An empty rectangle is about the shape of a digit’s candidates inside one box: they all lie on a single row and a single column, leaving the box’s remaining four cells — a 2×2 rectangle — empty of the digit. Wherever the box finally places it, the digit lands on that row or that column: the box’s whole influence is compressed into a cross.
The pattern fires when a conjugate pair joins in: another house where the digit has exactly two possible cells, one of which lies on the cross’s row (or column). The pair’s other end then points at a victim: the cell where its own line crosses the other arm of the box’s cross.
It works by cases — either the pair places the digit at its far end, which shares a line with the victim directly, or it places it on the cross’s row, forcing the box to use its column arm, which also sees the victim. Both roads strike the same cell, so the digit goes.
On the board
Follow the digit 3. In the top-right box its only homes are R1C7, R2C7, and R2C8 — everything sits on row 2 or column 7, and the rest of the box holds no 3 at all. Column 2 supplies the conjugate pair: its 3 sits at R2C2 or R6C2, with no third option. If R6C2 is the 3, then R6C7 loses its 3 along row 6. If instead R2C2 is the 3, row 2’s share of the box is dead, the box’s 3 must fall in column 7 — and R6C7 loses its 3 again, this time down the column. Both cases clear the same cell, so R6C7 drops to {5,9}.
This is the exact board the app's interactive Empty Rectangle demo uses — step 38 of its 78-step walkthrough, drawn here with its live pencil marks.
