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W-Wing

Points. W-Wings, like XY-Wings, are short chains made of three truths. The only difference is that the W-Wing has 2 cell truths and 1 row/column/box truth compared to the XY-Wing's 3 cells.  W-Wings are also rank 1. The truth in the center is linked on both ends to the 2 cells. The individual cells are bi-value and the total chain uses only 3 digits. Any digit that can see both ends of the chain cannot contain another candidate for this digit.

 

 

W-Wing Example 1, (row-truth) In this example, the center truth is the pair of digit 9s in row 6. The two cell truths are marked blue in r1c6 and r4c6. The digit 7 in r6c4 can see both ends of the chain and is thus eliminated.

 

Reasoning by truths and covers, 3 truths are covered by 4 covers thus anywhere 2 covers overlap will eliminate candidates.

 

 

 

 

W-Wing Example 1, (3D) A 3D view of the first example shows the looping chain clearly.

 

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