dailysudoku.com Forum Index dailysudoku.com
Discussion of Daily Sudoku puzzles
 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

Another UR

 
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Solving techniques, and terminology
View previous topic :: View next topic  
Author Message
tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Sun May 18, 2008 4:22 pm    Post subject: Another UR Reply with quote

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
Back to top
View user's profile Send private message
Marty R.



Joined: 12 Feb 2006
Posts: 5121
Location: Rochester, NY, USA

PostPosted: Sun May 18, 2008 5:22 pm    Post subject: Reply with quote

Ted, what you have there is a Type 2 UR, where the four corners are AB-AB-ABC-ABC. 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.
Back to top
View user's profile Send private message
tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Sun May 18, 2008 5:52 pm    Post subject: Reply with quote

Marty R. wrote:
Ted, what you have there is a Type 2 UR, where the four corners are AB-AB-ABC-ABC. 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
Back to top
View user's profile Send private message
Asellus



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

PostPosted: Sun May 18, 2008 7:59 pm    Post subject: Reply with quote

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.
Back to top
View user's profile Send private message Visit poster's website
Steve R



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

PostPosted: Sun May 18, 2008 9:37 pm    Post subject: Reply with quote

Well, I agree its 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
Back to top
View user's profile Send private message
tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Sun May 18, 2008 10:46 pm    Post subject: Reply with quote

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
Back to top
View user's profile Send private message
Asellus



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

PostPosted: Tue May 20, 2008 12:06 am    Post subject: Reply with quote

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 W-Wing 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?
Back to top
View user's profile Send private message Visit poster's website
keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Tue May 20, 2008 4:47 am    Post subject: Reply with quote

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
Back to top
View user's profile Send private message
Asellus



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

PostPosted: Sun Aug 17, 2008 3:39 am    Post subject: Reply with quote

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 uniqueness-based logic that exploits it... even if this seemed for a while, to me at least, to be a bit weird.
Back to top
View user's profile Send private message Visit poster's website
Display posts from previous:   
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Solving techniques, and terminology All times are GMT
Page 1 of 1

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum


Powered by phpBB © 2001, 2005 phpBB Group