Product of the AI hype
Considering that Sudoku is fairly simple to solve by a computer.
Have a bitfield for every field. (9 bits)
1. Set all bits to 1
2. For the fields with clue n, set all bits to 0 except for the n-th
3. Reset the n-th bit of all fields related to clue n
4. If while doing 3 one field has only one bit set, see it as a clue and continue with 3
5. If there are no new clues, select one field with the lowest number of bits set.
6. Loop through all possible solutions for that field and recursively set it as a clue
7. If there are no fields with more than 1 set bit left, output solution
This simple 7 step sketch will give you all possible solutions to a given Sudoku. The Bitfield easily fits on the stack, making it possible to simply copy the whole field for the recursive step 6. (the step where you try out several possibilities) It may give you the same solution multiple times, but that's easy to fix with sort and uniq.
Of course doing it with neural networks is an interresting idea, but not really usefull if you want to have results.