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  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.
It's 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
I have found an superb 'tough' Sudoku puzzle with a sequence of five Y-Wings and this illustrates teh full range of this strategy. The first three are pictured here but you can load the puzzle into the solver to see the remaining examples.

The first Y-Wing finds the AB cell in A2 which links 8 with the pair on B3 and the 3 in J2. Common to both the pincer cells is 4 which must go in either B3 or J2 so 4 in H3 can be removed. 		Y-Wing Example 1
Y-Wing Example 1: Load Example or : From the Start
The second Y-Wing gets two candidates because of the alignment in column 1. The 8s in B1 and C1 can both see the cells A2 and G1 which also contain 8. These pincer cells are linked to the pair [4,3] in J2.
 Y-Wing Example 2
Y-Wing Example 2: Load Example or : From the Start

The third step is included because it shows a very neat rectangular alignment which almost mirrors the theory diagram. You couldn't ask for a clearer example. 4 must go in B1 or D6 otherwise 7 and 8 would be used up and there'd be nothing to go in B6. The 4 in D1 is the lone candidate that can see the yellow cells and should be removed. 		Y-Wing Example 3
Y-Wing Example 3: Load Example or : From the Start


Go back to Multi-ColouringContinue to XYZ-Wings
 
Comments

Tuesday 28-Jun-2011

... by: Hans

Hallo Andrew,

Thanks for excellent explaining - although I got an other question.

y-wing explanations, figure 5, left side:
between green marked cells 18 and 15 there is the cell 12578 which contains also an 8. Why is this 8 not deleted?


Andrew Stuart writes:

Because that cell can't be "seen" by all the green ringed cells., only by two of them.

Sunday 17-Apr-2011

... by: senselocke

Thank you so much for the write-up, and the site as a whole.

Doing the step-by-step solving, with explicit reasons and links to the techniques, is exactly what I needed to be a better puzzler. Thank you so much!

Friday 15-Apr-2011

... by: zoph

I appreciate this Y-wing method/logic and follow the logic through your Figure 4 but Figure 5 baffles me.

I fail to understand the logic underlying one cell seeing another. Is it possible to easily explain the eliminations shown for Figure 5 without using the "seeing" concept.

Regarding Figure 5, and the "seeing" concept, could you explain exactly which cells see which other cells, why they do; and why some cells do not see other cells and why.

Thank you for your great site and your kind and patient instruction.

Tuesday 26-Oct-2010

... by: nihal

really good example. fantastic site.

Friday 17-Sep-2010

... by: Helen

Am I correct in assuming that finding a y-wing does not mean that the three cells forming the y-wing necessarily have to have those three numbers in the solution. It is only an eliminating strategy/

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: 118294
This page was last modified on 14-February-2012, at 08:08.
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Copyright Andrew Stuart @ Syndicated Puzzles Inc, 2012