W-Wing

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A W-Wing is an AIC (alternating inference chain) with a wing structure, formed by two bivalue cells (the pincers) and a conjugate pair (the pivot).

How to spot it

• Examine the conjugate pairs for each candidate. Suppose candidate w forms a conjugate pair in a row (or column); use it as the pivot.
• Find two bivalue cells that each see a different end of the conjugate pair and contain the same candidate pair {w, z}. These are the pincers.
• Once the pivot and pincers are in place, candidate z can be eliminated from any cell that sees both pincers.

How it works

• The two instances of w in the pivot conjugate pair form a strong link, so one of the two cells must contain w.
• Each end of the pivot sees one pincer. Whichever end contains w prevents its corresponding pincer from containing w.
• Within each bivalue cell, w and z form a strong link. The pincer that cannot contain w must therefore contain z.
• Thus, one of the two pincers must contain z, allowing candidate z to be eliminated from any cell that sees both pincers.

Examples

On the board above, the pincer cells R1C2 and R8C8 both contain candidates 2 and 6. Row 5 contains a conjugate pair for candidate 2 at R5C2 and R5C8, which serves as the pivot. This forms a W-Wing with w = 2 and z = 6. Candidate 6 in R1C8 sees candidate 6 in both pincers, so it can be eliminated.

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On the board above, the pincers lie on opposite sides of the pivot conjugate pair.

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On the board above, one pincer (R4C4) shares a box with one end of the conjugate pair (R6C6).