Avoidable Rectangle
What's an Avoidable Rectangle?
An Avoidable Rectangle is an expert-level Sudoku technique that extends the logic of Unique Rectangle to larger patterns. Like Unique Rectangle, it exploits the principle that valid Sudoku puzzles have exactly one solution. The difference is that Avoidable Rectangles span three boxes instead of two, creating a larger pattern that still produces deadly configurations if completed with just two candidates.
The technique identifies six cells arranged in a 2×3 or 3×2 rectangle spanning three boxes. When these cells contain the same two candidates, completing the pattern would allow swapping those candidates to create multiple solutions—violating the uniqueness constraint. This impossibility allows you to make eliminations.
This builds on the foundation of Unique Rectangle and requires strong pattern recognition skills across multiple boxes.
Why is it called "Avoidable Rectangle"?
It's called "Avoidable Rectangle" because the deadly pattern can be "avoided" through proper eliminations. The term distinguishes it from the simpler Unique Rectangle—both exploit uniqueness, but Avoidable Rectangle deals with more complex geometries that span additional boxes.
Some Sudoku resources also call this technique "Extended Rectangle" or "Type 3 Unique Rectangle," but "Avoidable Rectangle" is the most common name in the solving community.
Why It Matters
Avoidable Rectangle is a specialized technique for the hardest Sudoku puzzles. While rarer than standard Unique Rectangle, it can break deadlocks in diabolical-level puzzles where all other techniques fail. Like other uniqueness techniques, it's somewhat controversial but widely accepted for standard Sudoku puzzles.
Understanding Avoidable Rectangle completes your knowledge of uniqueness-based techniques and prepares you for the most challenging puzzles without resorting to trial and error.
Step-by-Step: How to Spot an Avoidable Rectangle
- Find six cells in a rectangle — They must span exactly two rows and three columns (or three rows and two columns), across three boxes.
- Check for the same two candidates — All six cells should contain the same two candidates (e.g., all have {4,9}).
- Identify cell configuration — Determine which cells have only the two candidates versus which have extras.
- Verify box spans — The pattern must cross exactly three boxes in a rectangular formation.
- Apply elimination rules — Similar to Unique Rectangle types, remove candidates that would create the deadly pattern.
Avoidable Rectangle Example
Imagine six cells in a 2×3 rectangle spanning three boxes:
- R1C1: {3,7}
- R1C4: {3,7}
- R1C7: {3,7}
- R2C1: {3,7}
- R2C4: {3,7,5}
- R2C7: {3,7}
Analysis: Five cells contain only {3,7}, and one cell (R2C4) has an extra candidate 5. This forms an Avoidable Rectangle spanning rows 1-2 and columns 1, 4, 7 (Boxes 1, 2, 3).
Logic: If R2C4 were 3 or 7, the six cells would form a deadly pattern where you could swap 3s and 7s to create multiple solutions. Therefore, R2C4 cannot be 3 or 7.
Elimination: Remove 3 and 7 from R2C4, solving it as 5.
Avoidable Rectangle Types
Type 1: One Cell Has Extras
Five cells contain only the two candidates {X,Y}, and one cell contains {X,Y} plus extra candidates. Eliminate X and Y from the cell with extras (similar to Unique Rectangle Type 1).
Type 2: Multiple Cells Have Extras
Multiple cells contain the two candidates plus extras. If these extra candidates form patterns like naked pairs or naked triples, you can make eliminations based on those patterns.
Type 3: Strong Links
When the extra candidates in different cells create strong links or chains, you can use those relationships for eliminations similar to coloring techniques.
Strategies for Spotting Avoidable Rectangles
- Master Unique Rectangle first — Don't attempt Avoidable Rectangle until you're comfortable with standard Unique Rectangle patterns.
- Look for bi-value cells in three boxes — Scan for cells with the same two candidates that span three consecutive boxes.
- Check 2×3 and 3×2 formations — The most common Avoidable Rectangles are these rectangular patterns.
- Use candidate highlighting — Highlight matching candidates to visualize the rectangular pattern across boxes.
