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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Mon Jul 21, 2008 1:55 am Post subject: |
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Yes, it was! Ravel, it was good to read that thread again.
Keith |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Jul 21, 2008 10:23 pm Post subject: |
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| keith wrote: | I tried Medusa, and got nowhere
[...]
Now, I need to figure out how to identify Medusa candidates! |
Well, starting with nataraj's grid again, I selected the 68 bivalue at r7c1 since both the <6> and <8> produce decent color chains each of which involve several other bivalues. So, it looks as if it will produce a large cluster. While larger isn't always better, it often is.
| Code: | +--------------------+------------------+----------------+
| 9 1 4 | 6 7 3 | 25 25 8 |
| 7 26 26 | 48 18 5 | 9 3 14 |
| 5 3a8A 3A8a | 2 9 14 | 7 6 14 |
+--------------------+------------------+----------------+
| 1 456 7 | 3458 3568 468 | 356 9 2 |
| 3A8a 9 3568A | 7 12 12 | 356 4 5a6A |
| 2 456 356 | 9 356 46 | 8 1 7 |
+--------------------+------------------+----------------+
| 6a8A 7 1 | 5A8a 4 9 | 256A 25 3 |
| 4 #2-58a 9 | 358 23568 268 | 1 7 5A6a |
| 3a6A 23A5 25 | 1 #2-56a 7 | 4 8 9 |
+--------------------+------------------+----------------+ |
The <5>s in the cells marked # are easily trapped by this cluster. There is now a 268 XYZ Wing in r89 that removes <2> from r8c5. Then, the cluster expands further:
| Code: | +--------------------+--------------------+----------------+
| 9 1 4 | 6 7 3 | 25 25 8 |
| 7 26 26 |#4A8a 1a8A 5 | 9 3 1A4a |
| 5 3a8A 3A8a | 2 9 1A4a | 7 6 1a4A |
+--------------------+--------------------+----------------+
| 1 456 7 | 34a58 3568 468 | 356 9 2 |
| 3A8a 9 3568A | 7 1A2a 1a2A | 356 4 5a6A |
| 2 456 356 | 9 356 46 | 8 1 7 |
+--------------------+--------------------+----------------+
| 6a8A 7 1 |#5A8a 4 9 | 256A 25 3 |
| 4 2A8a 9 | 358 3568 2a68 | 1 7 5A6a |
| 3a6A 23A5 25 | 1 2A6a 7 | 4 8 9 |
+--------------------+--------------------+----------------+ |
There are two 8a's in c4. So, all a's are false and all A's are true.
Had you started with a different cluster and it wasn't useful, that's no problem. Just start a second cluster, ignoring the first one. Eventually, if no single cluster works, then look for "bridges" between the clusters and check for multi-coloring eliminations. (And/or you can "extend" or "transport" the coloring, though I prefer to do this without markings because such markings are problematic and usually need to be erased.)
The sort of grid I posted here makes multi-cluster marking fairly easy to do on paper once you learn to work with it. (This sort of grid is only used when resorting to Medusa. Blank templates can be kept on hand.) |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Jul 21, 2008 10:29 pm Post subject: |
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| keith wrote: | | A "finned W-wing"? Very, very cool! |
Why, so it is! I didn't think of it in that way. Had I done so, I might only have noticed that it eliminates the <8> at r8c5 ... since the <2>-Fin can be transported to the <8> at r2c5 and the only common victim of that and the potential W-Wing is the <8> at r8c5. It requires also noticing that the potential W-Wing would result in r2c5 also being <8> to get the full benefit of the AIC (without having to think in AIC terms!). |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Jul 22, 2008 12:37 am Post subject: |
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I need to post a technical clarification about that "almost W-Wing" implication chain. The inference between the "fin" <2> and the potential W-Wing is not bidirectionally strong as far as I can tell. It is only a strong inference in the "left-to-right" direction. So, I should amend the notation to indicate this by using "=>" to indicated the unidirectional strong inference. Also, my claim of "r4c2<>8" is incoherent with the chain as shown. (Don't know how I did that.) So, this should be modified as well:
(8=1)r2c5 - (1=2)r5c5 - (2)r5c6=(2)r8c6 - (2)r8c2=>[58 W Wing in r78] - (8)r8c456=(8)r7c4 - (8)r2c4=(8)r2c5; r2c5=8
By the way, the "fin-wing" link is a bidirectional weak inference. However, I cannot think of any way in which determining the wing to be false is useful for chaining!
[Edit to change "can" to "cannot", shown in italics. Oops.] |
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