The XY-Wing — also called the Y-Wing — is an advanced sudoku elimination technique built from three cells that each hold exactly two candidates. It does not place a digit directly. Instead, it proves that a certain digit must appear in one of two cells, letting you delete that digit from every cell that sees both of them. It is often the key that unlocks a hard puzzle after all the basic techniques have stalled.
What Is the XY-Wing?
The pattern uses three bi-value cells (cells with exactly two candidates each):
- The pivot — holds candidates X and Y (for example, 3 and 7).
- Wing 1 (pincer) — holds candidates X and Z (for example, 3 and 9). It must "see" the pivot, meaning it shares a row, column, or box with it.
- Wing 2 (pincer) — holds candidates Y and Z (for example, 7 and 9). It must also see the pivot.
The two wings do not need to see each other. The shared digit Z — the one that appears in both wings but not in the pivot — is the elimination target. This pivot-and-pincers definition is the standard one used across sudoku communities (see the EnjoySudoku XY-Wing discussion; a visual walkthrough is also given in Sudoku Snake's XY-Wing guide).
The Logic: Why One Wing Must Be Z
The pivot can only be X or Y, and each case forces a different wing to become Z:
- If the pivot is X, then Wing 1 (which sees the pivot and holds X and Z) cannot be X, so it must be Z.
- If the pivot is Y, then Wing 2 (which sees the pivot and holds Y and Z) cannot be Y, so it must be Z.
Either way, one of the two wings ends up holding Z. That is the whole trick: no matter which way the pivot resolves, a Z appears in one of the wings.
The Elimination Rule
Because one wing is always Z, any cell that sees both wings can never be Z. Delete Z from the candidate list of every such cell. This often collapses a cell to a single candidate or exposes a hidden single, and the puzzle starts moving again. This candidate elimination is what makes the XY-Wing so powerful in hard puzzles.
Note the asymmetry: the elimination applies to cells that see both wings, not cells that see the pivot. The pivot's job was only to force the logic.
Worked Example: XY-Wing Step by Step
Imagine this pattern on the grid (using the digit sets from a real tutorial example):
- Find the pivot. Cell R4C4 holds candidates {3, 7}. This is X=3, Y=7.
- Find Wing 1. Cell R4C8 holds {3, 9}. It shares row 4 with the pivot, so it sees it. This is X=3, Z=9.
- Find Wing 2. Cell R7C4 holds {7, 9}. It shares column 4 with the pivot, so it sees it. This is Y=7, Z=9.
- Identify Z. Both wings share the digit 9, which is not in the pivot. Z = 9.
- Find cells that see both wings. Cell R7C8 shares column 8 with Wing 1 and row 7 with Wing 2 — it sees both. Delete 9 from R7C8.
- Follow through. With 9 eliminated, R7C8 may reduce to a single candidate or reveal a simpler pattern. Continue solving as normal.
The shape does not matter: the first examples of XY-Wings were drawn as an X or a Y, but the pincers only need to be buddies of the pivot — same row, column, or box. Bent and scattered shapes work identically. That flexibility is what makes the XY-Wing such a versatile elimination technique for hard sudoku: once your pencil marks are full of bi-value cells, the pattern can appear almost anywhere on the grid.
XY-Wing vs XYZ-Wing: What Is the Difference?
| Feature | XY-Wing | XYZ-Wing |
|---|---|---|
| Cells involved | 3 | 3 |
| Pivot candidates | 2 (X, Y) | 3 (X, Y, Z) |
| Wing candidates | 2 each (X,Z and Y,Z) | 2 each (X,Z and Y,Z) |
| Extra condition | None | All three cells must share one house |
| Elimination | Z removed from cells seeing both wings | Z removed from cells seeing all three |
The XYZ-Wing is the close cousin: the pivot carries three candidates instead of two, but all three cells must sit in the same row, column, or box. If you can spot XY-Wings, XYZ-Wings are a small step further.
How to Spot XY-Wings in a Real Puzzle
- Start with bi-value cells. XY-Wings only use cells with exactly two candidates, so scan for those first — many solvers circle bi-value cells in their pencil marks to spot them faster.
- Look for the XYZ pattern in candidates. When you see three bi-value cells whose candidate sets look like {X,Y}, {X,Z}, {Y,Z}, check whether the {X,Y} cell sees the other two.
- Check the pivot's buddies. Pick a bi-value cell and examine every other bi-value cell in its row, column, and box. Do two of them complete the pattern?
- Do not require the wings to see each other. This is the most common spotting mistake — the wings are independent of each other.
- Verify before eliminating. Confirm all three cells are bi-value, the pivot sees both wings, and the wings share exactly one candidate. Then delete Z only from cells that see both wings.
- XY-Wings are common. They appear far more often than fish patterns (X-Wing, Swordfish), so the effort of learning them pays off in nearly every hard puzzle.
When Should You Use the XY-Wing?
The XY-Wing is an intermediate-to-advanced technique. Reach for it when:
- Naked/hidden singles, pairs, triples, and locked candidates are exhausted.
- The grid is reduced mostly to bi-value cells with no obvious pairs.
- X-Wing and other fish patterns are not appearing.
It is the first technique that reasons about a chain rather than a single unit or a single digit — you split an unknown into cases and find what all cases agree on. Almost everything beyond it (XYZ-Wings, colouring, forcing chains) is the same move applied at greater length, so the XY-Wing is the natural doorway into expert solving. For more advanced patterns, see our guide to hard sudoku strategies.
What is the XY-Wing in sudoku?
The XY-Wing (also called Y-Wing) is an advanced elimination technique using three bi-value cells: a pivot holding {X,Y} and two wings holding {X,Z} and {Y,Z}. Because one wing must always be Z, you can delete Z from any cell that sees both wings.
What is the difference between XY-Wing and Y-Wing?
There is none — Y-Wing is simply an alternative name for the XY-Wing. Some solvers use “Y-Wing” because the three cells often form a Y shape on the grid.
Does the XY-Wing place a number?
No. Like most advanced patterns, the XY-Wing only eliminates candidates. Removing Z from cells that see both wings usually exposes a naked single, hidden single, or pair that moves the puzzle forward.
Do the two wings need to see each other in an XY-Wing?
No. Only the pivot must see both wings (share a row, column, or box with each). The wings are independent of each other — a common misconception that causes solvers to miss valid patterns.
What are the exact conditions for a valid XY-Wing?
Three cells, each with exactly two candidates; the pivot {X,Y} sees both wings; the wings are {X,Z} and {Y,Z}, sharing exactly one candidate Z. Then Z can be eliminated from every cell that sees both wings.
Is XY-Wing harder than X-Wing?
They are different skills. The X-Wing tracks one digit across rows and columns; the XY-Wing reasons about a three-cell chain of candidates. Most solvers find the XY-Wing slightly harder to spot but it occurs more often in hard puzzles.
What should I learn after the XY-Wing?
The XYZ-Wing (same idea, three-candidate pivot, all cells in one house), then simple colouring and forcing chains. Each builds on the case-splitting logic the XY-Wing introduces.