Two cells with identical bivalue candidates connected by a strong link on one of their shared digits.
Look for two cells with identical two-candidate lists, {A, B}, that need not share a unit. Then find a unit where A appears in exactly two cells, each seeing one of the pair — the strong link. One of the pair must be B, so remove B from every cell that sees both.
A W-Wing involves two bivalue cells that share the same two candidates, say {A, B}. These cells are connected by a strong link on one of the shared digits, meaning there is a unit where that digit appears as a candidate in exactly two cells, and those two cells each see one of the bivalue cells.
The logic: suppose the strong link is on digit A. If cell 1 is not A, then cell 1 is B. If cell 1 is A, the strong link forces the connecting cell to not be A, which in turn forces cell 2 to not be A, so cell 2 is B. Either way, at least one of the two bivalue cells contains B. Therefore, any cell that sees both bivalue cells cannot contain B.
W-Wings are a natural step beyond XY-Wings. They use strong links rather than direct unit sharing to connect the two endpoint cells, making them more flexible but also harder to spot.
Find two bivalue cells with the same candidates {A, B}. They do not need to share a unit.
Look for a strong link on digit A (or B): a unit where digit A appears in exactly two cells, and one of those cells shares a unit with bivalue cell 1 while the other shares a unit with bivalue cell 2.
If such a link exists, eliminate digit B from every cell that can see both bivalue cells. (If the link is on B, eliminate A instead.)
Step 1: R3C9 and R7C4 both have candidates {1, 5}. They don't share a row, column, or box.
Step 2: Look for a strong link on digit 1. In column 7, digit 1 appears in exactly two cells: R3C7 and R7C7. R3C7 shares row 3 with bivalue cell R3C9. R7C7 shares row 7 with bivalue cell R7C4. This is the W-Wing connection.
Step 3: If R3C9 = 1, the strong link forces R7C7 to be 1 (not R3C7), so R7C4 cannot be 1, meaning R7C4 = 5. If R3C9 = 5, then 5 is already placed. Either way, one bivalue cell contains 5. Eliminate 5 from R7C9, which sees both R3C9 and R7C4.
An XY-Wing uses three bivalue cells — cells with exactly two candidates — a pivot plus two wings that each share a unit with it, and the wings hold different candidate pairs. A W-Wing uses two bivalue cells with identical candidates that need not touch; a strong link on one digit does the work the pivot does.
A strong link is a pair of cells that are the only two places a digit can go in a unit, so one of them must hold it. In a W-Wing those two cells sit between the endpoints, each sharing a unit with one of the two identical bivalue cells, which transmits the deduction from end to end.
A W-Wing eliminates the digit the strong link is not on. If the link runs on A, then however it resolves, one of the two endpoint cells is forced to B, so B is the digit removed — and only from cells that see both endpoints. Put the link on B instead, and you eliminate A.
No — the two endpoint cells need only carry the same two candidates, and they can sit anywhere in the grid. The strong link supplies the connection between them, which is what makes W-Wings more flexible than XY-Wings, where each wing must share a unit with the pivot.
Start from bivalue cells and group them by their candidate pair, since a W-Wing needs two cells with an identical pair. For each such couple, pick one of the two digits and hunt for a unit where it has exactly two candidate cells, with one of those cells seeing each endpoint. Then check which cells see both endpoints.
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