XYZ-Wing
Like an XY-Wing, but the pivot has three candidates {x, y, z}; z is removed only from cells that see all three cells.
Rule
Pivot {x, y, z}, pincers {x, z} and {y, z} → remove z from cells that see the pivot and both pincers.
Pivot and pincers
The pivot r9c4 has three candidates 4, 8 and 9. It sees two "pincers": r8c4 (4, 8) and r9c7 (9, 8).
The idea
The pivot also holds z. If the pivot is x, the first pincer is z; if it is y, the second pincer is z; if it is z, the pivot itself is z. So z is in one of the three cells.
An eliminated cell must see all three cells, so the elimination area is narrower than for an XY-Wing — usually a cell in the pivot's box and in the same row (column) as one pincer.
How to spot it
- Find a three-candidate cell, then two bivalue cells it sees that are subsets of it and share exactly the digit z.
Common mistakes
- Eliminating from a cell that sees only the two pincers is wrong: it must see the pivot too.
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Related techniques
References
The examples on this page are generated from random puzzles, not taken from these sources.