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[Asellus]

Marty,

I agree with nataraj that, to some extent, T&E is in the eye of the beholder. I also believe that it has to do with the level of ones solving skills. An involved AIC looks like total T&E to someone who hasn't developed a comfort level with the implication concepts and with the sorts of links contained in various patterns. But someone who has come to look at a grid in terms of those patterns and links starts seeing such chains without spending time going: "If this is true, then that is true, that over there is false, then..." And, in really difficult puzzles, advanced coloring techniques are often necessary to help ferret out such implication chains. The coloring approach is itself a way of avoiding outright T&E, even if the coloring only gets one part way there.

For some, an XY Chain seems like T&E. It is true that you must often try various sequences of chained bivalues until you find a pair of useful pincer digits. But then, you usually have to try many sets of bivalues before you find a useful XY wing. Or, you have to try many different conjugate links in rows and columns before you find a useful X-Wing (and victimless X-Wings are often found when searching for X-Wings). This is true of any named technique: you TRY to find the pattern, not always succeeding (ERROR) and other times succeeding only to find there are no victims (ERROR again) and then occasionally succeeding. So, that is T&E, too. But nothing ventured nothing gained!

Using your grid, there is the straightforward XY Chain:
(7=9)r2c1 - (9=7)r7c1 - (7=3)r7c6 - (3=5)r7c8 - (5=8)r1c8 - (8=7)r3c9; r2c9|r3c3<>7

If that is accepted as not stepping over the T&E line, then why not also allow the use of a multi-cell ALS node rather than just bivalues? For instance, we could achieve the same thing with a slightly different chain:
(7=9)r2c1 - (9=7)r7c1 - (7=9)r8c3 - (9=6)r8c9 - (6=8)r9c8 - (8=7)r9c7 - (7=3)r8c7 - ALS[(3)r2c7=(8)r2c7|r1c8] - (8=7)r3c9; r2c9|r3c3<>7

It's really no different from the first chain (other than length). Both exploit easily seen patterns (ALS's) using a common underlying logical structure (alternating strong-weak inferences). By the way... this is a good time to mention that a "finned locked set" already has a name: ALS!

If we haven't yet crossed the line, then why not also exploit plain old conjugate links within such chains? That last chain can be shortened nicely by using the conjugate <3>s in r8:
(7=9)r2c1 - (9=7)r7c1 - (7=3)r7c6 - (3)r8c6=(3)r8c7 - ALS[(3)r2c7=(8)r2c7|r1c8] - (8=7)r3c9; r2c9|r3c3<>7

And, if that's okay, then how about exploiting the strong links induced in the extra digits of a UR? Here, we have (9)r2c3=(6)r2c9 induced by that 78 UR. Is it T&E to notice that the <9> in r2c3 sees conjugate <9>s in b7 and the <6> in r2c9 sees a {69} bivalue in r8? This gives what I consider to be a very elegant chain:
(9)r7c1=(9)r8c3 - UR[(9)r2c3=(6)r2c9] - (6=9)r8c9; r7c9|r8c3<>9

And then there's that "finned X-Wing" where we now allow a wing-induced link to serve as a node in our chain:
(3=7)r7c6 - XY-Wing[(7)r8c6=(7)r9c6|r8c7] - (7=8)r9c7 - (8=6)r9c8 - (6=3)r2c8; r7c8<>3

It is just an XY Chain with a "finned XY-Wing" node included. All of these chains have the same fundamental structure. The difference is merely one of ones ability to spot and exploit the various sorts of possible "nodes" (strong inferences) of the chain. Or at least that's how I see it.

[ravel]

I never liked these t&e discussions and fully agree with Asellus.

In my eyes this is just the wrong question. The right one is: What is a good way to continue, when you are stuck with your usual arsenal of techniques ?
Looking for xy-chains or multiple forcing chains is rather boring for me. There are so many possibilities to start without any way to decide, which is more promising. How long should i try, before i give up ? 5 cells, 7 cells, 10 or until i am stuck again or the puzzle is solved ?
So i prefer to explore the "almost" and "useless" patterns (like URs and wings) i already found.

No one posted full solution paths for the easy versions.

Here are mine:

Puzzle 1: UR, xy-wing
Puzzle 2: UR, BUG
Puzzle 3: wapati pointed out, that both versions solve with the finned x-wing (and a kite). The 2 URs are not needed.

Puzzle 4:
After the UR 18 and basics.

[wapati]