My Sudoku

Extreme Used in extreme puzzles.

XY-Chain

From pair to pair

An XY-Chain goes through cells with two candidates each, every cell seeing the next and sharing a digit with it.

Take Z, a digit of the first cell. If that cell is not Z, it is its other digit; the next cell, which shares that digit, is then its own other one, and so on along the chain. When the last cell comes out as Z, either the first cell or the last is Z.

So a cell that sees both ends cannot be Z: remove it there. An XY-Wing is the shortest XY-Chain, three cells long.

What to look for

Start from a two-candidate cell and hop from cell to cell through the digit they share, until the last cell's other digit is one the first cell holds.

Example

3415568589261278915725626341676234341589213634675468936898723461234646536453636893681721539245824582487618562815679341674936836828125 112233445566778899
XY-Chain: if R1C5 {5,8} is not 8, it is 5, so R1C3 {1,5} is 1, so R1C8 {1,2} is 2, so R9C8 {1,2} is 1, so R7C9 {1,8} is 8. Either R1C5 or R7C9 is 8: remove 8 from R7C5.
  • The cells the technique relies on
  • Cells where it removes candidates, struck out in red
  • Strong link (solid line) and weak link (dashed)

Practise it

In the app, Learn › XY-Chain sets exercises on real positions, then a full puzzle that needs this technique and nothing harder.

Practise in your browser