Unique Rectangles exploit the fact that valid puzzles have exactly one solution. Eliminate candidates that would create ambiguous rectangular patterns.
A Unique Rectangle pattern involves four cells that form a rectangle on the grid, occupying exactly two rows, two columns, and two 3x3 boxes. The key insight is this: if all four cells contained only the same two candidates (say 3 and 7), you could swap the diagonal pairs - putting 3 and 7 in either arrangement - and both configurations would satisfy all row, column, and box constraints. This would mean the puzzle has two solutions, which violates the Sudoku uniqueness rule.
Because the puzzle must have exactly one solution, this "deadly pattern" cannot be allowed to form. Therefore, at least one of the four cells must contain a candidate other than the pair - and this knowledge allows you to make eliminations. The most common form (Type 1) occurs when three cells are bi-value with candidates AB and the fourth cell has AB plus additional candidates. The AB candidates can be removed from the fourth cell, as they would complete the deadly pattern.
This technique is unique among Sudoku strategies because it relies not on constraint propagation within the grid, but on the meta-property that the puzzle has a unique solution. This makes it fundamentally different from techniques like X-Wing or Naked Pairs. For definitions of key terms, see our Sudoku glossary.
Unique Rectangles are useful whenever you spot rectangular patterns of bi-value cells across two boxes. They are a good technique to attempt alongside other advanced methods like X-Wing, Coloring, and XY-Wing when intermediate techniques have stalled.
They appear in hard and expert puzzles with moderate frequency. Because the pattern is based on structural properties rather than candidate counts, it provides a complementary approach to fish patterns and chain-based techniques. For the full technique progression, visit our strategy guide or review how to play Sudoku.
Unique Rectangles is classified as an advanced-level technique. The concept is straightforward once understood, but spotting the patterns requires familiarity with bi-value cells and rectangular alignments across boxes.
Never needed - basic techniques solve these
Rarely needed - intermediate methods usually suffice
Moderately common - a useful addition to your toolkit
Frequently applicable - complements other advanced methods
A Unique Rectangle is an advanced technique based on the principle that a valid Sudoku puzzle has exactly one solution. It identifies rectangular patterns of four cells (spanning two rows, two columns, and two boxes) where allowing certain candidates would create an ambiguous arrangement with multiple solutions - so those candidates can be eliminated.
It works because a properly constructed Sudoku puzzle has exactly one solution. If four cells form a rectangle across two boxes and contain only the same two candidates, the two numbers could be swapped between the diagonal pairs without affecting any constraint - creating two valid solutions. Since this cannot happen, at least one cell must contain an additional candidate, allowing eliminations.
There are several types. Type 1: Three cells are bi-value with candidates AB; the fourth cell has AB plus extra candidates. The extra candidates can be placed, and AB is eliminated from that cell. Type 2: Two cells have an extra candidate C; C can be eliminated from cells that see both of them. Type 3 and beyond involve more complex deductions based on the same uniqueness principle.
Unique Rectangle only works on puzzles that are guaranteed to have a single unique solution. This is true for all properly constructed puzzles. However, if you are solving a puzzle from an unknown source that might have multiple solutions, the uniqueness assumption may not hold, and this technique should not be applied.
Unique Rectangles are moderately common in hard and expert puzzles. They appear more frequently than fish patterns like Swordfish or Jellyfish. Because the pattern is based on the puzzle's structure rather than candidate distribution, solvers who learn to spot them find them surprisingly often.
Look at four cells forming a rectangle: R1C1, R1C2, R4C1, and R4C2. They sit in just two boxes (top-left and middle-left).
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