XY-Wing

An XY-Wing is a three-cell elimination pattern in Sudoku: a pivot cell and two wing cells, each holding exactly two candidates. The pivot shares one candidate with each wing; both wings share a third candidate. Because that third candidate must appear in one of the two wings, you can eliminate it from any unsolved cell that sees both wings simultaneously.

What's an XY-Wing?

XY-Wing is an advanced Sudoku technique using three bivalue cells: a pivot and two wings. Each holds exactly two candidates. Because one shared value must land in a wing regardless of the pivot's outcome, you can eliminate that candidate from any cell that sees both wings.

This is a more advanced technique that builds on your understanding of naked singles and naked pairs.

Practice tip: If you like solving offline, grab a printable Sudoku PDF pack and look for XY-Wing patterns in the harder difficulties.

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How It Works

1. Find the pivot — locate a cell with exactly two candidates, call them {x, y}.
2. Identify the wings — find two cells that each see the pivot: one holds {x, z}, the other holds {y, z}.
3. Trace the chain — if the pivot is x, the {y, z} wing must be z; if the pivot is y, the {x, z} wing must be z. Either way, z lands in a wing.
4. Eliminate z — remove z from every cell that can see both wings.

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A Simple Example

Suppose you have:

• Pivot cell: {2, 5}
• Wing A: {2, 9}
• Wing B: {5, 9}

Logic chain:

• If the pivot is 2 → wing B must be 9
• If the pivot is 5 → wing A must be 9

Either way, 9 is placed in one of the wings. Therefore, any other cell that sees both wings cannot contain 9 anymore.

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Spotting XY-Wings in Practice

• Always look for a pivot cell with two candidates.
• Scan outward for wings that share one candidate with the pivot, and a second candidate that overlaps between them.
• Check the eliminations: if there's at least one cell that sees both wings and contains that shared candidate, you've found a working XY-wing.

As you scan for bi-value cells, watch for four of them arranged in a rectangle across two rows and two boxes — that's the setup for a Unique Rectangle, a separate technique worth checking in the same pass.

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Common Pitfalls

• Not checking visibility: both wings must be in the pivot's row, column, or box, but they don't need to see each other - only the pivot does.
• False wings: sometimes two cells look like candidates, but the third link doesn't line up to form a true chain. Double-check before eliminating.
• Forgetting eliminations: spotting the shape is fun, but the real power is in removing that candidate elsewhere.

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Why XY-Wing Matters

This is often the first non-fish advanced technique players learn. It's elegant and shows the beauty of Sudoku's logic: without guessing, you use pure deduction to lock down candidates. XY-wings regularly appear in medium to hard puzzles and are great for breaking deadlocks.

It's a natural progression from X-Wing and prepares you for even more advanced techniques — including Forcing Chains, which extend this same if-then reasoning across the whole grid.

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Practice Tips

• Pencil in all candidates - it's almost impossible to see XY-wings without notes.
• Scan pivots systematically: look for {a, b}, then try to match them with {a, c} and {b, c}.
• Focus on areas where multiple cells are stuck at two candidates - XY-wings often hide there.

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Wrap-Up

XY-wings are all about chains of logic. Three cells, two candidates each, one neat elimination. Once you start seeing them, they'll become one of your go-to tools for unlocking puzzles that feel stuck.

Next step: XYZ-Wing is the natural follow-on — it uses the exact same pivot-and-wings structure, but the pivot holds three candidates instead of two, which means the elimination reaches further. Once you've worked through both wings variants, Swordfish gives you an entry point into three-row fish logic.

Frequently Asked Questions

Related Strategies

The wing technique family in sequence — go back if XY-Wing's logic still feels unclear, or move forward once it clicks:

• Go back if needed: Naked Pairs — bi-value cells are the building blocks of XY-Wing; revisit if the candidate logic feels shaky
• Natural next step: XYZ-Wing — same pivot-and-wings structure, pivot holds three candidates for a broader elimination reach
• Extended form: WXYZ-Wing — four-cell wing pattern; tackle this after XYZ-Wing
• Alternative approach: Unique Rectangle — easy to scan for in the same bi-value sweep; parallel technique at the same level
• Longer chains: Forcing Chains — extends XY-Wing's if-then reasoning across the whole grid
• XY-Wing in Sudoku — a blog post with additional worked examples and pattern variations

Practice XY-Wing

• Printable Expert Sudoku — PDF grids where wing patterns appear regularly
• Daily Sudoku puzzle — a new expert-level grid every day
• Sudoku a Day app — ad-free daily puzzles on iOS

Ready to extend the wing logic? The next step is XYZ-Wing — the same pivot-and-wings structure with a three-candidate pivot for a broader elimination reach. Or return to the strategy hub to map your full learning path.

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