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W-Wing

Points. Both W-Wings and XY-Wings are short chains made of three truths. The main difference is that W-Wings have 2 cell truths and 1 row/column/box truth while XY-Wing's have 3 cell  truths.  The center truth is linked to the 2 end cell truths. The end cells are bi-value with the same digits and the full chain uses the same 2 digits. Any digit that sees both ends of the chain cannot contain another candidate of that digit. W-Wings and XY-Wings are both rank 1.

 

 

W-Wing Example 1, (row-truth) In this example, the center row truth (red) is formed by the two 4s in row 6.  The two end truths are cell truth (blue) formed by candidates 34 in r5c8  and a cell truth (blue) formed by candidates 34 in r7c5.


Candidate  3 in r5c5 sees both ends of the chain and is thus eliminated.

 


 

 


 

3D view of W-Wing Example 1


A 3D view of the above example clearly showing the chain's loop and intersection with elimination candidate 3r5c5.

 

W-Wing Example 2, (column truth) The second example is essentially the same as the first, except the center truth is now a column truth  (green).