Unique Rectangle Type 4

Level 7 · Green Belt

Strategy:

Unique Rectangles

Requires:

Unique Rectangle Type 1

Overview

Unique Rectangle Type 4 occurs when one of the deadly pair digits forms a conjugate pair in the roof cells' shared house. Since that digit is locked in the roof, the other deadly pair digit can be eliminated from both roof cells.

How It Works

  1. Find a potential deadly rectangle with candidates {X,Y}.
  2. Two floor cells have only {X,Y}; two roof cells have extras.
  3. Check if digit X (or Y) forms a conjugate pair in the roof cells' shared row, column, or block.
  4. Since X must be in one of the roof cells, eliminate Y from both roof cells.

Example

Look for Unique Rectangle Type 4.

1

Unique Rectangle Type 4

Find four cells forming a rectangle across 2 boxes. Two cells have only { 5, 9 }.

2

Unique Rectangle Type 4

The roof cells r1c2 and r2c2 share column 2 with extra candidates.

3

Unique Rectangle Type 4

Digit 9 forms a conjugate pair in column 2 (appears only in the roof cells).

4

Unique Rectangle Type 4

Since 9 is locked in the roof, 5 can be eliminated from both roof cells: r1c2 and r2c2.

5

Result after applying the technique.

Tips & Patterns

  • Type 4 relies on one deadly pair digit being a conjugate pair in the roof's house.
  • The locked digit prevents the deadly pattern, so the other digit is safe to eliminate.
  • This often produces more eliminations than Type 2.