MathDB

067

Part of 1965 All Russian Mathematical Olympiad

Problems(1)

ASU 067 All Russian MO 1965 members of subcommittees

Source:

6/19/2019
a) A certain committee has gathered 4040 times. There were 1010 members on every meeting. Not a single couple has met on the meetings twice. Prove that there were no less then 6060 members in the committee.
b) Prove that you can not construct more then 3030 subcommittees of 55 members from the committee of 2525 members, with no couple of subcommittees having more than one common member.
combinatorics