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ALS Techniques (ALS-XZ, ALS Chains)

Visual diagram for als techniques als xz als chains Sudoku technique
See the pattern before reading the steps.

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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