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Ron Moore

Joined: 13 Aug 2006
Posts: 72
Location: New Mexico

Posted: Mon Mar 26, 2007 6:10 pm    Post subject: XY-Wing

The diagram below shows the relevant portion of the example position given in the "XY-Wing" section of the Solving Guide (http://www.sudocue.net/guide.php#XYWing).

 Code: col 1                            col 6         .--------------------------------------. row 7   | 2    #13   35   |*45-1 *3456-1  7    | row 8   | 567   378  3589 | 2     3456    3469 | row 9   |*67-1  4   #39   |#19    8       1369 |         '-----------------'--------------------'

The cells marked with "#" (r7c2, r9c3, and r9c4) form the XY wing pattern, from which the eliminations of digit 1 in the cells marked with "*" can be made.

Below, I've used bold font to highlight a portion of the last sentence of the penultimate paragraph in this section of the Solving Guide.
The green and blue arrows visualize peer relations that play a part in the two alternative solutions to this pattern.
Perhaps I'm quibbling over English language usage, but I would interpret those words to mean that there are exactly two solutions for the cells in the XY wing pattern.

Of course there are more. For the cells r7c2, r9c3, r9c4, in that order we have the possible solutions
1,3,1
1,3,9
1,9,1
3,9,1
We can say that an XY ring has exactly two solutions, but we need at least four cells for such a pattern.
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