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The Empty Rectangle
Learn the Empty Rectangle: when a digit's candidates in a box fit one row plus one column, a crossing strong link lets you eliminate the digit from a far cell.
An Empty Rectangle forms inside a box when all of a digit's candidates there fit into a single row and a single column of the box — leaving the other four cells of a 3×3 box empty of that digit, hence the name. The crossing row and column meet at the box's hinge.
That arrangement acts as a strong link: in the box, the digit must lie on the hinge row or the hinge column. Pair it with a conjugate pair of the same digit on a crossing line, and the chain forces an elimination at the cell where the strong link meets the box lines.
The Empty Rectangle catches eliminations that fish and kites miss, and it appears more often than people expect once you train your eye on boxes. The example highlights the box pattern, the strong link and the eliminated cell.
Practise the Empty rectangle
The best way to learn a technique is to use it. Play a puzzle at the level where it first appears, or drop a tricky board into the solver to watch it in action.
Frequently asked questions
What is an Empty Rectangle in Sudoku?
A box where a digit's candidates all lie in one row and one column of the box. Combined with a conjugate pair on a crossing line, it removes the digit from a far cell.
Why is it called "empty"?
Because the candidates concentrate on one row and one column of the box, the remaining cells of the box are empty of that digit — forming a rectangle of empty cells.
When should I look for an Empty Rectangle?
On expert boards, scan each box for a digit whose candidates collapse onto a single row plus a single column, then look for a conjugate pair on a line crossing that row or column.
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