XYZ-Wing
The XYZ-Wing is a direct extension of the XY-Wing. The difference is the pivot: instead of two candidates it has three, {X, Y, Z}. That means the pivot itself can be the shared digit Z — so the eliminations are tighter, but the logic is the same shape.
The three cells
- A pivot with three candidates {X, Y, Z} — here {5, 8, 3}.
- A pincer {X, Z} = {5, 3} the pivot can see.
- A pincer {Y, Z} = {8, 3} the pivot can see.
Whatever value the pivot takes, one of the three cells is a Z (3). So any cell that can see all three — pivot and both pincers — cannot be 3.
Indigo: the three-candidate pivot {5, 8, 3}. Amber: the pincers {5, 3} and {8, 3}. One of the three must be a 3, so a cell seeing all three (red) can't be 3.
Step by step
- Find a three-candidate pivot {X, Y, Z}.
- Look for two bi-value pincers it can see: one {X, Z} and one {Y, Z}, both carrying the pivot's third digit Z.
- Find the targets. Any cell that can see the pivot and both pincers is fair game.
- Eliminate Z from those target cells.
- Re-scan — the elimination often frees a single nearby.
XYZ-Wing vs XY-Wing
In an XY-Wing the pivot is bi-value, so eliminations happen where cells see both pincers. In an XYZ-Wing the pivot joins in, so the target must see all three cells — usually meaning it shares the pivot's box and line. That makes targets scarcer, but the payoff is the same satisfying logic, and the pattern reaches grids the plain XY-Wing can't. It also leads naturally toward the four-cell WXYZ-Wing and, beyond that, the general ALS family.
Common mistakes
- Target sees only two. It must see the pivot as well as both pincers.
- Pincers don't share Z. Both pincers must carry the pivot's third digit.
Which Sudoku types is this best for?
The same logic applies across variants, but it pays off more in some than others.