Unique rectangle: type 2

A worked example

This position comes from SudokuByte’s lesson on the Unique rectangle: type 2. Gold cells hold the evidence; green cells are the pattern’s ends.

1. Where to look

   Check the rectangle, then identify the same extra candidate in both roofs.

   Two pure-pair corners and two same-line roof corners share a single extra digit. At least one roof must take that extra digit.

2. Read the evidence in this position

   The rectangle r5c8, r5c9, r9c8, r9c9 spans exactly two rows, two columns, and two boxes. Its common pair is 3, 4; the extra candidates are in r5c9, r9c9.

3. Why the deduction must follow

   At least one roof must take the extra digit 8, or the pair would form an interchangeable rectangle. Any outside candidate seeing both roofs therefore cannot be 8.

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

4. Apply the result

   Erase 8 from r7c9. The pattern may remove candidates without immediately solving a cell.