I’ve recently gotten into Sudoku, and I’ve been wondering about some things.
Conversely…
[QUOTE=HeyHomie]
I’ve recently gotten into Sudoku, and I’ve been wondering about some things.
Yes, there is. The theoretical minumum for a 9x9 sudoku square is 17 clues. This site has a brief discussion on it and links to such sudokus.
[QUOTE=HeyHomie]
2) Is there a theoretical maximum number of spaces that can be filled in on a Sudoku puzzle, but yet the puzzle remains unsolvable? Again, if so, can you point to one such puzzle (or design one yourself)?
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According to this site (warning: pdf), the maximum number of clues for an unsolvable 9x9 sudoku is 33; there is not an example though.
That’s quite a confusing definition of solvable you’re using there. I’d say a sudoko puzzle is solvable if a solution exists. That is, if all the open spaces can be filled in in such a way that there are no contradictions.
So the answer to question 1 would be zero (the solution of any sudoko would be a solution) and 81 would be the other answer.
What you’re questioning here is the uniqueness of solutions.
Not that this answer is of any help…
[QUOTE=4.66]
That’s quite a confusing definition of solvable you’re using there. I’d say a sudoko puzzle is solvable if a solution exists. That is, if all the open spaces can be filled in in such a way that there are no contradictions.
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The rule of Sudoku is that there is always a unique solution. So by definition, a Sudoku puzzle which doesn’t have a unique solution is unsolvable.
[QUOTE=MissMossie]
Yes, there is. The theoretical minumum for a 9x9 sudoku square is 17 clues. This site has a brief discussion on it and links to such sudokus.
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As your link mentions, that result is more empirical than theoretical. As for the maximum, I think I’ve seen a grid with only four empty spaces and two solutions, but I can’t find a reference right now.
Four empty spaces and two possible solutions is relatively common – I have found a few of these in newspapers and such – you can use logic and deduction to complete everything except the final four squares. I will see if I can find one.
3 456 789
654 987 321
789 123 456
5 678 934
436 295 178
897 314 562
541 762 893
972 831 645
368 549 217
The above puzzle does not have a unique solution. You can fill the four blanks with 12/21 or 21/12.
As for the answer to the OP… well, I don’t know. But I think it is sensible to distinguish between legal solutions and unique solutions. A well designed puzzle will have a unique solution, but I think the OP was talking about legal solutions.
[QUOTE=Sage Rat]
The rule of Sudoku is that there is always a unique solution. So by definition, a Sudoku puzzle which doesn’t have a unique solution is unsolvable.
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Another rule of sudoku is that the clues don’t contradict each other. Combining our two rules, a sudoku puzzle is, by definition, solvable. But using the word (un)solvable in this way doesn’t make much sense in the context of the OP.
[QUOTE=j_sum1]
A well designed puzzle will have a unique solution, but I think the OP was talking about legal solutions.
[/QUOTE]
Her second question makes clear that she was talking about unique solutions. If she were talking about the other way in which the puzzles can be unsolvable (inconsistent clues: no legal solutions), the question doesn’t make any sense. Once you have such a sudoko you can just keep on adding clues and it remains inconsistent, so it would be a bit strange to ask for a maximum. I think she meant to ask:
What’s the maximum number of clues in a consistent sudoku, such that by adding a clue the sudoku would become either inconsistent or uniquely solvable?
Your example, combined with the fact that a consistent sudoku with three open spaces has a unique solution, makes clear that the answer is 77.
[QUOTE=4.66]
Her second question makes clear that she was talking about unique solutions.
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I’m a he.
The first rule of Sudoku is: DON’T TALK ABOUT SUDOKU!
Do you mean solvable as in, once x number of squares have been filled in you can use logic to solve the puzzle without resorting to guesses? If that’s what you meant I guess there would be a minimum, and going by j_sum1’s post it would be 3 blank squares.
[QUOTE=cooky173]
Do you mean solvable as in, once x number of squares have been filled in you can use logic to solve the puzzle without resorting to guesses? If that’s what you meant I guess there would be a minimum, and going by j_sum1’s post it would be 3 blank squares.
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Yes, that’s exactly what I meant. And that it would have a unique solution.