KURSCHAK 1996 Problem 2

Two countries ( $A$ and $B$ ) organize a conference, and they send an equal number of participants. Some of them have known each other from a previous conference. Prove that one can choose a nonempty subset $C$ of the participants from $A$ such that one of the following holds:

• the participants from $B$ each know an even number of people in $C$ ,
• the participants from $B$ each know an odd number of participants in $C$ .