- Don't overthink it — This technique is rare. Only search for it when stuck on expert puzzles after exhausting simpler methods.
Common Pitfalls
- Incorrect box spanning — The pattern must span exactly three boxes, not two or four. Verify the geometry carefully.
- Wrong cell count — Avoidable Rectangle requires exactly six cells (2×3 or 3×2). Other configurations are different patterns.
- Missing the extra candidates — Identify which cells have only the two candidates versus which have extras—this determines the elimination type.
- Confusing with Unique Rectangle — Unique Rectangle spans two boxes; Avoidable Rectangle spans three. Don't mix them up.
- Overthinking common puzzles — This technique is rare. Don't waste time hunting for it in easier puzzles.
Practice: Find the Avoidable Rectangle
Scenario: You have six cells:
- R3C2: {5,8}
- R3C5: {5,8}
- R3C8: {5,8,6}
- R7C2: {5,8}
- R7C5: {5,8}
- R7C8: {5,8}
Question: Is this an Avoidable Rectangle? What can you eliminate?
Answer: Yes! This is an Avoidable Rectangle Type 1 spanning rows 3 and 7, columns 2, 5, and 8 (three boxes: Box 1, 2, 3 or Box 7, 8, 9 depending on exact positions). Five cells contain only {5,8}, and R3C8 has an extra candidate 6. To prevent the deadly pattern, R3C8 cannot be 5 or 8. Therefore, R3C8 must be 6. Eliminate 5 and 8 from R3C8.
Why Avoidable Rectangle Matters
While Avoidable Rectangle is less common than Unique Rectangle, it's valuable for:
- Solving expert-level and diabolical puzzles without guessing
- Understanding advanced uniqueness logic
- Completing your knowledge of rectangle-based techniques
- Handling puzzles where simpler uniqueness patterns don't appear
Combined with techniques like Simple Coloring and X-Wing, Avoidable Rectangle gives you the tools to solve virtually any puzzle logically.
Quick Recap
| Technique | How it Works | Difficulty |
|---|---|---|
| Avoidable Rectangle | Uses uniqueness across three boxes to eliminate candidates | Expert |
| Unique Rectangle | Uses uniqueness across two boxes to eliminate candidates | Expert |
| X-Wing | 2×2 pattern allows column/row eliminations | Advanced |
Final Thought
Avoidable Rectangle is a specialized tool for the most difficult Sudoku puzzles. While you'll rarely need it, understanding this technique completes your mastery of uniqueness-based solving methods. When simpler techniques fail, Avoidable Rectangle might be the key to unlocking seemingly impossible puzzles.
Frequently Asked Questions
What is an Avoidable Rectangle in Sudoku?
An Avoidable Rectangle is an expert Sudoku technique similar to Unique Rectangle, but works with patterns that span three boxes instead of two. It identifies rectangular formations where completing them with just two candidates would create multiple solutions, allowing eliminations based on the uniqueness principle.
How is Avoidable Rectangle different from Unique Rectangle?
While Unique Rectangles span exactly two boxes (four cells in 2×2), Avoidable Rectangles span three boxes. Avoidable Rectangles are larger patterns (typically 2×3 or 3×2 formations) that still exploit uniqueness logic but with a more complex geometry.
Are Avoidable Rectangles common in Sudoku?
Avoidable Rectangles are relatively rare, appearing mainly in expert-level and diabolical puzzles. They're less common than Unique Rectangles because the pattern requirements are more specific and the configuration is larger.
Do I need to learn Avoidable Rectangle?
For most Sudoku players, Avoidable Rectangle is optional. It's primarily useful for solving the most difficult expert-level puzzles. Master Unique Rectangle first, as it's more common and builds the foundation for understanding Avoidable Rectangle.
Can Avoidable Rectangle work in all Sudoku variants?
No, Avoidable Rectangle (like all uniqueness techniques) only works on puzzles with guaranteed unique solutions. Don't use it on puzzle variants that allow multiple solutions or puzzles where uniqueness isn't guaranteed.
Practice Avoidable Rectangle
Ready for even more advanced techniques? Try Simple Coloring or Multi-Coloring.