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

5	8	47	9	2	47	3	1	6
6	9	1	3	8	5	7	4	2
2	3	467	1	46	467	8	9	5
3	1	9	6	5	2	4	7	8
7	5	2	8	4	9	6	3	1
4	6	8	7	3	1	2	5	9
1	2	3	5	9	8	14	6	47
9	7	47	2	6	479	5	8	3
8	4	6	13	1	3	9	2	57

Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

R1C3={4,7}, R1C6={4,7}, R8C3={4,7}, R8C6={4,7,9} → Deadly pattern broken only if R8C6≠4 and R8C6≠7 → R8C6 = 9.

Practice with a Real Puzzle

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

Medium26 givensStrict

5	8	47	9	2	47	3	1	6
6	9	1	3	8	5	7	4	2
2	3	467	1	46	467	8	9	5
3	1	9	6	5	2	4	7	8
7	5	2	8	4	9	6	3	1
4	6	8	7	3	1	2	5	9
1	2	3	5	9	8	14	6	47
9	7	47	2	6	479	5	8	3
8	4	6	13	1	3	9	2	57

5	8	47	9	2	47	3	1	6
6	9	1	3	8	5	7	4	2
2	3	467	1	46	467	8	9	5
3	1	9	6	5	2	4	7	8
7	5	2	8	4	9	6	3	1
4	6	8	7	3	1	2	5	9
1	2	3	5	9	8	14	6	47
9	7	47	2	6	479	5	8	3
8	4	6	13	1	3	9	2	57

5	8	47	9	2	47	3	1	6
6	9	1	3	8	5	7	4	2
2	3	467	1	46	467	8	9	5
3	1	9	6	5	2	4	7	8
7	5	2	8	4	9	6	3	1
4	6	8	7	3	1	2	5	9
1	2	3	5	9	8	14	6	47
9	7	47	2	6	479	5	8	3
8	4	6	13	1	3	9	2	57