Unique Rectangle Type 1

Level 4 · Yellow Belt (Orange Stripe)

Strategy:

Unique Rectangles

Requires:

Naked Pair

Learn after:

Unique Rectangle Type 2

Overview

Unique Rectangle Type 1 prevents a deadly pattern where four cells with identical candidate pairs would create multiple solutions. When three corners have only the pair and one has extras, the pair can be eliminated from the fourth.

How It Works

  1. Find four cells forming a rectangle across exactly two boxes.
  2. Three cells contain only candidates {X,Y}.
  3. The fourth cell contains {X,Y} plus additional candidates.
  4. Eliminate X and Y from the fourth cell to prevent the deadly pattern.

Example

Starting position

Look for Unique Rectangle Type 1.

1

Find a rectangle on 7 and 8

Find four cells forming a rectangle across exactly 2 boxes, all containing candidates 7 and 8.

2

Three corners hold only 7 and 8

Three of these cells have only { 7, 8 }. If the fourth did too, the rectangle would allow two interchangeable solutions.

3

The fourth corner must break the pair

Because a valid Sudoku has one solution, the fourth cell cannot stay limited to 7 and 8.

4

Only r9c3 has extra candidates

Cell r9c3 is the only rectangle cell with extra candidates, so it cannot be allowed to keep both 7 and 8.

5

Remove 7 and 8 from r9c3

Remove 7 and 8 from r9c3 to avoid the two-solution rectangle.

6

Result

Result after applying the technique.

Tips & Patterns

  • The rectangle must span exactly two rows, two columns, and two boxes.
  • This technique assumes the puzzle has a unique solution.
  • If X and Y remained in all four cells, they could be swapped infinitely.