Why must a sudoku have a unique solution. In my books I don't guarantee it. But I am sure there are not many which don't. I doubt if one in a thousand dont have. And even if they don't its only a matter of interchanging about four numbers. Why is there this obsession that it has to be only one unique solution. This of course applies to other puzzles too.
closed as unclear what you're asking by Kendall Frey, Doorknob, Aza, Ross Millikan, Joe Z. Jun 2 '14 at 21:51
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There is no law requiring that a published Sudoku have a unique solution. When I see a puzzle of any type, I expect from experience that the setter has promised a unique solution (or occasionally will say there are some number to be found). Some setters, Raymond Smullyan especially, create problems that challenge you to make use of the fact that there must be a unique solution. Cryptarithms are especially prone to multiple solutions.
Many of the advanced solving techniques rely on there being a unique solution. All of the Unique Rectangle techniques are predicated on this. To quote from that page:
Uniqueness Techniques are based on the fact that practically every Sudoku sudoku ever published has only one solution. More than that: Most Sudoku players consider sudokus with more than one solution invalid!
I would say that uniqueness is the default convention, in that unless you explicitly say otherwise, everyone will assume that any Sudoku puzzle has a unique solution, and failure to say that a given puzzle may not have a unique solution could result in unhappy customers.
You can solve Sudoku with different approaches. For instance, you can fill in all blank squares with random digits and see if the result meets the Sudoku 1-9 digit-set requirements; if not, try some other random digits. This is a trial-and-error approach. Most people, though, want to use deduction based on the digits previously established in puzzle squares.
If a Sudoku has multiple solutions, deduction will fail to solve the puzzle at some (late) point. The partial solution sequence will reach a point where no empty square can be deduced as having to be a specific digit. For people who do not use guessing (trial-and-error), this can be a frustrating barrier (probably making them curse the puzzle maker).