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14th May,2007.

 
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pipesmoker



Joined: 10 Sep 2005
Posts: 4
Location: Burton upon Trent

PostPosted: Mon May 14, 2007 8:38 am    Post subject: 14th May,2007. Reply with quote

Doing today's puzzle I have the following:

415xx7xx9
8x9354x61
36xx9x4x5
x98476x1x
x46x3x8xx
731825694
1x3x4xx2x
68x5129xx
9xx7x31xx

I was absolutely stuck. At this stage the hint given was a "2" in R4,C9 and I cannot work out why. Would some kind person please tell me?

Thanks in anticipation.

Graham
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David



Joined: 02 Jun 2006
Posts: 58
Location: Bedford, UK

PostPosted: Mon May 14, 2007 11:55 am    Post subject: Reply with quote

Pipesmoker

There is an xy wing (r4c7, r7c7, r8c9) which eliminates the 3 in cell r4c9 leaving the '2' that you were given in the hint.
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David



Joined: 02 Jun 2006
Posts: 58
Location: Bedford, UK

PostPosted: Mon May 14, 2007 11:58 am    Post subject: Reply with quote

Just for interest, there is also a 'BUG' removal at r8c8 which solves the puzzle.
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pipesmoker



Joined: 10 Sep 2005
Posts: 4
Location: Burton upon Trent

PostPosted: Mon May 14, 2007 2:25 pm    Post subject: Reply with quote

David

Thanks for your reply but I still can't see it. I must have another read up on xy wings.

The reason for my post was that my wife did it, but she sussed the "3" out in R8 C8 which you say was a bug?
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David



Joined: 02 Jun 2006
Posts: 58
Location: Bedford, UK

PostPosted: Mon May 14, 2007 3:13 pm    Post subject: Reply with quote

Pipesmoker

It probably is best to re-read the background on XY wings, but for clarity the pivot is the 57 in r7c7 and the two pincers are 35 in r4c7 and 37 in r8c9.

BUG removal is a very simple concept; easier than xy wings, and although it is not necessary for the current Daily Sudoku puzzles by Sam, other puzzles such as Brainbashers do use it. You may be interested to research it once you have mastered those pesky xy wings !
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David



Joined: 02 Jun 2006
Posts: 58
Location: Bedford, UK

PostPosted: Mon May 14, 2007 3:15 pm    Post subject: Reply with quote

Oh, and by the way, it was a 7 in r8c8, not a 3.
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pipesmoker



Joined: 10 Sep 2005
Posts: 4
Location: Burton upon Trent

PostPosted: Mon May 21, 2007 9:41 am    Post subject: Reply with quote

Thanks again David
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Mon May 21, 2007 11:15 pm    Post subject: Reply with quote

Code:
+-------------+-------------+-------------+
| 4   1   5   | 26  68  7   | 23  38  9   |
| 8   27  9   | 3   5   4   | 27  6   1   |
| 3   6   27  | 12  9   18  | 4   78  5   |
+-------------+-------------+-------------+
| 25  9   8   | 4   7   6   | 35b 1   23d |
| 25  4   6   | 19  3   19  | 8   57  27  |
| 7   3   1   | 8   2   5   | 6   9   4   |
+-------------+-------------+-------------+
| 1   57  3   | 69  4   89  | 57a 2   68  |
| 6   8   47  | 5   1   2   | 9   347 37c |
| 9   25  24  | 7   68  3   | 1   45  68  |
+-------------+-------------+-------------+

The BUG:

If each unsolved cell has only two candidates, the puzzle does not have a unique solution.

Furthermore, if each unsolved cell has only two candidates, each candidate occurs twice in each row, column, or box.

Look at R8. The unsolved cells are <47>, <347>, <37>. R8C8 must be <7>. If it is not <7>, it is <34>, and the solution is not unique.


The XY-wing:

If the cell marked a is <5>, b is <3>. If a is <7>, c is <3>. Any cell which sees both b and c cannot be <3>; d must be <2>.

Keith
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