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[Victor]

Hope you like this one, M3723414 (108)
After basics:

[nataraj]

First an ER (box 7) kills 2 in r2c3 (via strong link in col 6). Alas, nothing after that. How about this not-quite-xy-wing then:

Pincers 89 in r1c4 and 78 in r8c2.
If r1c4<>8 then r1c3=2 then r1c1=6 then r3c1=7 then r4c1=8 then r56c2<>8 then r8c2=8.

Therefore r8c4<>8 which gives a naked pair 17 in col 4 and a few steps later I found a kite to remove 8 from r4c5.

Nice going, but here , again, a difficult position:

[Steve R]

The X-wing on 8 in columns 1 and 5 eliminates 8 from r9c6. This leaves its candidates as (12), matching r3c5 and forming a W-wing using the conjugates with respect to 1 in column 4.

The W-wing places 2 r3c5 but the X-wing/skyscraper on 7 is still needed to complete the puzzle.

Thanks, Victor.

Steve

[nataraj]

[Steve R]

I think perhaps you know it as a skyscraper rather than a (finned) X-wing.

Steve

[nataraj]

finned! of course!

neat.

Thx, Steve

____


N.B. The "un-finned" or original X-wing looks like this (click to get full article)

[Steve R]

That’s interesting.

This is Wayne Gould in Extreme Su Doku (Harper Collins, 2007):

[Victor]

Working from Nataraj's grid:
There is a UR elimination of the 7 in r5c2 (to avoid a DP of 78s in R56C2^, but I don't think it helps much. I too needed a finned thing in 7s, based on R49C19 to finish (killing the 7s in r4c78). Isn't it called a sashimi finned x-w, because the 7 in r4c9 is actually missing?

And to start with, I just used 2 ERs, one to kill the 2 in r2c3, the other the 8 in r9c6, which as you've pointed out gives a pair of 12s which are linked .... equivalently? - wish we'd a word for a TT/FF link like this. (I actually noted that now R9C6 = 1 => R3C5 = 1 AND R4C5 = 1, which => R9C6 <> 1.)

[Asellus]

[Earl]

Is there such a thing as a "finned skyscraper?"

In Nataraj's grid, consider the 7's in C19.
If R5C9 is not a 7, the resultant skyscraper eliminates 7's in R4C78;
If R5C9 is a 7, the same 7's are also eliminated.

Am I correct? Is there a name for it?

"Earl's Skyscraper?"


Earl

[nataraj]

[Asellus]

[Victor]

I'd agree with anyone who said that seeing this sort of thing as a "grouped skyscraper" is easier than as a finned x-w. But Sashimi sort of rolls of the tongue!

[Victor]

Asellus, about the only thing you've written of which I think "Mmmm - not sure" is this:

[Asellus]

Victor,

I think we may be talking apples and oranges here.

I was referring to the sort of link that exists, for example, in an ER:

[Victor]

As you say, Asellus, apples & oranges. Silly of me really - I do know what a grouped link is. I don't quite agree with you about the lack of usefulness of the sort of link that I meant. If nothing else, it's the basis for Keith's splendid M-wings. In your abc 34 example, b could be 74 say. Because the 4s are * linked, then so are the 3s: now you can continue colouring on 3s. In general, I have met chains of all-conjugate links: if there's an even number of links, then you can (for instance) continue the chain with a strong link in either direction to get a valid AIC, because you can think of an even number of conjugate links as Either weak then strong Or strong then weak. So although I totally agree that these links aren't of much use, I think they are of some use. In his M-wing thread Keith calls this link complementary, but I'm not enthusiastic about that term (love the idea, don't like this name).

And to finish, THE most confusing thing I found when I was reading up about new techniques was the terminology for links / inferences - e.g. "There's a strong link from Cell A to Cell B in number x, but actually it's a weak link." I once made the mistake of treating a strong link (ends of an XY-chain as far as I remember) as a conjugate link & tried to continue colouring an odd number of steps from each end. And I'm not the only one - I've seen other people make this sort of mistake. There are just 4 kinds of bi-directional link that we meet (I think). Why not have a distinct and appropriate name for each? It would protect us from the kinds of mistake I've mentioned.

[Asellus]

Victor,

I am afraid the M-Wing is not a good example of the usefulness of this "complementary" sort of link. An M-Wing is a simple AIC involving only the usual strong and weak inferences. The presence of the "complementary" link in the structure is an artifact of the bivalue cell pattern that the M-Wing involves.

In my abc {34} schematic, I did not assume that the <3>s or the <4>s are strongly linked with each other in any way. The cells marked with "." can be anything. However, if you replace "b" with {47} then, indeed, the <4>s in c2 and in r5 must be strongly linked in order to have the "complementary" link between the "ac" <3>s.

The pincers at the ends of, say, an XY Chain have a strong inference between them (and are not a conjugate pair), as you note. This means that they are each attached to the ends of an AIC (that of the XY Chain for instance) with a strong link.

In the case of a "complementary" link pair, they are attached to the ends of an AIC with dissimilar links: one weak and one strong. I know you are not fond of Eureka, but...

In the case of the three "abc" {34} bivalues, we can write:
(3=4)r3c2-(4=3)r5c2-(3)r5c6
or we can write:
(3)r3c2-(3=4)r5c2-(4=3)r5c6
Reading from left to right, in the first chain, the <3>s on the ends are both false. In the second chain, they are both true. Note that the <4>s in the row and column do not need to be conjugates.

Now, with {47} at "b", we must have conjugate <4>s in the row and column and the AICs are different:
(3=4)r3c2-(4)r5c2=(4-3)r5c6
or
(3-4)r3c2=(4)r5c2-(4=3)r5c6
Again, in the first chain both <3>s are false and in the second both are true. In the first chain, the <4>s in r5 must be conjugate and in the second the <4>s in c2 must be conjugate. Since the "complementary" link depends upon both of these chains, then both the r5 and c2 <4>s must be conjugate.

It is true that you could use this "complementary" link in <3> coloring to "jump" in your color chain (using them to have two adjoining "red" or two adjoining "green" <3>s). This amounts to a "multi-coloring shortcut." As such, then I suppose it is useful.

[tlanglet]

[CORUJA]

Thanks for the fine discussion! Learned a lot!
Seems I finally understood what a skyscraper is.

[Asellus]