VWXYZ-Wing

A VWXYZ-Wing is a five-cell almost-locked-set pattern: four ALS cells share a restricted common with a bivalue pivot cell. If the pivot's other candidate appeared in all five 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 VWXYZ-Wing?

A VWXYZ-Wing extends the WXYZ-Wing from four cells to five. The pattern consists of a bivalue pivot cell (the "yz" cell) and four almost-locked-set cells that together share a restricted common candidate with the pivot. The four ALS cells hold four or more distinct candidates between them, but if the pivot's non-restricted candidate were placed in all five cells, the remaining ALS candidates would have to fill four cells with fewer than four 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 VWXYZ-Ring.

How to spot it

Start from a bivalue cell — the pivot — and look for four cells that all see the pivot and whose combined candidates include both pivot values plus at least two extras. The four cells form an almost-locked set: remove the restricted common (the pivot value they all share) and they would have too few candidates for four cells. The eliminations target the pivot's other candidate in cells that see every Wing cell holding that candidate. VWXYZ-Wings are very rare and appear only in the hardest 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 four ALS cells (they see the pivot). The ALS now has to fill four 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 five cells form a locked set, and any of the Ring's values can be eliminated from cells seeing all Ring cells holding that value.