The W-Wing is an elegant expert-level Sudoku technique that combines bivalue cells with strong links to achieve candidate eliminations. The pattern involves two bivalue cells that share the same pair of candidates (for example, both contain {3, 7}) and are connected by a strong link on one of those candidates. The strong link is formed by a conjugate pair in a row, column, or box where the linking digit appears in exactly two cells. When this configuration is found, the other shared candidate can be eliminated from any cell that sees both bivalue cells.
To understand why the W-Wing works, consider the logic: if the two bivalue cells both contain {A, B} and a strong link on digit A connects them indirectly, then at least one of the two bivalue cells must contain B. Here is the reasoning — if the first cell is A, then the strong link forces A elsewhere, which propagates to make the second cell B. If the first cell is B, then B is already placed. Either way, B must appear in at least one of the two bivalue cells. Therefore, any cell that can see BOTH bivalue cells cannot contain B, since B is guaranteed to be in one of them.
The W-Wing is often considered a stepping stone between Y-Wings and full XY-Chains. It appears more frequently than many expert techniques and can be easier to spot once you develop an eye for bivalue pairs and strong links. Practicing W-Wing recognition trains you to think in terms of logical implications and either-or reasoning, which are essential skills for tackling the hardest Sudoku puzzles. This technique is particularly useful when combined with other elimination methods to break through solving plateaus.
Try It Yourself
Walk through each step of the w-wing technique on a real puzzle. Follow the instructions and try entering the correct value when prompted.
Find two bivalue cells with the same candidate pair. Cell (0,4) has candidates {2,8} and cell (7,4) also has candidates {6,9}. Now look for cells (1,4) and (4,4) which both contain {2,8} — these form our W-Wing pair.
Step-by-Step Guide
Scan your candidate grid for bivalue cells — cells with exactly two candidates.
Find two bivalue cells that share the same pair of candidates, such as {A, B}.
Note that these two cells do NOT need to see each other directly.
Look for a strong link on one of the shared candidates (say A) that connects the two cells indirectly through a conjugate pair.
Verify the strong link: in the connecting row, column, or box, candidate A appears in exactly two cells, one of which sees each bivalue cell.
Conclude that candidate B must appear in at least one of the two bivalue cells.
Eliminate candidate B from any cell that can see BOTH bivalue cells simultaneously.
Imagine two twins who each must wear either a red or blue hat. A rule guarantees that if one wears red, the other must too -- so at least one of them is always wearing blue. Anyone standing between them can rule out blue for themselves.
The W-Wing works because the strong link on candidate A between the two bivalue {A, B} cells creates a logical guarantee: if the first cell is A, the strong link forces the second cell to also be A (impossible since they share the pair), so the second must be B; if the first cell is B, then B is already placed. In every case, at least one of the two cells must hold B, forming a virtual pair. Any cell that sees both endpoints therefore cannot contain B, because B is guaranteed to occupy one of them.
When to use: Use W-Wing when you find two bivalue cells with the same candidate pair that are not in the same row, column, or box, but can be connected by a strong link (conjugate pair) on one of their shared candidates.
Common Mistakes to Avoid
Using a weak link instead of a strong link (conjugate pair) to connect the two bivalue cells.
The connecting link must be a strong link -- the linking digit must appear in exactly two cells within the connecting unit. If there are three or more occurrences, the logic does not hold.
Eliminating the wrong candidate -- removing the linking digit instead of the other shared candidate.
You eliminate the non-linking candidate (the one NOT used for the strong link) from cells that see both bivalue cells.
Attempting W-Wing with bivalue cells that have different candidate pairs.
Both bivalue cells must contain the exact same pair of candidates. If the pairs differ, the W-Wing logic does not apply.
More Examples
See w-wing applied in different puzzle configurations to strengthen your pattern recognition.
W-Wing with strong link bridge
Highlighted cells show the w-wing pattern
Practice Puzzles
Apply the w-wing technique on these mini challenges. Tap a highlighted cell and enter the correct digit.
Quick Reference
- Pattern:
- Two bivalue cells with the same pair connected by a strong link on one of the digits
- Action:
- Eliminate the other shared digit from cells that see both bivalue cells
- Look for:
- Two identical bivalue cells linked through a strong link on one candidate