AHSME 1968 Problem 30

Convex polygons $P_1$ and $P_2$ are drawn in the same plane with $n_1$ and $n_2$ sides, respectively, $n_1\le n_2$. If $P_1$ and $P_2$ do not have any line segment in common, then the maximum number of intersections of $P_1$ and $P_2$ is: $\text{(A) } 2n_1 \text{(B) } 2n_2 \text{(C) } n_1n_2 \text{(D) } n_1+n_2 \text{(E) } \text{none of these}$