How many solutions can a sudoku have?

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How many solutions can a sudoku have?

Postby algernon » Sat Jul 15, 2006 9:36 pm

One, if it is legal, many otherwise:D

Seriously: Is there a sudoku with exactly 2006 solutions?
Or must the number of solutions be even, of have
special factors?

I cannot imagine an answer myself, and my solver
does not do brute force yet.

Anyway, I assume the "even" hypothesis is surely wrong, as ruuds
benchmark list has a sudoku with 3673 solutions, which isn't even
divisible by three.

Just curious, any clues?
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Postby JPF » Sun Jul 16, 2006 5:07 pm

Have a look at this thread.
You will get some answers to your questions.

Here :
Red Ed wrote:By random searching I've found N-solution grids for N=1,2,...,125332, with no sign that the first gap (at 125333 - at the moment) is at all significant...

JPF
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Postby Chessmaster » Sun Jul 16, 2006 6:11 pm

well you could have one with very many soultions suppose you give only one number that is the only number that gives any limitations.
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Postby algernon » Sun Jul 16, 2006 9:56 pm

JPF wrote:Have a look at this thread.
You will get some answers to your questions.


Thanks, that was exactly the information I was looking for.
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