Y-Wing Sudoku, also called XY-Wing, is an advanced candidate-elimination technique. It connects three unsolved cells containing three different candidates. The pattern does not normally place a digit immediately. Instead, it proves that one candidate cannot remain in a cell that sees both wings.
The name can make the method sound more complicated than it is. A valid Y-Wing follows one reusable structure: an XY pivot, an XZ wing, and a YZ wing. Once you can identify those three pairs and check how the cells see one another, the elimination becomes logical and repeatable.
Quick answer: A Y-Wing uses three bivalue cells arranged as XY, XZ, and YZ. The XY cell is the pivot. Because one wing must contain Z, remove Z from any other candidate cell that sees both wings.
Y-Wing Sudoku at a Glance
| Pattern detail | Meaning |
|---|---|
| Alternative name | XY-Wing |
| Difficulty | Intermediate to advanced |
| Pattern cells | Three bivalue cells |
| Pivot | Contains candidates XY and sees both wings |
| First wing | Contains candidates XZ |
| Second wing | Contains candidates YZ |
| Elimination digit | Z, the candidate shared by both wings |
| Valid targets | Candidate cells that see both wings |
| Main result | Candidate elimination rather than an immediate placement |
What Is a Y-Wing in Sudoku?
A Y-Wing is formed by three bivalue cells. A bivalue cell is an unsolved cell with exactly two remaining candidates. If a cell contains candidates 2 and 5, for example, it is a bivalue cell written as 25 or {2,5}.
The three Y-Wing cells use only three candidates in this arrangement:
- Pivot: XY
- First wing: XZ
- Second wing: YZ
The pivot shares X with one wing and Y with the other. The two wings share Z. The pivot must see both wings, but the wings do not need to see each other.
The final target is another cell containing Z that sees both wings. Since one of the wings must eventually contain Z, the target cannot also contain Z. That candidate can be removed.
Why the Y-Wing Elimination Works
The reasoning depends on the two possible values of the pivot. Suppose the pivot is XY.
- If the pivot becomes X, the XZ wing cannot use X and must become Z.
- If the pivot becomes Y, the YZ wing cannot use Y and must become Z.
Those are the only possibilities for the pivot. In either branch, one of the wings contains Z. A target cell that sees both wings therefore sees a guaranteed Z, even though you do not yet know which wing will contain it.
That is why Z can be removed from the target. The method tests both legal pivot outcomes and reaches the same conclusion without guessing.
A Complete Y-Wing Example
Candidate pattern
- Pivot at r4c4: {2,5}
- First wing at r4c8: {2,8}
- Second wing at r6c5: {5,8}
- Target at r6c8: includes candidate 8
The pivot at r4c4 sees the first wing because they share row 4. It sees the second wing because both cells are inside the same 3×3 box.
Now test the pivot:
- If r4c4 is 2, r4c8 cannot be 2, so r4c8 must be 8.
- If r4c4 is 5, r6c5 cannot be 5, so r6c5 must be 8.
The target at r6c8 sees the first wing through column 8 and the second wing through row 6. One of those wings must contain 8, so candidate 8 can be removed from r6c8.
The removal may create a single in the target or reveal another useful pattern elsewhere. A Y-Wing often acts as the small elimination that restarts progress in a difficult puzzle.
What Does It Mean for Cells to See Each Other?
Two Sudoku cells see each other when they belong to at least one common unit:
- The same row
- The same column
- The same 3×3 box
A Y-Wing can connect different types of units. One wing may see the pivot through a row while the other sees it through a box. The target may see one wing through a column and the other through a row.
Do not judge the pattern by its physical shape. The three cells do not need to draw a visible letter Y. Their candidate relationships and shared units are what matter.
How to Find a Y-Wing Step by Step
1. Update Your Candidate Notes
Remove candidates already ruled out by confirmed digits, singles, pairs, and locked candidates. A Y-Wing depends on accurate pencil marks. Missing candidates can hide the pattern, while outdated candidates can create a false pattern.
2. Mark the Bivalue Cells
Look for unsolved cells with exactly two candidates. Standard Y-Wings use three bivalue cells, so there is no need to scan every multi-candidate cell at first.
3. Choose a Possible Pivot
Select one bivalue cell and call its candidates X and Y. Search its row, column, and box for possible wings.
4. Find the XZ Wing
Find a visible bivalue cell that shares X with the pivot and introduces a third candidate, Z. If the pivot is {3,7}, a possible first wing could be {3,9}.
5. Find the YZ Wing
Find another bivalue cell that sees the pivot, shares Y, and contains the same Z. With a {3,7} pivot and a {3,9} first wing, the second wing must be {7,9}.
6. Identify the Shared Wing Candidate
The digit in both wings but not in the pivot is the elimination candidate. In the 37-39-79 pattern, that digit is 9.
7. Search for a Common Target
Find cells that see both wings and still contain the elimination candidate. Remove it only from those common peers.
8. Recheck the Grid
After the elimination, scan for a naked single, hidden single, pair, or locked candidate. The value of the technique often comes from the next deduction it creates.
Five-point validation check:
- All three pattern cells are bivalue.
- The pivot sees both wings.
- Each wing shares a different pivot candidate.
- Both wings share the same third candidate.
