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pipesmoker
Joined: 10 Sep 2005
Posts: 4
Location: Burton upon Trent
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 Posted: Mon May 14, 2007 8:38 am Post subject: 14th May,2007. |
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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
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| Posted: Mon May 14, 2007 11:55 am Post subject: |
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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
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| Posted: Mon May 14, 2007 11:58 am Post subject: |
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| 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
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| Posted: Mon May 14, 2007 2:25 pm Post subject: |
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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
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| Posted: Mon May 14, 2007 3:13 pm Post subject: |
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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
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| Posted: Mon May 14, 2007 3:15 pm Post subject: |
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| 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
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| Posted: Mon May 21, 2007 9:41 am Post subject: |
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| Thanks again David |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon May 21, 2007 11:15 pm Post subject: |
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| 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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