An advanced technique linking two bi-value cells with the same candidates via a strong link to eliminate a specific candidate.

W-Wing is an advanced technique that exploits the structure of two bi-value cells holding the same candidate pair {X, Y}, connected by a strong link on X (or Y). From any third cell that simultaneously 'sees' both bi-value cells, the digit not used in the strong link can be eliminated. The W-shaped logical chain gives it its name.

Conditions for Establishment

Three conditions are required for W-Wing to hold. First, two bi-value cells A and B with the same {X, Y} candidates must exist. They need not share a row, column, or block. Second, a strong link on X (or Y) connecting A and B must exist (in some relay unit, X is limited to 2 cells, and those 2 cells are visible from A and B respectively). Third, at least one third cell that 'simultaneously sees' both A and B must exist. When all three are met, Y can be eliminated from that third cell (when X has the strong link).

Contrast with XY-Wing

<a href="/en/glossary/xy-wing/">XY-Wing</a> uses 3 bi-value cells with different candidate pairs {X,Y}, {X,Z}, {Y,Z} sharing units directly. W-Wing uses 2 bi-value cells with the same {X, Y}, connected by a strong link as a relay relationship. While fewer cells are involved, W-Wing requires additional verification of the strong link. Both are complementary techniques worth having in the Expert+ solving repertoire.

Discovery in Practice

To efficiently find W-Wings, first list all bi-value cells on the board and identify groups of cells with the same candidate pair. Next, for each pair within a group, verify whether a strong link connects them. Strong link verification involves checking 'whether 2 cells visible from both via X (or Y) limit X's candidate positions to 2 cells in the same unit.' In Master/Extreme puzzles, W-Wing often serves as the decisive breakthrough.