sudokly

XY-Wing

An XY-wing is a three-cell pattern. The pivot cell has candidates {X, Y}. Two wing cells see the pivot, with one wing holding {X, Z} and the other holding {Y, Z}. Whatever digit the pivot takes, one of the wings must hold Z, so Z can be eliminated from any cell that sees both wings.

XY-wing is the first true chain technique. It tracks what happens across three cells linked by a shared digit, and the conclusion is forced regardless of which value any single cell takes.

How it works

Find a bivalue cell. Call its two candidates X and Y. This is the pivot. Now find a second bivalue cell that sees the pivot (shares a row, column or box) and holds candidates {X, Z}. Then find a third bivalue cell that also sees the pivot and holds {Y, Z}. Z is the shared digit. The pivot does not contain Z directly.

Now follow the logic. If the pivot takes X, the {X, Z} wing must take Z. If the pivot takes Y, the {Y, Z} wing must take Z. Either way one of the two wings ends up with Z. So any cell that sees both wings cannot contain Z.

XY-WING (pivot {3,4}, z=5)38291168429961879156159493512451357286458934356127913
Either pincer forces 5 → erase 5 where both pincers see.

When to look for it

After X-wing and fish techniques fail. The grid needs lots of bivalue cells. Late-game expert and evil puzzles, where candidate sets have collapsed, are the natural habitat.

Start by listing every bivalue cell. Try each one as a pivot in turn. The search is finite and almost always finds at least one wing within a few seconds.

Step-by-step example

  1. Pick a bivalue cell with candidates {X, Y}. Call it the pivot.
  2. List bivalue cells that see the pivot. From those, find one containing X plus a third digit Z. Call it the X-wing.
  3. From the same list, find another bivalue cell containing Y plus the same Z. Call it the Y-wing.
  4. Confirm both wings see the pivot. They do not need to see each other.
  5. Find cells that see both wings simultaneously. Erase Z from them.
  6. Re-scan. The Z eliminations often create a single or another chain opportunity.

Tips for spotting it

  • Find bivalue cells first. The chain is built from them.
  • The pivot must see both wings. Wings do not need to see each other.
  • Each of the three cells must be exactly bivalue. Three candidates anywhere kills the pattern.
  • Z is the elimination digit. Always.

Common mistakes

  • Wings with three candidates. The structure requires exactly two per cell.
  • Eliminating X or Y instead of Z.
  • Forgetting the visibility condition. The pivot must see both wings.
  • Confusing XY-wing with XYZ-wing, which has a trivalue pivot.

Practise it

Try expert sudoku. Mark every candidate fully and list the bivalue cells before doing anything else. Test each one as a pivot. After a few solves, XY-wing becomes the first technique you reach for when X-wing fails. Then graduate to XYZ-wing and coloring.

Put XY-Wing into practice

Play expert sudoku →Rate a puzzle's difficultyCheck your solution

XY-Wing FAQ

What is an XY-Wing in sudoku?
An XY-Wing is a three-cell pattern built from bi-value cells, meaning cells with exactly two candidates. A pivot cell holding candidates X and Y sees two pincer cells, one holding X and Z and the other Y and Z, where each pincer shares a unit with the pivot. Whichever value the pivot takes, one of the pincers is forced to be Z, so Z can be eliminated from any cell that sees both pincers.
How do you find an XY-Wing?
Look for a bi-value pivot cell with candidates XY, then find two other bi-value cells it can see, one containing XZ and the other YZ, so that the three cells together use exactly three digits X, Y and Z. Once located, identify the cells that both pincers can see, since those are where the shared candidate Z can be removed. The pivot and pincers can lie in any mix of rows, columns, or boxes as long as the required cells share units.
What's the difference between an XY-Wing and an X-Wing?
They are unrelated despite the similar names. An X-Wing is a single-digit fish using a rectangular pattern across two rows and two columns, while an XY-Wing is a multi-digit chain of three bi-value cells involving three different candidates. X-Wing reasoning is about one digit appearing twice per line, whereas XY-Wing reasoning follows a pivot forcing one of two pincers to hold the eliminating digit.
Why does an XY-Wing elimination always work?
The pivot cell must be either X or Y. If it is X, the XZ pincer is forced to Z; if it is Y, the YZ pincer is forced to Z. Either way one pincer becomes Z, so any cell seeing both pincers cannot be Z and the candidate can be safely removed regardless of which value the pivot actually holds.

Related strategies