- The target sees both wings and contains that third candidate.
Efficient Scanning Strategies
Scanning every bivalue cell against every other bivalue cell can be slow. A more focused method is to start with pivots in busy parts of the grid. A pivot that sees several bivalue cells has more possible wing combinations.
Write the candidate pairs in a consistent order. If you see 25, 28, and 58, the relationship is easier to recognize when you mentally rewrite it as XY, XZ, and YZ.
It can also help to scan by one pivot candidate at a time. For a pivot {2,5}, first locate every visible bivalue cell containing 2. Then locate every visible bivalue cell containing 5. Compare the extra candidate in each group. A matching extra digit creates the possible wings.
Finally, delay searching for the target until the three-cell pattern is confirmed. Looking for elimination cells too early adds unnecessary work.
Common Y-Wing Mistakes
Using a Pivot With Three Candidates
A standard Y-Wing pivot has exactly two candidates. A three-candidate pivot may belong to an XYZ-Wing, which follows different visibility requirements.
Letting Both Wings Share the Same Pivot Digit
If the pivot is {2,5}, one wing must connect through 2 and the other through 5. Pairs {2,8} and {2,9} do not form a Y-Wing with that pivot.
Using Different Third Candidates
The wings must share the same Z. A {2,8} wing and a {5,9} wing do not force one common digit, so they cannot support the elimination.
Removing Z From a Cell That Sees Only One Wing
The target must see both wings. A cell that sees only the XZ wing does not know whether Z will appear there or in the YZ wing.
Assuming the Wings Must See Each Other
The wings do not need to share a unit. The pivot connects the two branches of the logic. What matters is that the target sees both wing cells.
Forcing the Technique Into Every Puzzle
Not every hard Sudoku contains a useful Y-Wing. Use singles, pairs, locked candidates, and other simpler methods first. Search for a Y-Wing when the candidate grid is stable and easier deductions have stopped.
Y-Wing Compared With Similar Techniques
Y-Wing and XY-Wing
These names normally describe the same technique. XY-Wing emphasizes the candidate notation, while Y-Wing is the shorter common name.
Y-Wing and X-Wing
An X-Wing tracks one candidate in matching positions across two rows and two columns. A Y-Wing uses three different candidates across three bivalue cells. Despite the similar names, the structures are unrelated.
Y-Wing and XYZ-Wing
An XYZ-Wing has a three-candidate pivot, usually XYZ, plus XZ and YZ wings. Because Z also remains in the pivot, a valid XYZ-Wing target generally must see the pivot and both wings. A Y-Wing target only needs to see both wings.
How to Practise Y-Wing Sudoku
Pattern training is useful because a full Sudoku includes many competing candidates and techniques. Practising one pattern at a time helps separate recognition from general puzzle solving.
Use this routine:
- Identify the XY pivot.
- Find the XZ and YZ wings.
- Name the shared candidate Z.
- Find a candidate cell that sees both wings.
- Explain both pivot branches before eliminating Z.
Begin on Easy mode with fewer distracting pairs. Move to Medium when you can explain each elimination without using a hint. Hard mode adds more bivalue cells, so you must distinguish the real pattern from plausible-looking distractions.
Practise Y-Wing Patterns Online
Identify the pivot, both wings, the target, and the candidate to remove. Choose Easy, Medium, or Hard and solve 10 randomized Y-Wing challenges in each session.
Benefits of Learning the Pattern
Y-Wing expands your solving options when singles, pairs, and locked candidates no longer produce progress. It also develops the habit of testing every logical branch before removing a candidate.
The technique prepares you for patterns that connect candidates across several units, including XYZ-Wing, W-Wing, and short XY-Chains. More importantly, it teaches you to read relationships between cells instead of treating each empty square independently.
Frequently Asked Questions
What is a Y-Wing in Sudoku?
A Y-Wing is a three-cell candidate pattern arranged as XY, XZ, and YZ. It removes Z from cells that see both wing cells.
Is Y-Wing the same as XY-Wing?
Yes. Most Sudoku guides use Y-Wing and XY-Wing for the same technique.
Do all three Y-Wing cells need two candidates?
Yes. In a standard Y-Wing, the pivot and both wings are bivalue cells.
Do the wings need to see each other?
No. The pivot must see both wings. A valid elimination target must also see both wings, but the wings do not need to see one another.
Which candidate can be removed?
Remove the candidate shared by both wings but absent from the pivot. In XY-XZ-YZ notation, that candidate is Z.
Can a Y-Wing place a number directly?
Usually it removes a candidate rather than placing a digit. The removal may then create a single or another immediate deduction.
When should I search for a Y-Wing?
Search after updating all candidate notes and applying simpler techniques. A grid with several bivalue cells is a good place to begin.
Related Puzzle Resources
Continue developing Sudoku pattern recognition and candidate elimination with these guides:
Final Takeaway
A Y-Wing is easier to verify when you reduce it to five questions: Which cell is the XY pivot? Which cells are XZ and YZ? Do both wings see the pivot? What is the shared candidate Z? Which target cells see both wings?
Check both possible values of the pivot before making the elimination. If each branch forces Z into one of the wings, remove Z from their common peers. With accurate notes and regular practice, this advanced technique becomes a short and dependable chain of logic.
