Strategies for Number Puzzles of all kinds
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The Logic of Sudoku
  Y-Wing Strategy

This is an excellent candidate eliminator. The name derives from the fact that it looks like an X-Wing - but with three corners, not four. The forth corner is where the candidate can be removed but it leads us to much more as we'll see in a minute.

Lets look at Figure 1 for the theory.

A, B and C are three different candidate numbers in a rectangular formation. Three of the corners have two candidates AC, AB and BC. The cell marked AB is the key. If the solution to that cell turns out to be A then C will definitely occur in the lower left corner.If AB turns out to be B then C is certain to occur in the top right corner. C is a complementary pair. 		Y-Wing Figure 1
Y-Wing Figure 1
So whatever happens, C is certain in one of those two cells marked C. The red C can be 'seen' by both Cs - the cell is a confluence of both BC and AC.Its impossible for a C to live there and it can be removed.

In Figure 2 I'm demonstrating the sphere of influence two example cells have, marked red and blue. X can 'see' all the red cells, Z can 'see' all the blue ones. In this case there are two cells which overlap and these are 'seen' by both. 		Y-Wing Figure 2
Y-Wing Figure 2
If our A, B and C are aligned more closely they can 'see' a great deal more cells than just the corner of the rectangle they make. In Figure 3 BC can see AB because they share the same box. AC can see AB because they share the same row. BC and AC can see all the cells marked with a red C where this Y-Wing can eliminate whatever number C is. Y-Wing Figure 3
Y-Wing Figure 3
In this first example we have lots of 1s, 2s and 3s, but three cells - marked in green rings - form a Y-Wing. The two 2s on the end form the pincer - one of them must be a 2. Therefore the 2 marked in a red box can be eliminated.
 Y-Wing Example 1
Y-Wing Example 1: Load Example
The second example in Figure 5 shows three candidate 8s being eliminated from a single Y-Wing. The Y-Wing consists of 1/8, 1/5 and 5/8.
 Y-Wing Example 2
Y-Wing Example 2: Load Example

breakline

Comments...

Thursday 10-Jun-2010

... by: Reggie

With the techniques in your "Logic of Sudoku" book, I am only able to solve up to level 5 in Dr. Arto Inkala AI Escargot book. Level 6 to 10 make me feel like I know nothing about sudoku

Do you have another more advanced book? Where in the world can I learn strategies that will let me crack those Arto Inkala puzzles?

Friday 26-Feb-2010

... by: Vidyasagar

I have not seen such lucid explanation of XY wing as you have done. The reasoing given by you makes one understand this difficult concept.
thanks

Saturday 30-Jan-2010

... by: Ed Wieder

The Y-Wing explaination is very good. It can be improved on by being consistent in numbering examples and figures. It might also be mentioned that the Y-Wing can only be used when one of the canidates is not in the same 3X3 box where the other two are located.

Andrew Stuart writes:
Good point.

Tuesday 12-Jan-2010

... by: Jody

The image of the pincer really brought the Y-wing concept into focus.

Monday 11-Jan-2010

... by: William Balzar

Just learned the "Y-Wing" from your site.... WOW how elegant!!! I am like blown away. I will soon order that book. The best part of all of this is that there is still more to learn!!!! Like in that "Wayne's World" Movie: I am not worthy!!!

Bill (NOT over the hill and just 5 months from 65)

THANKS

Saturday 2-Jan-2010

... by: John

Nice work! I now can understand the Y-wing concept. Thanks for taking the time to teach those of us with lesser skills.

Tuesday 29-Dec-2009

... by: John Myfrianthousis

Brilliant! I am a medium-advanced player who often falls after a specific point. I believe now = especially with y-wing one I will recognize this formation

Thursday 17-Dec-2009

... by: ChandaMija

I call this a Crooked L-Wing. But I now get this. Thank you!

Tuesday 7-Jul-2009

... by: Malikov

Easy to understand concept.

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Article created on 11-April-2008. Views: 55655
This page was last modified on 11-April-2008, at 20:20.
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Copyright Andrew Stuart @ Scanraid Ltd, 2008