## a multisolutional sudoku solved by uniqueness

Advanced methods and approaches for solving Sudoku puzzles

### Re: Uniqueness shortens the way to validity

Mauricio wrote:
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`+-------+-------+-------+| 1 . . | . 6 . | . . 5 || . 9 . | . . 2 | . 7 . || . . . | 8 . . | 3 . . |+-------+-------+-------+| . . 2 | 1 . . | . 4 . || 4 . . | . . . | . . 8 || . 8 . | . . 9 | 6 . . |+-------+-------+-------+| . . 7 | . . 4 | . . . || . 3 . | 6 . . | . 1 . || 5 . . | . 2 . | . . 9 |+-------+-------+-------+`

There exists a uniqueness technique that guarantees r3c3=r5c5=r7c7=5, and r6c4=r4c6={3,7}, the rest is singles.

Where does this puzzle come from? Are you sure it has a unique solution?
denis_berthier
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wintder wrote:As far as I can see uniqueness can only lead to possible correct answers.
Show me a case where uniqueness eliminates a solution that MAY be valid, and does not present an alternate solution, no less correct.
T&E will present many not possible "solutions".

T&E (if applied crorrectly) cannot produce wrong solutions.
Uniqueness, used on a non unique puzzle, can eliminate correct solutions. Can it produce wrong solutions? I don't think so, at least for rules that only eliminate candidates. But in theory, it could incorrectly lead to the conclusion that there is no solution; I've no example of this case (I've never looked for one).
denis_berthier
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### Re: Uniqueness shortens the way to validity

denis_berthier wrote:Where does this puzzle come from? Are you sure it has a unique solution?
I created this puzzle a few months ago, I am sure it has a unique solution. If you do not then try to find 2 solutions.
Mauricio

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denis_berthier wrote:Uniqueness, used on a non unique puzzle, can eliminate correct solutions. Can it produce wrong solutions? I don't think so, at least for rules that only eliminate candidates.

999_Springs wrote:
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`. .  .   |. .  . |. . . . .  .   |. .  . |. . . . .  .   |. .  . |. . . ---------+-------+----- . .  .   |. .  . |. . . . 12 12  |. .  . |. . . . .  .   |. .  . |. . . ---------+-------+----- . .  .   |. .  . |. . . . 12 1234|. 13 . |. . . . .  13  |. 13 . |. . . `

Suppose that a puzzle with 3 solutions contained the above pattern. Uniqueness would say that r8c3=4, but this could eliminate all 3 solutions and produce a "wrong" solution if the 4 could have been eliminated with some other sort of technique.

That is one of the reasons why I don't use uniqueness techniques unless I am solving against the clock (which never occurs in not-all-singles puzzles).
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999_Springs

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999_Springs wrote:That is one of the reasons why I don't use uniqueness techniques unless I am solving against the clock (which never occurs in not-all-singles puzzles).

I hope that any solvers relatively new to Sudoku are not being misled by some of the statements in this thread that infer that even now uniqueness is somehow something that may or may not be present in a given puzzle. Virtually every puzzle in Sudoku books or newspapers published these days has one solution guaranteed, not to mention the more advanced puzzles such as the Extremes on the UK forum. In addition, all the popular free and/or commercial Sudoku solvers, PC-based or PDA-based, ensure a unique solution for their created puzzles and when you enter your own puzzle, they warn you if it is not unique. With that in mind, I can't for the life of me understand why anyone would remove uniqueness-based methods from their solving tool bag.

There is another reason why an advanced player would not want to even fool with a non-unique puzzle (other than their own personal satisfaction) and that is because no one else would really take their solution to the puzzle very seriously since there would not be any common denominator to measure it against. For instance, say I come up with one of 4 possible solutions to the puzzle- maybe that solution was more easily arrived at than the other 3 and so on. One puzzle solution means that everyone is working towards the same end and that is probably the most important reason why puzzle uniqueness became standard some time ago.
sirdave
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999_Springs wrote:
Code: Select all
`. .  .   |. .  . |. . . . .  .   |. .  . |. . . . .  .   |. .  . |. . . ---------+-------+----- . .  .   |. .  . |. . . . 12 12  |. .  . |. . . . .  .   |. .  . |. . . ---------+-------+----- . .  .   |. .  . |. . . . 12 1234|. 13 . |. . . . .  13  |. 13 . |. . . `

Suppose that a puzzle with 3 solutions contained the above pattern. Uniqueness would say that r8c3=4, but this could eliminate all 3 solutions and produce a "wrong" solution if the 4 could have been eliminated with some other sort of technique.
[/quote]
But this is a case where the uniqueness rule asserts a value. I spoke of a rule that only eliminates candidates. In such a case, I don't think you can produce a wrong solution (but, of course, you can produce a no-solution even if a solution exists).
denis_berthier
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The uniqueness rules eliminate (12) and (13) respectively, leaving a naked 4. The eliminations precede the placement.
Ruud

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999_Springs wrote:Uniqueness would say that r8c3=4, but this could eliminate all 3 solutions and produce a "wrong" solution if the 4 could have been eliminated with some other sort of technique.

That is one of the reasons why I don't use uniqueness techniques unless I am solving against the clock (which never occurs in not-all-singles puzzles).
Again, you can't use uniqueness techniques on a multisolution puzzle, neither can you use them if you need or want to prove that a puzzle has a unique solution (for personal satisfaction or whatever other reason).

By the way, what is a "wrong" solution in a multisolutional puzzle?
Mauricio

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denis_berthier wrote:But this is a case where the uniqueness rule asserts a value.

OK, let r8c3={123456789}.

Mauricio wrote:what is a "wrong" solution in a multisolutional puzzle?

oops, I meant to put the word "solution" in quote marks. I interpret it as a "solved" number which destroys ALL of the solutions.
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999_Springs

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