XY-Wing

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An XY-Wing is a mixed-digit alternating inference chain built from three bivalue cells. One bivalue cell contains candidates X and Y and serves as the pivot cell. The other two contain X and Z, and Y and Z, and serve as the pincer cells. Candidate X in one pincer and candidate Y in the other each form a weak link with the matching candidate in the pivot. If candidate Z in another cell forms weak links with candidate Z in both pincers, it can be eliminated.

X, Y, and Z can be any three distinct digits, as long as the structure has the form ZX-XY-YZ.

For example, in the board below, R7C7 is the pivot cell. Candidate 2 in R5C7 forms a weak link with candidate 2 in R7C7, and candidate 5 in R7C3 forms a weak link with candidate 5 in R7C7. So R5C7 and R7C3 are the two pincer cells. Here, candidates 2 and 5 play the roles of X and Y, and candidate 3 is Z. Candidate 3 in R5C3 forms weak links with candidate 3 in both pincer cells, so it can be eliminated from R5C3.

This is a very direct XY-Wing, with the pivot and the two pincers in different boxes and linked by a shared row or column.

When the pivot cell and one pincer cell lie in the same box, an XY-Wing can sometimes eliminate multiple candidates, as in the next example.