XY-Wing in Sudoku: How to Find & Use This Technique

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Published April 12, 2026 · 10 min read

You’ve mastered naked pairs, hidden pairs, and even the X-Wing. Yet some grids still refuse to budge, packed with pencil marks that basic and intermediate techniques can’t crack. Sound familiar?

Enter the XY-Wing — also known as the Y-Wing — an advanced elimination strategy that connects three bi-value cells in a logical chain. Once you see how it works, an entire class of stubborn puzzles suddenly becomes solvable.

In this guide we’ll explain exactly what an XY-Wing is, walk through the logic behind it, and demonstrate the technique on a real puzzle with before-and-after diagrams.

✅ What Is an XY-Wing in Sudoku?

The XY-Wing (sometimes written Y-Wing) is an advanced candidate-elimination technique that uses exactly three bi-value cells. Each cell contains precisely two candidates, and they share digits in a specific pattern.

The name comes from the three candidate pairs. The pivot holds X and Y, while the pincers each contribute the elimination digit Z. Together, they form a “wing” with the pivot at the centre.

🧠 How the XY-Wing Works (The Logic)

The reasoning is surprisingly clean. Consider three bi-value cells on a real grid:

• Pivot R1C1 has candidates {4, 5}.
• Pincer R1C9 has candidates {5, 7} — shares digit 5 with the pivot.
• Pincer R2C3 has candidates {4, 7} — shares digit 4 with the pivot.

The pivot can only be 4 or 5. Let’s trace both possibilities:

• If the pivot is 4: Pincer R1C9 still has {5, 7}, unaffected. But Pincer R2C3 loses its 4 (same box), so it must be 7.
• If the pivot is 5: Pincer R2C3 still has {4, 7}, unaffected. But Pincer R1C9 loses its 5 (same row), so it must be 7.

Either way, at least one pincer is always 7. That means any cell that can see both pincers can never be 7 — it would conflict with whichever pincer holds the 7.

🔎 Step-by-Step Example

Let’s walk through a real XY-Wing. The pivot sits at R1C1 in Box 1, one pincer is at R1C9 (connected by Row 1), and the other pincer is at R2C3 (connected by Box 1). The elimination digit is Z = 7.

Step 1: Identify the three cells

• Pivot R1C1: candidates {4, 5} — sees both pincers.
• Pincer R1C9: candidates {5, 7} — shares 5 with pivot (same row).
• Pincer R2C3: candidates {4, 7} — shares 4 with pivot (same box).

Step 2: Confirm the pattern

Check the requirements: all three cells are bi-value ✔, the pivot sees both pincers ✔, each pincer shares exactly one digit with the pivot ✔, and the “other” digit in each pincer is the same (Z = 7) ✔.

Step 3: Find the elimination targets

Which cells can see both pincers (R1C9 and R2C3) and contain candidate 7?

• R1C2 — {4, 5, 7, 8}: sees R1C9 (same row) and R2C3 (same box). Remove 7 → {4, 5, 8}.
• R2C7 — {7, 8}: sees R1C9 (same box) and R2C3 (same row). Remove 7 → {8} — solved!
• R2C8 — {2, 7, 8}: sees R1C9 (same box) and R2C3 (same row). Remove 7 → {2, 8}.

That’s 3 eliminations from a single XY-Wing, and R2C7 is instantly resolved as 8!

Step 4: Continue solving

Resolving R2C7 as 8 creates a cascade: R2C8 becomes {2}, further constraining the grid. One well-spotted XY-Wing can unlock an entire puzzle.

🕵️ How to Find an XY-Wing

🔄 XY-Wing vs X-Wing

Despite the similar names, XY-Wing and X-Wing are completely different techniques.

Think of X-Wing as a row/column pattern and XY-Wing as a candidate-chain pattern. Both are advanced, but they solve different types of bottlenecks.

📌 How the Pivot Connects to Pincers

The pivot must “see” both pincers, meaning it shares a row, column, or box with each. Common connectivity patterns:

• Row + Column: Pivot connects to one pincer by row, the other by column — forming an L-shape.
• Row + Box: One pincer in the same row, another in the same box (as in our example above).
• Column + Box: One pincer in the same column, another in the same box.
• Box + Box: In rare cases, both pincers share the pivot’s box (all three cells in the same box).

⚠️ Common Mistakes to Avoid

1. Using cells that aren’t bi-value

All three cells (pivot and both pincers) must have exactly two candidates. A cell with three or more candidates cannot participate in an XY-Wing.

2. Getting the shared digits wrong

Each pincer must share exactly one digit with the pivot, and the two shared digits must be different. The “leftover” digit in each pincer must be the same — that’s your Z.

3. Eliminating from the wrong cells

You can only eliminate Z from cells that see both pincers. Seeing just one pincer is not enough. Double-check the row, column, and box relationships.

4. Confusing XY-Wing with X-Wing

They look nothing alike in practice. X-Wing is a rectangle; XY-Wing is a chain of three bi-value cells.

📅 When to Look for XY-Wings

1. Basic techniques: Naked Singles, Hidden Singles, Full House.
2. Intermediate techniques: Naked Pairs, Hidden Pairs, Naked Triples, Pointing Pairs, Box/Line Reduction.
3. Advanced techniques: X-Wing, Swordfish, XY-Wing.
4. Expert techniques: XYZ-Wing, W-Wing, Chains, Almost Locked Sets.

🚀 Beyond XY-Wing: XYZ-Wing & W-Wing

Master the XY-Wing first. The logical reasoning — tracing what happens when the pivot is X versus Y — transfers directly to its more complex cousins.

🎯 Practice XY-Wings

• Fill in all pencil marks: XY-Wing depends on knowing every candidate in every cell.
• Scan for bi-value cells: Cells with exactly two candidates are your building blocks.
• Check connections: For each bi-value cell, ask “can two other bi-value cells I can see form a wing?”
• Verify with the solver: Use our Sudoku solver to confirm your findings.