GridWits
Extreme tier Technique 28 of 46 Used by Smart Hint

Alternating Inference Chains (AIC)

The most general chaining technique: follow a chain of candidates that alternates "at least one of these is true" with "at most one of these is true", hopping between digits as it goes. Whichever way it resolves, one of the two chain ends must be true.

How it works

  1. 1Read the highlighted cells as a chain of candidates. It alternates two kinds of link — strong ("at least one of these is true") and weak ("at most one is") — and starts and ends on a strong one.
  2. 2A1 holds only {3, 5}, so if it isn't 5 it is 3: strong, inside one cell. A1's 3 and C3's 3 share the top-left box, so at most one of them is a 3: weak. Row 3 has only C3 and G3 left for 3, so that link is strong again.
  3. 3G3 carries three candidates, so its 3 and its 5 are only a weak link — but column G has just G3 and G6 left for 5, which is strong, and closes the chain.
  4. 4Follow it end to end: if A1 isn't 5, G6 is. A6 sees A1 down column A and G6 across row 6, so its 5 goes. Strong links from a unit's last two homes — not only from two-candidate cells — are the reach that lets AIC cover X-Chains, XY-Chains and most wings as one pattern.

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 3 5 3 4 3 5 8 2 5 5 9 5 3 3 3 5 5 5
  • 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 Exocet →

Two "base" cells constrain two "target" cells elsewhere on the board so tightly that the targets' candidates must come entirely from the base cells' digits.