When a digit's candidates in a box all lie on one row and one column of it, the digit must be on that row or that column. Pair it with a line where the digit has just two places, one of them on the box's row: either that cell is the digit, or the box's digit is on its column. Both ways rule out the cell where the column meets the line's other end.
The name comes from the empty corner of the box: the digit fills an L or a cross, leaving a rectangle of the box without it.
It works like a 2-String Kite, but the box only needs its candidates on two lines, not exactly two cells.
An Empty Rectangle
Where the pattern lives
The pattern
Candidates removed
Solved as a result
In box 3, the 9 fits only along row 1 and column 7. In row 7, it fits in just two cells, R7C7 and R7C4. If R7C7 is the 9, the box's 9 isn't on column 7, so it's on row 1; if it isn't, R7C4 is the 9. Either way R1C4, on row 1 and seeing R7C4, can't be the 9. That leaves R1C4 with only one candidate: 2.
Only the 9s are shown, so the pattern stands out.
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
1Pick a digit and look at each box's candidates for it.
2Find a box where they all sit on one row and one column of it (an L or a cross, with at least one off each line).
3Look for a column where the digit has just two places, one of them on the box's row (or a row with one on the box's column).
4Find the cell where the box's column meets the other end's row. If it can hold the digit, remove it.
Why it works
If the line's cell on the box's row is the digit, the box can't use that row, so its digit is on the column.
If it isn't, the line's other cell is the digit.
The target cell is on the box's column and in line with that other cell, so in both cases it can't hold the digit.
Common mistakes
A box whose candidates aren't all on one row and one column. One stray candidate breaks it.
A line with three places for the digit. It needs exactly two.
Removing the digit from cells inside the box. The target is always outside it.
Questions
Why is it called an Empty Rectangle?
The digit occupies one row and one column of the box, leaving a rectangle of the box where it can't go.
Is it related to the 2-String Kite?
Yes. A kite needs exactly two cells in the box; an Empty Rectangle allows more, as long as they lie on one row and one column.
How often does it come up?
Fairly often in hard puzzles, once the simpler single-digit patterns are used up.
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