Skip to content

Wings ​

Wings are a family of techniques based on an AIC (alternating inference chain) built around strong links of the bivalue-cell type. Structurally, a wing is a six-node, five-link AIC 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, the XYZ-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.

The W-Wing also has a variant, Chute Remote Pairs: the entire structure is confined to one band or stack, and the pivot is supplied by a grouped strong link.