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Wings

Wings are a family of alternating inference chains built around strong links of the bivalue-cell type. Structurally, a wing is a six-node, five-link alternating inference chain of the form strong-weak-strong-weak-strong, with the first and last strong links both coming from bivalue cells. As a result, wing patterns usually involve only three or four cells and are relatively easy to spot.

Two important structures appear in wings: the pincers and the pivot. A wing has two pincers and one pivot. The two strong links at the ends of the chain are the pincers, and because they each correspond to a single bivalue cell, they are also called pincer cells. The strong link in the middle is the pivot. It can be either a bivalue cell or a conjugate pair. If the pivot is a bivalue cell, the pattern is an XY-Wing, and that bivalue cell is called the pivot cell. If the pivot is a conjugate pair, the pattern is a W-Wing.

There is also an extended form of the XY-Wing: if the pivot cell also contains the elimination candidate Z, the structure no longer follows the strict alternating-chain rule, but it still supports eliminations.