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[Marty R.]

I offer this one up only because I used a variety of techniques, some of which aren't everyday for me. All in all, I played eight moves, but usually people can find ways to solve puzzles more quickly than I can.

[nataraj]

this, I think, is the first "crunch" point

[storm_norm]

nataraj, that was so nice

and just in case anyone was puzzled at the first grid in nataraj's post, there is a xy-wing present in the grid after basics which eliminates the 2 in r3c8. but after that, its smooth sailing with those sweet W and M wings.

[daj95376]

[Withdrawn:]

[cgordon]

To get to the same position as the last posted grid I used:
an xyz wing <456>
an ER on <8> (from R5)
and an xy wing <237>

But I also used what I think is an extended xy-wing - except I'm not really clear on these. In the grid below - is the <4> in R7C7 a victim.

[cgordon]

Here’s another question for anyone out there. See the two 5’s in C4. The bottom one uses the ER hinge in Box6 to remove the 5v from R1C6. The top one leaves the 5a in R1C2 which also removes the 5v. Now is this elegance or just a form of trial and error?

[Marty R.]

[nataraj]

I use the term "extended xy-wing" in two situations. Both involve pincer cells with two candidates each: xa .... bx, but the connection is not made by a single cell ab, but is a little wider (hence "extended", like in extension cord):

a) the connection is made by TWO cells xa-an-nb-bx (the n-n really looks like an extension cord, doesn't it?)

b) the connecting cell ab is repeated an odd number of times: xa-ab-ab-ab-bx

ALL of these (including the "simple" xy-wing) are, of course, xy-chains. That's why I don't fancy the term xy-wing-chain.

[Asellus]

[cgordon]

Asellus: Thanks for explanation. I like the "transported pincer" thing. I've seen the term used quite a bit recently. Seems it's not as complex as it sounds. In fact, my other post for this puzzle asked if a solution was an extended xy wing. Unless I'm mistaken - these also involve transported pincers.
I kinda understood the colour wing alternative but had to struggle a bit with the with the choice of 5B or 5b in C2. Need more time for that one.

Cheers, Craig

[Asellus]

Craig,

You're welcome.

I don't see your extended XY Wing (or XY Chain) as what folks usually mean by pincer transport. The pincers are the two <4>s. In a transport, you would find a third <4> somewhere in the grid that must be true when one of the pincer <4>s is true. Then, that pincer <4> is "transported" to that third <4> and can produce eliminations against the other (non-transported) pincer. Instead, what you did in this case is take something that can be seen as based upon a basic XY Wing and "extended" the pincer ends to new locations from where they might otherwise be. You are still dealing just with two pincer <4>s, so there's no transport as such.

As for the coloring, I should stress that the letters used for coloring are just symbols. If you're wondering how I chose to color the <5> in r2c2 "5b" instead of "5B", my answer is that it doesn't matter. However, since there is a choice, it is easier to visualize the strong and weak pairs if they share upper or lower case. So, since there is a 5a in row 2, I find it easier to assign "b" to the <5> in r2c2. That way, the weak pair is lower case, "ab", and the strong pair upper case, "AB".

If there had, instead, been "5A" in row 2, I would do it the opposite way, with "5B" in r2c2. Then, "AB" would be weak and "ab" would be strong and perform the eliminations.

You could mix the upper and lower cases if you like, since they are just symbols. So, you could have "aB" as the weak pair and "Ab" as the strong pair. But, this makes it a bit trickier to see the correct eliminations in the grid. (In more advanced multi-coloring, with many different simultaneous clusters, this mix of symbols is unavoidable. But, that's for when you are ready to go whole hog with coloring!)

The essential point in multi-coloring is to understand that one or both of the weakly linked colors (in row 2 in this case) between the two clusters must be false and, therefor, one or both of the colors complementary to these must be true (that is, they become strongly linked to each other in the same way that pincer digits are strongly linked). Once you are comfortable with that, multi-coloring with two clusters should be an easy thing to add to your arsenal.

[Myth Jellies]

[tlanglet]