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.