Y-Wing (XY-Wing) Sudoku Strategy

Note: The Y-Wing is also reffered to as the XY-Wing or Bent Triple strategy. The shape of this strategy is that of the letter "Y" where as the "XY" placed importance on the candidates involved in the strategy.

What is the Y-Wing Sudoku Strategy?

The XY Wing Sudoku strategy will help you solve complex problems. This is a strategy that can be used when there are three cells with two candidates in each cell – where one of the numbers in each cell matches with one of the numbers in the other cells.For it to be an XY Wing strategy the middle cell has to intersect with both of the outside cells also known as the wings.

The Y-Wing Setup

Look for three cells in the Sudoku grid, each with exactly two candidates (pencil marks). These three cells form a “Y” shape: one cell acts as the stem, and the other two are the branches. The stem cell must intersect both branch cells (i.e., they share a row, column, or block). Crucially, the two branch cells cannot intersect each other.

Understand the Y-Wing Logic

Suppose we have three cells: A (stem), B (branch 1), and C (branch 2). A and B share a candidate (e.g., both have a “1”), and A and C share another candidate (e.g., both have a “9”). The third candidate (e.g., “3”) appears only in B and C. If A were the “9,” then B would be the “1.” If A were the “3,” then C would be the “1.” Either way, one of the branch cells must be a “1.” Now, any cell that intersects both branch cells cannot be a “1.”

Y-Wing Sudoku Example

  • The green cell (A) has candidates “3” and “9.”
  • The blue cells (B and C) have candidates “1” and either “3” or “9.”
  • The pink cells intersect both blue cells.
  • Since the green cell dictates that one of the blue cells must be a “1,” we can eliminate the “1” candidate from the pink cells.
  • This creates a Lone Single in the right pink cell, solving it.

How to find an Y-Wing (XY-Wing)?

To help find situations where the Y-Wing strategy can be used look for cells with only two candidates in your sudoku problems grid. If you find three cells that match the conditions of the Y-Wing, you can apply the logic from this strategy as outlined above.

Once you have had practice correctly identifying the Y-Wing problem within sudoku problems, you will be able to find situations where you can use the Y-Wing strategy eaiser and apply it faster. This will help you become more efficient at solving more complex sudoku problems.