Peak Sudoku
Fish, wings, chains & uniquenessPeak Score 55–70

Unique Rectangle

A pattern that would create two solutions – logic forces it to break.

Also known as: UR, Deadly Pattern, Uniqueness Test

Quick Summary

Because every proper Sudoku has exactly one unique solution, four cells forming a rectangle across two rows, two columns, and two boxes cannot all share the exact same two candidates. Logic forces the pattern to break.

Understanding the Unique Rectangle Technique

The Unique Rectangle technique leverages a fundamental premise of Sudoku: every well-formed puzzle has a single unique solution. If four cells forming a rectangle across two rows, two columns, and exactly two 3×3 boxes were all to contain only the same two candidates, the puzzle would have two valid solutions (swapping the numbers in opposite corners). Since a valid puzzle forbids this 'deadly pattern', any candidate that would force the deadly pattern must be eliminated.

Visual Examples

Green cells highlight the Unique Rectangle pattern, amber cells denote where candidates are affected, and struck-through pencil marks show the eliminations. Use the buttons or arrow keys to browse examples.

Example 1 of 5
R3C1, R3C2, R9C1, R9C2 form a rectangle across two boxes, and three corners hold only {5,6}. If R3C2 were also just {5,6}, 5 and 6 could swap for a second solution. The puzzle has one solution, so remove 5 and 6 from R3C2.
Removes: 5 from R3C2 · 6 from R3C2

How to Spot & Solve a Unique Rectangle (Step-by-Step Guide)

The complete visual scanning and logical deduction process to execute this technique:

  • 1Find four cells forming a rectangle across two rows, two columns, and exactly two 3×3 boxes.
  • 2Confirm that three of the corners are bivalue cells with the exact same two candidates (for example, 4 and 9).
  • 3Notice that the fourth corner contains 4 and 9 plus one or more extra candidate numbers.
  • 4If that fourth corner were to take 4 or 9, all four corners would be locked on {4, 9}, creating an invalid puzzle with two solutions.
  • 5Because every proper Sudoku has only one unique solution, the deadly pattern cannot be allowed to form.
  • 6Eliminate 4 and 9 from that fourth corner cell, leaving behind only its extra candidates.

Common Traps & Mistakes to Avoid

  • Attempting a Unique Rectangle where the four cells sit in four different boxes. The cells MUST sit in exactly two boxes.
  • Applying uniqueness on puzzles that might not have a guaranteed unique solution (though all Peak Sudoku puzzles are mathematically guaranteed unique).
  • Confusing Type 1 (direct elimination) with Type 2 or Type 4.

Frequently Asked Questions

Why must the cells span exactly two boxes?

If the rectangle spanned four boxes, placed digits in the boxes could differentiate the solutions. Only when the four cells span exactly two boxes does the deadly interchangeable pattern occur.

Is using uniqueness considered 'pure' Sudoku logic?

Yes! While some purists prefer constructive proofs, uniqueness deductions are 100% mathematically sound for all valid puzzles published with a single solution.

Expand your repertoire by learning prerequisites and advanced counterparts:

BUG+1Peak Score 65–75

All unsolved cells are bivalue except one – that cell's odd digit is forced.

Read guide →
Naked PairPeak Score 30–45

Two cells in the same house contain exactly the same two candidates.

Read guide →

Ready to Practice Unique Rectangle?

Try a puzzle in the Hard tier (Peak Score 51–60), or browse all 25 techniques.

Play Hard puzzleAll 25 techniques