XYZ-Wing Technique
advancedExtended XY-Wing where the pivot has three candidates
The XYZ-Wing is a natural extension of the XY-Wing. The pivot cell has three candidates {X,Y,Z}, and two bi-value wings provide the same elimination logic — but the elimination zone is more restricted because the target must also see the pivot.
Understanding the Concept
Pivot has candidates {X,Y,Z}. Wing 1 has {X,Z}. Wing 2 has {Y,Z}. All three cells contain the common digit Z.
The Pivot must see both Wings (share a house with each).
If Pivot = X, then Wing 1 must be Z. If Pivot = Y, then Wing 2 must be Z. If Pivot = Z, then the pivot itself holds Z.
In every case, at least one of the three cells holds Z.
Therefore, any cell that sees ALL THREE cells (the pivot and both wings) cannot contain Z.
Because the elimination target must see the pivot too (not just the wings), there are fewer eliminations than with XY-Wing.
The most common configuration has both wings in the same box as the pivot.
Examples
XYZ-Wing: Pivot {2,5,8}, Wings {2,8} and {5,8}
Pivot at R4C4 has {2,5,8}. Wing 1 at R4C3 has {2,8} (same row and box). Wing 2 at R3C4 has {5,8} (same column and box). The common digit is 8. Any cell seeing all three cannot be 8. Cell R3C3 sees all three: same row as Wing 2, same box as all three. Eliminate 8 from R3C3.
Pro Tips
- •Look for cells with exactly 3 candidates as potential pivots
- •Each wing must share exactly 2 of the pivot's candidates, and the common digit Z must be in all three cells
- •Eliminations are only in cells that see ALL THREE cells — more restrictive than XY-Wing
- •When both wings are in the same box as the pivot, look for eliminations in that box
- •XYZ-Wings are actually more common than XY-Wings because the 3-candidate pivot is easier to match
