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.
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Why don't they make jigsaw puzzles so that every piece connects with every other piece? What's the point of a puzzle that you have to make up a solution? – Kendall Frey Jun 02 '14 at 13:00
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You still have to decide a correct solution. A puzzle (in almost all cases) is something that you have to find the solution, not create your own. – Kendall Frey Jun 02 '14 at 13:08
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Actually it doesn't. Although most sudoku you find will usually have a unique solution it is not fully true. It is possible to find ones that does have more than one solution. All this is vague as Sudoku doesn't come with official rules as to what exactly constitutes a Sudoku. – minusSeven Jun 02 '14 at 13:08
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3In the case of Sudoku, it was originally intended to be a puzzle to be completely filled out using nothing but logic. If multiple solutions exist, this defeats the purpose, as you can't complete it with logic alone. – Kendall Frey Jun 02 '14 at 13:15
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@AlanRoss Is this an actual question, or do you just want to argue that puzzles with multiple solutions are valid puzzles too? – SQB Jun 05 '14 at 10:23
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@AlanRoss - if there is a point which can be reached, where there are two equally viable answers, and both are correct, then there is no logical way to distinguish between them. Thus the puzzle can't be solved by logic and must be solved by arbitrarily choosing one of the two paths. It is thus no longer a pure logic puzzle, but a logic-and-guess puzzle. – Bobson Jun 09 '14 at 18:49
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@KendallFrey - There are jigsaw puzzles where every piece is identical - See this example of a Smuzzle Puzzle. There's still only one right answer, though. – Bobson Jun 09 '14 at 18:53
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@AlanRoss - "Considered solving a sudoko" by who? You appear to be alone in that opinion here. However, this link defines a single-solution Sudoku as "well-formed", which implies that multiple-solution ones are still sudoku but not well-formed. The equivalent for chess problems would probably be having pawns in the first or last rows - it's still a solvable configuration, but it's not a well-formed one. – Bobson Jun 09 '14 at 21:00
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@Bobson I am alone in many of my opinions I dont follow the herd and that seems to be the reason I am banned here. I maintain when I write my books which again are unique (and contain many X-Wing ones which no one here seems to manage to make, since no answer is yet forthcoming to that question and I am banned from answering) that this is what the public wants and are not concerned if it is not the 'defined' sudoku. – Alan Ross Jun 10 '14 at 05:33
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@AlanRoss - Sometimes being alone means you're thinking outside the box. Sometimes it just means you're wrong. It depends on whether the subject at hand is one that requires consensus or not. If I think sudokus are supposed to use the numbers 0-8, then I'm just wrong, because everyone else accepts them as using 1-9. – Bobson Jun 10 '14 at 13:18
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@Bobson Thanks I always also think out of the box but that is after I have been 'in' the box. This site 'follows' the herd and has never been out of it and bans me and is 'dead' by all accounts. I can only be proved wrong if my many books don't sell or that large publishers dont use me to make their books. As the latest post shows that they cant make x-wings although my books contain many and I offer them free. I have tried in my few questions to explain how sudoku works from my programmers viewpoint.Believe when I say my programs didnt take me long to make and the books followed in 'minutes'. – Alan Ross Jun 10 '14 at 13:44
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Take this question for example. The same people who closed it because they were 'unclear' what I was asking 'answered' it! On this site thats no contradiction! This has applied to all my questions. They answer and then say they dont know what I am asking and then ban me. As you understand my question so do they, make no mistake. It is just they are trying to 'kill' this site and succeeding. – Alan Ross Jun 10 '14 at 13:52
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There is no such thing as a Sudoku with more than one solution. The objective of a Sudoku puzzle is to reason out what the numbers must be based on the constraints imposed by the given numbers. If the given numbers are insufficient to compel the remaining squares, then the problem has no solution. – David Schwartz Mar 15 '17 at 05:09
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@Bobson: the link is broken. Here's another one: http://www.shmuzzles.com/ – Nav Jan 15 '21 at 11:51
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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.
Ross Millikan
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3I understand what you are saying. I think most Sudoku solvers would be disappointed to find there were multiple solutions. It is quite possible to remove four numbers and have two solutions. I believe most Sudoku setters run the final product through a solver to make sure there is a unique solution. They certainly do not have a fixed number of clues. You can do what you want-I was saying what I believe is the expectation of most of the puzzling community. – Ross Millikan Jun 02 '14 at 14:01
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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.
Donald.McLean
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From that article: "Most Sudoku players consider sudokus with more than one solution invalid!". I would want evidence to quantify "most". +1 though for stating the link between "default convention" and "happy customers". – ClickRick Jun 22 '14 at 08:32
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Well, as evidence I present all of the sites that mention uniqueness techniques (such as unique rectangles). ALL of these techniques rely on puzzles having unique solutions. – Donald.McLean Jun 22 '14 at 16:29
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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).
mgkrebbs
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A Sudoku with 81 empty squares can also be solved logically; you just fill in digits that don't conflict. If a digit to be added next logically conflicts with all possible remaining permutations, then it is not logical to add it; use a different digit. This is the same sort of logic, just carried back to 81 empty spaces instead of only 4 empty spaces. – mgkrebbs Jun 03 '14 at 00:00
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1I'm sorry, @AlanRoss, but your argument is completely meaningless. A "solution" is, by most people's accepted definition, unique. You don't have to accept their definition, but trying to tell them they are wrong just because you disagree accomplishes nothing positive. – Donald.McLean Jun 03 '14 at 00:11