The Y-Wing (often called XY-Wing) is a strategy that works with three cells, each containing exactly two candidates (bi-value cells).
It is sometimes described as a "Bent Triple". While a Naked Triple has three cells all in the same group, a Y-Wing connects them across different groups (e.g., a box and a column).
Interactive Example
7
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
8
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
4
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
3
1
2
3
4
5
6
7
8
9
5
1
2
3
4
5
6
7
8
9
3
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
7
1
2
3
4
5
6
7
8
9
4
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
2
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
4
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
3
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
7
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
1
2
3
4
5
6
7
8
9
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
7
1
2
3
4
5
6
7
8
9
8
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
4
1
2
3
4
5
6
7
8
9
4
1
2
3
4
5
6
7
8
9
7
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
3
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
3
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
4
1
2
3
4
5
6
7
8
9
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
7
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
6
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
2
1
2
3
4
5
6
7
8
9
5
1
2
3
4
5
6
7
8
9
4
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
7
1
2
3
4
5
6
7
8
9
2
1
2
3
4
5
6
7
8
9
5
1
2
3
4
5
6
7
8
9
3
1
2
3
4
5
6
7
8
9
8
1
2
3
4
5
6
7
8
9
6
1
2
3
4
5
6
7
8
9
7
1
2
3
4
5
6
7
8
9
9
1
2
3
4
5
6
7
8
9
4
1
2
3
4
5
6
7
8
9
1
1
2
3
4
5
6
7
8
9
8
1
2
3
4
5
6
7
8
9
4
1
2
3
4
5
6
7
8
9
7
1
2
3
4
5
6
7
8
9
1
1
2
3
4
5
6
7
8
9
3
1
2
3
4
5
6
7
8
9
9
1
2
3
4
5
6
7
8
9
6
1
2
3
4
5
6
7
8
9
5
1
2
3
4
5
6
7
8
9
2
1
2
3
4
5
6
7
8
9
Click "Apply Logic" to see the strategy in action.
Real Example Explanation
In the interactive example above, we are looking for the elimination of the number 1:
- Identify the Pivot: Look at the cell highlighted in Purple (R1C6). It contains candidates
{2, 5}. - Identify the Wings:
- Wing 1 (Green): R3C5 contains
{1, 2}. It "sees" the Pivot (they are in the same Box). - Wing 2 (Green): R6C6 contains
{1, 5}. It "sees" the Pivot (they are in the same Column).
- Wing 1 (Green): R3C5 contains
- The Logic:
- Imagine the Pivot is a 2. Then Wing 1 forces its other number: 1.
- Imagine the Pivot is a 5. Then Wing 2 forces its other number: 1.
- We don't know which one is true, but we know one of them must start a chain that ends with a 1.
- The Elimination: Since one of the two Green wings must be a 1, any cell that can see both Green wings cannot contain a 1. We remove 1 from the Red cells (R2C6 and R5C5).
How it Works
The Y-Wing relies on a chain reaction.
- Structure: Three cells (Pivot, Wing A, Wing B).
- Candidates: They share three numbers between them (X, Y, Z).
- Pivot:
{X, Y} - Wing A:
{X, Z} - Wing B:
{Y, Z}
- Pivot:
- Geometry: The Pivot sees both Wings, but the Wings don't necessarily see each other.
The "Z" is the Target The number shared by the two wings (Z) is the candidate we can eliminate. No matter what the Pivot turns out to be (X or Y), it forces one of the wings to become Z.
How to Spot It
- Find Bi-Value Cells: This strategy only works with cells having exactly 2 candidates.
- Find a Pivot: Look for a cell with
{A, B}. - Check Neighbors: Look for two other cells that see the Pivot.
- One has
{A, C}. - One has
{B, C}.
- One has
- Check Intersection: If you find this pattern, look for cells that see both wings. You can eliminate
Cfrom those intersection cells.