Advanced Sudoku Strategy
W-Wing Sudoku: How to Find and Use W-Wings
Discover how two matching candidate pairs and one strong link create a logical elimination in challenging Sudoku puzzles.
Two Matching Pairs + One Strong Link
Two cells contain {3, 7}. A strong link on 3 forces at least one of them to be 7.
What Is a W-Wing in Sudoku?
A W-Wing involves two cells with exactly the same two candidates, such as 3 and 7. These are the wings.
A strong link for one candidate connects the logic between the wings. If the strong link is on 3, at least one wing must contain 7.
Any other cell that sees both wings cannot contain 7. This is a candidate elimination, not an immediate placement.
The W-Wing Rule
Find two bivalue cells containing the same pair {X, Y}. Find a strong link for X whose endpoints see the two wings respectively. Then remove Y from any other cell that sees both wings.
W-Wing Example: Candidates 3 and 7
Wing A: R2C2 contains candidates {3, 7}.
Wing B: R8C8 contains candidates {3, 7}.
Strong link: Candidate 3 appears only in R2C5 and R8C5 within column 5.
R2C5 sees Wing A along row 2. R8C5 sees Wing B along row 8.
Eliminate 7 from R2C8
R2C8 sees Wing A along row 2 and Wing B along column 8. Therefore, candidate 7 can be removed from R2C8 if present.
This is a candidate-position example, not a complete playable Sudoku grid. The candidate restrictions must first be verified.
Why the W-Wing Elimination Works
Column 5 must contain candidate 3 at R2C5 or R8C5.
If R2C5 is 3, Wing A cannot be 3, so Wing A must be 7.
If R8C5 is 3, Wing B cannot be 3, so Wing B must be 7.
In either case, at least one wing contains 7. Because R2C8 sees both wings, R2C8 cannot contain 7.
How to Find a W-Wing: Step by Step
Find Two Bivalue Cells
Look for two cells with identical two-candidate lists, such as {3, 7}.
Choose the Linking Candidate
Pick one candidate, such as 3, to connect the two wings.
Find a Strong Link
Find two possible positions for 3 in a row, column, or box. One of them must be 3.
Check Visibility
Each strong-link endpoint must see a different wing.
Find a Common Peer
Locate another cell that sees both wings.
Eliminate the Other Candidate
Remove 7 from that common peer, if it is a candidate there.
Rescan the Puzzle
Look for newly revealed singles, pairs, or other eliminations.
W-Wing vs. XY-Wing
Read our XY-Wing Sudoku guide to learn the related but different technique.
When Should You Look for a W-Wing?
W-Wings are useful in Hard and Expert Sudoku after simpler techniques stop making progress.
Start with bivalue cells containing the same pair, then check for a strong link that connects them logically.
Candidate notes make this pattern easier to recognize.
Common W-Wing Mistakes
❌ Different Wing Pairs
The wings must contain exactly the same two candidates.
❌ No Strong Link
Two arbitrary cells containing the linking candidate are not enough.
❌ Incorrect Visibility
Each strong-link endpoint must see its corresponding wing.
❌ Wrong Elimination
Remove the non-link candidate only from cells that see both wings.
Related Sudoku Learning Pages
Frequently Asked Questions
What is a W-Wing in Sudoku?
A W-Wing uses two matching bivalue cells and a strong link to eliminate a candidate from cells seeing both wings.
How do you find a W-Wing?
Find two matching bivalue cells, then a strong link for one candidate whose endpoints see the two wings respectively.
What candidate can be removed?
Remove the non-link candidate from another cell that sees both wings.
Is W-Wing the same as XY-Wing?
No. W-Wing uses an external strong link and two matching bivalue cells. XY-Wing uses a pivot and two pincers.
W-Wing Example: Why the Elimination Is Valid
Suppose Wing A at R2C2 and Wing B at R8C8 each contain exactly candidates 2 and 7. Candidate 2 has a strong link in column 5: only R2C5 and R8C5 can contain 2 in that column.
Wing A — R2C2
Candidates: 2, 7
Wing B — R8C8
Candidates: 2, 7
Link endpoint — R2C5
Candidate 2; sees Wing A in row 2
Link endpoint — R8C5
Candidate 2; sees Wing B in row 8
If R2C5 is 2, Wing A must be 7. If R8C5 is 2, Wing B must be 7. At least one link endpoint is 2, so at least one wing is 7.
Eliminate 7 from R2C8
R2C8 sees Wing A through row 2 and Wing B through column 8. Therefore R2C8 cannot contain 7.
This is an illustrative candidate configuration, not a full Sudoku puzzle. The stated candidates and strong-link restrictions are assumed.
Practise W-Wing Sudoku
Open a Hard or Expert puzzle, turn on Notes, and look for two matching bivalue cells connected through a strong link.