UVWXYZ-Wing

A UVWXYZ-Wing is a six-cell almost-locked-set pattern: five ALS cells share a restricted common with a bivalue pivot cell. If the pivot's other candidate appeared in all six cells, the ALS would collapse to fewer candidates than cells — an impossibility. So that candidate can be removed from any cell that sees all Wing cells containing it.

What is a UVWXYZ-Wing?

A UVWXYZ-Wing extends the VWXYZ-Wing from five cells to six. The pattern consists of a bivalue pivot cell (the "yz" cell) and five almost-locked-set cells that together share a restricted common candidate with the pivot. The five ALS cells hold five or more distinct candidates between them, but if the pivot's non-restricted candidate were placed in all six cells, the remaining ALS candidates would have to fill five cells with fewer than five values — a contradiction. The single-link case (one restricted common) eliminates the pivot's other candidate from cells that see all Wing cells containing it. When both pivot candidates are restricted commons, the pattern becomes a UVWXYZ-Ring.

How to spot it

Start from a bivalue cell — the pivot — and look for five cells that all see the pivot and whose combined candidates include both pivot values plus at least three extras. The five cells form an almost-locked set: remove the restricted common (the pivot value they all share) and they would have too few candidates for five cells. The eliminations target the pivot's other candidate in cells that see every Wing cell holding that candidate. UVWXYZ-Wings are extraordinarily rare and appear only in the most diabolical puzzles once every smaller ALS pattern has been exhausted.

The logic

Suppose the pivot's non-restricted candidate is the true value in the pivot cell. Then that candidate is removed from all five ALS cells (they see the pivot). The ALS now has to fill five cells with its remaining candidates — but the restricted common is also locked, leaving fewer candidates than cells. That's impossible, so the non-restricted candidate cannot be the pivot's true value in any cell that sees all Wing cells containing it. The same logic with two restricted commons (both pivot values locked) creates a Ring: the six cells form a locked set, and any of the Ring's values can be eliminated from cells seeing all Ring cells holding that value.