The XY-Wing Technique in Sudoku Explained

When to reach for it

The XY-Wing is an advanced move for hard and extreme boards, the kind where singles, pairs and even the X-Wing have run dry. Unlike those techniques, it links three separate cells together, which lets it reach candidates sitting far apart on the grid.

The three cells

Every XY-Wing is built from three cells that each hold exactly two candidates. One cell is the pivot. It shares a row, column or box with each of the other two, which are called the pincers. The trick is in how their candidates overlap.

Label the pivot's two candidates X and Y. One pincer must hold X and a third value Z, so it reads X and Z. The other pincer must hold Y and that same Z, so it reads Y and Z. The pivot sees both pincers, but the two pincers do not need to see each other.

The forcing that makes it work

Whatever the pivot turns out to be, one of the pincers is forced to become Z. If the pivot is X, the first pincer cannot be X, so it becomes Z. If the pivot is Y, the second pincer cannot be Y, so it becomes Z. Either way, one of the two pincers ends up as Z.

That certainty is the payoff. Any cell that can see both pincers at once cannot be Z, because one of the pincers is going to claim it. You can safely remove Z from every one of those shared cells, which often breaks a stubborn board wide open.

How to find an XY-Wing

1. Keep clean notes, since the whole pattern lives in two-candidate cells.
2. Find a pivot cell with candidates X and Y.
3. Look for a pincer it sees that reads X and Z, and another it sees that reads Y and Z.
4. Remove Z from any cell that sees both pincers.

Take it slowly

The XY-Wing rewards patience more than speed. Trace the logic once or twice by hand until the forcing feels obvious, and it will start to jump out at you. Load an extreme board in Shapedoku, keep your notes tidy, and hunt for a pivot with its two matching pincers.