The Y-Wing, also known as XY-Wing, is a powerful advanced Sudoku technique that uses three bivalue cells (cells with exactly two candidates each) arranged in a specific logical configuration. The pattern involves a pivot cell and two wing cells. The pivot cell shares one candidate with each wing cell, and the two wing cells share a common candidate with each other but not through the pivot. The pivot can see both wings, but the wings do not need to see each other.
The logic works as follows: suppose the pivot has candidates {A, B}, one wing has {A, C}, and the other wing has {B, C}. If the pivot is A, then the first wing (which the pivot sees) cannot be A, so it must be C. If the pivot is B, then the second wing cannot be B, so it must be C. In either case, at least one wing cell must contain C. Therefore, any cell that can see both wing cells and contains candidate C can have C safely eliminated — because C is guaranteed to be in at least one wing.
The Y-Wing is the simplest member of the XY-Chain family and serves as an excellent introduction to chain-based reasoning in Sudoku. It appears frequently in hard and very hard puzzles and can produce eliminations that no amount of basic or intermediate techniques can achieve. Learning to identify the pivot-wing-wing configuration and trace the logical implications trains your mind for the longer XY-Chains and other advanced chain strategies used in expert-level solving.
Try It Yourself
Walk through each step of the y-wing (xy-wing) technique on a real puzzle. Follow the instructions and try entering the correct value when prompted.
Look for bivalue cells to form a Y-Wing. Cell (3,0) has candidates {4,1}, cell (3,3) has candidates {2,8}, and cell (4,0) has candidates {6,4}. We need to find a pivot-wing-wing arrangement among bivalue cells.
Step-by-Step Guide
Identify all bivalue cells in the grid (cells with exactly two candidates).
Select a potential pivot cell with candidates {A, B}.
Find a wing cell visible to the pivot that shares candidate A and has a second candidate C, giving it {A, C}.
Find another wing cell visible to the pivot that shares candidate B and has second candidate C, giving it {B, C}.
Confirm that both wings share the common candidate C.
Eliminate candidate C from any cell that can see both wing cells simultaneously.
Check if the elimination resolves any cells or enables further techniques.
Imagine a fork in the road where both paths lead to the same destination — no matter which way the pivot cell goes, the shared candidate must show up in one of the wings, so anything visible to both wings is blocked.
The pivot cell's bivalue constraint creates an exhaustive case split: it must resolve to either A or B. Each case activates a different visibility constraint — choosing A eliminates A from the first wing (forcing it to C), while choosing B eliminates B from the second wing (forcing it to C). Since both branches of the case split independently force C into at least one wing cell, C is guaranteed to occupy one of the two wings in every valid solution, and any cell seeing both wings is thereby excluded from holding C.
When to use: Use Y-Wing when you spot three bivalue cells where a pivot sees two wings, each sharing one candidate with the pivot, and the two wings share a common candidate between themselves. Look for this after pencil marks reveal many bivalue cells.
Common Mistakes to Avoid
Choosing a pivot that cannot see both wings.
The pivot must share a row, column, or box with EACH wing cell. The wings do not need to see each other, but the pivot must see both.
Eliminating the wrong candidate — removing a pivot candidate instead of the shared wing candidate.
The elimination target is always the candidate shared between the two wings (C), not the candidates shared between the pivot and each wing (A or B).
Trying to apply Y-Wing with cells that have more than two candidates.
All three cells (pivot and both wings) must be bivalue — exactly two candidates each. If any cell has three or more candidates, consider XYZ-Wing instead.
More Examples
See y-wing (xy-wing) applied in different puzzle configurations to strengthen your pattern recognition.
Y-Wing with Pivot and Two Wings
Highlighted cells show the y-wing (xy-wing) pattern
Practice Puzzles
Apply the y-wing (xy-wing) technique on these mini challenges. Tap a highlighted cell and enter the correct digit.
Quick Reference
- Pattern:
- Three bivalue cells forming a pivot-wing-wing chain with candidates AB, AC, BC
- Action:
- Eliminate C from cells that see both wing cells
- Look for:
- Three bivalue cells sharing candidates in a hinge pattern