Box–Line Reduction (Locked Candidates Type 2)

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Box–Line Reduction (Locked Candidates Type 2)

What It Is

Box–line reduction (claiming) is the inverse of pointing: if all candidates for a number in a row/column sit inside one box, that number is claimed there; other cells in the box outside the line can’t hold it.

When to Use

Mid-game while scanning rows/columns with penciled candidates; look for a line whose remaining spots for a digit all fall in one box.

How to Apply (Step-by-Step)

  1. Pick a line: examine each incomplete row/column; mark candidate positions for missing numbers.
  2. Spot one-box concentration: if a number’s possible positions in that line are all in the same box, you have a box–line scenario.
  3. Eliminate in the box: remove that candidate from other cells of that box not in the line.
  4. Repeat across lines; these reductions can chain into new singles or subsets.

If row 8 can place digit 3 only inside the top-right box, eliminate 3 from the other cells of that box outside row 8 to reveal fresh options.

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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