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December 23 VH

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5181
Location: Rochester, NY, USA

PostPosted: Sun Dec 23, 2012 4:48 am    Post subject: December 23 VH Reply with quote

Code:

+---------+--------------+------------+
| 9 34 7  | 14  8    13  | 5  6    2  |
| 5 8  6  | 2   379  379 | 39 1    4  |
| 1 34 2  | 469 369  5   | 7  39   8  |
+---------+--------------+------------+
| 3 27 19 | 579 2579 6   | 8  4    15 |
| 4 27 8  | 57  1    37  | 6  235  9  |
| 6 5  19 | 8   239  4   | 13 23   7  |
+---------+--------------+------------+
| 2 6  4  | 3   579  789 | 19 5789 15 |
| 8 1  5  | 679 679  2   | 4  79   3  |
| 7 9  3  | 15  4    18  | 2  58   6  |
+---------+--------------+------------+

I needed three moves, but I'm not confident that it couldn't be done in less.

X-Wing on 9 in c67 and X-Wing on 5 in c59. That gets me here where an XY-Wing on 78-5 pivoted in r7c8 finishes it off.


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Code:

+---------+--------------+-----------+
| 9 34 7  | 14  8    13  | 5  6   2  |
| 5 8  6  | 2   37   379 | 39 1   4  |
| 1 34 2  | 469 369  5   | 7  39  8  |
+---------+--------------+-----------+
| 3 27 19 | 79  2579 6   | 8  4   15 |
| 4 27 8  | 57  1    37  | 6  235 9  |
| 6 5  19 | 8   239  4   | 13 23  7  |
+---------+--------------+-----------+
| 2 6  4  | 3   57   789 | 19 78  15 |
| 8 1  5  | 679 679  2   | 4  79  3  |
| 7 9  3  | 15  4    18  | 2  58  6  |
+---------+--------------+-----------+

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arkietech



Joined: 31 Jul 2008
Posts: 1734
Location: Northwest Arkansas USA

PostPosted: Sun Dec 23, 2012 8:47 am    Post subject: Reply with quote

Code:
 *-----------------------------------------------------------*
 | 9     34    7     | 14    8     13    | 5     6     2     |
 | 5     8     6     | 2     379   379   | 39    1     4     |
 | 1     34    2     | 469   369   5     | 7     39    8     |
 |-------------------+-------------------+-------------------|
 | 3    d27    19    | 579  e279-5 6     | 8     4    a15    |
 | 4    c27    8     | 57    1     37    | 6    b235   9     |
 | 6     5     19    | 8     239   4     | 13    23    7     |
 |-------------------+-------------------+-------------------|
 | 2     6     4     | 3     579   789   | 19    5789  15    |
 | 8     1     5     | 679   679   2     | 4     79    3     |
 | 7     9     3     | 15    4     18    | 2     58    6     |
 *-----------------------------------------------------------*
L-wing
5r4c9=(5-2)r5c8=r5c2-r4c2=2r4c5 => -5r4c5; stte
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George Woods



Joined: 28 Mar 2006
Posts: 239
Location: Dorset UK

PostPosted: Sun Dec 23, 2012 10:17 am    Post subject: Has this variation of an xy wing got a name? Reply with quote

After the x wing in 5 we can 'pivot' r4c4 if it is 9 then r4c3 denies a 1 to r4c9 which becomes 5. aliter if r4c4 is 7 then r5c4 is 5 which forces r4c9 to be 5

so r4c9 =5

but it is not an xy wing

I came to this by observing that r3c23 must contain a 1 or a2 (ellse r4c4 cannot be satisfied) this leads to a similar artgument to that given above. So it was frustrating to find that I couldn't force the argument into any known (by me) formal structure
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JC Van Hay



Joined: 13 Jun 2010
Posts: 373
Location: Charleroi, Belgium

PostPosted: Sun Dec 23, 2012 11:55 am    Post subject: Re: Has this variation of an xy wing got a name? Reply with quote

George Woods wrote:
...So it was frustrating to find that I couldn't force the argument into any known (by me) formal structure

Code:
+-------------+-------------------+----------------+
| 9  34  7    | 14     8      13  | 5   6     2    |
| 5  8   6    | 2      379    379 | 39  1     4    |
| 1  34  2    | 469    369    5   | 7   39    8    |
+-------------+-------------------+----------------+
| 3  27  (19) | (579)  279-5  6   | 8   4     (15) |
| 4  27  8    | (57)   1      37  | 6   235   9    |
| 6  5   19   | 8      239    4   | 13  23    7    |
+-------------+-------------------+----------------+
| 2  6   4    | 3      579    789 | 19  5789  15   |
| 8  1   5    | 679    679    2   | 4   79    3    |
| 7  9   3    | 15     4      18  | 2   58    6    |
+-------------+-------------------+----------------+
(5=7)r5c4-(7=159)r4c349 :=> -5r4c5

Extended WXYZ-Wing Type 1 or ALS X-Z Rule : W=7(restricted common), X=1, Y=9, Z=5 (common); WXYZ as r4c4, XYZ and XYZ as r4c39, WZ as r5c4 --> (Z=W)-(W=XYZ) :=> -Z.
XY Chain if 5r4c4 is already eliminated. In this case, -5r4c5 and -5r5c8.

In both case, the XWing on 5 is solved.
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