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

19
479
6
1369
4273
6
28
169
3
258
6
18
4
38
4
369
479
1
169
6573
3
139
69
6
58
4
18
2
38
1
479
179
4
149
23
57
6
2
269
469
561743
4
158
258
9
369
7186
3
468
368
5
256
8497
5
257
157
3
478
8269
Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

Pivot R5C5={2,4,6}. Wing1 R5C1={2,6}, Wing2 R4C5={4,6}. → Any cell seeing the pivot and both wings: eliminate 6.

Practice with a Real Puzzle

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

Medium26 givensStrict