Good, complete explanation of XY wings

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Good, complete explanation of XY wings

Postby mchassoc » Thu Aug 06, 2015 7:28 pm

I have read several explanations of XY wings, and have attempted using this technique. However, using my understanding, most times it gives a good result, but not always. Therefore I conclude that I do not have an all inclusive understanding of the method. I'm hoping someone has the patience to give an all encompassing explanation of this powerful "trick".
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Re: Good, complete explanation of XY wings

Postby JasonLion » Thu Aug 06, 2015 10:21 pm

Have you read the Sudopedia description, or SadMan Software's description?

While neither is "ideal", both are reasonably good.
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Re: Good, complete explanation of XY wings

Postby mchassoc » Thu Aug 06, 2015 11:57 pm

Jason, thank you so much: the Sudopedia explanation is both succinct, complete in explanation, and the reasoning is clearly presented. It is undoubtedly my lack of completely following previously read descriptive reasoning behind the method that did not allow consistent results. I thought only two of the three had to "see" one another (for which XY wings would be much easier to spot), and that this would allow deleting the common candidate that could see the two pincers. Its now obvious why that is not feasible.

My wife and I were introduced to Sudoku about 5 years ago and have made good progress in solving some of the most difficult puzzles. We have completed solutions in Steve Soto and Monica Jones "Soduko Puzzles, Hard to Very Hard", and are presently more than 1/3 through Frank Longo's "Beyond the Black Belt", encountering very few puzzles that we cannot solve. Most of these I have been able to solve using only Chad Barker's "1 to 9" technique over and over. But on a few a more sophisticated "trick" was required. I am just now starting to investigate solutions based on use of the SAS method.

Early in learning Sudoku I wrote a short computer macro to populate all candidates for all cells in any given puzzle. Once a cell candidate, or group of candidates, is determined the macro can be rerun, eliminating unnecessary candidates from all cells. These are eliminated based on "no legitimate candidate can occupy more than one cell on the board". Whereas we don't use this "Sudoku Aid" in the solving process, it is comforting to use it as a check.

Thanks again for solving my quandary re XY wings.

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Re: Good, complete explanation of XY wings

Postby mchassoc » Sat Aug 08, 2015 4:46 pm

Pardon me for responding to my own inquiry. After reading Jason Lion's reference recommendations, followed by a few applications in actual potential XY wings, I concluded that there are only two conditions that need be satisfied to determine if candidate(s) can be eliminated by this technique. First, the definitions: an XY cell is called the "pivot", the XZ and YZ cells are "pinchers"; also the word "share" between two cells means "be in the same row, or column, or box.

(1) Each pincher must share with the pivot. (2) Any candidate for elimination must share with both pinchers. That's it!

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