Home › Learn › The Unique Rectangle
The Unique Rectangle
Learn the Unique Rectangle: four cells in two boxes sharing a bi-value pair would create two solutions, so you can eliminate candidates that would allow it.
The Unique Rectangle exploits the promise that a proper Sudoku has exactly one solution. Four cells forming a rectangle across just two boxes, all carrying the same two candidates {X,Y}, would be a "deadly pattern" — the X’s and Y’s could swap to give a second solution. A valid puzzle must avoid it.
In the common Type 1, three of the corners are exactly {X,Y} and the fourth has extra candidates. To dodge the deadly pattern, that fourth corner cannot be X or Y, so both are removed — usually placing it immediately. In Type 2, two corners carry an extra digit Z, which can be eliminated from any cell seeing them both.
Uniqueness techniques only work when the puzzle is known to have a single solution, which the solver verifies first. The example highlights the rectangle and the candidates the uniqueness argument removes.
Practise the Unique rectangle
The best way to learn a technique is to use it. Play a puzzle at the level where it first appears, or drop a tricky board into the solver to watch it in action.
Frequently asked questions
What is a Unique Rectangle?
Four cells in two boxes that all share the same two candidates would allow two solutions. Since a proper puzzle has one, you can eliminate the candidates that would complete the deadly pattern.
Is it cheating to use uniqueness?
It assumes the puzzle is properly set with a single solution — true of essentially all published Sudoku. If a puzzle might have multiple solutions, uniqueness techniques do not apply.
What is the deadly pattern?
Four cells at the corners of a rectangle, spanning two boxes, each holding only the same two candidates. Their two digits could be arranged two ways, so no valid single-solution puzzle contains it.
More guides on the Learn hub.