Unique Rectangle Type 1

Level 3 · Yellow Belt

Strategy:

Unique Rectangles

Requires:

Naked Pair

Learn after:

Avoidable RectangleHidden Unique RectangleUnique Rectangle Type 2Unique Rectangle Type 3Unique Rectangle Type 4Unique Rectangle Type 5

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

Look for Unique Rectangle Type 1.

1

Unique Rectangle Type 1

Find four cells forming a rectangle across exactly 2 boxes, all containing candidates 3 and 8.

2

Unique Rectangle Type 1

Three of these cells have ONLY { 3, 8 }. This would create a 'deadly pattern' with 2 solutions.

3

Unique Rectangle Type 1

If the fourth cell also stayed limited to 3 and 8, the rectangle could swap those two digits and create multiple solutions.

4

Unique Rectangle Type 1

Cell r8c2 is the only rectangle cell with extra candidates, so it cannot be allowed to keep both 3 and 8.

5

Unique Rectangle Type 1

Remove 3 and 8 from r8c2 to break the deadly pattern.

6

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.