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Clement
Joined: 24 Apr 2006
Posts: 1110
Location: Dar es Salaam Tanzania
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 Posted: Wed Aug 18, 2010 10:54 pm Post subject: Aug 19 VH |
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| 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
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| Posted: Thu Aug 19, 2010 7:51 am Post subject: |
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| 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
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| Posted: Thu Aug 19, 2010 2:31 pm Post subject: |
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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
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| Posted: Thu Aug 19, 2010 3:57 pm Post subject: |
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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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