Uniqueness Techniques (Unique Rectangle etc.)

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Uniqueness Techniques (Unique Rectangle etc.)

What It Is

Uniqueness techniques rely on a puzzle’s single solution. A unique rectangle arises when four cells forming a rectangle hold the same two candidates; an extra candidate or elimination breaks the pattern to avoid multiple solutions.

When to Use

Mid-to-late game when you spot two rows and two columns forming a rectangle with paired candidates.

How to Apply (Step-by-Step)

  1. Identify the rectangle: four corner cells in two rows/columns with the same two candidates.
  2. Assess the danger: without intervention, swapping those two digits could give another solution.
  3. Find the hint: often one corner has an extra candidate.
  4. Eliminate via uniqueness: place the extra candidate or remove symmetry-breaking candidates per the pattern type.
  5. Continue with the now-unique grid.

If four corners share {5,8} and one corner also has 3, that corner must be 3 to prevent multiple solutions—place it and proceed.

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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