by **ab** » Thu May 08, 2008 5:19 pm

So long as you don't rely on uniqueness tests (ER, BUG, etc.) then if you solve a sudoku using logical techniques, then yes it proves that it has a unique solution.

The thing about logical techniques is that they exclude other possibilities. For example if two cells in the same house have a naked pair in 3 and 5 then if one of those cells is 3 the other must be 5, so you can eliminate 3 and 5 from other cells in that house.

If you use strategies that rely on the uniqueness of the puzzle, such as ER, then you are assuming the puzzle has a unique solution. If you then go on to find a solution, you cannot be certain that it is unique, although if indeed the puzzle has a unique solution, uniqueness tests will guide you to it. HTH