Two cells with identical bivalue candidates connected by a strong link on one of their shared digits.
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.
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