Multiple solutions?

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Multiple solutions?

Postby shurd12 » Wed Mar 08, 2006 2:40 am

I just started doing these (the first 10 in a book that I got) and several of them seem to have more than one solution. I read on sudoku.com that the puzzles are supposed to have only one solution. Is that correct? Am I doing something wrong?
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Postby shurd12 » Wed Mar 08, 2006 3:12 am

OK, after doing some reading on this forum, it seems that multiple solutions are possible. However, I would think that a beginner's book of puzzles would be simple and contain only puzzles with unique solutions. Maybe I should look for another source? Or, is this pretty common?
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Postby tso » Wed Mar 08, 2006 3:40 am

Sudokus, by definition, have one and only one solution. If the puzzle has multiple solutions without explicitly saying so*, the puzzle is flawed and/or a misprint. It's much more common now then it was two years ago before Sudoku became a worldwide fad.

See this post on the subject.


*Puzzles can be constructed that have multiple solutions, the solver's task being to find both. For example:

Code: Select all
 1 . . | . . . | 5 8 .
 8 . . | . . 1 | . . 6
 . 6 . | . 2 . | . . .
-------+-------+------
 . . . | 5 9 . | . . .
 . . . | . 7 . | . . .
 . 9 3 | . . 2 | . . .
-------+-------+------
 . 1 . | . . . | 8 . 4
 . . . | 9 . 7 | . 5 .
 6 . . | 2 . . | 7 1 .


This puzzle (from this thread) has exactly two solutions. Can you find them both?
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Postby shurd12 » Wed Mar 08, 2006 5:38 am

The book I have is "Sudoku ?" book #2 out of 4, published by Hinkler Books, Pty Ltd. Out of the first 10 puzzles, 3 have two solutions. This is a very elementry book so I guess they are just sloppy??

Thanks for the example. I'll work on it.
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Postby Moschopulus » Wed Mar 08, 2006 10:57 am

shurd12 wrote:The book I have is "Sudoku ?" book #2 out of 4, published by Hinkler Books, Pty Ltd. Out of the first 10 puzzles, 3 have two solutions. This is a very elementry book so I guess they are just sloppy??

Thanks for the example. I'll work on it.


Thanks for letting us know. Could you post one of the puzzles with multiple solutions?

I'm sure this book is supposed to have ordinary sudokus with one solution, so yes, they are being very sloppy.
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Postby shurd12 » Wed Mar 08, 2006 6:12 pm

Here's one (sorry for the crude representation. I'm not sure how you guys draw these on here):

. . . ! 7 . . ! . 4 6
8 1 . ! 4 . 2 ! . . 5
4 6 . ! 3 . . ! 1 . .
--------------------------------
. . . ! . . 5 ! 4 2 .
5 . 4 ! 8 . 1 ! . . .
6 7 . ! . 9 . ! 5 . 8
--------------------------------
2 4 . ! . 8 . ! 3 5 1
7 . 5 ! 1 . . ! 8 . .
. . . ! 5 4 . ! . . .

Solution 1: 359718246817462935462359187981675423524831679673294518246987351735126894198543762
Solution 2:
352718946819462735467359182981675423524831679673294518246987351735126894198543267
(I hope I didn't make a typo! lol)
Last edited by shurd12 on Wed Mar 08, 2006 2:26 pm, edited 1 time in total.
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Postby ab » Wed Mar 08, 2006 6:25 pm

Yep that has multiple solutions.

PS to see how the pictures are made in posts press the quote button on a post with a picture and you'll be able to play with the code:)

What the heck here's one for you to play with:
Code: Select all
 *-----------*
 |...|..9|8..|
 |...|.5.|.6.|
 |...|.7.|.2.|
 |---+---+---|
 |...|..5|1..|
 |.34|...|...|
 |2..|6..|45.|
 |---+---+---|
 |7..|4.8|..5|
 |.96|..3|..7|
 |...|...|93.|
 *-----------*


This is a valid sudoku puzzle
Last edited by ab on Wed Mar 08, 2006 2:30 pm, edited 1 time in total.
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Postby shurd12 » Wed Mar 08, 2006 6:28 pm

Thanks.
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Postby Chessmaster » Wed Mar 08, 2006 10:17 pm

iff a sudoku has one soultion it is valid. nowdays sudokus need to have symmetry in them as well.
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Postby ab » Thu Mar 09, 2006 4:29 pm

Chessmaster wrote:iff a sudoku has one soultion it is valid. nowdays sudokus need to have symmetry in them as well.


That's ok, the one I posted has symmetry along the minor diagonal.
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