Avoidable Rectangle

Level 8 · Blue Belt

Strategy:

Unique Rectangles

Overview

Avoidable Rectangle is similar to Unique Rectangle but involves solved cells. When three cells of a rectangle are already solved with two alternating values, the fourth cell must avoid completing the deadly pattern.

How It Works

Find four cells forming a rectangle across two boxes.
Three corners are already solved, using two values that alternate.
The fourth (unsolved) cell has one of these values as a candidate.
Eliminate that candidate to prevent the deadly pattern that would allow multiple solutions.

Example

Starting position

Look for Avoidable Rectangle.

Sudoku grid showing the initial puzzle state for Look for Avoidable Rectangle.

1

Rectangle with three corners determined

Cells r4c9, r4c7, r7c9, and r7c7 form a rectangle across 2 boxes. Three corners are determined with values 5 and 7.

Sudoku grid illustrating step 1: Rectangle with three corners determined — Cells r4c9, r4c7, r7c9, and r7c7 form a rectangle across 2 boxes. Three corners are determined with values 5 and 7.

2

7 at r4c9 would allow two solutions

If r4c9 were 7, these four non-given cells would form a two-solution rectangle.

Sudoku grid illustrating step 2: 7 at r4c9 would allow two solutions — If r4c9 were 7, these four non-given cells would form a two-solution rectangle.

3

Why the rectangle must be avoided

Avoidable Rectangle assumes a valid puzzle has one solution, so this rectangle must be avoided.

Sudoku grid illustrating step 3: Why the rectangle must be avoided — Avoidable Rectangle assumes a valid puzzle has one solution, so this rectangle must be avoided.

4

7 at r4c9 is the target

So 7 at r4c9 is the candidate that must be removed.

Sudoku grid illustrating step 4: 7 at r4c9 is the target — So 7 at r4c9 is the candidate that must be removed.

5

Remove 7 from r4c9

Eliminate 7 from r4c9.

Sudoku grid illustrating step 5: Remove 7 from r4c9 — Eliminate 7 from r4c9.

6

Result

Result after applying the technique.

Sudoku grid showing the result after applying the technique

Tips & Patterns

Avoidable Rectangles use the same uniqueness logic as Unique Rectangles but with solved cells.
Types 2, 3, and 4 parallel the UR types.
Look for rectangles where three corners are filled with two alternating digits.