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Mar 9 VH

 
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Clement



Joined: 24 Apr 2006
Posts: 1110
Location: Dar es Salaam Tanzania

PostPosted: Mon Mar 08, 2010 10:19 pm    Post subject: Mar 9 VH Reply with quote

XYZ-Wing 57 578 58 eliminating 5 in r8c1 solves the puzzle Smile
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Tue Mar 09, 2010 2:21 am    Post subject: Reply with quote

This was an interesting puzzle in terms of the number of solutions. I found it solves in one step with examining the ramifications of a UR, or two XYZ-Wings, two XY-Wings or two W-Wings.
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Wendy W



Joined: 04 Feb 2008
Posts: 144

PostPosted: Tue Mar 09, 2010 10:41 pm    Post subject: Reply with quote

I used Clement's xyz-wing and then needed an x-wing on 7 as well.
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Toole130



Joined: 05 Feb 2010
Posts: 3

PostPosted: Wed Mar 10, 2010 12:41 am    Post subject: Cryptic Replies Reply with quote

Sorry, but as one trying to learn the novelties of XYZ wings, U's, etc. I find the responses hear too cryptic for me to learn anything. I understand that the XYZ wing will ultimately eliminate 5 in r8c6, but I have absolutely no idea how logic got me there/ What are the parts to and XYZ wing?
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Wed Mar 10, 2010 1:20 am    Post subject: Reply with quote

Hi Toole, welcome to the forum.

An XYZ-Wing is defined as: start with a trivalue cell we'll call XYZ. Find another cell in the same box we'll call XZ. Then find a cell in another box we'll call YZ. Any cell that sees all three of XYZ-XZ-YZ cannot contain Z. This is my grid after basic moves.

Code:

+-------------+----------+-----------+
| 489 689 1   | 268 5 3  | 7 248 248 |
| 48  5   3   | 28  1 7  | 9 6   248 |
| 7   68  2   | 68  4 9  | 5 3   1   |
+-------------+----------+-----------+
| 6   1   9   | 7   8 4  | 3 25  25  |
| 2   37  58  | 35  9 1  | 4 78  6   |
| 58  37  4   | 35  6 2  | 1 9   78  |
+-------------+----------+-----------+
| 3   4   57  | 1   2 6  | 8 57  9   |
| 589 2   578 | 49  3 58 | 6 1   457 |
| 1   89  6   | 49  7 58 | 2 45  3   |
+-------------+----------+-----------+

Play this puzzle online at the Daily Sudoku site

Note the 578 cell in r8c3 and the 57 cell in r7c3. The 578 cell also sees the 58 cell in r8c6. R8c1 sees all three cells and cannot contain a 5.

Feel free to ask questions, there are lots of people here happy to help out.
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Wendy W



Joined: 04 Feb 2008
Posts: 144

PostPosted: Wed Mar 10, 2010 1:41 am    Post subject: Reply with quote

Hi Toole,
xyz-wings were confusing to me at first, too. I found it helped to write them out like an algebra problem: e.g., x = 5, y = 7, z = 8 and then xy = 57, xz = 58. What digit do the "pincers" have in common? x, or 5.
This is a beautiful example of a helpful xyz-wing.
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keith



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

PostPosted: Wed Mar 10, 2010 2:25 am    Post subject: Reply with quote

After basics:
Code:
+-------------+-------------+-------------+
| 489 689 1   | 268 5   3   | 7   248 248 |
| 48  5   3   | 28  1   7   | 9   6   248 |
| 7   68  2   | 68  4   9   | 5   3   1   |
+-------------+-------------+-------------+
| 6   1   9   | 7   8   4   | 3   25  25  |
| 2   37  58@ | 35  9   1   | 4   78# 6   |
| 58  37  4   | 35  6   2   | 1   9   78  |
+-------------+-------------+-------------+
| 3   4   57# | 1   2   6   | 8   5-7 9   |
| 589 2   578 | 49  3   58  | 6   1   457 |
| 1   89  6   | 49  7   58  | 2   45  3   |
+-------------+-------------+-------------+

The 5-78 XY-wing is a 1-step solution.

