WXYZ-Ring
A WXYZ-Ring is the double-linked form of a WXYZ-Wing: both pivot candidates are restricted commons, creating a loop. The four cells form a locked set — four distinct values in four cells — so any of the Ring's values can be removed from cells that see all Ring cells containing that value.
What is a WXYZ-Ring?
A WXYZ-Ring is a WXYZ-Wing where both of the pivot's candidates are restricted commons — each pivot value is locked into the ALS, so the pattern forms a closed loop rather than a single chain. The four cells (three ALS + one bivalue pivot) must contain four distinct values between them, making them a locked set. Any of the Ring's values can be eliminated from cells that see all Ring cells holding that value. The Ring is rarer than the single-linked Wing because it requires both pivot candidates to be restricted commons simultaneously.
How to spot it
Look for a bivalue pivot cell where both candidates appear as restricted commons across three ALS cells that all see the pivot. The tell-tale sign is that both pivot values are locked: removing either one from the ALS would leave too few candidates for three cells. When both are locked, the four cells form a ring — a closed loop of mutual restrictions. The eliminations are broader than a Wing: any Ring value can be stripped from cells seeing all Ring cells containing it, not just the pivot's non-restricted candidate.
The logic
Both pivot candidates are restricted commons, so whichever value the pivot takes, the other is locked into the ALS. The three ALS cells plus the pivot must therefore hold four distinct values — one per cell — forming a locked set. A locked set behaves like a naked subset: any candidate that appears in cells seeing all locked-set cells holding that value can be eliminated. The Wing is the single-link special case (one restricted common, one elimination value); the Ring is the double-link general case (both restricted commons, multiple elimination values).