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XY-Wing

Points. An XY-Wing is a short chain made of three bi-value cell truths. The cell in the center is called the pivot and the other 2 cells are called pincers. An XY-Wing uses only 3 digits usually named X, Y and Z. The pivot contains the XY candidates while the pincers contain candidates XZ and YZ. Any cell that can see both pincers cannot contain another candidate for digit Z. What Sudopedia says.

 

XY-Wing Theory, (row-column) There are two types of XY-Wings depending on which houses are lapping. The example on the right is a theoretical drawing of the row-column type. Note, there can be only one elimination.

 

In this example, the center cell is r4c5 with digits 4 and 9.  The 2 pincers cells contain the candidates 46 and 69 respectively for XZ and YZ.

 

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

 

 

 

 

XY-Wing Theory, (box-row) The other type of XY-Wing has overlapping box and row (or column) houses. The example on the right is a theoretical drawing of the box-row type XY-Wing. Note, this type can have two sets of overlapping covers and eliminate several candidates.

 

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

XY-Wing Example 1, (row-column) An example of a row-column XY-Wing from a puzzle.

XY-Wing Example 2, (box-row)  An example of a box-row XY-Wing from a puzzle. Note the two sets of overlapping covers that eliminate 2 candidates for digit 7.