Like an XY-Wing, but the pivot has three candidates instead of two. Eliminations are restricted to cells seeing ALL three pattern cells.
An XYZ-Wing is the bigger sibling of the XY-Wing. The pivot cell has three candidates {X, Y, Z} instead of two, and connects to two wing cells: one with {X, Z} and one with {Y, Z}. The shared digit Z must appear in at least one of the three cells, so any cell that can see all three cannot be Z.
The crucial difference from XY-Wing is the elimination zone. In an XY-Wing, the pivot has two candidates and the elimination digit isn't in the pivot, so you can eliminate from cells seeing just the two wings. In an XYZ-Wing, Z IS in the pivot too, so you can only eliminate from cells that see ALL three cells (pivot and both wings). This makes the elimination zone much smaller.
Because of this restriction, XYZ-Wings are most useful when the pivot and one wing share a box, and the target cell is in that same box while also seeing the other wing.
Find a pivot cell with exactly three candidates {X, Y, Z}. Find two wing cells connected to the pivot (sharing a row, column, or box): one wing has {X, Z} and the other has {Y, Z}.
The digit Z appears as a candidate in all three cells. No matter how the puzzle resolves, at least one of these three cells must contain Z: if the pivot is X, wing 1 must be Z. If the pivot is Y, wing 2 must be Z. If the pivot is Z, done.
Therefore, any cell that can see all three pattern cells (pivot + both wings) cannot contain Z, it would conflict with whichever cell Z ends up in. Find such cells and eliminate Z from them.
Example 1: XYZ-Wing
Pivot R3C3 has candidates {1, 3, 8}. Wing R2C1 has {1, 3}, and wing R3C4 has {1, 8}. The shared digit among all three is 1, it must appear in at least one of these cells.
Which cells see all three? R3C1 and R3C2 share row 3 with R3C3 and R3C4, and share box 1 with R2C1 and R3C3. They see all three pattern cells, so digit 1 is eliminated from both.
Eliminated digit 1 from R3C1 and R3C2. Only cells seeing ALL three pattern cells are affected, this is more restrictive than XY-Wing.
Explore all 28 solving techniques in our complete technique guide.