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XY-Wing Chain

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Tue Sep 04, 2007 4:52 am    Post subject: XY-Wing Chain Reply with quote

This is the first one I've seen in awhile. When you have a chain of an odd number of cells with the same pair, the start and end of the chain act as the XY cell of an XY-Wing. Note the chain (ABC) of 35 cells in boxes 2 and 3. One end (A) sees D and the other end (C) sees E. The 2s in D and E act as pincers and knock out the 2 from r7c6. Not much help, but I thought I'd post it since it comes up only occasionally and never gets discussed here.

Code:

+--------------+------------+----------+
| 6    8   1   | 7   4 35A  | 35B 2 9  |
| 35   9   2   | 356 1 36   | 8   7 4  |
| 357  57  4   | 8   2 9    | 6   1 35C|
+--------------+------------+----------+
| 4    257 8   | 9   6 25D  | 257 3 1  |
| 257  3   57  | 4   8 1    | 257 9 6  |
| 1    6   9   | 25  3 7    | 4   8 25 |
+--------------+------------+----------+
| 278  27  367 | 1   5 268  | 9   4 23E|
| 9    1   36  | 236 7 4    | 23  5 8  |
| 258  4   35  | 23  9 238  | 1   6 7  |
+--------------+------------+----------+
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Wed Sep 05, 2007 11:20 pm    Post subject: Extended XY-wing? Reply with quote

Marty is exactly correct. I have used this technique a couple of times in a couple of years.

If an XY-wing is XZ-XY-YZ, it excludes Z at any cell that "sees" both of the end "pincer" cells. Then, XZ-XY-YX-XY-YZ makes the same exclusions.

I might call it an extended XY_wing. Except, we do not need any new terminology.

Name claims, anyone?

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Thu Sep 06, 2007 12:46 am    Post subject: Reply with quote

I first read about it at Scanraid, where it is called a Y-Wing Chain. However, he calls the XY-Wing a Y-Wing, so he's really calling this technique an XY-Wing Chain in the language most of us use.

I've used it four or five times and one of those times it was a five-cell chain.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sun Sep 16, 2007 3:57 pm    Post subject: Reply with quote

Hey Marty,

This is the thread I was fuzzily remembering when I referred to an "extended XY-wing" in this thread, but I thought you originated that term, not Keith. And apparently my remembering was really fuzzy, because what I used there and what you used here aren't the exactly the same.

Since I often complain about others use of what I consider redundant or unnecessary terminology, and then go and do it myself in an incorrect manner to boot, I guess I should be banned from posting for a week and made to do only puzzles with hidden singles. Sad
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Sun Sep 16, 2007 9:11 pm    Post subject: Reply with quote

Quote:
but I thought you originated that term


I'm sorry to say that when it comes to Sudoku, I have originated NOTHING. Embarassed
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Mon Sep 17, 2007 1:23 am    Post subject: Reply with quote

For my 2 cents...

Hearing only the term "XY-Wing Chain" I would have imagined that it referred to an AIC that employed one or more XY-Wings as a node. Needless to say, that's not what is explained here.

What is explained here is an XY Chain that just happens to have some identical bivalues in the middle. I don't see why that merits a new name to learn. If one learns the XY Chain name/technique, then one has this puppy covered!
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