Advanced Sudoku Strategy
XY-Wing Sudoku: How to Find and Use the XY-Wing Technique
Learn how three bivalue cells work together to eliminate candidates. Identify the pivot, find the two pincers, and use their shared candidate to make safe eliminations without guessing.
Pivot + Two Pincers
Three bivalue cells create a logical chain. The two pincers share one candidate that can be eliminated from cells seeing both pincers.
Find the Pivot
Start with a cell containing exactly two candidates, which we can call X and Y.
Find Two Pincers
One pincer contains XZ and the other YZ. Both must see the pivot.
Eliminate Z
Any cell that can see both pincers cannot contain their shared candidate Z.
What Is an XY-Wing in Sudoku?
An XY-Wing is an advanced Sudoku candidate-elimination technique formed by three bivalue cells.
A bivalue cell is an unsolved cell containing exactly two candidates.
The central cell is called the pivot. Suppose the pivot contains candidates X and Y.
Two other cells, called pincers, must each see the pivot. One pincer contains X and Z, while the other contains Y and Z.
The two pincers therefore share candidate Z.
No matter whether the pivot eventually becomes X or Y, one of the pincers must become Z. Therefore, any other cell that can see both pincers cannot contain Z.
The XY-Wing Pattern
XY → XZ + YZ
The central bivalue cell.
Shares candidate X with the pivot.
Shares candidate Y with the pivot.
Remove Z from every other candidate cell that can see both pincer cells.
How to Find an XY-Wing
Find a Bivalue Pivot
Choose an unsolved cell containing exactly two candidates. Call them X and Y.
Find a Pincer Sharing X
Find another bivalue cell that sees the pivot and contains X plus a third candidate Z.
Find a Pincer Sharing Y
Find another bivalue cell that sees the pivot and contains Y together with the same Z candidate.
Confirm Both Pincers Share Z
The first pincer must be XZ and the second pincer YZ. Their shared candidate is the elimination candidate.
Find Cells Seeing Both Pincers
Look for other cells that share a row, column, or 3×3 box with both pincer cells.
Remove Z
Remove candidate Z from any cell that sees both pincers.
XY-Wing Example
Suppose three cells contain the following candidate pairs:
The pivot contains 2 and 7. One pincer contains 2 and 9, while the other contains 7 and 9.
Therefore:
If R5C5 = 2, then R5C2 cannot be 2, so R5C2 must be 9.
If R5C5 = 7, then R8C5 cannot be 7, so R8C5 must be 9.
No matter what value the pivot takes, one of the pincers must contain 9.
Any other cell that sees both R5C2 and R8C5 can therefore remove candidate 9.
Why XY-Wing Works
The logic comes from the two possible values of the pivot.
Assume the pivot is XY.
The XZ pincer cannot use X because it sees the pivot. It must therefore use Z.
The YZ pincer cannot use Y because it sees the pivot. It must therefore use Z.
The Guaranteed Result
One of the two pincers must contain Z. Therefore any cell seeing both pincers cannot also contain Z.
What Does "See" Mean in XY-Wing?
In Sudoku, one cell can see another cell when both cells belong to at least one common unit.
A unit can be:
Each pincer must see the pivot, but the two pincers themselves do not need to see each other.
Do the Pincers Need to See Each Other?
No
The defining relationship is between each pincer and the pivot.
Pincer XZ must see the pivot XY, and pincer YZ must also see the pivot.
The two pincers do not need to share a row, column, or box with each other.
However, an elimination cell must see both pincers because candidate Z is guaranteed to appear in one of them.
The Three Cells Must Be Bivalue
A standard XY-Wing uses three cells that each contain exactly two candidates.
If one of these cells contains an additional candidate, you cannot apply the standard XY-Wing logic in the same way.
XY-Wing vs. X-Wing
The names sound similar, but the logic is different. Learn the grid-based fish pattern in our X-Wing Sudoku guide .
XY-Wing vs. Swordfish
For a larger fish pattern, continue with our Swordfish Sudoku guide .
XY-Wing vs. Hidden Pair
If you are still practising candidate subsets, review our Hidden Pair Sudoku guide .
