Step 21 · Master
What is Empty Rectangle? How to Solve Killer Sudoku
When a digit's candidates in a box fit inside one row and one column (a cross), you can combine it with a line where the digit has only two spots to remove that digit from a cell.
What it is
Use one digit (say 2) when its candidates in a box fit inside a cross: one row plus one column. The rest of the box is empty of 2s — hence the name.
That box's 2 must be on the cross's row or its column. Combine it with a column (or row) where 2 fits in only two places, and you'll find a cell that can't be 2 either way.
How to spot it
Pick one digit, find a box where its candidates sit in just one row and one column, then look along those lines for a column (or row) with only two spots.
Example
Dotted outlines are cages, with their total in the top-left corner. Yellow cells are where to look, orange cells are the reason, red digits are candidates you can remove, and the green digit is the answer.
box 5's 5 must be on column 5 or row 6. In row 9, 5 fits only in R9C5 or R9C8. If R9C5 is 5, box 5's 5 ends up on row 6 and blocks R6C8. If R9C8 is 5, it blocks R6C8 directly. Either way, R6C8 can't be 5.