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Alternating Inference Chains (AICs)

Visual diagram for alternating inference chains aics Sudoku technique
See the pattern before reading the steps.

What It Is

AICs build chains alternating strong and weak links. Starting and ending on a strong link forms a loop that can force contradictions or guarantee eliminations where both ends are seen.

When to Use

Tough puzzles when simpler patterns fail; after coloring or fish patterns, to avoid guessing.

How to Apply (Step-by-Step)

  1. Identify strong links (two-only candidates in a unit or bi-value cells).
  2. Alternate with weak links between candidates.
  3. Construct a chain loop: True → False → True → … back to start.
  4. Look for conclusions: contradictions eliminate; matching endpoints seen by a cell eliminate that candidate there.
  5. Eliminate and simplify, then repeat.

If two endpoints of a chain are both candidate 5 and at least one must be true, any cell seeing both cannot be 5—an immediate elimination.

See also

Scanning / Cross-Hatching Single Candidate (Naked Single) Single Position (Hidden Single) Naked Pairs / Triples / Quads Hidden Pairs / Triples / Quads Pointing Pairs / Triples (Locked Candidates Type 1) Box–Line Reduction (Locked Candidates Type 2) X-Wing Swordfish Jellyfish XY-Wing XYZ-Wing W-Wing Alternating Inference Chains (AICs) Forcing Chains / Forcing Nets Nishio Coloring Multi-Coloring Uniqueness Techniques (Unique Rectangle etc.) Fish Variants (Finned X-Wing, Sashimi etc.) ALS Techniques (ALS-XZ, ALS Chains) Sue de Coq Pattern Overlay / Template Method
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