Peak Sudoku

XY-Wing

Three bivalue cells – a hinge and two pincers.
All techniques

Overview

Tier 4
Fish, wings, chains & uniqueness
Typical difficulty
Peak Score 55–70
Also known as
Y-Wing, Bent Triple, Hinge and Pincers

An XY-Wing uses three two-candidate cells: a pivot and two wings. Whichever value the pivot takes, one of the wings is forced to a shared common digit, eliminating it from any cell seeing both wings.

The XY-Wing (often called Y-Wing) is one of the most elegant and common expert techniques. It consists of three cells, each having exactly two candidates. One cell acts as the 'pivot' or 'hinge' holding two candidates (such as 3 and 8). The other two cells are 'pincers' or 'wings' seeing the pivot: one holding 3 and 5, and the other holding 8 and 5. If the pivot is 3, the first wing becomes 5. If the pivot is 8, the second wing becomes 5. In all possible outcomes, at least one wing MUST be 5. Therefore, any cell that sees both wings can never be 5.

Worked examples

1 / 5
Reading the exampleCells forming the patternCells losing candidatesEliminated candidates
The pivot R4C3 holds {5,8}, one wing R9C3 holds {5,6} and the other wing R4C8 holds {6,8}. Whichever digit the pivot takes, one wing must be 6, so 6 can be removed from any cell that sees both wings.
Removes: 6 from R9C8

How to apply it

Spotting the pattern and making the deduction, in order.

  1. Find a two-candidate pivot cell (for example, with candidates 3 and 8).
  2. Locate two wing cells that each share a house with the pivot: one holding 3 and a new digit 5, and the other holding 8 and 5.
  3. If the pivot is 3, the first wing is forced to be 5.
  4. If the pivot is 8, the second wing is forced to be 5.
  5. In either outcome, at least one of the wings must be 5.
  6. Eliminate candidate 5 from any cell in the grid that has a direct line of sight to both wings.

Common mistakes

  • Choosing wings that do not both see the pivot cell.
  • Eliminating the wrong digit: you must eliminate the digit shared by the two wings, not the digits in the pivot.
  • Eliminating from cells that only see one of the two wings.

Frequently asked questions

Do the two wings have to see each other?
No! The wings only need to see the pivot cell. They do not need to see each other.
Can an XY-Wing be contained within a single 3x3 box?
If all three cells were in one box, they would simply form a Naked Triple. An XY-Wing is powerful because the wings reach outside the box across rows and columns.
Peak Score 65–75XYZ-WingXY-Wing with a three-candidate hinge.Peak Score 65–80W-WingTwo bivalue cells with identical candidates, bridged by a strong link on one digit.Peak Score 70–85XY-ChainA chain of bivalue cells that forces a digit at both endpoints.

Put XY-Wing into practice

Try a puzzle from the Hard tier (Peak Score 51–60).

Play a Hard puzzleAll 25 techniques