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tlanglet
Joined: 17 Oct 2007 Posts: 2468 Location: Northern California Foothills

Posted: Sun May 18, 2008 4:22 pm Post subject: Another UR 


Recently I have experience several puzzles where I find a UR that is nearly a simple Type 1, but the extra candidate occurs in 2 cells. I am not sure how to handle this circumstance where I seemed to have a pseudo <5>. For example, the code for the Times Online puzzle 1895 after basics is :
Code: 
**
 1 5 8  6 9 2  4 3 7 
 9 27 4  37 1 358  6 28 258 
 3 267 26  47 458 458  258 9 1 
++
 245 8 25  249 3 49  1 7 6 
 6 1 3  5 28 7  28 4 9 
 24 9 7  1 6 48  3 5 28 
++
 8 246 256  249 245 4569  7 1 3 
 25 246 1  234 7 3456  9 28 258 
 7 3 9  8 25 1  25 6 4 
**

Note the possible UR on <28> in r28c89. An extra candidate, <5>, occurs in two cells, r28c9. Is it possible to pursue eliminations with this condition?
I have solved the puzzle with other strategies, but am wondering specifically if something positive is possible with this potential UR.
Ted 

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Marty R.
Joined: 12 Feb 2006 Posts: 5446 Location: Rochester, NY, USA

Posted: Sun May 18, 2008 5:22 pm Post subject: 


Ted, what you have there is a Type 2 UR, where the four corners are ABABABCABC. In your example, one of the 258 cells must be =5, therefore, all other 5s in that column can be eliminated. Unfortunately, there are no 5s to be eliminated. Maybe somebody could do something, but I can't. 

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tlanglet
Joined: 17 Oct 2007 Posts: 2468 Location: Northern California Foothills

Posted: Sun May 18, 2008 5:52 pm Post subject: 


Marty R. wrote:  Ted, what you have there is a Type 2 UR, where the four corners are ABABABCABC. In your example, one of the 258 cells must be =5, therefore, all other 5s in that column can be eliminated. Unfortunately, there are no 5s to be eliminated. Maybe somebody could do something, but I can't. 
Thanks Marty for your timely response.
I recognized it as a Type 2 UR, but was hoping that something could be pursued . Some time back, I read about an "almost UR" but did not really understand it and was wondering if this was an example of that condition.
Do you have any insight into an "almost UR"?
Ted 

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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA

Posted: Sun May 18, 2008 7:59 pm Post subject: 


This particular example is not a UR. The deadly pattern isn't possible due to the 28 bivalue at r6c9. It's just a plain old locked triple. However, if this weren't the case, then the Type 2 logic would apply. 

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Steve R
Joined: 24 Oct 2005 Posts: 289 Location: Birmingham, England

Posted: Sun May 18, 2008 9:37 pm Post subject: 


Well, I agree it’s not a very useful UR. It nevertheless eliminates 2 from r2c9.
This is because the two cells in row 8 are conjugate with respect to 8. If r8c9 contains 5, r8c8 must contain 8 and so r2c8 contains 2. On the other hand, if r8c9 does not contain 5, r2c9 does. Either way there is no room for 2 in r2c9.
A corresponding elimination is always possible in a UR of the type:
Code:  xy xyU
xy –x xyV 
where U and V are any sets of candidates.
Steve 

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tlanglet
Joined: 17 Oct 2007 Posts: 2468 Location: Northern California Foothills

Posted: Sun May 18, 2008 10:46 pm Post subject: 


So, it was possible to obtain an elimination from that code. I recall someone once commented to try substituting the "odd" candidates in a UR to see if something evolves. In fact, I did try the <5> in both locations, r28c9, but failed to recognize that the <2> could be deleted from r2c9.
The lesson I have learned is to look for conjugates and substitute the required "odd" candidates.
Thanks all ..........
Ted 

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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA

Posted: Tue May 20, 2008 12:06 am Post subject: 


I'd still quibble that the <2> elimination in r2c9 is not really due to the "UR" since no deadly pattern is possible here. I see it as a result of the 28 WWing in r2c8 and r6c9. The strong <8> pair in r8 means that one or both of these bivalues is <2>. We never really "get to" the DP logic.
Perhaps it is not a legitimate concern, but I always worry that if an ALS is present that prevents what looks like a possible DP from actually being possible, then inferences based upon the apparent DP may not be valid. In this case, there was no problem. But, I'm not certain if that is always the case. Is there someone who can shed light on this? 

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keith
Joined: 19 Sep 2005 Posts: 3253 Location: near Detroit, Michigan, USA

Posted: Tue May 20, 2008 4:47 am Post subject: 


Asellus,
I think the logic is quite valid.
Assume there is a unique solution. Look at facts a, b, c, ... to make an elimination.
Observe that there is a fact d that guarantees a unique solution. This does not invalidate any conclusions from a, b, c.
Keith 

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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA

Posted: Sun Aug 17, 2008 3:39 am Post subject: 


keith wrote:  Asellus,
I think the logic is quite valid. 
I was remiss in not posting long ago that I concur. The fact that additional information in the grid makes the apparent Deadly Patttern impossible does not invalidate the uniquenessbased logic that exploits it... even if this seemed for a while, to me at least, to be a bit weird. 

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