Keith
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strmckr



Joined: 18 Aug 2009
Posts: 64

PostPosted: Wed Mar 10, 2010 4:05 am    Post subject: Reply with quote

alternative to the noted above xy-wing

XY-Wing: 8/7/5 in r5c38,r7c8 => r7c3<>5
Code:
.---------------.------------.-------------.
| 489  689  1   | 268  5  3  | 7  248  248 |
| 48   5    3   | 28   1  7  | 9  6    248 |
| 7    68   2   | 68   4  9  | 5  3    1   |
:---------------+------------+-------------:
| 6    1    9   | 7    8  4  | 3  25   25  |
| 2    37   58@ | 35   9  1  | 4  78@  6   |
| 58   37   4   | 35   6  2  | 1  9    78  |
:---------------+------------+-------------:
| 3    4    7-5 | 1    2  6  | 8  57@  9   |
| 589  2    578 | 49   3  58 | 6  1    457 |
| 1    89   6   | 49   7  58 | 2  45   3   |
'---------------'------------'-------------'


other single step solutions.

{interesting how all of them seem to run around the same cells, either as the elimination or part of the move}

XYZ-Wing: 5/9/8 in r8c16,r9c2 => r8c3<>8
Code:
.---------------.------------.-------------.
| 489  689  1   | 268  5  3  | 7  248  248 |
| 48   5    3   | 28   1  7  | 9  6    248 |
| 7    68   2   | 68   4  9  | 5  3    1   |
:---------------+------------+-------------:
| 6    1    9   | 7    8  4  | 3  25   25  |
| 2    37   58  | 35   9  1  | 4  78   6   |
| 58   37   4   | 35   6  2  | 1  9    78  |
:---------------+------------+-------------:
| 3    4    57  | 1    2  6  | 8  57   9   |
| 589@ 2    57-8| 49   3  58@| 6  1    457 |
| 1    89@  6   | 49   7  58 | 2  45   3   |
'---------------'------------'-------------'


W-Wing: 8/5 in r5c3,r8c6 connected by 5 in r68c1 => r8c3<>8
Code:

.---------------.------------.-------------.
| 489  689  1   | 268  5  3  | 7  248  248 |
| 48   5    3   | 28   1  7  | 9  6    248 |
| 7    68   2   | 68   4  9  | 5  3    1   |
:---------------+------------+-------------:
| 6    1    9   | 7    8  4  | 3  25   25  |
| 2    37   58@ | 35   9  1  | 4  78   6   |
| 58@  37   4   | 35   6  2  | 1  9    78  |
:---------------+------------+-------------:
| 3    4    57  | 1    2  6  | 8  57   9   |
| 589@ 2    57-8| 49   3  58@| 6  1    457 |
| 1    89   6   | 49   7  58 | 2  45   3   |
'---------------'------------'-------------'


W-Wing: 8/5 in r5c3,r8c6 connected by 5 in r68c1 => r8c3<>8

Code:
.---------------.------------.-------------.
| 489  689  1   | 268  5  3  | 7  248  248 |
| 48   5    3   | 28   1  7  | 9  6    248 |
| 7    68   2   | 68   4  9  | 5  3    1   |
:---------------+------------+-------------:
| 6    1    9   | 7    8  4  | 3  25   25  |
| 2    37   58@ | 35   9  1  | 4  78   6   |
| 58@  37   4   | 35   6  2  | 1  9    78  |
:---------------+------------+-------------:
| 3    4    57  | 1    2  6  | 8  57   9   |
| 89-5 2    578@| 49   3  58@| 6  1    457 |
| 1    89   6   | 49   7  58 | 2  45   3   |
'---------------'------------'-------------'
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Toole130



Joined: 05 Feb 2010
Posts: 3

PostPosted: Thu Mar 11, 2010 2:49 am    Post subject: Thanks Reply with quote

Thanks to all your help. I guess I was a little frustrated in not being able to follow the clues. I really appreciate the time each of you took.

Bart
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