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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Sun Apr 24, 2011 5:18 pm Post subject: Rambling: UR with a Chain Segment |
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While working through Mike Barker's collection of UR puzzles designed to crack with one technique, I encountered this puzzle ... and a different UR solution.
First, there is an X-Wing on <2> in the UR cells. This limits r4c3=6 and/or r5c5=6 as the only exterior possibilities in [b4] and [b5] to break the <26> UR. So, at least one of these statements must be true. Normally, this leads to eliminations r4c6,r5c2<>6 and nothing more. They don't crack the puzzle.
| Code: | +--------------------------------------------------------------+
| 7 369 68 | 49 2 56 | 38 345 1 |
| 2 4 5 | 8 13 13 | 6 9 7 |
| 89 369 1 | 49 56 7 | 2 345 358 |
|--------------------+--------------------+--------------------|
| 89 *26+9 68 | 1 4 *26+39 | 7 35 359 |
| 3 *26+9 7 | 5 68 *26+9 | 4 1 89 |
| 5 1 4 | 7 38 39 | 389 6 2 |
|--------------------+--------------------+--------------------|
| 6 5 3 | 2 9 8 | 1 7 4 |
| 1 8 9 | 3 7 4 | 5 2 6 |
| 4 7 2 | 6 15 15 | 39 8 39 |
+--------------------------------------------------------------+
# 43 eliminations remain
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However, this chain segment also exists:
| Code: | (6)r4c3 = r45c2 - r3c2 = r3c5 - (6)r5c5
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It says: if r4c3<>6 then r5c5<>6 as well. This leaves only one conclusion: r4c3=6 -- which cracks the puzzle. |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Sun Apr 24, 2011 8:45 pm Post subject: |
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Nice. Another view of it would be like a turbot/er where one strong link on 6 is created by the UR?
| Code: | | (6)r1c6=r3c5 - ur(26)r45c26[(6)r5c5=r4c3] ; r1c3<>6 so r4c3=6 |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sun Apr 24, 2011 11:21 pm Post subject: Chains with UR segments |
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| daj95376, I think Chain with a UR segment would be a better description than UR with a chain segment. [edit: Hmm, guess that's what peterj already said.] |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sun Apr 24, 2011 11:48 pm Post subject: |
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It's even easier to see as an ER (or conjugate pair) in box 2 resulting in r1c3<>6. (Same as Peterj again.)
Or, you could state the external UR inference as (6)r13c2=(6)r1c6 and get r1c3<>6 directly. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Apr 25, 2011 12:26 am Post subject: |
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Thanks Peter, Ron, and Asellus !!! I like your general consensus.
I'm hoping to soon add internal/external strong inferences to my chains() routine. With the altered perspective you (pl.) provided, that will now prove productive on puzzles (like this one) where it won't be necessary to include the inner workings of the UR.
Regards, Danny |
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