View the example grid
This form of Unique Rectangle requires a puzzle with a guaranteed unique solution. Four cells occupy two rows, two columns and exactly two boxes; three cells contain only the same pair of candidates.
An example from the app
The four corners D4, H4, D5, H5 lie in two rows, two columns and exactly two boxes. Three corners have only 4, 9. Corner D5 has extra candidates.
If D5 also used one of 4, 9, swapping the two digits in the rectangle would produce a second solution. The uniquely solvable puzzle does not allow this. D5 must use another digit.
These notes are therefore ruled out: D5: 4, 9.
The image shows the candidates relevant to this step. A note being hidden does not mean it has been logically eliminated.
Practice the next step
The fourth cell cannot be left with just that pair, which would allow two interchangeable completions. This Type 1 deduction is not valid without the uniqueness assumption.
In the app, follow the reasoning in the matching lesson and try a task yourself. With a new puzzle, always start from its actual candidate state.
Questions about Unique Rectangle
Why does Unique Rectangle need a unique solution?
The elimination prevents a second solution obtained by swapping the pair. Without guaranteed uniqueness, that argument is invalid.
Why must the corners occupy exactly two boxes?
The pair can then be swapped at the four corners without changing the box constraints. An arbitrary rectangle need not allow this.
What remains in the fourth cell?
In the illustrated Type 1, remove both pair digits there. If several additional candidates remain, the cell is not yet determined.
Can I remove the pair from all four corners?
No. This case eliminates from the corner with extra candidates, not from the three pure pair cells.
What if the other three corners have extra candidates?
The conditions of this Type 1 case are absent. The rectangle’s shape alone proves no elimination.
Keep practicing in Unisu
Download Unisu for iPhone or Android. Solve a puzzle or work through a guided lesson on the technique.
