An XYZ-wing upgrades the XY-wing’s pivot from two candidates to three: the pivot holds X, Y, and Z, and its two pincers hold {X,Z} and {Y,Z}. All three cells now contain the shared digit Z — and that changes where the eliminations land.
Run the cases. If the pivot is X, the {X,Z} pincer collapses to Z; if it is Y, the {Y,Z} pincer does; and the pivot may simply be Z itself. One of the three cells is always Z — so only a cell that sees all three of them can be cleared. That is a smaller net than the XY-wing casts, which is why this pattern pays less often, but just as decisively.
To spot one, start from cells with exactly three candidates and try them as pivots: the pincers are bivalue cells it sees whose candidates are drawn entirely from the pivot’s three. Because an elimination cell must see the pivot and both pincers, it always shares a house with the pivot — look in the pivot’s own box first.
On the board
The pivot is R8C6, holding {3,5,6}. Up column 6 it sees the pincer R2C6 {5,6}; along row 8 — inside the bottom-middle box — the pincer R8C4 {3,5}. If R8C6 is 6, R2C6 becomes 5; if it is 3, R8C4 becomes 5; and R8C6 can be the 5 itself. Every case puts a 5 in one of the three cells. R7C6 sees all three — it shares column 6 with the pivot and R2C6, and the box with R8C4 — so its 5 is struck, taking the cell from {5,6,9} to {6,9}.
This is the exact board the app's interactive XYZ-Wing demo uses — step 32 of its 76-step walkthrough, drawn here with its live pencil marks.
