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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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 Posted: Sun Apr 18, 2010 10:05 pm Post subject: Handling UR implications |
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Here is my code after basics for Danny's 10/04/18 (C) puzzle.
| Code: | *--------------------------------------------------------------------*
| 2 35 9 | 478 68 47 | 35 1 67 |
| 1 67 678 | 3 26 5 | 489 79 2467 |
| 5678 3567 4 | 27 9 1 | 358 57 267 |
|----------------------+----------------------+----------------------|
| 4678 1 2678 | 24789 28 47 | 459 5679 3 |
| 467 2467 5 | 2479 1 3 | 49 679 8 |
| 478 9 3 | 478 5 6 | 1 2 47 |
|----------------------+----------------------+----------------------|
| 457 2457 27 | 1 47 8 | 6 3 9 |
| 3 467 67 | 5 47 9 | 2 8 1 |
| 9 8 1 | 6 3 2 | 7 4 5 |
*--------------------------------------------------------------------* |
Notice the type 5 UR 67 in r28c23 and look at the outside box implications.
Digit 6: r3c12
Digit 7: r3c12 & r7c123
r3c12 therefore forms a 67 pseudocell that combines with the 67 bivalue in r2c2 to delete 67 in r8c2,
r7c123=7 will also delete the 7 in r8c2, and
r3c12=6 deletes 6 in r2c23.
Thus, r8c2<>7 is the only valid deletion.
My question is the validity of forming the 67 pseudocell in r3c12. Comments appreciated.
Ted
Edited to correct typo in location and type of UR. |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Mon Apr 19, 2010 1:24 am Post subject: |
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I don't see a UR here. I may well be wrong.
I don't see enough strong links. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Apr 19, 2010 2:10 am Post subject: |
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| wapati wrote: | I don't see a UR here. I may well be wrong.
I don't see enough strong links. |
This is what my solver found.
| Code: | r28c23 <67> UR via s-link <> 6 r2c3
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Note: r2c2=67 prevents r35c12 from ever forming a <67> DP. Anything else is just icing on the cake.
More specifically, there are 32 companion cells to each UR pattern. If any of these cells is a bivalue cell containing the UR candidates, then you can never force a UR condition.
| Code: | 32 "companion" cells to a UR
+-----------------------+
| . . . | * * * | . . . |
| * * * | X * X | * * * |
| . . . | * * * | . . . |
|-------+-------+-------|
| . . . | * . * | . . . |
| . . . | * . * | . . . |
| . . . | * . * | . . . |
|-------+-------+-------|
| . . . | * * * | . . . |
| * * * | X * X | * * * |
| . . . | * * * | . . . |
+-----------------------+
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Apr 19, 2010 1:48 pm Post subject: |
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Danny & Wapati,
Thanks for the feedback.
It seems that it is time for me it review the fundamental considerations for URs. I verified that the companion cells of the "potential" UR67 in r28c23 did not contain a bivalue 67, but otherwise viewed the pattern as a "almost" UR. To prevent a deadly pattern, either r2c3=8 or r8c2=4 was sufficient for me to be valid.
I do not understand the strong link issue.
Ted |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Apr 19, 2010 7:09 pm Post subject: |
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The only elimination I see in the 67 UR is R2C3 is not 6, because of the string link on 6 in R8.
| Quote: | | More specifically, there are 32 companion cells to each UR pattern. If any of these cells is a bivalue cell containing the UR candidates, then you can never force a UR condition. |
That is correct. However, you can still make any UR eliminations you may find.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Apr 19, 2010 7:28 pm Post subject: |
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| tlanglet wrote: | I do not understand the strong link issue.
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Strong links are the backbone of many numbered and named UR patterns. The strong links just get downplayed when these UR patterns are explained. For other, unnamed UR patterns, the strong links play a major factor in explaining how they work.
Consider your <67> UR pattern above. It doesn't fit any of the "standard" UR patterns, but a UR elimination still exists because of strong links.
First, it's important to remember that all bivalue cells represent a strong link between the two candidates. This means that cells r2c2,r8c3 have a strong link between the candidate values <6> and <7>. In addition, there's a strong link on <6> in [r8] between r8c2 and r8c3.
If r2c3=6, then strong links force the bivalue cells r2c2,r8c3 to be <7>. The strong link in [r8] then forces r8c2=6. We now have a DP in r28c23.
Deduction: r2c3<>6.
If there had been a strong link on <6> in [r2] between cells r2c2 and r2c3, then we could have also deduced r8c2<>6. Of course, if we had the second strong link on <6>, then we would have an X-Wing pattern on <6> ... and the <67> UR would qualify as a Type 6. 
I have occasionally been tempted to post examples of these half-Type URs because they are so common. Then, I remember how often I get into trouble by tackling such issues ... and I don't. 
