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Conjugate-Linked ALS's with 5 eliminations

 
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Bud



Joined: 06 May 2010
Posts: 47
Location: Tampa, Florida

PostPosted: Mon Jun 06, 2011 7:26 pm    Post subject: Conjugate-Linked ALS's with 5 eliminations Reply with quote

200041000306000500000500090021000000040126080000000200070008000002000703000470806

After basic moves the puzzle is as shown in the diagram. The 2 ALS's are labeled A and B in Box 1 and 3. The 1 grouped conjugates in row 2 are labeled C and D. The logic is as follows. If C=1, A=478 or if D=1, B=3678. In either case r1c3 and r3c9<>78 and r1c2<>8. This move results in 8 cells being identified. I have another example of this technique which I can add to this post if someone wants to see it. I don't think that this technique is new. It would be hard to believe that someone has not used it before.

Code:

+----------------------+--------------------+---------------------+
| 2       5-89   5-7-89| 36789  4     1     | 36B   367B    78B   |
| 3       189C   6     | 2789   89    279   | 5     1247D   12478D|
| 1478A   18A    478A  | 5      368   237   | 136B  9       12-7-8|
+----------------------+--------------------+---------------------+
| 56789   2      1     | 3789   3589  34579 | 3469  34567   4579  |
| 579     4      3579  | 1      2     6     | 39    8       579   |
| 56789   35689  35789 | 3789   3589  34579 | 2     134567  14579 |
+----------------------+--------------------+---------------------+
| 1456    7      345   | 236    1356  8     | 149   1245    12459 |
| 145689  15689  2     | 69     1569  59    | 7     145     3     |
| 159     1359   359   | 4      7     2359  | 8     125     6     |
+----------------------+--------------------+---------------------+
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Tue Jun 07, 2011 12:18 am    Post subject: Reply with quote

Bud, without the grouped strong inference (link) in r2, you already have two ALS-xz's for the same eliminations. The 'x' is digit <1> in r3. Either way, it's a nice move.
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Bud



Joined: 06 May 2010
Posts: 47
Location: Tampa, Florida

PostPosted: Tue Jun 07, 2011 12:13 pm    Post subject: Reply with quote

Thanks for your reply Ron. I still think that 1 move is better than 2 but I respect your opinion. In a sense, the conjugate linked ALS's are quasi or psuedo ALS-XZ's since the 2 ALS's have the same rcd and logically there is no difference between a direct link and and indirect link between the rcd's in the 2 ALS's. In fact in the old forum I had a post about ALS-XZ's that were ER linked.

One other comment. This puzzle has a Sudoku Explainer (SE) rating of 8.3 which usually takes a lot of moves to work. The same is true of my almost doubly-linked ALS-XZ post. Since SE does not use ALS logic, one way I have found to reduce the number of moves is to look for ALS's.
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Tue Jun 07, 2011 1:02 pm    Post subject: Reply with quote

Bud wrote:
I still think that 1 move is better than 2 but I respect your opinion. In a sense, the conjugate linked ALS's are quasi or psuedo ALS-XZ's since the 2 ALS's have the same rcd and logically there is no difference between a direct link and and indirect link between the rcd's in the 2 ALS's.

How the digit <1> weak link is made between sets A and B has nothing to do with counting this as one move or two. The chain is terminated with both digits <7> and <8> in each instance.

(478=1)r3c123 - (1=3678)r3c7,r1c789
(478=1)r3c123 - (1)r2c2 = (1)r2c89 - (1=3678)r3c7,r1c789
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Bud



Joined: 06 May 2010
Posts: 47
Location: Tampa, Florida

PostPosted: Wed Jun 08, 2011 12:06 pm    Post subject: Reply with quote

I apologize Ron, My Bad. I now clearly see that the conjugate linkage is redundant. So your way is better. I will say that this is the most powerful singly-linked ALS-XZ I have ever seen. Because of the redundancy I need to trot out my other example.

605420301000050000408700900000080020300000007050010000003206508500090000002005004

After basic moves, the puzzle is as shown in the diagram below. The pattern of interest is in boxes 2 and 8. The ALS labeled A =1389. The ALS labeled B =138. These two ALS's do not even see each other so they need the help of the 3 conjugate labeled C and D in column 5. If C=3, A=189 and if D=3, B=18. In either case r2c4 and and r8c6<>18.

Code:

+--------------------+------------------+--------------------+
| 6     79     5     | 4      2   89A   | 3      78     1    |
| 1279  12379  179   |-136-89 5   1389A | 24678  4678   26   |
| 4     123    8     | 7      36C 13A   | 9      56     256  |
+--------------------+------------------+--------------------+
| 179   14679  14679 | 3569   8   3479  | 146    2      3569 |
| 3     28     1469  | 569    46  249   | 1468   14568  7    |
| 28    5      4679  | 369    1   23479 | 468    3468   369  |
+--------------------+------------------+--------------------+
| 179   1479   3     | 2      47  6     | 5      179    8    |
| 5     14678  1467  | 138B   9  -134-8 | 1267   1367   236  |
| 1789  16789  2     | 138B   37D 5     | 167    13679  4    |
+--------------------+------------------+--------------------+
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Wed Jun 08, 2011 7:20 pm    Post subject: Reply with quote

Bud wrote:
Because of the redundancy I need to trot out my other example.

