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Sudoku techniques

XY-Wing

Three cells with two candidates each, linked through a pivot, make one digit impossible wherever both ends can see.

The idea

Find a pivot cell with two candidates, X and Y. Then find two cells it sees: one with X and Z, the other with Y and Z (the same Z).

If the pivot is X, the first cell can't be X, so it is Z. If the pivot is Y, the second cell is Z. Either way, one of the two outer cells is Z.

So any cell that sees both outer cells can't be Z. This is also called a Y-Wing.

How to spot it

  • Collect the cells with exactly two notes. Pick one as the pivot and look for two cells it sees that each share one of its digits and share a third digit with each other.
  • Then look at the cells both outer cells see (often in a box corner or at a row-column crossing) for that third digit.

Worked example

XY-Wing on a real puzzle

From our master puzzle #12 (26 clues), after 26 earlier steps of our solver. Gold cells make the pattern; red notes are the ones it rules out.

Before. XY-Wing: whatever goes in row 4, column 7, one of the two marked cells it sees must be 3. So any cell that sees both of them can't be 3.
After. Remove 3 from row 3, column 8; row 5, column 7.

Play this puzzle

How often our puzzles need it

Our solver works like a careful player: it always uses the easiest technique that still makes progress. Counting the puzzles where it had to use xy-wing at least once:

  • 918 of our 1000 master puzzles

The easiest level that can need it is master Sudoku.