XYZ-Wing
An XYZ-Wing is a three-cell elimination pattern — the bigger sibling of the XY-Wing. The pivot cell has three candidates, and two pincer cells each see the pivot with overlapping candidate pairs. Whichever value the pivot takes, one of the three cells must hold the shared digit, so any cell that sees all three can have that digit eliminated.
What is an XYZ-Wing?
An XYZ-Wing is a three-cell pattern built on the same idea as the XY-Wing, but with a key difference: the pivot cell has three candidates {X, Y, Z} instead of two. Two pincer cells each see the pivot — one has candidates {X, Z}, the other has {Y, Z}. The pivot must be X, Y, or Z. If it's Z, the pivot itself holds Z. If it's X, the first pincer can't be X (it sees the pivot), so it must be Z. If it's Y, the second pincer can't be Y, so it must be Z. In every branch, one of the three cells ends up with Z. Any cell that sees all three — pivot plus both pincers — can't be Z, so Z gets eliminated from it. The catch is that the elimination target is smaller than an XY-Wing's: a cell must see all three pattern cells, not just both pincers, because the pivot itself might be the one holding Z.
How to spot it
XYZ-Wings are rarer and harder to spot than XY-Wings because the pivot needs three candidates and the geometry has to line up just right. The way in is to scan for cells with exactly three candidates that share a house with two other bivalue cells. Once you've found a candidate pivot, check whether two of its candidates appear as a pair in cells that see it — those are your pincers. The shared candidate across all three cells is the one you can eliminate. Because the elimination only hits cells that see all three, the target zone is tight, so XYZ-Wings often remove just one or two candidates. They're worth checking once you've exhausted singles, subsets, and the simpler wings.
The logic
The pivot has candidates {X, Y, Z}, so it must take one of those three values. The first pincer has {X, Z} and sees the pivot, so it can't take the same value the pivot takes. The second pincer has {Y, Z} and also sees the pivot. If the pivot is Z, the pivot holds Z. If the pivot is X, the first pincer can't be X and must be Z. If the pivot is Y, the second pincer can't be Y and must be Z. Every case forces Z into one of the three cells, so any cell that sees all three can't be Z itself. That's why the elimination requires visibility to all three cells rather than just the two pincers — unlike an XY-Wing, where the pivot only has two candidates and can never hold the shared digit, here the pivot might be the one carrying Z.