Nice example. However, someone looking for smaller sets might first find ... (1=3)r3c6 - (3)r3c5 = (3)r9c5 - (3=81)r89c4 ==> r2c4,r8c6<>1
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Jun 08, 2011 9:10 pm    Post subject: Reply with quote

Ron, why didn't you use?

Code:
 (189=3)r123c6 - r3c5 = r9c5 - (3=18)r89c4  =>  r2c4,r8c6<>18
 +-----------------------------------------------------------------------+
 |  6      79     5      |  4      2      89     |  3      78     1      |
 |  1279   12379  179    |  13689  5      1389   |  478    478    26     |
 |  4      123    8      |  7      36     13     |  9      56     256    |
 |-----------------------+-----------------------+-----------------------|
 |  179    14679  14679  |  3569   8      3479   |  146    2      3569   |
 |  3      28     1469   |  569    46     249    |  1468   14568  7      |
 |  28     5      4679   |  369    1      23479  |  468    3468   369    |
 |-----------------------+-----------------------+-----------------------|
 |  179    1479   3      |  2      47     6      |  5      179    8      |
 |  5      14678  1467   |  138    9      1348   |  2      1367   36     |
 |  1789   16789  2      |  138    37     5      |  167    13679  4      |
 +-----------------------------------------------------------------------+
 # 125 eliminations remain


My alternative:

Code:
(18=3)r89c4 - r9c5 = (3-6)r3c5 = (6)r2c4  =>  r2c4<>18

The eliminations in r8c6 follow from a subsequent Hidden Pair.
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PIsaacson



Joined: 13 Jun 2011
Posts: 11
Location: Campbell, CA

PostPosted: Tue Jun 14, 2011 1:24 am    Post subject: Reply with quote

Bud,

Your last example, 2 ALSs linked via a conjugate, is what I would call a Death Blossom. I'm not sure where it was proposed, but it's not necessary for a DB to be confined to a single stem cell with ALSs hanging off as petals. The stem can be any set of mutually exclusive candidates with ALSs linked to each of the members. In this case, you have the bi-local 3 in column 5 acting as the stem of the DB.

Cheers,
Paul
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Tue Jun 14, 2011 1:43 am    Post subject: Reply with quote

PIsaacson wrote:
Your last example, 2 ALSs linked via a conjugate, is what I would call a Death Blossom.

I'm super-surprised you would take that position for a simple chain. We ought to be "reserving" the Death Blossom name for nets, not chains. Yes, I know there are examples to the contrary ... but I obviously don't agree.
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PIsaacson



Joined: 13 Jun 2011
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Location: Campbell, CA

PostPosted: Tue Jun 14, 2011 8:03 am    Post subject: Reply with quote

Ron,

I guess I view DBs as patterns rather than chains/nets. But being of the school that believes there's little (if any) practical difference between the two, I'll concede that the example is a also a fairly simple AIC containing 2 ALSs. Could you supply an example of a DB that satisfies the requirement of needing to be a net? I'm having trouble visualizing this - perhaps because I'm biased to seeing them as patterns???

Cheers,
Paul
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Bud



Joined: 06 May 2010
Posts: 47
Location: Tampa, Florida

PostPosted: Tue Jun 14, 2011 1:03 pm    Post subject: Reply with quote

Hi Paul,
First of all, let me say that Allan Barker initiated the Death Blossom. I have been able to contact him in the past to ask questions at his site Sudokuone.com and he is very gracious about answering. I think my last post is a good example of a death blossom. Your definition of the db in your first reply is accurate. The problem is you are equating conjugates to a stem cell which is a single cell with two or more candidates. I think Allan would simply call my example "multiple ALS logic". He also uses "single ALS logic" which is a combination of an ALS and conjugates.

Cheers,
Bud
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Tue Jun 14, 2011 3:33 pm    Post subject: Reply with quote

Bud wrote:
First of all, let me say that Allan Barker initiated the Death Blossom.

Mike Barker, not Allan Barker, initiated usage of the Death Blossom term here.

Unfortunately, there is no comprehensive definition for Death Blossom, Kraken Blossom, or Kraken/Death Blossom, just a small collection of examples which often don't yield the same conclusion. For the later, I don't even know if "Kraken" and "Death" are two different terms for the same thing, or if Kraken is a specific class of Death Blossom.

Moreover, many examples give one the impression that part of the definition is the requrement for an ALS at the end of each chain segment that sees the target, but I know of some Mike Barker examples where that's not true either
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DonM



Joined: 15 Sep 2009
Posts: 51

PostPosted: Wed Jun 15, 2011 6:01 am    Post subject: Reply with quote

Bud, here's another view about the subject above.

