I have a very strange idea.
When I solve a puzzle using a Unique Rectangle, and that puzzle happens to have multiple solutions because of that unique rectangle, it is unavoidable (pun intended) that a conflict arises in the subsequent solving path. The remainder of the puzzle has to find a place for a digit that would otherwise be part of the UR. In exchange, a digit has been used in the UR that will surely leave some holes outside the UR.
What I'm aiming at is that being able to find a solution using a UR proves that there is a unique solution, otherwise it would be impossible to completely solve the puzzle.
I have 3 questions
1. Is it possible to irrefutably prove that using a 'wrong' UR will always cause an error?
2. If so, wouldn't this effectively 'legalize' UR techniques?
3. Can we extrapolate this to other uniqueness-based techniques?
Ruud