Y-Wing

The Y-Wing is a three-cell pattern that lets you eliminate a candidate by linking two bi-value cells through a shared pivot. The pivot has two candidates, A and B. Each wing shares exactly one candidate with the pivot: one wing is A with C, and the other wing is B with C. If both wings see a common cell, you can eliminate C from that cell because whichever value the pivot takes, one wing will force C to be false there.

When To Look For It

• You find a pivot cell with exactly two candidates, A and B.
• There is a second bi-value cell in the same row, column, or box as the pivot that contains A and C.
• There is a third bi-value cell that sees the pivot and contains B and C.
• The two wing cells are not in the same cell and are positioned so that at least one other cell can see both wings.

How It Works

1. Identify a pivot cell with candidates A and B.
2. Find a first wing cell that sees the pivot and has candidates A and C.
3. Find a second wing cell that sees the pivot and has candidates B and C.
4. Locate any cells that can see both wing cells. In those cells, eliminate candidate C.

Quick Example

Suppose the pivot has candidates 2 and 7. One wing has candidates 2 and 9, and the other wing has candidates 7 and 9. If a target cell sees both wings, it cannot be 9. If the pivot is 2, the 9 in the 2-9 wing is false for the target; if the pivot is 7, the 9 in the 7-9 wing is false for the target. Either way, the target cannot be 9.

Why It Works

The pivot must take either A or B. In each case, one of the wings loses its shared candidate with the pivot and forces the other candidate C within that wing, which prevents C from appearing in any cell that sees both wings. Since this is true regardless of which value the pivot takes, C can be safely eliminated from the intersection.

Tips

• Search for bi-value cells first. Mark cells with exactly two candidates; they are the building blocks of Y-Wings.
• Check visibility. The wings must each see the pivot, and your elimination works only on cells that see both wings.
• Avoid same-house traps. If both wings are in the same box and see each other in a way that blocks a common target, the pattern may not yield an elimination.
• Chain with basics. After Y-Wing eliminations, rescan for singles using Last Possible Number and Last Remaining Cell to convert progress into placements.

Common Mistakes To Avoid

• Using a pivot with more than two candidates. The pivot must be bi-value.
• Choosing wings that share the same pair as the pivot. Each wing must share exactly one candidate with the pivot and carry a different second candidate C.
• Eliminating in cells that do not see both wings. Only cells that see both wings are valid targets.

Where You Will Use It

Y-Wing appears frequently from medium through hard difficulties. It is especially helpful when singles dry up but the grid has many bi-value cells. Use it to clear stubborn candidates and reopen progress without guessing.