WXYZ-wing

A WXYZ-wing is the four-cell extension of the wing series. Y-wing uses three bivalue cells; XYZ-wing uses three cells where the pivot has an extra candidate; WXYZ-wing uses four cells, where three "pincer" cells each share two of four candidates with a "pivot" cell that holds all four.

The shape

The pattern has four cells and four candidates — call them w, x, y, z. One cell, the pivot, has all four candidates: {w, x, y, z}. Three other cells, the pincers, each see the pivot and each carry exactly two candidates that overlap with the pivot's set. Between the three pincers, all four pivot candidates are covered, but the candidate z appears in all three pincers (and the pivot).

The reasoning runs as in Y-wing and XYZ-wing. Whichever digit the pivot turns out to be, one of the four cells will hold z. Either the pivot itself is z, or one of the three pincers is. Therefore any cell that sees all four — the pivot and all three pincers — can have z eliminated.

Why it's rare

Four cells with the right candidate distribution and the right visibility relationships is a tight constraint. Most stuck states are unblocked by simpler techniques before a WXYZ-wing's conditions appear. When WXYZ-wing fires, it's usually on a master-or-extreme puzzle where every fish, every Y-wing, and most XY-chains have already been exhausted.

The technique generalises further to VWXYZ-wing (five cells, five candidates, four pincers), but those are rare enough that most published solvers don't bother cataloguing them as a separate technique. They fall under the broader Almost Locked Set framework instead.

A note on Almost Locked Sets

WXYZ-wing is the boundary case where the wing technique starts to look like an ALS-XZ pattern. The pivot plus the three pincers form an Almost Locked Set on {w, x, y, z}. From the ALS perspective, WXYZ-wing is a particular shape of an ALS interaction with another (degenerate) ALS — the eliminating cell. Solvers who become fluent in ALS reasoning often skip the wing labels entirely and just see the ALSes.