XYZ-wing extends XY-wing by upgrading the pivot from two candidates to three. The wings stay bivalue. The eliminations get tighter, but the logic is the same family of forced-branch reasoning.

How it works

The pivot is a trivalue cell with candidates {X, Y, Z}. One wing is bivalue {X, Z} and sees the pivot. The other wing is bivalue {Y, Z} and sees the pivot. The two wings do not need to see each other.

Whichever digit the pivot resolves to, one of the three cells must hold Z. If the pivot is X, the {X, Z} wing takes Z. If the pivot is Y, the {Y, Z} wing takes Z. If the pivot is Z, the pivot itself holds Z. So Z is locked into the pivot or one of the two wings.

Any cell that sees all three of them. pivot, X-wing, and Y-wing. cannot hold Z. That is the elimination.

Trivalue pivot {X,Y,Z}, bivalue wings {X,Z} and {Y,Z}. Z is locked into the three. eliminate it from cells that see all three.

When to look for it

After XY-wing fails. The pivot now has three candidates, which widens the search but tightens the eliminations because the target cell must see all three of the pattern's cells.

Most XYZ-wings fit inside two or three units that overlap. Pivots in the centre of a 3x3 box are common because they see eight neighbours plus all column and row peers.

Step-by-step example

Find a trivalue cell {X, Y, Z}. Treat it as the pivot.
List bivalue cells that see the pivot. Find one with candidates {X, Z} and another with {Y, Z}.
Find cells that see all three: the pivot and both wings.
Erase Z from every such cell.
Re-scan. XYZ-wing eliminations sometimes yield a single, more often they prune candidates that feed into the next chain.

XY-wing vs XYZ-wing

	XY-wing	XYZ-wing
Pivot candidates	{X, Y}	{X, Y, Z}
Wings	{X, Z} and {Y, Z}	{X, Z} and {Y, Z}
Target sees	Both wings	Pivot and both wings
Cells holding Z	Two wings	Pivot plus two wings

The trivalue pivot tightens the visibility condition on the target.

Tips for spotting it

Search XY and XYZ patterns together. Many bivalue chains have a trivalue cousin nearby.
The pivot must be exactly trivalue. Four candidates breaks the pattern.
Wings stay bivalue. Use the wing's candidates to identify Z.
Pivots inside a box are productive because the box gives extra visibility into the cells around it.

Common mistakes

Using a bivalue pivot. That is plain XY-wing.
Eliminating Z from cells that only see two of the three.
Confusing XYZ-wing with WXYZ-wing (four cells), a different pattern.
Skipping the visibility check. Targets must see the pivot too, not just the wings.

Practise it

On expert sudoku, mark every candidate and list both bivalue and trivalue cells. Run XY-wing first, then run XYZ-wing using each trivalue cell as a pivot. The habit unlocks puzzles where pure XY-wing falls short.

XYZ-Wing