some OT: how to solve this kind of problem in our program?

[Chris Mellon]

On 12/26/06, Gabriel Genellina <gagsl-py at yahoo.com.ar> wrote:
> At Monday 25/12/2006 21:24, Paul McGuire wrote:
>
> >For example, for all the complexity in writing Sudoku solvers, there are
> >fewer than 3.3 million possible permutations of 9 rows of the digits 1-9,
> >and far fewer permutations that match the additional column and box
> >constraints.  Why not just compute the set of valid solutions, and compare
> >an input mask with these?
>
> Are you sure? There are 9!=362880 rows of digits 1-9; taking 9 of
> these at random gives about 10**50 possibilities. Of course just a
> few match the additional constraints. Maybe you can trivially reduce
> them (just looking for no dupes on the first column) but anyway its a
> laaaaarge number... (Or I'm wrong computing the possibilities...)
>

According to Wikipedia, there are 6,670,903,752,021,072,936,960
possible classical Sudoku layouts. Ref.
http://www.research.att.com/~njas/sequences/A107739