XYZ-Wing
A pivot cell holding {X, Y, Z} with two pincer cells {X, Z} and {Y, Z}. Any cell that sees all three loses Z.
Advanced sudoku technique
What it is
XYZ-Wing is XY-Wing with a heavier pivot. Instead of two candidates, the pivot holds THREE — {X, Y, Z}. Pincer A is a bivalue cell {X, Z} sharing a unit with the pivot; pincer B is a bivalue cell {Y, Z} also sharing a unit with the pivot. Whatever the pivot ends up holding, ONE of the three cells holds Z. If pivot is X, pincer A is Z. If pivot is Y, pincer B is Z. If pivot is Z, pivot itself is Z. Either way, one of the three cells is Z. Therefore Z can be eliminated from every cell that sees ALL THREE — the pivot AND both pincers. The 'sees all three' constraint is stricter than XY-Wing's 'sees both pincers' because the pivot is now part of the chain.
Want the full theory?
The XYZ-Wing guide on Sudoku247Wiki walks through the logic step by step, with worked examples, diagrams and FAQs.
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