Naked Pairs / Triples / Quads

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Naked Pairs / Triples / Quads

What It Is

Naked subsets occur when cells in the same unit hold a limited set of candidates that exactly matches their count (pair=2 cells/2 numbers, triple=3/3, quad=4/4). Those candidates are locked there, so they disappear from other cells in the unit.

When to Use

Mid-game after singles; whenever you notice multiple cells sharing the same small candidate sets.

How to Apply (Step-by-Step)

  1. Scan for twin cells: in each row/column/box, find two cells with the exact same two candidates—potential naked pair.
  2. Confirm the pair: ensure no other cell in that unit has those candidates; those numbers are then locked.
  3. Eliminate elsewhere: remove those candidates from all other cells in the unit.
  4. Repeat for triples/quads: find three cells sharing three numbers or four cells sharing four numbers; eliminate those numbers from others.
  5. Use the cleanup: after elimination, recheck for new singles or simpler patterns.

Think of naked pairs/triples as a team of candidates saying, “These spots are ours.” A row with two {3,9} cells forms a naked pair—erase 3 and 9 from every other cell in that row to trigger new placements.

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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