You may be aware of the following links, but your first post indicates you may not be. In the first thread below, you will find examples of ALS Chains using conjugate links just as you do above. The first 3 examples in the 2nd thread below are of the most common form of Death Blossom- which, in that form, is nothing but a 3-Set ALS Chain with a bivalue single-cell middle/second ALS set. There are more complex Death Blossoms, but you don't come across them very often. Incidentally, on the subject of Death Blossom as a net or not: I have the same view as Paul above: When it comes to patterns, the question as to whether the pattern is a net or not is not relevant. Pattern-solving does not involve recognition of nets vs. chains: patterns are patterns, nothing more, nothing less. However, I also agree that the pattern referred to was not a DB as I know it.

http://forum.enjoysudoku.com/als-chains-a-tutorial-asi-3-t6443.html

http://forum.enjoysudoku.com/advanced-als-chains-a-tutorial-asi-3b-t30098.html

The two ALS patterns you came up with are both the same: a 2-set ALS Chain using a conjugate link for the RC. (In this case, the term, 'set' refers specifically to an Almost Locked Set, lest the terminology police choose to make an issue of the number of sets.) They are clever finds in and of themselves and it takes skill to find them. Keep in mind that it is always easier for others to find 'simpler' patterns than the one you used to reach the same eliminations than it is for them to find your pattern in the first place. As one gets more skilled, one will find oneself waking up the next morning and simplifying one's own patterns.

Pattern-solving is a unique skill, different from finding chains. I started as a pure pattern solver and ended up also using AIC chains to solve more difficult puzzles, but the graduation to AICs does not make pattern-solving obsolete. If you find that you can increasingly find ALS patterns such as yours above, you will likely be able to not only find the eliminations from those patterns faster than someone who uses an AIC to find those same eliminations, but you will also be better able to find ALS patterns to use in AICS.

Pattern solving is not only useful in solving in general, it's also fun. As is indicated in the threads those two links refer to, one can often solve some puzzles with nothing but basic methods and ALS chains.

But to repeat myself: those were 2 nice finds, just the way they are.
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Bud



Joined: 06 May 2010
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PostPosted: Wed Jun 15, 2011 11:55 am    Post subject: Reply with quote

Thanks Don,
I learned a lot about ALS's from your tutorial. Also thanks to everyone else for your helpful comments.
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ronk



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PostPosted: Wed Jun 15, 2011 12:24 pm    Post subject: Reply with quote

DonM wrote:
The first 3 examples in the 2nd thread below are of the most common form of Death Blossom- which, in that form, is nothing but a 3-Set ALS Chain with a bivalue single-cell middle/second ALS set.

Which makes them ALS xy-wings, or simply ALS-xy patterns. Why baptize them with the Death Blossom name?
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DonM



Joined: 15 Sep 2009
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PostPosted: Wed Jun 15, 2011 3:24 pm    Post subject: Reply with quote

ronk wrote:
DonM wrote:
The first 3 examples in the 2nd thread below are of the most common form of Death Blossom- which, in that form, is nothing but a 3-Set ALS Chain with a bivalue single-cell middle/second ALS set.

Which makes them ALS xy-wings, or simply ALS-xy patterns. Why baptize them with the Death Blossom name?


Why indeed! That' exactly what 'Death Blossom...is nothing but a 3-Set ALS Chain with a bivalue single-cell middle ALS set' is meant to imply. Unfortunately, when it comes to confusing things, it is just this type of pattern that is used as an example of DB at Sudopedia and elsewhere.

But, on the same general subject, why further confuse the issue with confusing names like ALS-xz rule or ALS xy-wings or ALS-xy patterns as if they are distinctly different patterns rather than simply ALS patterns connected by RCCs with the only difference being the number of sets ie. ALS chains?
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ronk



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PostPosted: Wed Jun 15, 2011 4:11 pm    Post subject: Reply with quote

DonM wrote:
But, on the same general subject, why further confuse the issue with confusing names like ALS-xz rule or ALS xy-wings or ALS-xy patterns as if they are distinctly different patterns rather than simply ALS patterns connected by RCCs with the only difference being the number of sets ie. ALS chains?

Sure DonM, and while we're at it, let's just dispense with the xy-wing term and call those little thingies xy-chains.
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DonM



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PostPosted: Wed Jun 15, 2011 4:39 pm    Post subject: Reply with quote

ronk wrote:
DonM wrote:
But, on the same general subject, why further confuse the issue with confusing names like ALS-xz rule or ALS xy-wings or ALS-xy patterns as if they are distinctly different patterns rather than simply ALS patterns connected by RCCs with the only difference being the number of sets ie. ALS chains?

Sure DonM, and while we're at it, let's just dispense with the xy-wing term and call those little thingies xy-chains.


I concede the point that a single link does not a chain make, but that doesn't change the (IMO) more important point that the oft-used terminology for the single-link form of these structures creates the false impression that they are some sort of separate unique pattern and not simply the first link of will be a chain when there are 2 or more of them.

Edit: I hereby decree that the ALS-xz rule will be known as an ALS-link and the xy-wing known as the xy-link. Wink
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