MathDB

061

Part of 1965 All Russian Mathematical Olympiad

Problems(1)

ASU 061 All Russian MO 1965 100 men help the police, 3 every evening

Source:

6/19/2019
A society created in the help to the police contains 100100 men exactly. Every evening 33 men are on duty. Prove that you can not organise duties in such a way, that every couple will meet on duty once exactly.
combinatorics