Avoidable Rectangle

Level 6 · Orange Belt (Green Stripe)

Strategy:

Unique Rectangles

Requires:

Unique Rectangle Type 1

Overview

Avoidable Rectangle is similar to Unique Rectangle but involves solved cells. When three cells of a rectangle are already solved with two alternating values, the fourth cell must avoid completing the deadly pattern.

How It Works

  1. Find four cells forming a rectangle across two boxes.
  2. Three corners are already solved, using two values that alternate.
  3. The fourth (unsolved) cell has one of these values as a candidate.
  4. Eliminate that candidate to prevent the deadly pattern that would allow multiple solutions.

Example

Look for Avoidable Rectangle.

1

Avoidable Rectangle

Cells r2c9, r2c8, r4c9, and r4c8 form a rectangle across 2 boxes. Three corners are determined with values 4 and 1.

2

Avoidable Rectangle

If r2c9 were 1, these four non-given cells would form a two-solution rectangle.

3

Avoidable Rectangle

Avoidable Rectangle assumes a valid puzzle has one solution, so this rectangle must be avoided.

4

Avoidable Rectangle

So 1 at r2c9 is the candidate that must be removed.

5

Avoidable Rectangle

Eliminate 1 from r2c9.

6

Result after applying the technique.

Tips & Patterns

  • Avoidable Rectangles use the same uniqueness logic as Unique Rectangles but with solved cells.
  • Types 2, 3, and 4 parallel the UR types.
  • Look for rectangles where three corners are filled with two alternating digits.