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Unique rectangle

Assume the puzzle has one solution — and avoid creating a deadly pattern.

Unique rectangle (Type 1) is the simplest of the uniqueness techniques. It assumes the puzzle has exactly one solution — which any well-formed sudoku does.

Find four cells arranged in a rectangle (two rows × two columns) confined to exactly two boxes. If three of the four cells hold only candidates {X, Y}, the fourth cell — which currently shows {X, Y, …extras} — cannot be just X or Y. If it were, both X-Y and Y-X arrangements of the four cells would be valid, giving the puzzle two solutions. So X and Y must be removed from the fourth cell.

Some solvers regard uniqueness techniques as cheating — they use a property of the puzzle's construction rather than pure logic. We document them because they're standard in the community, but mark them with a 'uniqueness assumption' label.

When to look for it

When the candidate grid is dense and you spot a near-deadly pattern of four cells in a 2×2 that all share {X, Y} as candidates.

How to apply it

  1. Identify four cells in a 2×2 across two boxes where three cells are bivalue {X, Y}.
  2. The fourth cell will currently list X, Y, plus at least one other candidate.
  3. Remove X and Y from the fourth cell.

Example

47
Three corners hold only {4,7}. The fourth must hold its extras, not 4 or 7.