Advanced Sudoku Strategy
Unique Rectangle Sudoku: How to Find and Use Unique Rectangles
Learn how four cells forming a rectangle can reveal a dangerous two-solution pattern. Use the Unique Rectangle technique to remove candidates while preserving the puzzle's single valid solution.
Four Cells, One Rectangle
Track two candidates across four rectangle corners. The goal is to prevent a pattern that could allow the two candidates to swap positions.
Find the Rectangle
Look for four unsolved cells occupying two rows and two columns across exactly two 3×3 boxes.
Spot the Pair
Check whether the same two candidates repeat around the rectangle and could become interchangeable.
Break the Pattern
Use an extra candidate or another restriction to prevent the deadly rectangle from forming.
What Is a Unique Rectangle in Sudoku?
A Unique Rectangle is an advanced Sudoku technique based on the assumption that a properly constructed Sudoku puzzle has exactly one solution.
The pattern uses four cells positioned at the corners of a rectangle. These cells occupy exactly two rows, two columns, and two 3×3 boxes.
Two candidates appear repeatedly among the four cells.
If all four corners were allowed to contain only those same two candidates, the values could potentially be exchanged around the rectangle without violating any row, column, or box.
This interchangeable configuration is often called a deadly pattern.
Because the Sudoku is assumed to have one solution, you can sometimes eliminate candidates that would otherwise complete that deadly pattern.
The Unique Rectangle Structure
Two Rows + Two Columns + Two Boxes
The four rectangle corners must occupy two rows and two columns.
They must also span exactly two 3×3 boxes rather than four separate boxes.
What Is a Deadly Rectangle?
Suppose four rectangle cells all contain exactly the candidates 2 and 7.
Why Is This Dangerous?
One valid arrangement could place 2 and 7 around the rectangle one way, while reversing all four values could create another valid arrangement.
If nothing else distinguishes the two arrangements, the puzzle could have multiple solutions.
Unique Rectangle techniques use this observation to prevent the deadly pattern from becoming possible.
Unique Rectangle Type 1
Type 1 is the simplest and most useful Unique Rectangle pattern to learn first.
Three of the four rectangle cells contain exactly the same two candidates.
The fourth corner contains those same two candidates plus one or more extra candidates.
Example Candidate Pattern
Remove candidates 2 and 7 from the fourth cell. The fourth corner must use its extra candidate 9 to prevent all four corners from becoming the deadly 2/7 rectangle.
How to Find a Type 1 Unique Rectangle
Find a Bivalue Pair
Look for cells containing the same two candidates, such as 3 and 8.
Search for Rectangle Corners
Find four unsolved cells lying on the same two rows and same two columns.
Check the Boxes
Verify that the four cells lie within exactly two 3×3 boxes.
Confirm Three Pure Pair Cells
Three corners should contain exactly the same two candidates.
Inspect the Fourth Corner
The fourth cell must contain the rectangle pair plus at least one additional candidate.
Remove the Rectangle Candidates
Remove the two rectangle candidates from the fourth cell, leaving only its extra candidate or candidates.
Type 1 Unique Rectangle Example
Suppose the four corners of a valid rectangle are:
If R8C5 were allowed to become either 4 or 6, all four corners could be restricted to candidates 4 and 6.
That would create the deadly rectangle.
Remove candidate 4 and candidate 6 from R8C5.
R8C5 must therefore be 9.
Why Type 1 Unique Rectangle Works
The logic depends on preventing all four cells from becoming interchangeable pairs.
Three corners are already restricted to X and Y.
If the fourth corner also became X or Y, the rectangle could become a deadly pattern.
The Key Conclusion
The fourth corner must use something other than X or Y. Therefore X and Y can be removed from that cell.
Why the Rectangle Must Use Two Boxes
The geometry of a Unique Rectangle matters.
The four cells must occupy exactly two rows and two columns, but they must also lie across only two 3×3 boxes.
Why?
The deadly-pattern argument requires the two candidate values to be interchangeable without creating a duplicate inside any affected box.
Checking the box arrangement is therefore an essential part of verifying the pattern.
The Unique-Solution Assumption
Unique Rectangle is different from many ordinary Sudoku techniques because its reasoning relies on puzzle uniqueness.
Important
Use Unique Rectangle logic only when the Sudoku puzzle is intended to have exactly one solution.
If uniqueness is not guaranteed, avoiding a second solution is not enough by itself to justify an elimination.
Unique Rectangle vs. Naked Pair
If you are still practising candidate pairs, review our Naked Pair Sudoku guide .
Unique Rectangle vs. Hidden Pair
For candidate-position logic, continue with our Hidden Pair Sudoku guide .
Unique Rectangle vs. X-Wing
The shapes can look similar, but the reasoning is very different. Learn the single-candidate pattern in our X-Wing Sudoku guide .
Unique Rectangle vs. XY-Wing
For another advanced candidate technique, read our XY-Wing Sudoku guide .
