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x-y wing

 
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Poppa
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PostPosted: Mon Oct 31, 2005 5:58 pm    Post subject: x-y wing Reply with quote
I'm new at this and I must admit I thought I was pretty clever but you guys are WAY ahead of me. Is there anywhere I can go to see a quick-and-dirty review of techniques and shorthand without taking another college course in symbolic logic? Wink
By the way, what is an x-y wing?
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
PostPosted: Mon Oct 31, 2005 7:13 pm    Post subject: Techniques; "XY-Wing" Reply with quote
Poppa wrote:
Is there anywhere I can go to see a quick-and-dirty review of techniques and shorthand without taking another college course in symbolic logic? Wink

The SadMan Software site has a good introduction to several advanced techniques.

Poppa wrote:
By the way, what is an x-y wing?


The "XY-Wing" is a formation that appears in some Sudoku puzzles. In general, there are four cells in the formation, and the information in three of the cells allows us to eliminate one possibility from the fourth cell. Here's an abbreviated example.
Code:
 1/5   .    .    .    .    .   1/8   .    .
  .    .   5/7   .    .    .   1/7   .    .
  .    .    .    .    .    .    .    .    .

In this example the only values possible at r1c1 are {1, 5}; the only possibilities at r2c3 are {5, 7}; and the only possibilities at r1c7 & r2c7 are {1, 8} and {1, 7} respectively. We can reason as follows:
If r2c3 = 5 then r1c1 = 1 and r1c7 = 8.
If r2c3 = 7 then r2c7 = 1 and r1c7 = 8.
Either way, r1c7 = 8, so r1c7 must be an "8".

The logic works just as well in reverse:
If r1c8 = 1 then r1c1 = 5 and r2c7 = 7.
But then there's no way to fill in r2c3.
Therefore r1c7 cannot be "1", and it must be "8".

There are a lot of examples of "XY-Wing" over in the Other puzzles section of this forum. dcb

Last edited by David Bryant on Wed Nov 02, 2005 5:12 pm; edited 1 time in total
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Lulu



Joined: 21 Sep 2005
Posts: 11
Location: Manchester, England
PostPosted: Wed Nov 02, 2005 4:39 pm    Post subject: X-Y wing Reply with quote
David

At last you've explained X-Y wing in simple terms that I can finally understand.
Thank you very much.
Lulu
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