XY-Wing
XY-Wing uses three cells with two candidates each to eliminate a shared candidate elsewhere. It's a powerful advanced technique that often unlocks stuck puzzles.
What is an XY-Wing?
An XY-Wing consists of three special cells:
- Pivot cell: Contains candidates [X,Y]
- Wing 1: Contains [X,Z], can "see" the pivot
- Wing 2: Contains [Y,Z], can "see" the pivot
The key: both wings share candidate Z, but the pivot doesn't have Z.
Visual Pattern
The three cells:
- Pivot A1: [X,Y] — the "hinge" of the wing
- Wing 1 at C1: [X,Z] — shares X with pivot
- Wing 2 at A3: [Y,Z] — shares Y with pivot
The Logic Explained
Think about what happens when you place a number in the pivot:
If the pivot becomes X:
- Wing 1 can't be X anymore (they share a row)
- Wing 1 must be Z
- Z is placed!
If the pivot becomes Y:
- Wing 2 can't be Y anymore (they share a column)
- Wing 2 must be Z
- Z is placed!
Either way, one of the wings MUST be Z!
The result: Any cell that can "see" BOTH wings cannot contain Z.
Making Eliminations
Finding elimination targets:
- Identify both wing cells
- Find cells that can "see" both wings (same row/column/box)
- Eliminate Z from those cells
The pivot doesn't matter for eliminations — only the wings!
Concrete Example
The XY-Wing:
- X = 3, Y = 7, Z = 9
- Pivot at A1: [3,7]
- Wing 1 at A4: [7,9] — shares 7 with pivot (same column A)
- Wing 2 at B7: [3,9] — shares 3 with pivot (same box)
Elimination: Cell C7 sees both wings (same row as Wing 2, same box as Wing 1). Eliminate 9 from C7!
How to Find XY-Wings
Method 1: Start from Bi-Value Cells
- Find all cells with exactly 2 candidates
- Pick one as a potential pivot [X,Y]
- Look for a cell with [X,Z] that sees the pivot
- Look for a cell with [Y,Z] that sees the pivot
- Check if Z is the common candidate in both wings
- Eliminate Z from cells seeing both wings
Method 2: Candidate Focus
- Pick a candidate Z that you want to eliminate
- Find two bi-value cells with Z that share a common peer
- Check if that peer forms a valid pivot with them
Method 3: Pattern Recognition
With practice, XY-Wings become visual:
- Look for three bi-value cells forming a "bent" shape
- The pivot is in the middle, wings are on the ends
- Check that candidates interlock correctly
The "Seeing" Requirement
For an XY-Wing to work:
| Cell | Must see... |
|---|---|
| Pivot | Both wings |
| Wing 1 | The pivot |
| Wing 2 | The pivot |
| Wings | Don't need to see each other! |
"Seeing" means: Same row, same column, or same box.
Types of XY-Wings
Same-Box Wing
Both wings are in the same box as the pivot:
Different-Unit Wing
Wings see the pivot through different units:
Practice Exercises
Exercise 1: Identify the XY-Wing
Hint
Find three cells with exactly 2 candidates each. Check if they form the [XY], [XZ], [YZ] pattern.
Answer
The bi-value cells are:
- A: [2,4]
- D: [4,7]
- H: [2,7]
Check the pattern:
- A [2,4] as pivot: X=2, Y=4
- D [4,7] as wing: shares 4 (Y), has 7 as Z
- H [2,7] as wing: shares 2 (X), has 7 as Z
XY-Wing found! Pivot [2,4], Wing 1 [4,7], Wing 2 [2,7]. Z = 7.
Elimination: Find cells that see both D and H. Eliminate 7 from them!
Exercise 2: Find the elimination target
Answer
- Pivot [2,4] at A1
- Wing 1 [4,7] at D1 (shares row with pivot)
- Wing 2 [2,7] at A3 (shares column with pivot)
- Z = 7
Find cells seeing both wings:
- Wing 1 is in row 1, column 4
- Wing 2 is in row 3, column 1
- Cell D3 (row 3, column 4) sees both!
Eliminate 7 from D3!
XYZ-Wing: The Extension
An XYZ-Wing is similar, but the pivot has three candidates [X,Y,Z]:
- Pivot: [X,Y,Z]
- Wing 1: [X,Z]
- Wing 2: [Y,Z]
The logic: Same as XY-Wing, but the pivot could also be Z.
Elimination: Any cell seeing ALL THREE cells (pivot and both wings) cannot be Z.
See XYZ-Wing for a full explanation with examples.
Common Mistakes
Mistake 1: Wrong candidate assignment
Make sure X,Y,Z are correctly identified:
- X: shared between pivot and wing 1
- Y: shared between pivot and wing 2
- Z: shared between both wings (NOT in pivot)
Mistake 2: Eliminating from wrong cells
Only eliminate from cells that see BOTH wings. Not cells that see only one wing or only the pivot.
Mistake 3: Wings must see pivot
Both wings must see the pivot. If a wing doesn't see the pivot, the logic breaks.
Mistake 4: Confusing with other patterns
XY-Wing requires specific candidates:
- Pivot has exactly [X,Y]
- Wing 1 has exactly [X,Z]
- Wing 2 has exactly [Y,Z]
When XY-Wings Appear
- Easy puzzles: Never needed
- Medium puzzles: Rarely needed
- Hard puzzles: Occasionally useful
- Expert puzzles: Common and often essential
- Extreme puzzles: Frequently required
Quick Reference
XY-Wing structure:
- Pivot: [X,Y] — the center cell
- Wing 1: [X,Z] — sees the pivot
- Wing 2: [Y,Z] — sees the pivot
- Z: common in wings, absent from pivot
Finding XY-Wings:
- Find bi-value cells (exactly 2 candidates)
- Look for pivot-wing-wing patterns
- Verify X,Y,Z assignment
- Find elimination targets
Elimination rule:
- Eliminate Z from cells that see BOTH wings
- Pivot is irrelevant for eliminations
- Wings don't need to see each other
Why it works:
- If pivot = X → Wing 1 = Z
- If pivot = Y → Wing 2 = Z
- Either way, one wing must be Z!
What's Next?
Once you master XY-Wing:
- XYZ-Wing — Same pattern with a three-candidate pivot
- W-Wing — Four-cell pattern with strong links
- Remote Pairs — Chain of bi-value cells
- XY-Chains — Extended chains through bi-value cells