When Should You Look for Unique Rectangles?
When Repeated Pairs Appear
Several cells containing the same candidate pair can be a good reason to check for rectangle geometry.
When Three Corners Match
If three corners of a rectangle contain exactly the same pair, inspect the fourth corner carefully.
In Hard or Expert Sudoku
Unique Rectangles are most useful when ordinary singles, pairs, and candidate interactions have stopped producing progress.
Before Long Chains
A simple Type 1 Unique Rectangle can often be easier to spot than a long chain or coloring pattern.
When Is It Not a Unique Rectangle?
❌ The Four Cells Do Not Form a Rectangle
The cells must occupy exactly two rows and exactly two columns.
❌ The Rectangle Uses Four Boxes
A standard Unique Rectangle must span exactly two 3×3 boxes.
❌ The Pair Is Not Consistent
The same two candidates must form the underlying rectangle pair.
❌ Puzzle Uniqueness Is Unknown
If the puzzle is not guaranteed to have exactly one solution, uniqueness-based eliminations should not be assumed.
Common Unique Rectangle Mistakes
❌ Ignoring the Box Layout
A visual rectangle is not enough. Confirm that its corners occupy exactly two boxes.
❌ Removing the Extra Candidate
In Type 1, the extra candidate is what prevents the deadly rectangle. Remove the rectangle pair from the fourth corner, not the extra candidate.
❌ Applying Type 1 to the Wrong Candidate Pattern
Three corners must contain only the rectangle pair. The fourth corner contains the pair plus extra candidates.
❌ Forgetting the Uniqueness Assumption
This technique depends on the puzzle having one intended solution.
How to Practise Unique Rectangles
1. Start With Bivalue Cells
Scan the grid for cells containing exactly two candidates.
2. Look for Repeated Pairs
If the same candidate pair appears repeatedly, check whether the cells could form rectangle corners.
3. Verify Two Rows and Two Columns
Confirm the four cells align into a true rectangle.
4. Check the Two-Box Requirement
Make sure all four corners occupy exactly two 3×3 boxes.
5. Learn Type 1 First
Become comfortable with the simplest Unique Rectangle before studying more complicated variations.
6. Rescan After Eliminations
A Unique Rectangle elimination may reveal a single, pair, Locked Candidate, XY-Wing, or another advanced pattern.
Unique Rectangle Practice Checklist
- 1. Do the four cells occupy exactly two rows?
- 2. Do they occupy exactly two columns?
- 3. Do the corners span exactly two 3×3 boxes?
- 4. Are you tracking the same two rectangle candidates?
- 5. For Type 1, do three corners contain only the pair?
- 6. Does the fourth corner contain the pair plus an extra candidate?
- 7. Are you keeping the extra candidate rather than removing it?
- 8. Is the puzzle intended to have a unique solution?
- 9. Did you rescan the puzzle afterward?
Related Sudoku Learning Pages
🧠 Advanced Sudoku Techniques
Explore advanced Sudoku strategies including pairs, fish patterns, wings, strong links, rectangles, and chains.
👯 Naked Pair Sudoku
Master matching candidate pairs before moving into rectangle-based patterns.
🕵️ Hidden Pair Sudoku
Find two candidates restricted to the same two cells within a unit.
✖️ X-Wing Sudoku
Learn another rectangle-shaped pattern that follows one candidate across two rows and columns.
🔺 XY-Wing Sudoku
Learn how three bivalue cells create a shared-candidate elimination.
🏙️ Skyscraper Sudoku
Use two strong links to eliminate candidates from cells seeing both roof positions.
Frequently Asked Questions
What is a Unique Rectangle in Sudoku?
A Unique Rectangle is an advanced technique involving four cells across two rows, two columns, and two boxes. It prevents a repeating two-candidate pattern that could otherwise allow more than one solution.
What is a deadly pattern?
A deadly pattern occurs when two candidates can be exchanged around four rectangle corners while keeping all Sudoku rules satisfied, potentially producing two solutions.
What is a Type 1 Unique Rectangle?
Type 1 occurs when three rectangle cells contain only the same two candidates and the fourth contains those candidates plus one or more extras. The rectangle candidates can be removed from the fourth cell.
Why must a Unique Rectangle span only two boxes?
The two-box layout is required for the candidate pair to be interchangeable around the rectangle without creating an immediate box conflict.
Does Unique Rectangle depend on puzzle uniqueness?
Yes. The technique assumes the puzzle has exactly one valid solution, so it should not be used when uniqueness is unknown.
Is Unique Rectangle an advanced Sudoku technique?
Yes. It is generally considered an advanced strategy and is most useful in Hard and Expert Sudoku puzzles.
Practise Unique Rectangles
Open a Hard or Expert Sudoku puzzle, turn on Notes, look for repeated candidate pairs, and check whether four related cells form a rectangle across two rows, two columns, and two boxes.