GridWits
Extreme tier Technique 21 of 46 Used by Smart Hint

XY-Chain

A longer alternating chain of links that traces a digit (or a sequence of digit pairs) across the board to find a single elimination.

How it works

  1. 1Every highlighted cell holds exactly two candidates. A1 and A4 share column A and the digit 5; A4 and D4 share row 4 and the digit 6; D4 and D8 share column D and the digit 7.
  2. 2Suppose A1 isn't 1. Then it's 5, so A4 must be 6, so D4 must be 7, so D8 must be 1 — a two-candidate cell that loses one candidate has no choice left.
  3. 3So A1 is 1, or D8 is; one end of the chain always holds it. D1 sees A1 along row 1 and D8 down column D, so its 1 goes.
  4. 4Three links is already past anything a wing can reach, and a real chain often runs much longer before its two ends line up on one digit.

Play a Sudoku that needs this technique →

A 1 B 2 C 3 D 4 E 5 F 6 G 7 H 8 I 9 1 5 1 9 5 6 6 7 1 7 1 5 5 6 6 7 7 1 1
  • First colour in the chain
  • Second colour in the chain
  • Where the conclusion lands
  • Candidate ruled out
  • Strong link — At least one endpoint must be true.
  • Weak link — At most one endpoint can be true.
Next in the ladder X-Cycles →

A single digit's strong and weak links are traced into a closed loop — a continuous loop yields eliminations at its weak links, a discontinuous one pins or clears its meeting cell outright.