Empty Rectangle
A box where a digit forms an L-shape, combined with a conjugate pair on a line, forces an elimination at their intersection.
An empty rectangle is a single-digit technique. Within one box, the candidates for a digit all lie on one row and one column that cross at a "hinge" cell — the rest of the box is empty of that digit, leaving an L-shape. Pair this with a conjugate pair for the same digit on a line elsewhere, and one cell is forced to lose the candidate.
It captures eliminations that an X-Wing misses, using just one box plus one strong link.
How to spot it
In a box, check that a digit’s candidates occupy only one row and one column (an empty-rectangle / L pattern). Find a conjugate pair for that digit on a line: one end aligns with the box’s row, the other with its column. The cell where the far end’s line crosses the hinge line loses the candidate.
- A box where the digit forms an L on one row + one column.
- A conjugate pair for the digit on a crossing line.
- Eliminate at the intersection the pattern forces.
Worked example
- In the centre box, digit 3 appears only on one row and one column of the box.
- Column 8 has 3 as a conjugate pair (only two cells).
- One of those cells lines up with the box’s row.
- The other end fixes the row to test.
- Remove 3 from the cell where that row meets the box’s column.
Try it yourself
Tap a cell, then a number, to practise.
Frequently asked questions
- Why is it called an empty rectangle?
- Because four cells of the box — the corners away from the hinge row and column — are empty of the candidate, leaving the L-shaped pattern the technique relies on.
- How does it compare to an X-Wing?
- Both are single-digit techniques, but the empty rectangle needs only one box plus one conjugate pair, so it fires in positions where no X-Wing exists.
Related techniques
Practice: Empty Rectangle
Put the Empty Rectangle to work on a live board — free puzzles with notes, hints and four difficulty levels.
Try it on a live board