Invalid Sudoku Puzzles

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Invalid Sudoku Puzzles

Postby Solgor » Mon Dec 10, 2012 5:35 am

I have read that if you have mirror images in a puzzle it is invalid as there can be more than one solution. However I run into a lot of these "invalid" puzzles and it doesn't seem right. For example I just ran into a puzzle that contained the following mirror image:

R2C2 Given Number 6

R5C2 Given Number 4

R2R3 Given Number 4

R5C3 Given Number 6

Is this an invalid Puzzle because it can have more than one solution? Sometimes I run into two or three of these mirror images in one puzzle. What's happening?
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Postby Pat » Mon Dec 10, 2012 8:54 am

Solgor wrote:I just ran into a puzzle that contained the following mirror image:

R2C2 Given 6
R5C2 Given 4

R2c3 Given 4
R5C3 Given 6

Is this an invalid Puzzle because it can have more than one solution?


it is customary to require that the Givens stay where they are
i.e. you cannot switch them around

therefore,
you cannot use this to claim multiple answers
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Re: Invalid Sudoku Puzzles

Postby Solgor » Mon Dec 10, 2012 10:01 pm

But suppose that there were only three givens and the fourth cell contained a few candidates. In order to defend against making an invalid puzzle I have been eliminating the candidate that would make it a mirror image. That is often very helpful in solving the puzzle. However, that technique seems to work all the time when there are more than two candidates in the cell but not 100% of the time when there are only two candidates. I have no idea why this is so.

It is pretty difficult to describe this situation in words but I hope it is understandable.
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Re: Invalid Sudoku Puzzles

Postby David P Bird » Tue Dec 11, 2012 1:07 am

Solgor, the chances of a randomly chosen candidate in a cell being false fall from 80% with 5 candidates down to 50% for 2 candidates. You would need to run a large number of trials to test if your theory gave better results. However even if that was so, a single case that fails will demonstrate that your reasoning isn't watertight.
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Re: Invalid Sudoku Puzzles

Postby Solgor » Tue Dec 11, 2012 1:58 am

You are absolutely right. I thought I had hit on something really helpful but I won't rely on this technique any more. Thanks.
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