Empty Rectangle
We define an Empty Rectangle as a rectangle that is inside a Square and the corners of which do not contain a particular Candidate.
In this strategy we are considering Strong Links and Squares including Empty Rectangles involving one particular Candidate.
If we can find a Strong Link that has one of its ends on the same Row as one of the Rows of the Square that contains the Empty Rectangle and if that Row does not contain any corner of the Empty Rectangle, then the Candidate can not be the solution in the Cell that is located on the same Row as the other end of the Strong Link and on the Column of the Square that does not contain any corner of the Empty Rectangle.
Indeed, either the Candidate is the solution for one of the Cells in the Column of the Square that does not contain any corner of the Empty Rectangle, which eliminates the Candidate from all other Cells in that Column, or it is the solution for one of the Cells in the Row of the Square that does not contain any corner of the Empty Rectangle, which eliminates the Candidate from one Cell of the Strong Link, which in turn implies that the Candidate must be the solution for the other Cell of the Strong Link, which finally eliminates the Candidate from all Cells in the same Row.
The reasoning is also applicable when you replace "Row" by "Column" and "Column" by "Row".
In this example, an Empty Rectangle for Candidate 1 is made of D4, D6, E4 and E6 in Square "5".
In Column "2" Candidate 1 must be the solution in either F2, or G2.
If it is the solution in G2, then Candidate 1 can be eliminated from all cells in Row "G" (in particular in G5).
If it is the solution in F2, then it must be the solution in E5, wich eliminates Candidate 1 from all cells in Column "5" (in particular in G5).
Whichever the solution for Candidate 1 in Column "2" it can never be the solution in G5.
You can practice this strategy by installing the SudokuCoach application on your Android™ device.