Regards, Danny
Now, take a close look at the <47> UR pattern in r78c25, and the <47> UR pattern in r14c46. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Apr 19, 2010 8:18 pm Post subject: |
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Also, the type 4 UR 35.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Apr 19, 2010 9:09 pm Post subject: |
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| keith wrote: | Also, the type 4 UR 35.
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Yes, I almost used that UR to demonstrate that any UR based on an X-Wing is derived from 2x URs through strong links. Then I decided that my message was long enough. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Apr 19, 2010 9:39 pm Post subject: |
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| Quote: | | Now, take a close look at the <47> UR pattern in r78c25, and the <47> UR pattern in r14c46. |
OK. I can eliminate 7 in R4C4 and R7C2. Is there anything else?
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Apr 19, 2010 11:44 pm Post subject: |
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| keith wrote: | OK. I can eliminate 7 in R4C4 and R7C2. Is there anything else?
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No. You found the eliminations. Too bad they don't contribute more towards a solution in this puzzle.
What I really tried to do was combine the <47> UR in [band 3] with the overlapping <67> UR in [stack 1], but I failed to find anything productive.  |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Tue Apr 20, 2010 12:38 am Post subject: |
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| Quote: | | No. You found the eliminations. Too bad they don't contribute more towards a solution in this puzzle. |
Danny,
I have a theory that these Type-6 etc. UR's are not very useful, in that they do not often crack a puzzle. You have a UR on an X-wing, or a strong link or two. The elimination tends to be on one or two diagonal cells, and does not propagate to the rest of the puzzle.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Apr 20, 2010 1:26 am Post subject: |
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| keith wrote: | I have a theory that these Type-6 etc. UR's are not very useful, in that they do not often crack a puzzle. You have a UR on an X-wing, or a strong link or two. The elimination tends to be on one or two diagonal cells, and does not propagate to the rest of the puzzle.
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Yes, but then there's always the exception.
| Code: | +-----------------------+
| 7 . . | . 8 1 | . . . |
| . . . | . . . | . 8 . |
| . . 3 | 9 . 4 | 7 . . |
|-------+-------+-------|
| . . 6 | . . 9 | . 2 . |
| 2 . . | . . 7 | . . 3 |
| 3 . 9 | 4 2 . | . 1 . |
|-------+-------+-------|
| . . 7 | . . . | 8 . . |
| . 3 . | 8 . 2 | . 5 4 |
| . . . | . 4 . | . 7 . |
+-----------------------+ Ext_Out Puzzle #61
c4b8 Locked Candidate 1 <> 1 r45c4
c4b5 Locked Candidate 1 <> 5 r79c4
c37 X-Wing <> 2 r2c2,r9c29
r37 X-Wing <> 2 r2c2,r9c29
<28+4> XY-Wing r9c3/r5c3+r7c2 <> 4 r5c2
+-----------------------------------------------------+
| 7 6 5 | 2 8 1 | 3 4 9 |
| 149 149 24 | 7 36 36 | 12 8 5 |
| 18 128 3 | 9 5 4 | 7 6 12 |
|-----------------+-----------------+-----------------|
| 14 7 6 | 35 13 9 | 45 2 8 |
| 2 18 48 | 56 16 7 | 45 9 3 |
| 3 5 9 | 4 2 8 | 6 1 7 |
|-----------------+-----------------+-----------------|
| 45 24 7 | *16 9 56 | 8 3 *16+2 |
| 6 3 1 | 8 7 2 | 9 5 4 |
| 589 89 28 | *16+3 4 356 | 12 7 *16 |
+-----------------------------------------------------+
# 37 eliminations remain
r79c49 <16> UR via s-link <> 6 r7c4
r79c49 <16> UR via s-link <> 1 r7c9
r79c49 <16> UR via s-link <> 1 r9c4 *** important
r79c49 <16> UR via s-link <> 6 r9c4 *** important
Solution:
765281349942763185813954762176539428284617593359428617427195836631872954598346271
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It can also be solved with the network
<16> UR[(3)r9c4 = (2)r7c9] - {(2=1)r9c7 - (1=6)r9c9} - (16=3)r9c4
Ted: My apologies for hijacking your thread!!! |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Tue Apr 20, 2010 1:49 am Post subject: |
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| Quote: | | Yes, but then there's always the exception. |
Danny,
Yes, there is.
When I first discovered the Type 6 UR, Mike Barker and others used it to solve a number of their previously "unsolvable" puzzles.
However, I stand by my statement. I think that, in general, W- and M-wings are much more effective puzzle busters than unnamed UR's with strong links.
But then, I will use any tool in the toolbox!
Keith |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Tue Apr 20, 2010 8:35 am Post subject: |
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| Quote: | But then, I will use any tool in the toolbox!
Keith |
[Fargo]You got dat right[/Fargo] |
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