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Almost Doubly-Linked ALS-XZ Example

 
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Bud



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

PostPosted: Mon Aug 02, 2010 1:11 pm    Post subject: Almost Doubly-Linked ALS-XZ Example Reply with quote

This example has 3 almost patterns which are linked by the restrictive common digit (rcd) 8. When A=27 it forms a doubly-linked (DL) ALS-XZ with the ALS labeled B. This ALS-XZ gives 1 an 9 cell eliminations in column 3 as shown. It also gives 2 cell eliminations in column 2 box1 but this is not useful here. When A=8 ALS R2C3 becomes a locked single 9 and the ALS B becomes a locked set 1679. These ALS's also result in the same 1 and 9 eliminations as the ALS-XZ. Therefore the 1 and 9 eliminations are valid independent of whether the DL-ALS-XZ is true or false. In fact in the final solution to the puzzle it is false. A more general name for this example is almost continuous loop (ACL). Unfortunately, the only other ACL example I have at this time is another DL-ALS-XZ. I do have a number of almost examples some of which I may post in the future.

Almost Doubly-Linked ALS-XZ Example
Code:

 |-------------------+--------------------+--------------------|
 |  278A  124  127B  |   25    34     9   |    6    35     78C |
 |    5     3    89B |   67    17   167   |  289    29      4  |
 |    6    249  279B |   25    34     8   |   35     1     79C |
 |-------------------+--------------------+--------------------|
 |   28     7   -136 |    9    28     5   |    4    36     16C |
 |    4    159  189B |   78     6     3   | 1579   579      2  |
 |   29   2569 236-9 |    1    27     4   | 3579     8    679C |
 |-------------------+--------------------+--------------------|
 |   279   8     4   |    3   179  1267   | 1279  2679      5  |
 |    1    269  267-9|  678     5   267   | 2789     4      3  |
 |    3    269    5  |    4  1789  1267   |  1279 2679  16789  |
 |-------------------+--------------------+--------------------|


This puzzle is the Sudoku.com.au daily tough July 5, 2010. An 8 swordfish is the only advanced move I used to reach this point in the puzzle.
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Thu Aug 05, 2010 8:26 pm    Post subject: Reply with quote

That is beautiful Bud. It deserves the full coloured square treatment!
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Aug 05, 2010 10:10 pm    Post subject: Reply with quote

[Withdrew alternate perspective and alternate solution.]

Last edited by daj95376 on Fri Aug 06, 2010 6:43 am; edited 1 time in total
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Bud



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

PostPosted: Fri Aug 06, 2010 2:30 am    Post subject: Reply with quote

Hi Mogulmeister and DAJ,
DAJ, a doubly-linked ALS-XZ is one that has 2 restricted common digits. When this occurs the ALS-XZ is a continuous loop and eliminations are possible for all the digits. In this example 2 and 7 would be the rcds. If R1C1 is either of these, then B becomes a locked set.
The overall pattern works something like an ALS-XZ. The rcd for the overall pattern is 8. If R!C! is not equal to 8, the dl-ALS-XZ is true. If R1C1 = 8, then the 2 ALS's both become locked sets. Either way you get the 1 and 9 eliminations.
This is a general technique for making any almost pattern that can be linked to one or more ALS useful. It really isn't new, because I am borrowing from techniques that have been used for ALS"s for some time. One example I have resembles an ALS-XY-Wing with a bivalue pivot cell which is linked to an ALS and an almost XY-Wing. I will be posting other almost examples as time permits.
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Fri Aug 06, 2010 8:17 am    Post subject: Reply with quote

Thanks Bud - that will be good -- I am (as you can see from some of my solutions) interested in almost ALS patterns.
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Fri Aug 06, 2010 11:21 am    Post subject: Re: Almost Doubly-Linked ALS-XZ Example Reply with quote

Bud wrote:
When A=8 ALS R2C3 becomes a locked single 9 and the [edit: ALS C] becomes a locked set 1679. These ALS's also result in the same 1 and 9 eliminations as the ALS-XZ. Therefore the 1 and 9 eliminations are valid independent of whether the DL-ALS-XZ is true or false.

You have an almost [edit: doubly-linked] ALS-xz for r68c3<>9 and an ALS chain for r4c3<>1. IOW ALS C has nothing to do the exclusions for digit 9. In chain form:

In AIC notation:
(9)r68c3 - (9=8)r2c3 - (8=27)aals:r1c1 - (27=189)als:r1235c3 - (9)r68c3 => r68c3<>9

(1)r4c3 - (1=8927)als:r1235c3 - (27=8)aals:r1c1 - (8=7)r1c9 - (7=591)als:r346c9 - (1)r4c3 => r4c3<>1

And in NL notation:
r68c3 -9- r2c3 - 8- aals:r1c1 - 27- als:r1235c3 -9- r68c3 => r68c3<>9

r4c3 - 1- als:r1235c3 - 27- aals:r1c1 -8- r1c9 - 7- als:r346c9 -1- r4c3 => r4c3<>1

Note that dual links are required between an AALS and an ALS. For the ALS chain, r1c19 could be viewed as an ALS, but the chain notation then becomes awkward.


Last edited by ronk on Fri Aug 06, 2010 1:37 pm; edited 1 time in total
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Bud



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

PostPosted: Fri Aug 06, 2010 1:15 pm    Post subject: Reply with quote

Hi Romk,
I agree that the ALS C has nothing to do with the 9 eliminations when it is locked at 1679, but I needed this locked set for the 1 elimination. That's why I also needed the locked single 9 in R3C2. This is what gives the 9 eliminations. As I look at the quote this is not very clear in my initial writeup and maybe I should edit it for clarification.
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Fri Aug 06, 2010 1:46 pm    Post subject: Reply with quote

Bud, in my experience an almost-"anything" rarely, if ever, has the same exclusions as the "anything." To search for additional strong inferences to make it the same, well ... it seems labored to me.
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Bud



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

PostPosted: Sat Aug 07, 2010 1:50 am    Post subject: Reply with quote

Ron.
You have a valid point. If for example I had to use a long chain to link the almost dl-als-xz to an ALS it may be better to use a chain for something else. But in this example there is a direct rcd link between the ALS's and the almost pattern. Also one of the ALS's is a bivalue cell. Finding these was not laborious.
In this example I did get the 1 and 9 eliminations of the dl-ALS-XZ but I made no attempt to get the 2 eliminations. I do have an example in which I get the same eliminations for the almost anything as for the anything. I will post it when I have more time. I think you have to consider the labor on a case by case basis.
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Mon Aug 09, 2010 12:22 pm    Post subject: Reply with quote

Bud wrote:
Ron.
Finding these was not laborious.


Agreed - got to say I enjoy it. Smile
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Mon Aug 09, 2010 2:07 pm    Post subject: Reply with quote

Mogulmeister wrote:
Bud wrote:
Ron.
Finding these was not laborious.

Agreed - got to say I enjoy it. Smile

There are meanings for 'labored' other than 'laborious.'
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Mon Aug 09, 2010 3:12 pm    Post subject: Reply with quote

I was seconding the word Bud used which was "labourious*" and, I suspect, one of the more common synonyms of laboured* but I do appreciate the subtle differences. I am still fighting the good fight with "disinterested" and "uninterested".

Labored also means someone who has had enough of Los Angeles.

*Pardon my English English
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