Unique solutions

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Unique solutions

Postby Willo » Mon Nov 10, 2014 1:06 am

I am having an argument with a co-solver of sudokus. We have a puzzle with three solutions, two containing a deadly pattern. He argues that this puzzle has three solutions, is not unique and is therefore not a sudoku. I argue that the third solution is the unique solution and the two solutions with a deadly pattern are therefore not valid solutions …. but the puzzle does have a unique solution and is therefore a sudoku. Any opinions or answers?
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Re: Unique solutions

Postby JasonLion » Mon Nov 10, 2014 3:26 am

Puzzles with more than one solution are not generally considered valid puzzles. Of course opinions vary a little bit, but that is the majority view.
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Re: Unique solutions

Postby eleven » Mon Nov 10, 2014 10:26 am

If it has 3 solutions, each one is as good (or bad) as the others, it does not matter, if two can be eliminated, when you forbid a deadly pattern.
It is not allowed to use uniqeness methods for multisolution puzzles, because it can result in getting one (or some) of the possible solutions or leaving no solution at all.
I cannot see much sense in deviding multisolution puzzles in those, which have a unique solution after applying uniqueness methods and others.
There should also be puzzles, which then have different "unique" solutions depending on, which uniqueness pattern is used.
{Added:] Here is a simple example:
Code: Select all
+----------------+----------------+----------------+
| 1    7    9    | 25   235  23   | 4    6    8    |
| 5    8    2    | 6    4    7    | 3    1    9    |
| 4    3    6    | 1    8    9    | 5    2    7    |
+----------------+----------------+----------------+
| 6    9    3    | 7    1    5    | 8    4    2    |
| 7    4    1    | 8    23   23   | 9    5    6    |
| 8    2    5    | 4    9    6    | 7    3    1    |
+----------------+----------------+----------------+
| 3    5    7    | 9    6    1    | 2    8    4    |
| 9    1    8    | 25   25   4    | 6    7    3    |
| 2    6    4    | 3    7    8    | 1    9    5    |
+----------------+----------------+----------------+

You can use the 25 or the 23 UR to get different "unique" solutions.
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