Lesson 19

Empty Rectangle

The rule

When a box's only spots for a number lie on one row and one column, placing that number in an outside cell can block the row and eliminate one end of a strong link, forcing the other end to block the column. This would leave the box with nowhere to put the number, so the candidate is removed from the outside cell. The same reasoning applies with rows and columns swapped.

Step by step

1. In the outlined box, every occurrence of candidate 4 lies in either the same row or the same column, or at their intersection. Whichever of the two finally holds 4, the box always claims one of those two lines.
2. The connected line outside is a strong link: it holds 4 in exactly two cells, one of them on one of the box's two lines. The red cell lies on the box's other line and sees the far end of the strong link. If the red cell were 4, it would clear its own line inside the box and remove 4 from the far end, so the strong link's other cell would have to be 4, clearing the box's remaining line. The box would have nowhere left for 4, so 4 can be removed from the red cell.