RO-TST 1999 Problem 15

The participants to an international conference are native and foreign scientist. Each native scientist sends a message to a foreign scientist and each foreign scientist sends a message to a native scientist. There are native scientists who did not receive a message.

Prove that there exists a set $S$ of native scientists such that the outer $S$ scientists are exactly those who received messages from those foreign scientists who did not receive messages from scientists belonging to $S$ .

Radu Niculescu