Unique rectangle
Don't paint the puzzle into having two solutions.
Unique rectangle (Type 1) leans on a property of every well-formed sudoku: it has exactly one solution. Find four cells arranged as a rectangle (two rows × two columns) that together span only two boxes. If three of those cells are bivalue with the same {X, Y}, the fourth — currently listing X, Y, and something extra — cannot collapse to just X or Y.
If it did, you could swap X and Y around the rectangle without breaking any constraint, and the puzzle would have two solutions. Since it doesn't, the fourth cell is forced to take the "something extra," and X and Y can be dropped from it.
Uniqueness moves use a fact about how the puzzle was constructed, not a fact deducible from the partial grid. Some solvers consider that a soft cheat; we include them because every reasonable sudoku does have a single solution and the moves are standard in the community.
When the move applies
Near the end of dense puzzles, look for four cells arranged in a 2×2 across two boxes where three of them already share the same bivalue candidate set.
The procedure
- Locate four cells forming a 2×2 across exactly two boxes.
- Confirm three of the cells are bivalue {X, Y}, and the fourth lists X, Y, plus at least one more candidate.
- Strike X and Y from the fourth cell.