ASU 067 All Russian MO 1965 members of subcommittees
Source:
June 19, 2019
combinatorics
Problem Statement
a) A certain committee has gathered times. There were members on every meeting. Not a single couple has met on the meetings twice. Prove that there were no less then members in the committee. b) Prove that you can not construct more then subcommittees of members from the committee of members, with no couple of subcommittees having more than one common member.