Unique Rectangle Type 3

Level 7 · Green Belt

Strategy:

Unique Rectangles

Requires:

Unique Rectangle Type 1

Overview

Unique Rectangle Type 3 has two floor cells with only the deadly pair and two roof cells with extra candidates. The extras in the roof cells form a pseudo-locked set with other cells in their shared house, allowing eliminations.

How It Works

  1. Find a potential deadly rectangle with candidates {X,Y} across two boxes.
  2. Two cells (floor) have only {X,Y}; two cells (roof) have extras beyond {X,Y}.
  3. The roof cells' extra candidates, combined with other cells in their shared house, form a locked set.
  4. Eliminate the locked set's candidates from other cells in that house.

Example

Look for Unique Rectangle Type 3.

1

Unique Rectangle Type 3

Find four cells forming a rectangle across 2 boxes. Two cells have only { 2, 3 }.

2

Unique Rectangle Type 3

The roof cells r7c2 and r9c2 have extra candidates { 5, 7 } beyond the UR pair.

3

Unique Rectangle Type 3

r2c2 in column 2 also contain { 5, 7 }, forming a pseudo-locked set with the roof extras.

4

Unique Rectangle Type 3

That pseudo-locked set has already claimed { 5, 7 } inside column 2, so other cells there cannot keep those digits.

5

Unique Rectangle Type 3

Remove { 5, 7 } from the other cells in column 2: r1c2.

6

Result after applying the technique.

Tips & Patterns

  • Type 3 is more complex than Types 1 and 2 because it involves a pseudo-locked set.
  • The roof cells' extras effectively act as a Naked Pair/Triple with neighboring cells.
  • Check the shared row, column, or block of the roof cells.