Like an XY-Wing, but the pivot has three candidates instead of two. Eliminations are restricted to cells seeing ALL three pattern cells.
Find a pivot cell with exactly three candidates and two cells it sees that hold two candidates each — {X, Z} and {Y, Z} — so digit Z appears in all three. Z must land in one of them, so eliminate Z from any cell that sees all three at once.
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.
The pivot. An XY-Wing has a two-candidate pivot that does not contain Z, so eliminations reach any cell seeing both wings. An XYZ-Wing has a three-candidate pivot that does contain Z, so eliminations are limited to cells seeing the pivot as well as both wings — a much smaller zone.
Because Z is also a candidate in the pivot. If Z ends up in the pivot itself, a cell that sees only the wings is unaffected, so the elimination would be unsound. Only cells seeing all three pattern cells are covered no matter which of the three actually takes Z.
Start from cells with exactly three candidates, since those are the only possible pivots. For each one, look among the cells it sees for two two-candidate cells whose digits are both drawn from the pivot's three and which share exactly one digit with each other. That shared digit is Z.
No. Each wing must see the pivot, sharing a row, column or box with it, but the wings need not see one another — in the worked example R2C1 and R3C4 share no unit at all. Eliminations still require a cell that sees all three, because Z is a candidate in the pivot as well.
Most often inside the box shared by the pivot and one wing. Because the target must see all three pattern cells, the practical case is a pivot and wing sitting in the same box, with the target in that box while also lining up with the second wing by row or column.
A WXYZ-Wing is the next size up in the same family: four cells whose combined candidates cover exactly four digits, with one non-restricted common digit as the elimination target. XY-Wing, XYZ-Wing and WXYZ-Wing form a progression, and each step widens the pattern while making it harder to find.
Explore all 28 solving techniques in our complete technique guide.