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.
When to use it
On expert and master puzzles when XY-Wing yields no move. Hunt for trivalue pivot cells with two bivalue neighbours whose candidate sets complete the {X, Y, Z} triangle.
Worked example
Pivot R5C5 = {2, 5, 8}. Pincer A R5C2 = {2, 8} sees pivot via row 5. Pincer B R3C5 = {5, 8} sees pivot via column 5. Shared third digit Z = 8. Cells that see ALL THREE (pivot + pincer A + pincer B) are limited to box 5's overlap with row 5 + column 5. Any such cell drops 8 from its candidates.
Try it
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