W-Wing: Two Matching Cells, One Strong Link

If you've got XY-Wing down, the W-Wing will feel familiar and unfamiliar at the same time — same two-pincer shape, but the middle piece is completely different.

What is a W-Wing?

A W-Wing uses two cells that both hold exactly the same two candidates, A and B, but do not see each other. Somewhere else, a unit has only two spots for B — a strong link — and each of those two spots sees one of the bi-value cells.

If one bi-value cell is B, the link forces the other end to be B too, which then rules B out of the other bi-value cell, making it A. If neither is B, both are A. Either way, at least one of them is A, so any cell that sees both cannot be A.

How this differs from XY-Wing

Both use bi-value cells and end in an elimination, which is why they're easy to mix up. The difference is the middle piece: an XY-Wing chains three different cells that share pairs of digits, with a pivot cell doing the connecting. A W-Wing uses two identical-pair cells, connected not by a shared cell but by an outside strong link — a row, column, or box where the linking digit has only two possible homes.

A worked example

Here's the exact board the app uses for its own W-Wing lesson:

Singles alone take this puzzle most of the way:

When they stop, look for a pair of matching bi-value cells. R7C7 and R9C3 both read {3, 7} and don't see each other — and row 8 has a 7 in only two cells, R8C3 and R8C7, each sitting in the same column as one of the two:

Blue & violet: the cells the logic runs on · Rose: where the elimination lands

That's a strong link on 7 joining both pincers. Follow the logic through: whichever pincer turns out to be 7, the link forces the other pincer to be 3. So one of the two pincers is always 3, and R7C3, R9C8, and R9C9 — each visible to both pincers — can't be.

How to spot one

1. Look for two separate cells with the same pair of candidates that don't see each other.
2. Pick one of the two digits and look for a row, column, or box where it fits in only two cells.
3. Check that each of those two cells sees one of your pair cells.
4. Eliminate the other digit from any cell that sees both pair cells.