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Aug 19 VH

 
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Clement



Joined: 24 Apr 2006
Posts: 1111
Location: Dar es Salaam Tanzania
PostPosted: Wed Aug 18, 2010 10:54 pm    Post subject: Aug 19 VH Reply with quote
XY-Wing 59 58 89 Pivoted in BOX 5 removes the 9's in r6c13 solving the puzzle.
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peterj



Joined: 26 Mar 2010
Posts: 974
Location: London, UK
PostPosted: Thu Aug 19, 2010 7:51 am    Post subject: Reply with quote
Or a w-wing(89) with pincers r4c8 and r6c4 with strong link (8)r4c2=r6c2 eliminates 9 from r4c6
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Thu Aug 19, 2010 2:31 pm    Post subject: Reply with quote
How about a Type 4 UR (59) in r78c34 for those times when a xy-wing is not present?

Here is the code after basics.
Code:
*--------------------------------------------------*
 | 3    5    1    | 2    4    6    | 89   7    89   |
 | 2    9    8    | 1    57   57   | 4    3    6    |
 | 7    6    4    | 3    9    8    | 2    5    1    |
 |----------------+----------------+----------------|
 | 459  78   2    | 6    1    59   | 3    89   47   |
 | 59   1    3    | 7    58   4    | 6    2    89   |
 | 46   78   69   | 89   3    2    | 5    1    47   |
 |----------------+----------------+----------------|
 | 89   4   *59   |*589  2    1    | 7    6    3    |
 | 689  3   *569  |*589  78   79   | 1    4    2    |
 | 1    2    7    | 4    6    3    | 89   89   5    |
 *--------------------------------------------------*


The Type 4 UR, marked *, has a x-wing 5 overlay which means that r8c4<>9 because that would allow the deadly pattern. However, this does not solve the puzzle and is not very helpful otherwise.

Another possible deletion using the "almost" UR (AUR) pattern is to follow the implications of all the non-UR digits in the UR cells. That is, if one or more of r7c4=8, r8c3=6 or r8c4=8, then the deadly pattern is prevented.
If r7c4=8, then r6c4=9 and r6c1<>9
If r8c3=6, then r6c3=9 and r6c1<>9
If r8c4=8, then r6c4=9 and r6c1<>9
Thus all three of the conditions within the UR cells needed to prevent the deadly pattern result in r6c1<>9. However, this deletion is also not very useful.

But Wait! There is More!
The three implications really provide two pincers on 9 in r6c3 and r6c4 which can be extended as follows:
If r6c3=9, then r5c1=5 and
If r6c4=9, then r4c6=5
These two pincers on 5 now delete 5 from r4c1, r4c1<>5, and the puzzle is completed in one step.

Ted
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Thu Aug 19, 2010 3:57 pm    Post subject: Reply with quote
There is also a W-Wing on 59.

As to the 59 UR: the 6 in r8c3 leads to an invalidity, after which it's a conventional Type 4 which solves it.
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