VWO 1993 Problem 1

The 20 pupils in a class each send 10 cards to 10 (different) class members. [note: you cannot send a card to yourself.] (a) Show at least 2 pupils sent each other a card. (b) Now suppose we had $n$ pupils sending $m$ cards each. For which $(m,n)$ is the above true? (That is, find minimal $m(n)$ or maximal $n(m)$ )