Unique Rectangle

Hard

Uses the principle that a valid Sudoku cannot have a deadly pattern (multiple solutions) to eliminate candidates.

How It Works

If four cells forming a rectangle across two rows, two columns, and two boxes all share only the same two candidates, the puzzle would have multiple solutions (a "deadly pattern") — which is impossible in a valid puzzle. Therefore, the candidate that breaks the pattern must be the solution.

Type 1: Three corners {A,B}, one corner {A,B,+extra} → Eliminate A,B from the extra corner. Type 2: Two corners {A,B}, two corners {A,B,C} → Eliminate C from cells seeing both type-2 corners. Types 3–6: More complex variations.

Example

37
37
2496518
145238
67
67
9
689157234
216743985
8
37
347
569
147
2
17
95
47
8123
47
6
34
6
13
97
14
852
52
17
68
14
47
93
47
98325
1467
467
17
Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

Practice with a Real Puzzle

This 9×9 puzzle is solver-verified to require this technique on its solution path.

Medium26 givensStrict