The Empty Rectangle Technique, Explained

Picture the empty rectangle

Take one digit and look at a single box. If every candidate for that digit in the box sits within one row and one column of the box, the rest of the box is empty of that digit. Those empty cells form a rectangle, which is where the name comes from. The live candidates make an L shape.

Adding a strong link

On its own the empty rectangle does nothing. You pair it with a strong link elsewhere, a row or column where the same digit appears in only two cells. One end of that link points back toward the box. The logic then forces the digit at the crossing point of the box row or column and the far end of the link.

The elimination

The result is that a single cell, sitting where the box line and the link cross, cannot hold the digit. You erase it there. It is one of the most efficient single-digit removals once the shape clicks, and it appears more often than the rarer fish.

A tip for finding it

Scan box by box for a digit whose candidates hug just one row and one column. When you find such a box, look outward along that row and column for a conjugate pair of the same digit. The two together are your empty rectangle.