Step 17 · Master
What is Empty Rectangle? How to Solve 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
Yellow cells are where to look, orange cells are the reason, red digits are candidates you can remove, and the blue digit is the answer.
box 3's 1 must be on row 2 or column 7. In column 3, 1 fits only in R2C3 or R6C3. If R2C3 is 1, box 3's 1 ends up on column 7 and blocks R6C7. If R6C3 is 1, it blocks R6C7 directly. Either way, R6C7 can't be 1.