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[keith]

Here is the generalized XY-wing:

[Asellus]

As long as those cells are all bivalues, as seems to be the case, then there is no need for a strong link on S. It is just an XY Chain. Perhaps I'm missing something.

[storm_norm]

ZX...XS...SY...YZ

Z(X...X)(S...S)(Y...Y)Z

23...34...45...52

2(3...3)(4...4)(5...5)2

(2=3)-(3=4)-(4=5)-(5=2)... cells in ()... this is an AIC.

in all xy-chains, which this is, the first and last candidate has to be the same and the cells have to be bivalue. therefore creating a pincer and eliminating any other candidates they see.

this is also called a bidirectional y-cycle because you can make the same chain in both directions and the candidate not used in connecting the prior two cells must be used to connect the next two. thus called "y". and the cells must "see" each other.

so you would logically look for bivalue cells that have one number in common...( and can see each other ) (2,3) with (3,4) then (4,5) then (5,2) creating a pincer with candidate 2.

if 2 than not 3, 3 than not 4, 4 than not 5, 5 than not 2... then reverse...

if 2 than not 5, 5 not 4, 4 not 3, 3 not 2

so when seen in both directions, either end has to have a 2 thus eliminating any 2's the two ends see.

this works because the cell with two candidates is actually a strong link...cell (2,3) is 2=3 ... so am I correct that this is a formation of a AIC?? strong link for each cell, weak when connecting cells. srong-weak-strong-weak-etc. two directions?? I just want to be sure of that.

this is the same foundation that a w-wing is based on... and the xy-wing is a three cell xy-chain. its the same technique.

the misconceptions about what is and isn't a xy-chain might stem from the multitude of bivalue cells and the numerous geometric shapes they create around the puzzle board and possibly what kind of eliminations they do make, but all in all, it has its roots in one particular technique.

IMO, the hardest xy-chains to spot have 3 or more cells in the same row or column and don't interact in any specific order. the chain then overlaps but still works.

[Asellus]

[storm_norm]

the three cell xy-chain or commonly known as the xy-wing

23...34...42

2(3...3)(4...4)(2

[Victor]

Norm, you've written slightly carelessly - a syndrome that I'm personally very familiar with!