7.27 Draw 1 line on a rectangular grid paper of $m \times n$ squares. Find the maximum number of squares that this line can intersect.
[Solution] Apart from the boundary, this grid paper has $m+n-2$ grid lines internally. When drawing any straight line on the grid paper, it intersects with at most one point on each internal grid line, and can be divided into at most $m+n-1$ segments by these grid lines. Since each intersected square contains exactly one segment of the line, a straight line can intersect with at most $m+n-1$ squares.

On the other hand, the diagonal of the rectangle (when $m=n$, the diagonal can be slightly moved) intersects with exactly $m+n-1$ squares. Therefore, the maximum number of squares a straight line can intersect is $m+n-1$.