When Should You Look for an XY-Wing?
When Many Bivalue Cells Appear
XY-Wings depend on cells with exactly two candidates, so a grid containing several bivalue cells is worth examining.
After Simpler Techniques Stop
Check singles, pairs, and Locked Candidates before searching for a wing pattern.
In Hard or Expert Sudoku
XY-Wing is most useful when straightforward candidate eliminations no longer make progress.
Before Long Chains
XY-Wing is a compact three-cell pattern and is often easier to identify than longer chaining techniques.
When Is It Not an XY-Wing?
❌ The Pivot Has Three Candidates
A standard XY-Wing pivot must contain exactly two candidates.
❌ A Pincer Does Not See the Pivot
Both pincers must share a row, column, or box with the pivot.
❌ The Pincers Do Not Share Z
The two pincers must contain the same third candidate Z.
❌ The Elimination Cell Sees Only One Pincer
Z can be removed only from a cell that can see both pincer cells.
Common XY-Wing Mistakes
❌ Removing X or Y Instead of Z
The elimination candidate is the candidate shared by the two pincers, not the two candidates inside the pivot.
❌ Requiring the Pincers to See Each Other
They do not need to see each other. Each only needs to see the pivot.
❌ Ignoring Candidate Counts
The pivot and both pincers should be bivalue cells in a standard XY-Wing.
❌ Eliminating Z Everywhere
Remove Z only from cells that can see both pincers, not from every cell that contains Z.
How to Practise XY-Wing
1. Highlight Bivalue Cells
Focus first on cells containing exactly two candidates.
2. Choose a Possible Pivot
Pick one bivalue cell and search its peers for two cells that each share one of its candidates.
3. Look for a Shared Third Candidate
The two pincer cells must share the same third candidate.
4. Find the Intersection of Their Peers
Locate cells that can see both pincers and check whether any contain the shared candidate.
5. Rescan After Every Elimination
Removing Z may reveal a Naked Single, Hidden Single, pair, Locked Candidate, or another advanced pattern.
XY-Wing Practice Checklist
- 1. Does the pivot contain exactly two candidates XY?
- 2. Does pincer 1 contain exactly XZ?
- 3. Does pincer 2 contain exactly YZ?
- 4. Can pincer 1 see the pivot?
- 5. Can pincer 2 see the pivot?
- 6. Do both pincers share the same candidate Z?
- 7. Does the elimination cell see both pincers?
- 8. Are you removing only candidate Z?
- 9. Did you rescan the puzzle afterward?
Related Sudoku Learning Pages
🧠 Advanced Sudoku Techniques
Explore advanced Sudoku strategies including pairs, fish patterns, wings, coloring, and chains.
✖️ X-Wing Sudoku
Learn how one candidate forms a four-corner elimination pattern across two rows and columns.
🐟 Swordfish Sudoku
Study the larger three-row and three-column fish pattern.
🔒 Locked Candidates Sudoku
Learn how candidate restrictions between a box and a line create safe eliminations.
Frequently Asked Questions
What is an XY-Wing in Sudoku?
An XY-Wing is a three-cell pattern consisting of a pivot XY and two pincers XZ and YZ. Because one pincer must contain Z, Z can be removed from cells that see both pincers.
What is the pivot in an XY-Wing?
The pivot is the bivalue cell containing candidates X and Y. Both pincer cells must see this pivot.
Do the two pincers need to see each other?
No. Each pincer must see the pivot, but the pincers themselves do not need to see one another.
What candidate does XY-Wing eliminate?
XY-Wing eliminates candidate Z, which is the candidate shared by both pincer cells.
Is XY-Wing an advanced Sudoku technique?
Yes. It is an advanced candidate-elimination method that becomes useful in Hard and Expert Sudoku puzzles.
Does XY-Wing place a number directly?
Usually not. It removes a candidate from one or more cells and may reveal the next logical placement afterward.
Practise the XY-Wing Technique
Open a Hard or Expert Sudoku puzzle, turn on Notes, find cells with exactly two candidates, and search for an XY pivot connected to XZ and YZ pincers.