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[Bud]

In this example the S-Wing cells are denoted by an * and the 45 pivot cell is r2c1. When I look for an S-Wing, I use transport on both of the pivot digits to find that either r4c2=4 or r7c2=5 which => r6c2<>4. But in this example, r4c2 or r7c2 must also be 6, so the only possibilities or r4c2=46 or r7c2=56. Hence the 129 cell eliminations. Essentially, the 6 conjugates make the 45 S-Wing pattern become a 456 continuous loop.
I'm not sure how common this is, but since I almost overlooked the 6 conjugate in this S-Wing, it is possible I may have overlooked this in other S-Wings that I have found. This also means that it is possible to find a Hybrid-Wing which is also a continuous loop. Although this is beyond the scope of this post, there is a second 78 S-Wing with a pivot at r8c8 and a hybrid wing with a 35 pivot at r6c9 in this puzzle. Neither of these is a continuous loop.

S-Wing Continuous Loop Example

[Luke451]

Good to hear from you again, Bud.

Descriptions of a move are nice. If you do notation, would it be possible to include it as well as the description? It would help a lot of us in picking up on the move, esp with all those typos in there.

If this is where you're going...

[Bud]

Hi Luke,
Good to hear from you again. I thought I was describing it, but I'll try to make this clearer. This isn't about a chain. It is about a 2 digit pattern technique called an S-Wing. This sometimes can be extended (see some of my other posts) and sometimes is a continuous loop as in this example. If you recall I made some posts at the old forum about 2 and three digt inclusive-or elimination techniques. These posts have since been lost. Both the S-Wing and the Hybrid-Wing are patterns that use this type of elimination. The logic is as follows. If cell A is 4 or cell B is 5, then A cannot be 5 and B cannot be 4. These are both possible S-Wing eliminations. But if 6 is a conjugate in cell A or cell B. Then the only possible candidates for cell A are 46 and cell B are 56. Note that all the 456 links in the continuous loop are already strong. To establish which is cellA and which is cell B start at the pivot. From the pivot there is a simple 4=not4 =4 path to cell A and a simple 5=not5=5 path to cell B in the pattern.

The intent of this poat is this. After finding an S-Wing what should one look for to see if this is a continuous loop? I think this is easier than finding a continuous loop from scratch.

I think I fixed the typos.

Bud

[Luke451]

Bud, it’s OK. I understood your first description, and I’m not trying to jam you up. When I said, “Descriptions of a move are nice,” I meant your descriptions were nice. It was a compliment .

I like the idea of pattern recognition. I like the idea of pattern recognition of S-wings. S-rings, even. I like “Any-Letter-Of-The-Alphabet”-wings. I’m very much down with seeing how to extend any wing into a loop, because that's where the power is.

My suggestion was only to throw in the notational version on the side, as an afterthought, if you are so inclined.

Your idea “is not about a chain,” but it can be expressed as such, and instantly recognized. When I know where you’re going, it’ll help me to more quickly learn the process you used to get there for yourself.

Maybe I’m just getting too mechanical….

[Bud]

Hi Luke,
There are a few more comments I'd like to make. I don't want to sound like an expert on NL's because I am far from it, but I think that it is safe to say that any S-Wing is an NL, so the only question is if it is continuous or discontinuous. If it is discontinuous, the discontinuity will occur in the link between what I called the A-cell and the B-cell. In this example this is a strong 6 link so the NL is continuous. I suspect that this is rare but an almost continuous S-Wing is probably less rare, and I have a strong interest in ALS almost continuous loop techniques.

I think my forte is pattern techniques. As a result I am very grateful for the 2 and 3 digt pattern techniques.

There are a handful of A-List AIC guys at Sudoku.com.au who use almost no other techniques. I am always amazed at how quickly they can pick out a useful multi-digit AIC. They could probably find this continuous loop directly. I am not programmed that way. I struggle when I use DNL's and when I use multidigit AIC's. I would have to review NL notation for the continuous loop, but I would have no objection if you want to add it.

[ronk]

Bud, I think you've posted an "extended" m-ring or s-ring. Non-extended wings/rings except for x-wings, have three strong inferences (links), not four. Also, an s-ring is also an m-ring.

[Bud]

Hi Ron,
You are the expert on terminolgy so I am willing to change the title to whatever you think it should be. The important thing to me is that the extra strong link is something to look for when you find an S-Wing. I thought about calling it an extended pattern but the number of cells is the same as if the strong link isn't there. Also, it is a 3 digit contiuous loop, whereas the M-Ring is a 2 digit continuous loop so I am confused.

Bud

[strmckr]

the s wing is two digits specifically

[Bud]

Hi Strm Ckr,
Good to hear from you again. As I see it an S-Wing is a 2 digit pattern, but it may also be a 3 digit S-Ring. The entire continuous-loop lies inside of a typical 5 cell S-Wing pattern. Nothing was added so it isn't really an extension. A simple way to solve any conflict with existing definitions is this. Put a simple statement in your S-Wing post sa follows.

"These patterns are S-Wings only if they are discontinuous NL's. Otherwise they are 3 digit S-Rings."

[strmckr]

i don't think they fit as a pseudo s-ring either as any of the patterns i have for s-wings to be continuous using two digits are already covered by m-rings

the overlap of cells with +1 digits is the kicker that allows the extension to contribute to addition eliminations.

the overlap is very specifically arranged in the case as well there is only 1 way for it to work

specifically the +1 digit is found in both end points sharing a common row,box,column.

if anything i would include it as a "check for overlapping strong links shared by the end points contained with in the s-wig shape.

[Bud]

OK, Strmckr I accept your interpretation of the continuous loop in the interest of harmony. I will no longer refer to this as a 3 digit S-Ring. It is simply a 3 digit continuous loop which should be looked for in an S-Wing pattern.

[ronk]