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
wforms 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
zcan be eliminated from any cell that sees both pincers.
How it works
- The two instances of
win the pivot conjugate pair form a strong link, so one of the two cells must containw. - Each end of the pivot sees one pincer. Whichever end contains
wprevents its corresponding pincer from containingw. - Within each bivalue cell,
wandzform a strong link. The pincer that cannot containwmust therefore containz. - Thus, one of the two pincers must contain
z, allowing candidatezto 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.
On the board above, the pincers lie on opposite sides of the pivot conjugate pair.
On the board above, one pincer (R4C4) shares a box with one end of the conjugate pair (R6C6).