dailysudoku.com

[Bud]

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

[Mogulmeister]

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

[daj95376]

[Withdrew alternate perspective and alternate solution.]

[Bud]

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.

[Mogulmeister]

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

[ronk]

[Bud]

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.

[ronk]

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.

[Bud]

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.

[Mogulmeister]

[ronk]

[Mogulmeister]

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