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An XYZ-Wing has a pivot X/Y/Z and two cells it sees, X/Z and Y/Z. At least one of these three cells must contain Z.
Two cells see each other when they share a row, column or 3×3 box. An elimination needs the specific visibility relationships described in the reasoning.
An example from the app
These are the complete notes of the three cells: E8: 1, 2, 7; G8: 1, 2; E9: 1, 7. E8 is the pivot with three candidates. The other two cells are its wings.
E8 either contains 1 or forces it into G8 or E9. So one of these three cells contains 1. Only cells sharing a row, column or box with each of the three may lose it.
These notes are therefore ruled out: D8: 1.
The image shows the candidates relevant to this step. A note being hidden does not mean it has been logically eliminated.
Practice the next step
The elimination cell must see both wings and the pivot. That extra condition distinguishes it from an XY-Wing.
In the app, follow the reasoning in the matching lesson and try a task yourself. With a new puzzle, always start from its actual candidate state.
Questions about XYZ-Wing
How does its pivot differ from XY-Wing?
An XYZ-Wing pivot has X, Y and Z. Each wing contains two of those candidates.
Is seeing both wings enough for elimination?
No. The target must also see the pivot, because Z could be placed there.
Can both wings contain the same pair?
This pattern needs the two different pairs X/Z and Y/Z beside the X/Y/Z pivot.
Why must a target see all three cells?
Z is either at the pivot or forced into a wing by its other value. The target must conflict with Z in every case.
Which digit may I remove?
Only the shared digit Z at a valid target. The pattern does not allow arbitrary eliminations around the pivot.
Keep practicing in Unisu
Download Unisu for iPhone or Android. Solve a puzzle or work through a guided lesson on the technique.
