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Handling UR implications

 
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tlanglet



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

PostPosted: Sun Apr 18, 2010 10:05 pm    Post subject: Handling UR implications Reply with quote

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.

PostPosted: Mon Apr 19, 2010 1:24 am    Post subject: Reply with quote

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: 3855

PostPosted: Mon Apr 19, 2010 2:10 am    Post subject: Reply with quote

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

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: 2461
Location: Northern California Foothills

PostPosted: Mon Apr 19, 2010 1:48 pm    Post subject: Reply with quote

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: 3174
Location: near Detroit, Michigan, USA

PostPosted: Mon Apr 19, 2010 7:09 pm    Post subject: Reply with quote

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: 3855

PostPosted: Mon Apr 19, 2010 7:28 pm    Post subject: Reply with quote

tlanglet wrote:
I do not understand the strong link issue.

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. Smile

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. Laughing

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: 3174
Location: near Detroit, Michigan, USA

PostPosted: Mon Apr 19, 2010 8:18 pm    Post subject: Reply with quote

Also, the type 4 UR 35.

Keith
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Mon Apr 19, 2010 9:09 pm    Post subject: Reply with quote

keith wrote:
Also, the type 4 UR 35.

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: 3174
Location: near Detroit, Michigan, USA

PostPosted: Mon Apr 19, 2010 9:39 pm    Post subject: Reply with quote

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: 3855

PostPosted: Mon Apr 19, 2010 11:44 pm    Post subject: Reply with quote

keith wrote:
OK. I can eliminate 7 in R4C4 and R7C2. Is there anything else?

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. Sad
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keith



Joined: 19 Sep 2005
Posts: 3174
Location: near Detroit, Michigan, USA

PostPosted: Tue Apr 20, 2010 12:38 am    Post subject: Reply with quote

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: 3855

PostPosted: Tue Apr 20, 2010 1:26 am    Post subject: Reply with quote

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.

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

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: 3174
Location: near Detroit, Michigan, USA

PostPosted: Tue Apr 20, 2010 1:49 am    Post subject: Reply with quote

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: 695

PostPosted: Tue Apr 20, 2010 8:35 am    Post subject: Reply with quote

Quote:
But then, I will use any tool in the toolbox!

Keith


[Fargo]You got dat right[/Fargo]
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