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Rambling: UR with a Chain Segment

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sun Apr 24, 2011 5:18 pm    Post subject: Rambling: UR with a Chain Segment Reply with quote

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

However, this chain segment also exists:

Code:
(6)r4c3 = r45c2 - r3c2 = r3c5 - (6)r5c5

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

PostPosted: Sun Apr 24, 2011 8:45 pm    Post subject: Reply with quote

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: 397

PostPosted: Sun Apr 24, 2011 11:21 pm    Post subject: Chains with UR segments Reply with quote

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

PostPosted: Sun Apr 24, 2011 11:48 pm    Post subject: Reply with quote

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: 3855

PostPosted: Mon Apr 25, 2011 12:26 am    Post subject: Reply with quote

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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