Forcing Chains / Forcing Nets

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Forcing Chains / Forcing Nets

What It Is

Forcing chains assume a candidate, follow implications, and see if they lead to contradiction or a shared result. Forcing nets generalize to multiple branches. They prove eliminations by exploring both possibilities.

When to Use

Last-resort logic in very challenging puzzles when pattern-based tactics fail; ideal for bi-value cells or stubborn candidates.

How to Apply (Step-by-Step)

  1. Select a target cell/candidate.
  2. Assume one value and propagate forced placements/eliminations.
  3. Note outcomes: contradiction means the assumption is false; common results across branches confirm a placement or elimination.
  4. Test the alternative if needed.
  5. Apply findings and continue solving.

If assuming a cell = 7 breaks rules, eliminate 7 there; if both branches force another cell to 9, place that 9 with certainty.

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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