Multiple Solutions

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

Multiple Solutions

Postby JC » Thu Feb 02, 2006 12:55 pm

Which one do you think is harder, a multiple solutions or a puzzle with one solution in an evil level puzzle...???
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Postby Wolfgang » Thu Feb 02, 2006 1:24 pm

It depends on the technique you use. If you try numbers for good luck, a multiple solutions puzzle will give you better chances, if you use logical steps only, it will be unsolvable (and in this sense harder) for you.
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Postby TKiel » Thu Feb 02, 2006 3:04 pm

It seems to depend on why one plays Sudoku. Is it the end that's important? Or is it the means to the end?

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Postby tso » Thu Feb 02, 2006 8:00 pm

The question has no meaning without defining your terms. The rating of "evil" has no agreed upon meaning -- we've all come across puzzles that were nearly trivial that were rated "evil" as well has very tough once rated "easy".

Things get only worse when you say "multiple solution" puzzle. A puzzle can be presented as having exactly 2 (or N) solutions -- the puzzle could be either trivial or as hard as the hardest puzzle ever seen. Mutiple solution puzzle of this type do have added difficulties: You can't use Unique Rectangles or BUG, you might have to make multiple copies of the grid, etc. You're basically solving two (or N) separate puzzles.

Then there are puzzles that *look* like multiple solution puzzles but aren't. "What is the number in the central cell?" might have one answer -- the answer the puzzle construtor is looking for -- though the Sudoku might have any number of solutions.

Then there are puzzles that are simply broken, posed as having a unique solution, but actually having dozens or hundreds. A puzzle like this is no better than one that has *no* solution. It is neither hard nor easy. It is impossible.
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Postby Chessmaster » Fri Feb 03, 2006 10:25 pm

well if it has more than one soultion it is invalid
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