Intersection

An intersection is the group of $1\times 3$ or $3\times 1$ cells shared by a row (or column) and a box.

Every intersection must involve one box together with one row or one column. In Sudoku, no two boxes share any cells, so two boxes cannot form an intersection. As for a row and a column, their intersection is just a single cell, which is why a row number and a column number uniquely identify a cell.

For example, in the grid below, the highlighted cells are the intersection of row $2$ and box $2$.

In the grid below, the highlighted cells are the intersection of column $5$ and box $5$.

Because an intersection is shared by a box and a row or column, it leads to some very useful techniques:

• Locked Candidates: If a candidate is “locked” inside an intersection in one house (a row, column, or box), then that candidate cannot appear in the other cells of the other house that forms the same intersection, which allows candidate eliminations.