Sudoku techniques · Extreme
Unique Rectangle in Sudoku
A Unique Rectangle rests on the promise that the puzzle has exactly one solution. Four cells at the corners of a rectangle spanning two rows, two columns and two boxes, all limited to the same two candidates, could be filled two ways, so that arrangement is impossible, and whatever prevents it must be true.
Also known as: Deadly Pattern, UR.
Why it works
The puzzle has a single solution, so a pattern that would allow two solutions must be avoided.
How to spot it
Look for three cells that already form three corners of the trap.
- The four cells must span exactly two boxes. Four corners across four boxes are harmless.
- Three cells holding only AB and a fourth holding AB plus extras is Type 1: the fourth cell must be one of its extras.
- Other types handle two roof cells with matching extras, a conjugate pair in the roof, or roof extras forming a naked pair with neighbours.
Builds on
Worked examples
These are the app's own lesson boards. Step through them the same way a hint does.
Type 1
Three bivalue cells and one with extras.
- 1
These four cells form a rectangle in exactly two boxes, and each contains the candidates 3 and 7. If all four were limited to only those two candidates, they would form a deadly pattern.
- 2
To avoid two solutions, the candidates 3 and 7 can be removed from the cell with extra candidates.
Type 2
Two roof cells share the same extra candidate.
- 1
These four cells form a rectangle in exactly two boxes, and each contains the candidates 3 and 7. If all four were limited to only those two candidates, they would form a deadly pattern.
- 2
These two cells with the extra candidate are in different boxes but share a row or column. At least one must hold 5, so we can remove the candidate 5 from any other cell that sees both of them.
Type 3
Roof extras form a naked pair or triple with nearby cells.
- 1
These four cells form a rectangle in exactly two boxes, and each contains the candidates 3 and 7. If all four were limited to only those two candidates, they would form a deadly pattern.
- 2
Together, the rectangle's extra candidates act as one member of a naked pair in a shared row or column. The candidates 5, 6 can be removed wherever they appear in that row or column, outside the naked set.
Type 4
A conjugate pair in the roof forces elimination of the other candidate.
- 1
These four cells form a rectangle in exactly two boxes, and each contains the candidates 3 and 7. If all four were limited to only those two candidates, they would form a deadly pattern.
- 2
In a row, column, or box shared by the two cells with extra candidates, 3 is a candidate only in those two cells. The candidate 7 can then be removed from both of them to prevent a deadly pattern.