XYZ-Wing
An XY-Wing whose pivot carries three candidates {X,Y,Z}. Because the pivot could also be Z, eliminations apply only to cells seen by all three cells.
A pivot cell has three candidates: 1, 2, and 3. One cell sharing its row shows {1,3}; one sharing its column shows {2,3}.
How to spot it
- 1Find a pivot with three candidates {X,Y,Z}.
- 2Find pincers {X,Z} and {Y,Z} the pivot sees.
- 3Remove Z from cells seen by the pivot and both pincers.
When to use
As an extension once XY-Wings feel natural.
Common mistake
Forgetting the target must also be a peer of the pivot, not just the pincers.
Worked Example
An XYZ-Wing extends the XY-Wing by giving the pivot a third candidate: {X,Y,Z} instead of just {X,Y}. It still needs two pincers, {X,Z} and {Y,Z}, sharing a house with the pivot. Now there are three possibilities for the pivot instead of two — but in every one of them, a Z ends up somewhere among the pivot and its two pincers.
Because the pivot itself might also be the Z, eliminations only apply to cells that see all three cells at once — the pivot and both pincers — rather than just the two pincers as in a regular XY-Wing. That tighter requirement is what makes XYZ-Wings a step harder to spot.