XY-wing in Simple Sudoku

Advanced methods and approaches for solving Sudoku puzzles

Postby vidarino » Tue Jan 10, 2006 2:45 pm

ronk wrote:
tarek wrote:Most of XY wings have one of the braches having a Box relationship with the Stem, fewer examples invlove a strictly "Line" relationship for both branches, or a "Box" relationship for both:D

Do you have an example of a "Box" relationship for both?


Code: Select all
  13    x   12
   x    x    x
  32    x    x


A.k.a. Naked Triple.:)

(Edit: Well, not entirely "a.k.a", since there are naked triples that arent' XY-wings, but still... Close enough.) ;)
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Postby tarek » Tue Jan 10, 2006 6:27 pm

Now even for a naked triple to have a 222 formation in a box with no shared lines is also rare.

I haven't particularly looked for those in my database (the 5k database that is:) ), but if I find one I'll post it here.
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Postby tarek » Tue Jan 10, 2006 6:35 pm

vidarino wrote:
Code: Select all
  13    x   12
   x    x    x
  32    x    x

A.k.a. Naked Triple.:)


Although this is a valid examples of both, I think ronk was looking for an example where there are no lines shared by the candiates in the box. By the way it is interesting that in your example vidarino, as a naked triple we will miss all eliminations outside the box, then as we treat it as an XY wing the eliminations outside the box will happen.

[rearranging your example vidarino]

Code: Select all
  13    x    x
   x    x   12
   x   32    x


XY wing will only eliminate 1s from the boxes marked with an X
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Postby ronk » Tue Jan 10, 2006 6:50 pm

Hi tarek and vidinaro,

OK, OK, I'll acknowledge an xy-wing can degenerate into a naked triple ... but to call a naked triple an xy-wing is a stretch IMO. So I'm going to try to forget I ever asked the question.:D
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Postby vidarino » Tue Jan 10, 2006 8:18 pm

tarek wrote:
Code: Select all
  13    x    x
   x    x   12
   x   32    x


XY wing will only eliminate 1s from the boxes marked with an X


To continue (and hopefully end) our dead horse massacre, you can also eliminate 2s and 3s with the XY-wing rules, since the three pairs technically form three separate XY-wings. ;)
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