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Rectangle Elimination technique in Sudoku
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Rectangle Elimination

Breaking Deadly Patterns

By Minimal Sudoku TeamLast updated:

Rectangle Elimination encompasses various techniques for avoiding deadly rectangle patterns — configurations that would allow multiple solutions. It's closely related to Unique Rectangle.

⚡Quick Summary
  • Goal: Prevent formations that would create multiple solutions
  • Pattern: Rectangles spanning 2 rows, 2 columns, and 2 boxes
  • Method: Eliminate candidates that would complete deadly patterns
  • Difficulty: Advanced — requires understanding uniqueness

The Concept

A valid Sudoku has exactly one solution. Rectangle Elimination uses this fact: if completing a rectangle with specific candidates would allow diagonal swapping (creating multiple solutions), those candidates can be eliminated.

Deadly Patterns

💀 The Deadly Rectangle
Four cells in a rectangle (2 rows × 2 columns × 2 boxes) all containing the same two candidates = deadly pattern. The candidates can swap diagonally, giving 2+ solutions.
Deadly rectangle patternFour cells across two boxes and two rows with the same pair allow diagonal swapping.Box 1Box 2Box 7Box 8Row 2Row 73,73,73,73,7can swap
Diagonal swapping produces multiple solutions — break the rectangle.

Types of Rectangle Elimination

Type 1: One Corner Extra

3 corners locked (only the pair), 1 corner has extra candidates → eliminate the pair from that corner.

Type 2: Two Corners Same Extra

2 corners have the same extra candidate → that candidate must be true in one; eliminate from cells seeing both.

Extended Types

Types 3-6 handle more complex configurations with different extra candidates and positions.

Detection Tips

Look for Bi-Value Pairs
Scan for cells containing the same two candidates. If they could form a rectangle across 2 boxes, investigate further.
Must Span 2 Boxes
The rectangle must cover exactly 2 boxes. All-in-one-box or spanning 4 boxes doesn't create the deadly pattern.
Assumes Uniqueness
Like all uniqueness techniques, this only works for puzzles with exactly one solution.

Related Techniques

Uniqueness Techniques

🔲Unique Rectangle🐛BUG
Unique RectangleAdvanced

Unique Rectangle

The foundational technique for rectangle-based uniqueness eliminations.