XYZ-Wing

Hard

Like XY-Wing but the pivot has three candidates {X,Y,Z}; Z is eliminated from cells seeing the pivot and both wings.

How It Works

The pivot has candidates {X,Y,Z}. One wing has {X,Z}, the other {Y,Z}. Whatever value the pivot takes, one of the wings must contain Z. Any cell seeing the pivot AND both wings can have Z eliminated.

Unlike XY-Wing, the eliminating cell must see all three cells (narrower scope), but the pivot is more flexible.

Example

53
78
78
19642
124
36
5
36
789
6
79
789
2
48
478
135
2
146
16
348
468
3468
957
7
469
69
52
46
318
385971264
49
5213
47
8
79
6
8
167
167
67
95423
49
67
3
478
468
25
79
1
Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

Practice with a Real Puzzle

This 9×9 puzzle is solver-verified to require this technique on its solution path.

Medium26 givensStrict