The XYZ-Wing Technique, Explained

A quick recap of the XY-Wing

In an XY-Wing you have a pivot cell with two candidates, say X and Y, that sees two other cells. One of those cells holds X and Z, the other holds Y and Z. Whatever value the pivot takes, one of the two wings is forced to be Z. So any cell that sees both wings cannot be Z, and you erase it.

What changes in the XYZ-Wing

The XYZ-Wing keeps the same shape but the pivot now carries three candidates, X, Y and Z, instead of two. The two wings are still bivalue cells holding X and Z, and Y and Z. The name simply lists what the pivot contains. Because the pivot itself can also be Z, the logic tightens by one cell.

The elimination it gives you

1. Find a three-candidate pivot XYZ that sees a wing with XZ and a wing with YZ.
2. Notice that between the pivot and its two wings, one of the three cells must end up as Z.
3. Look for any cell that sees all three of these cells at once, the pivot and both wings.
4. That cell cannot be Z, because a Z is already committed among the three. Erase Z from it.
5. Rescan, since clearing that candidate often frees a fresh single.

Why the target must see the pivot too

This is the one difference to remember. In an XY-Wing the pivot cannot be Z, so a target only needs to see both wings. In an XYZ-Wing the pivot can be Z, so a target must see the pivot as well as both wings before you are allowed to remove Z. In practice this usually means the target sits in the same box as the pivot.

When it is worth hunting for

Reach for the XYZ-Wing when scanning, singles and basic pairs have run dry and the board still has three-candidate cells sitting near bivalue neighbours. It is a mid-level tool, harder than a naked pair but far less work than a chain. Finding one on a stuck board feels like picking a lock.