Sudoku solver: reduction + brute force

[ago]

Anton,

Do you think it is possible to reduce the set of all possible solutions
to a small enough set? I personally doubt it, but IF that was the case
an efficient solver could be easily created.

In reducing the set of all solutions for instance you could always swap
the numbers (3rd axis) so that the first submatrix reads
[[1,2,3],[4,5,6],[7,8,9]]. By this we reduced the set of solutions by
362880. You can then always move blocks, columns and rows to fix the
following elements (1,4)=4, (4,1)=2, (9,9)=9. Further reductions are
still possible, but I do not know how far can this go and if the end
result is a small enough set. 

Just my 2c.