VWXYZ-Ring
A VWXYZ-Ring is the double-linked variant of the VWXYZ-Wing — a five-cell pattern where both pivot candidates are restricted commons, closing the chain into a loop. The five cells form a locked set, so any Ring value can be eliminated from cells that see all Ring cells containing it.
What is a VWXYZ-Ring?
The VWXYZ-Wing is already a challenging pattern — four ALS cells plus a bivalue pivot, linked by a single restricted common. When both of the pivot's candidates happen to be restricted commons, the chain closes on itself: the five cells form a ring. A ring is a locked set (five cells, five distinct values), and locked sets behave like naked subsets — any value in the set can be stripped from external cells that see every Ring cell holding that value. The Ring is harder to find than the Wing because both pivot candidates must be restricted commons at the same time, which is a much rarer configuration.
How to spot it
Start from a bivalue cell and check whether both of its candidates are restricted commons across four ALS cells that all see it. A restricted common is a candidate that appears only within the ALS in some shared house — if it's removed from the ALS, the set collapses. When both pivot values satisfy this condition, the five cells are locked. The pattern is easy to miss because the ALS cells may not all contain both pivot values; what matters is the union of candidates across all four ALS cells, not individual cell contents.
The logic
Each pivot candidate is a restricted common, so whichever value the pivot takes, the other is forced into the ALS. The ALS then has exactly four values for four cells — a perfect fit. Together with the pivot, the five cells contain five distinct values, one per cell: a locked set. Any external candidate sharing a house with all Ring cells of that value can be eliminated, because one of those Ring cells must hold it. The Wing is the single-link case (one restricted common, one elimination); the Ring generalises to two restricted commons and potentially multiple eliminations.