## Unique solutions fo Sudoku

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

### Unique solutions fo Sudoku

I, i am new to the forum, and also a new player when it comes to Sudoku

I would like to know, if a puzzle is solvable using only logical strategies (pairs, hidden singles etc.), does this prove that the puzzle has a unique solution? And Why?

Thank You
037936

Posts: 2
Joined: 08 May 2008

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
ab

Posts: 451
Joined: 06 September 2005

thanks for the help ab

not familiar with uniqueness tests

What you are trying to say is that, the proof is generally based on the fact that the solving techniques exclude possiblities from each cell

Thank You
037936

Posts: 2
Joined: 08 May 2008

ab wrote:.... If you use strategies that rely on the uniqueness of the puzzle .... 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 ....

Worse yet, if you rely on uniqueness, you might eventually reach the conclusion that there is NO solution, even though there might be two or more.

Bill Smythe
Smythe Dakota

Posts: 546
Joined: 11 February 2006