XY-Wing

What's an XY-Wing?

An XY-wing is a pattern formed by three cells (often called the pivot and two wings) that each contain exactly two candidates. Together, these three cells create a logical chain that lets you eliminate a candidate from other cells.

The magic is: even though you can't solve the cells outright, you know one number will definitely appear in a wing, which means you can safely remove it from other cells in the grid.

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

How It Works (The Setup)

  1. Pick a pivot cell with two candidates, let's call them {x, y}.
  2. Find two other cells (the wings) that "see" the pivot (in the same row, column, or box).
  3. One wing has candidates {x, z}
  4. The other wing has candidates {y, z}
  5. Together, they create a chain: if the pivot is x, then the {y, z} wing must be z; if the pivot is y, then the {x, z} wing must be z.
  6. In either case, z is guaranteed to land in one of those wings.
  7. That means any other cell that can "see" both wings cannot contain z—it can be eliminated.

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.

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.

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.

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.

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.

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: Let's tackle Swordfish—the bigger, badder cousin of X-Wing.

Frequently Asked Questions

What's an XY-Wing in Sudoku?

An XY-wing is a pattern formed by three cells (often called the pivot and two wings) that each contain exactly two candidates. Together, these three cells create a logical chain that lets you eliminate a candidate from other cells. The magic is: even though you can't solve the cells outright, you know one number will definitely appear in a wing, which means you can safely remove it from other cells in the grid.

How does XY-Wing work?

XY-Wing works by: 1) Pick a pivot cell with two candidates {x, y}, 2) Find two other cells (the wings) that "see" the pivot, 3) One wing has candidates {x, z} and the other has {y, z}, 4) Together, they create a chain: if pivot is x, then {y, z} wing must be z; if pivot is y, then {x, z} wing must be z, 5) In either case, z is guaranteed to land in one of those wings, so it can be eliminated from other cells that see both wings.

What's the difference between XY-Wing and other techniques?

XY-Wing is often the first non-fish advanced technique players learn. It's different from fish techniques like X-Wing because it uses three interlinked cells with logical chains rather than rectangular patterns. It's elegant and shows the beauty of Sudoku's logic: without guessing, you use pure deduction to lock down candidates.

When should I look for XY-Wing patterns?

Look for XY-Wing patterns when you're stuck and basic techniques aren't working. Focus on areas where multiple cells are stuck at two candidates - XY-wings often hide there. Pencil in all candidates as it's almost impossible to see XY-wings without notes. Scan pivots systematically by looking for {a, b}, then trying to match them with {a, c} and {b, c}.

What are common pitfalls with XY-Wing?

Common pitfalls include: 1) Not checking visibility - both wings must be in the pivot's row, column, or box, but they don't need to see each other, 2) False wings - sometimes two cells look like candidates, but the third link doesn't line up to form a true chain, 3) Forgetting eliminations - spotting the shape is fun, but the real power is in removing that candidate elsewhere.

Practice XY-Wing

Need more firepower? Try Swordfish next — it's like X-Wing's big cousin.

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