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. modular arithmeticcombinatorics unsolvedcombinatorics