Unique Rectangle Type 3

Level 8 · Blue Belt

Strategy:

Unique Rectangles

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

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

Example

Starting position

Look for Unique Rectangle Type 3.

Sudoku grid showing the initial puzzle state for Look for Unique Rectangle Type 3.

1

Find a rectangle on 4 and 8

Find four cells forming a rectangle across 2 boxes. Two cells have only { 4, 8 }.

Sudoku grid illustrating step 1: Find a rectangle on 4 and 8 — Find four cells forming a rectangle across 2 boxes. Two cells have only { 4, 8 }.

2

Roof cells carry extra candidates

The roof cells r3c5 and r4c5 have extra candidates { 2, 7 } beyond the UR pair.

Sudoku grid illustrating step 2: Roof cells carry extra candidates — The roof cells r3c5 and r4c5 have extra candidates { 2, 7 } beyond the UR pair.

3

A pseudo-locked set forms in column 5

r8c5 in column 5 also contain { 2, 7 }, forming a pseudo-locked set with the roof extras.

Sudoku grid illustrating step 3: A pseudo-locked set forms in column 5 — r8c5 in column 5 also contain { 2, 7 }, forming a pseudo-locked set with the roof extras.

4

The locked set claims its digits in column 5

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

Sudoku grid illustrating step 4: The locked set claims its digits in column 5 — That pseudo-locked set has already claimed { 2, 7 } inside column 5, so other cells there cannot keep those digits.

5

Remove 2, 7 from the rest of column 5

Remove { 2, 7 } from the other cells in column 5: r6c5.

Sudoku grid illustrating step 5: Remove 2, 7 from the rest of column 5 — Remove { 2, 7 } from the other cells in column 5: r6c5.

6

Result

Result after applying the technique.

Sudoku grid showing the 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.