XY-Wing

The XY-Wing — also known as the Y-Wing — is one of the most satisfying intermediate techniques to learn. It uses three cells, each with just two candidates, arranged so that whatever happens, one particular digit is forced out of a fourth cell. Once you see the shape, you can't unsee it.

The three cells

An XY-Wing is built from three bi-value cells (two candidates each):

• A pivot holding {X, Y} — here {5, 8}.
• A pincer holding {X, Z} — here {5, 3} — that the pivot can see.
• A pincer holding {Y, Z} — here {8, 3} — that the pivot can also see.

Now follow the logic. If the pivot is 5, the first pincer must be 3. If the pivot is 8, the second pincer must be 3. Either way, one of the two pincers is a 3 — so any cell that can see both pincers cannot be 3.

Step by step

1. Find a bi-value pivot — any cell with exactly two candidates, {X, Y}.
2. Look for pincers it can see: one cell {X, Z} and one cell {Y, Z}, sharing a third digit Z with each other.
3. Find the targets. Any cell that can see both pincers is fair game.
4. Eliminate Z from those target cells.
5. Re-scan. The elimination often triggers a single nearby.

Why it's called Y-Wing

The three cells fan out from the pivot like the arms of a Y, which is where the older name comes from. It's closely related to the X-Wing family, but where the X-Wing tracks a single digit across a rectangle, the XY-Wing juggles three digits across three cells. Both are worth having in your kit for harder grids.

Common mistakes

• Pincers that don't share Z. The two pincers must have a common third digit — {5,3} and {8,3} share the 3. {5,3} and {8,9} do not, and form no wing.
• A target that sees only one pincer. The elimination only works on cells that see both pincers.
• Using cells with three candidates. All three wing cells must be strictly bi-value.

Which Sudoku types is this best for?

The same logic applies across variants, but it pays off more in some than others.