Unique Rectangles is a powerful Sudoku solving technique that exploits one of the fundamental rules of valid Sudoku puzzles: every well-formed puzzle must have exactly one solution. When four cells in two rows and two columns within two boxes share only two candidates, they form a potential "deadly pattern" that would allow two valid solutions. Since a proper Sudoku cannot have multiple solutions, at least one of those four cells must contain a different digit, allowing you to eliminate candidates.
The most common form is the Type 1 Unique Rectangle. In this scenario, three of the four rectangle cells contain only the same two candidates (say 3 and 7), while the fourth cell contains those two candidates plus one or more extras. Because placing only 3 and 7 in all four cells would create the deadly pattern with two solutions, you can safely eliminate 3 and 7 from the fourth cell, leaving only the extra candidate as the solution. This deduction is purely logical and relies on the uniqueness constraint rather than direct elimination.
Mastering Unique Rectangles requires careful identification of candidate pairs across rows, columns, and boxes. This technique is especially valuable in harder puzzles where basic and intermediate methods have been exhausted. It is closely related to other advanced elimination strategies such as Naked Pairs and X-Wing patterns. Understanding deadly patterns and uniqueness-based reasoning opens the door to many expert-level Sudoku deductions and significantly boosts your puzzle-solving toolkit.
Try It Yourself
Walk through each step of the unique rectangles technique on a real puzzle. Follow the instructions and try entering the correct value when prompted.
Look at rows 2 and 6. Notice that cells (1,2) and (1,5) both contain candidates {3,5}. These two candidates appear in two rows across two columns.
Step-by-Step Guide
Scan your candidate grid for two rows that share the same two candidates in exactly two columns.
Verify that the four cells span exactly two boxes — this is required for a Unique Rectangle.
Check if three of the four cells contain ONLY those two candidates (bivalue cells).
Identify the fourth cell, which should contain the two candidates plus at least one extra candidate.
Recognize that placing only the two shared candidates in all four cells would create a deadly pattern with two solutions.
Since the puzzle must have a unique solution, eliminate the two shared candidates from the fourth cell.
The remaining candidate(s) in the fourth cell are now confirmed — place the value if only one remains.
Imagine a square table with four legs -- if all four legs were identical, the table could be flipped two ways and still look the same. A valid Sudoku cannot have that kind of symmetry, so at least one leg must be different.
Unique Rectangles exploit the constraint that a valid Sudoku must have exactly one solution. If four cells spanning two rows, two columns, and two boxes all contained only the same two candidates, you could swap those two digits across all four cells and produce a second valid solution. Since this violates the uniqueness guarantee, at least one cell must contain a digit outside the pair, and the shared pair candidates can be eliminated from the cell with extras to prevent the deadly pattern.
When to use: Use Unique Rectangles when you spot four cells forming a rectangle across two boxes where three corners are bivalue with the same pair of candidates, and the fourth corner has those candidates plus extras.
Common Mistakes to Avoid
Applying Unique Rectangle logic when the four cells do not span exactly two boxes.
The rectangle must cross a box boundary. If all four cells are within the same box, the deadly pattern argument does not apply.
Assuming any rectangle of bivalue cells is a Unique Rectangle, even when the candidate pairs differ.
All four corners must share the same two candidate digits. If the pairs are different, the pattern is not a Unique Rectangle.
Eliminating the wrong candidates from the fourth cell -- removing the extras instead of the shared pair.
You eliminate the shared candidates (the pair) from the cell with extras, not the extra candidates. The extras are what break the deadly pattern.
More Examples
See unique rectangles applied in different puzzle configurations to strengthen your pattern recognition.
Unique Rectangle across two boxes
Highlighted cells show the unique rectangles pattern
Practice Puzzles
Apply the unique rectangles technique on these mini challenges. Tap a highlighted cell and enter the correct digit.
Quick Reference
- Pattern:
- Four cells forming a rectangle across two boxes, with a potential deadly pattern
- Action:
- Eliminate candidates that would create a non-unique (deadly) pattern
- Look for:
- A rectangle of cells in two rows, two columns, and two boxes sharing candidates