Unique rectangle: type 1

A worked example

This position comes from SudokuByte’s lesson on the Unique rectangle: type 1. Gold cells hold the evidence; green cells are the pattern’s ends.

1. Where to look

   Find four unsolved corners in two rows, two columns, and exactly two boxes.

   Three corners are the same pair. The fourth must break that pair, or swapping the rectangle would give a second solution.

2. Read the evidence in this position

   The rectangle r2c8, r2c9, r6c8, r6c9 spans exactly two rows, two columns, and two boxes. Its common pair is 2, 9; the extra candidates are in r6c9.

3. Why the deduction must follow

   If the roof also took a member of the pair, all four corners would form an interchangeable rectangle. Swapping its two digits preserves all row, column, and box constraints but creates another solution. Uniqueness therefore forces an extra digit into the roof.

   Extra assumption: the original puzzle has exactly one solution. This is checked for every included practice puzzle.

4. Apply the result

   Erase 2 from r6c9. Erase 9 from r6c9. The pattern may remove candidates without immediately solving a cell.