How it works
XYZ-wing is XY-wing with the pivot upgraded from bivalue to trivalue. The pivot still has X and Y, and now also Z directly.
Whichever digit the pivot resolves to, one of the three cells holds Z: the pivot itself, the X-Z wing, or the Y-Z wing. So Z is forced into one of those three cells.
Any cell that sees all three of them cannot be Z. That elimination is the payoff.
When to look for it
When XY-wing fails and a similar three-cell shape suggests itself with a trivalue pivot.
Tips for spotting the pattern
- The eliminations are tighter than XY-wing because the cell must see all three of the pivot and both wings.
- Bivalue wings only. The trivalue is the pivot.
- Searching for both XY and XYZ patterns together is efficient.
Common mistakes
- Bivalue pivot. That would be plain XY-wing, not XYZ.
- Eliminating Z from cells that only see two of the three. They must see all three.
- Confusing the shape with WXYZ-wing (four cells), which is a different and more advanced pattern.