Find a cell with exactly three options, x, y or z (the pivot), that sees a cell that can only be x or z and another that can only be y or z. Whatever the pivot is, one of the three cells is z: a pincer, or the pivot itself. So no cell that sees all three can be z.
XYZ-Wing is the XY-Wing's bigger sibling. Because the pivot itself might be z, only cells that see all three cells can lose z, which usually means one or two cells next to the pivot.
It comes up when an XY-Wing almost works but the pivot has one candidate too many.
An XYZ-Wing
The pattern
Candidates removed
Solved as a result
R9C7 can only be 4, 6 or 7; R7C7 can only be 6 or 7, and R9C5 only 4 or 7. If R9C7 is 6, R7C7 must be 7; if it is 4, R9C5 must be 7; otherwise it is the 7 itself. Either way one of the three is the 7, so the 7 can be removed from every cell that sees all three: R9C8. That leaves R9C8 with only one candidate: 3.
This position comes from a puzzle generated on this site, after every single has been filled in. Boxes are numbered 1–9 from the top left, row by row; R5C4 means row 5, column 4.
How to spot it
1Look for a cell with exactly three candidates. Call them x, y and z.
2Find a cell it sees with only two of them, say x and z, and another with y and z. The digit they share is z.
3Look for cells that see all three: the pivot and both pincers.
4Remove z from those cells.
Why it works
If the pivot is x, the x/z pincer is z. If it is y, the y/z pincer is z. If it is z, it holds z itself.
So one of the three cells is always z, and a cell that sees all three can't be.
Common mistakes
Removing z from cells that see only the two pincers. With an XYZ-Wing they must see the pivot too.
Picking pincers with the same two digits. One must be x/z and the other y/z.
A pivot with more than three candidates. It needs exactly x, y and z.
Questions
How is it different from an XY-Wing?
The pivot has a third option, z. That covers one more case, so fewer cells lose z: only those that see the pivot as well as both pincers.
Why are there so few eliminations?
A cell has to see three cells at once, which usually limits it to the pivot's box.
What comes next?
W-Wing links two identical two-option cells through a digit that has only two places in a row, column or box.
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