Killer Sudoku

The cages form an irregular pattern, preventing us from most scramble operations. The following operations can still be used:

It is also possible to alter Killer puzzles by systematically exchanging digits (for example, swapping all 4s and 9s) and updating the cage totals; the result will be an entirely different puzzle, however, which may well have a different difficulty-level and may or may not have a unique solution. It is also possible to combine, split or redraw the cages in an existing puzzle in order to make it easier or harder; again, one must be careful to avoid creating a puzzle with multiple solutions. Both of these quasi-scrambling techniques are frequently used by Killer aficionados to create more difficult variants of already-solved puzzles.


The diagonals limit row and column permutations.


The irregular nonets prevent all row and column permutations. Only a few might be possible if the jigsaw pattern is symmetrical. Digit relabeling as usual. Swapping rows and columns and reflection is also possible.


The extra constraints leave room to swap rows 2 & 3, 7 & 8 and columns 2 & 3, 7 & 8. Other than that, total reflection and swapping rows and columns is possible, as well as relabeling the digits.

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See Also

This page was last modified 13:55, 21 July 2010.