Learn / Uniqueness
Sudoku technique · Uniqueness · first needed in Expert puzzles
Unique rectangle: type 4
A strong link on one rectangle digit between the two roofs forces the other rectangle digit out of both roofs.
How to spot it
Confirm the roof strong link inside an entire shared house.
The common mistake
Both roofs being candidates is not enough: they must be the only two places for the linked digit in that house. Requires uniqueness.
Learn this first
Unique rectangle: type 1 and strong links.
A worked example
This position comes from SudokuByte’s lesson on the Unique rectangle: type 4. Gold cells hold the evidence; green cells are the pattern’s ends.
Where to look
Confirm the roof strong link inside an entire shared house.A strong link on one rectangle digit between the two roofs forces the other rectangle digit out of both roofs.
Read the evidence in this position
The rectangle r3c4, r3c5, r9c4, r9c5 spans exactly two rows, two columns, and two boxes. Its common pair is 2, 3; the extra candidates are in r9c4, r9c5.Why the deduction must follow
row 9 puts 2 in one of the two roofs. If the other roof took 3, all four corners would become the interchangeable pair. Uniqueness rules that out, so neither roof can take 3.Extra assumption: the original puzzle has exactly one solution. This is checked for every included practice puzzle.
Apply the result
Erase 3 from r9c4, r9c5. The pattern may remove candidates without immediately solving a cell.
Further reading: hodoku.sourceforge.net