Unique Rectangle Sudoku Technique

Updated 6 October 2026

A Unique Rectangle is a uniqueness technique: when three corners of a rectangle spanning two rows, two columns and exactly two boxes hold the same two candidates and nothing else, the fourth corner cannot take either of those two digits, because doing so would give the puzzle a second solution.

When a Unique Rectangle applies

Every proper sudoku has exactly one solution, and every puzzle Suuudokuuu serves is checked for that before it reaches you. A Unique Rectangle turns that promise into a deduction. Picture four cells at the corners of a rectangle, in two rows and two columns, with the rectangle sitting in exactly two boxes. If all four corners ended up holding only the digits a and b, the corners could be filled in two ways — a and b on one diagonal, or the swap — and nothing else in the grid could tell the two apart. That arrangement is called a deadly pattern, and a puzzle with one solution can never reach it.

The two-box condition is what makes the swap invisible. Each row, each column and each of the two boxes contains exactly two corners, so exchanging a and b keeps every unit valid. A rectangle that spreads across four boxes does not give the same guarantee, because each box only sees one corner and the swap can break a box elsewhere.

The pattern that fires is the near miss. Three corners, the floor, hold exactly a and b. The fourth corner, the roof, holds a and b plus at least one more digit. If the roof became a or b, all four corners would collapse into the deadly pattern, so the roof must take one of its other candidates. This is the most common form, often called type 1, and it is the one Suuudokuuu’s solver checks for.

Worked example

Look at rows 8 and 9 near the bottom of the grid. Column 2 holds the pair 1 and 9 in both r8c2 and r9c2, and column 5 holds the same pair in r9c5. The rectangle sits in exactly two boxes: the column 2 corners in the bottom-left box, the column 5 corners in the bottom-middle box. Those three cells are the floor.

r8c5 is the roof, with candidates 1, 3, 8 and 9. Suppose it were 1. Then r8c2 would have to be 9, r9c2 would have to be 1, and r9c5 would have to be 9 — and the same grid with every 1 and 9 in those four cells exchanged would also be valid. Suppose it were 9 instead and the same swap appears. Both choices lead to two solutions, which the puzzle does not have, so r8c5 is neither 1 nor 9. The solver removes both and leaves 3 and 8, a much smaller choice for the next step to work with.

How to spot a Unique Rectangle

1. Look for repeated bivalue pairsScan for the same two-candidate pair appearing in several cells, especially in two rows or two columns near each other.
2. Check the rectangle shapePick three cells holding that pair that form three corners of a rectangle, and confirm the four corners sit in exactly two boxes.
3. Inspect the fourth cornerThe fourth corner must be empty and must hold both digits of the pair plus at least one extra candidate.
4. Erase the pair from the roofRemove both digits of the pair from the fourth corner. Whatever is left there is the corner’s real set of options.

Common mistakes

• Using a rectangle that spans four boxes. Without the two-box condition the swap is not invisible, and the deduction is not valid.
• Counting a given as a corner. The deadly pattern only threatens cells that are still empty; a corner that holds a given or a digit you placed by logic breaks the swap.
• Applying it to a puzzle that might have several solutions. The technique proves nothing on a grid you typed in yourself unless you know it has exactly one solution.
• Erasing the extra candidates instead of the pair. The roof keeps its extras; it is the shared pair that cannot go there.