What is a Unique Rectangle in Sudoku?

A Unique Rectangle (UR) is a pattern involving 4 cells that form a rectangle spanning exactly 2 boxes, 2 rows, and 2 columns. If those 4 cells all share the same 2 candidates, it would create a Deadly Pattern (two solutions), which violates the uniqueness rule of Sudoku. This allows powerful eliminations.

How many types of Unique Rectangle are there?

There are several types. Type 1 is the simplest: one corner cell has extra candidates beyond the 2 shared digits, so the shared candidates can be eliminated there. Type 2 involves two cells with the same extra candidate. Types 3, 4, 5, and 6 involve more complex patterns requiring Naked Subsets or strong links.

Can Unique Rectangle be used in Easy Sudoku?

Rarely. Unique Rectangle requires that the puzzle has a unique solution (which all standard Sudoku do), and the UR pattern must be present. It is primarily useful in Expert, Evil, and Extreme Sudoku.

Unique Rectangle Sudoku Strategy — How to Spot Deadly Patterns & Beat Expert Sudoku

1. The "Deadly Pattern" Principle

Imagine a rectangular box formed by four cells spanning across two rows, two columns, and exactly two separate 3x3 blocks. If all four cells were to contain only the candidate pair [4, 7], you could swap the 4s and 7s diagonally:

The Unusable "Deadly Pattern" (Invalid Sudoku):

Because a computer-generated puzzle like those on iLoveSudoku is mathematically verified by Donald Knuth’s DLX solver to have strictly one solution, this deadly loop CANNOT be allowed to form. You can use this guarantee to instantly deduce or eliminate candidates!

2. Unique Rectangle Type 1 (The Instant Win)

Type 1 is the easiest and most common form. Three of the corner cells contain strictly the bivalue pair [4, 7], while the fourth corner contains [4, 7, 9].

Type 1 Elimination Layout:

Corner A: [ 4, 7 ] Corner B: [ 4, 7 ] | | Corner C: [ 4, 7 ] Corner D: [ 4, 7, 9 ] <-- TARGET CELL!

Type 1 Deduction Rule:

If Corner D were to take 4 or 7, the deadly pattern would trigger and invalidate the entire puzzle. Therefore, Corner D CANNOT be 4 or 7. Both candidates are eliminated, meaning Corner D MUST BE 9!

3. Unique Rectangle Type 2 (Locked Guardian Elimination)

In Type 2, two corner cells contain the pair [4, 7], and the other two corners both contain a shared extra candidate, for example [4, 7, 9]:

Type 2 Elimination Layout:

Corner A: [ 4, 7 ] Corner B: [ 4, 7 ] | | Corner C: [ 4, 7, 9 ] <-> Corner D: [ 4, 7, 9 ] (Both have extra '9')

Type 2 Deduction Rule:

One of the cells (Corner C or D) MUST contain the 9 to break the deadly pattern. Because both cells share the same row/block, the candidate 9 acts as a pointing pair: you can safely eliminate candidate 9 from all other cells in that unit!

4. How to Spot Unique Rectangles in Under 10 Seconds

Step 1: Look for Bivalue CellsScan for cells with only two pencil marks (e.g. 2/5, 4/7, 1/9).

Step 2: Check Two Different 3x3 BoxesThe rectangle must span exactly two 3x3 boxes (never inside a single box).

Step 3: Strike Out the Dangerous DigitsIdentify the fourth corner (Type 1) or line (Type 2) and eliminate the repeating digits immediately.

Frequently Asked Questions (FAQ)

Is the Unique Rectangle technique considered guessing?

No! Unique Rectangle is a 100% rigorous deductive logic technique. It is built on the mathematical theorem of puzzle uniqueness. High-quality platforms like iLoveSudoku mathematically verify that only one valid solution exists, making this deduction completely sound.

Can a Unique Rectangle be inside a single 3x3 box?

No. If all four cells were inside the same 3x3 box, classic Sudoku rules would automatically prevent duplicates, so a deadly pattern would never be possible. A valid UR must span across exactly two 3x3 boxes.

At what difficulty level do Unique Rectangles appear?

Unique Rectangles typically appear on Hard, Expert, and Evil Sudoku levels where basic techniques like Naked Singles, Hidden Pairs, and Pointing Pairs are insufficient to break the board.

Put Unique Rectangles into Action!

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