Y-Wing

Three cells. Three candidates. One elimination.

The Y-Wing — also called XY-Wing — is an advanced elimination technique built from three cells instead of the four-cell rectangle an X-Wing relies on. It requires a pivot cell with exactly two candidates, {A, B}, plus two pincer cells visible to the pivot — sharing its row, column, or box — with candidates {A, C} and {B, C}.

If the pivot holds A, the first pincer can't also hold A, so it's forced to C; if the pivot holds B, the same logic forces the second pincer to C. Either way, at least one pincer ends up holding C, even though you can't say which one. That guarantee means any cell visible to both pincers — sharing a row, column, or box with each — can never be C, and the candidate can be eliminated there. Y-Wings are easy to miss since the three cells can sit far apart on the grid, connected only by shared lines.

How It Works

A Y-Wing involves three cells, each with exactly two candidates:

  • Pivot: a cell with candidates {A, B}
  • Pincer 1: a cell visible to the pivot (same row, column, or box) with candidates {A, C}
  • Pincer 2: a cell visible to the pivot (same row, column, or box) with candidates {B, C}

The pivot must be either A or B. Whichever it is, one of the pincers is forced to C:

  • If pivot = A, then Pincer 1 ≠ A, so Pincer 1 = C.
  • If pivot = B, then Pincer 2 ≠ B, so Pincer 2 = C.

Either way, one of the two pincers must hold C. Therefore, any cell that is visible to both pincers — sharing a row, column, or box with each — cannot be C. Eliminate it.

  1. Find a pivot cell with two candidates {A, B}.
  2. Find two pincer cells, each visible to the pivot, with candidates {A, C} and {B, C}.
  3. Identify every cell visible to both pincers. Eliminate C from those cells.

Example

Below board presents an example of a Y-Wing pattern with pivot cell {1, 2} and pincers {1, 3} and {2, 3}.

pivot — {1, 2}
pincers — {1, 3} and {2, 3}
sees both pincers — 3 eliminated

The pivot shares a box with one pincer and a row with the other. If the pivot is 1, the first pincer is forced to 3. If the pivot is 2, the second pincer is forced to 3. Either way, one of the two pincers holds 3 — so any cell that can see both pincers (here, sharing a row with one and a column with the other) cannot be 3.

On Evil Boards

The Y-Wing is often very hard to spot. The pivot and its two pincers may be scattered very wide across the board, connected only through shared rows or columns. It's difficulty combined with its low yield — at most one elimination — makes it most useful as a late game technique. If the board shows a repeating pattern across rows or columns, try checking for an x-wing or a swordfish instead.