## May 31, 2005

### Sudoko Problem SOLVED!

Well, the number of solutions problem has been solved. I can't claim any credit, of course, but plenty of kudos for this Felgenhauer guy.

The number of valid Sudoku solution grids for the standard 9×9 grid with 3×3 regions was calculated by Bertram Felgenhauer to be 6,670,903,752,021,072,936,960 This number is equivalent to 9! × 722 × 27 × 27,704,267,971, the last factor of which is prime.

Still awaiting confirmation, of course, but it seems pretty sound.

The mechanics of the solution isn't terribly technical, though. Basically, it's a brute force search by computer for unique solutions, which we then multiply by the appropiate number of symmetries. (From above, 27,704,267,971 are the unique solutions, and the rest we multiply by are symmetries.)

The code used is available here. It's in C++ and python, so you should be able to test it yourself. The solution was found based on discussions on an internet forum, so obviously these things are useful, after all!

The minimum givens problem is still open, though.

### 5 comments by 1 or more people

1. Surely a brute force search by computer would find all solutions INCLUDING symmetries? It seems strange that such an "irregular" prime would appear in the answer.

05 Jun 2005, 13:32

2. No, because if you take into account the symmetries, you can say that a number of squares or patterns or stuff can uniquely determine the rest of the grid. You just need to find out which ones these are, which would give you the weird prime.

OK, I'm not terribly certain on the details, myself. Snoop around the links I gave…

05 Jun 2005, 15:21

3. #### joão

não entendi nada
hauhauhauh

16 Jun 2005, 17:15

4. #### anbu

hai

20 Aug 2005, 13:20

5. #### arun

cool…

07 Oct 2005, 07:54

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