Four cells on two rows, two columns and two boxes that could all only be the same two digits would let those digits swap places, giving the puzzle two solutions. A proper sudoku has exactly one, so that pattern can never be completed, and that rules candidates out.
Unique rectangles are the only technique here that uses a rule about the puzzle itself: a proper sudoku has exactly one solution. Every puzzle on this site does, and so does every puzzle the solver accepts.
They come in several types. The three below are the most common.
Type 1: one corner with extras
The pattern
Candidates removed
Solved as a result
R4C3, R7C1 and R7C3 can only be 4 or 6. If R4C1 were 4 or 6 too, the four corners R4C1, R4C3, R7C1 and R7C3 could swap 4 and 6 and the puzzle would have two solutions. It has one, so 4 and 6 can be removed from R4C1. That leaves R4C1 with only one candidate: 1.
Type 2: one extra digit
The pattern
Candidates removed
Solved as a result
R3C2 and R3C3 can only be 1 or 2, and R7C2 and R7C3 can only be 1, 2 or 3. If neither of them were 3, the four corners could swap 1 and 2: two solutions. So one of them is 3, and the 3 can be removed from every cell that sees both: R7C4 and R8C3. That leaves R7C4 with only one candidate: 2.
Type 4: a strong link
Where the pattern lives
The pattern
Candidates removed
Solved as a result
R3C2 and R3C3 can only be 1 or 2. In row 7, the 1 fits only in R7C2 and R7C3, so one of them is 1. If the other were 2, the four corners would hold only 1 and 2 and could swap: two solutions. So 2 can be removed from both: R7C2 and R7C3. Now the 2 has just one place left in row 7: R7C4.
This position comes from a puzzle generated on this site, after every single has been filled in. Boxes are numbered 1–9 from the top left, row by row; R5C4 means row 5, column 4.
How to spot it
1Look for two cells in the same row (or column) that can only be the same two digits, a and b.
2Find the matching pair of cells in another row, in the same two columns, so the four cells span exactly two boxes.
3If three corners are just a/b, remove a and b from the fourth (type 1).
4If the other two corners both have one extra digit, and it is the same, remove that digit from cells that see both (type 2).
5If a or b fits only in those two corners within their row, the other digit can be removed from both (type 4).
Why it works
If all four corners were just a and b, you could swap a and b around the rectangle and both grids would follow the rules.
That would be two solutions. A proper sudoku has one, so the four corners can never end up as just a and b.
Each type uses that fact to show which candidates must go.
Common mistakes
Corners in four boxes (or one). The rectangle must span exactly two boxes.
Using it on a puzzle that might have several solutions. The logic depends on there being exactly one.
Mixing up the types: check what the "roof" cells hold before deciding what to remove.
Questions
Is it cheating to use the puzzle having one solution?
No. A proper sudoku is defined by having exactly one solution, so it is a fact you are allowed to use. Some purists avoid it anyway.
Does it work on every puzzle?
Only on puzzles with a single solution. Every puzzle here has one, and the solver checks any puzzle you bring.
Are there more types?
Yes, types 3, 5 and 6 and hidden rectangles, but they are rarer and harder to spot.
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