Unique Rectangle Type 4

Level 8 · Blue Belt

Strategy:

Unique Rectangles

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

Starting position

Look for Unique Rectangle Type 4.

1

Find a rectangle on 1 and 6

Find four cells forming a rectangle across 2 boxes. Two cells have only { 1, 6 }.

2

Roof cells share column 3

The roof cells r5c3 and r9c3 share column 3 with extra candidates.

3

1 is a conjugate pair in column 3

Digit 1 forms a conjugate pair in column 3 (appears only in the roof cells).

4

Remove 6 from both roof cells

Since 1 is locked in the roof cells, remove 6 from both roof cells: r5c3 and r9c3.

5

Result

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.