(no subject)
I've done several hundred of these little things, but I don't recall ever coming across this particular solution technique before. Here's my puzzle, with the upper and lower rows of the right-hand column magnified.
> > > >
As you can see, I've filled in current potential values for all undetermined squares. Leaving aside the possibility that I might've made a mistake somewhere, or that there are further reductions that could be done, take a look at the squares in yellow. I propose that the lower right of these has to be a 5 (circled). Why? Because if it weren't, then in the final solution, the 1's and 2's in these squares could be freely swapped without affecting anything else in the puzzle or the correctness of the solution, contradicting the "unique solution" property of Sudoku.
In all the Sudokus I've done, I've never come across a case like this where I've appealed to the uniqueness-of-solution to perform a reduction. Has anyone else? Does anyone have any thoughts about the validity of this technique?
> > > >
As you can see, I've filled in current potential values for all undetermined squares. Leaving aside the possibility that I might've made a mistake somewhere, or that there are further reductions that could be done, take a look at the squares in yellow. I propose that the lower right of these has to be a 5 (circled). Why? Because if it weren't, then in the final solution, the 1's and 2's in these squares could be freely swapped without affecting anything else in the puzzle or the correctness of the solution, contradicting the "unique solution" property of Sudoku.
In all the Sudokus I've done, I've never come across a case like this where I've appealed to the uniqueness-of-solution to perform a reduction. Has anyone else? Does anyone have any thoughts about the validity of this technique?