ALS Techniques (ALS-XZ, ALS Chains)

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ALS Techniques (ALS-XZ, ALS Chains)

What It Is

An ALS has one more candidate than its cells. ALS-XZ links two ALSes sharing candidates X (restricted common) and Z. One ALS must take X, forcing the other to take Z; any cell seeing all Zs in an ALS can’t be Z. ALS chains extend this through multiple links.

When to Use

Expert level when simpler chains fail; with clustered cells having nearly locked candidate sets.

How to Apply (Step-by-Step)

  1. Identify two ALSes.
  2. Check shared candidates: X (restricted common) and Z (elimination target) appear in both.
  3. Ensure ALSes see each other on X (mutually exclusive).
  4. Eliminate Z from any cell that sees all Z positions in one ALS.
  5. For ALS chains, link multiple ALSes via different restricted commons similarly.

If ALS-A {2,7,9} and ALS-B {2,3,9} share 2 (X) and 9 (Z), one ALS gets 2, the other must use 9; eliminate 9 from cells seeing all ALS-B 9s.

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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