Alternating Inference Chains (AICs)

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Alternating Inference Chains (AICs)

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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