## How many solutions can a sudoku have?

Everything about Sudoku that doesn't fit in one of the other sections

### How many solutions can a sudoku have?

One, if it is legal, many otherwise

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?
algernon

Posts: 25
Joined: 26 June 2006

Have a look at this thread.

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
JPF
2017 Supporter

Posts: 4018
Joined: 06 December 2005
Location: Paris, France

well you could have one with very many soultions suppose you give only one number that is the only number that gives any limitations.
Chessmaster

Posts: 191
Joined: 21 December 2005

JPF wrote:Have a look at this thread.