ASU 310 All Soviet Union MO 1981 90 inhabitants out of 1000, news in 10 days
Source:
July 23, 2019
combinatorics
Problem Statement
There are inhabitants in a settlement. Every evening every inhabitant tells all his friends all the news he had heard the previous day. Every news becomes finally known to every inhabitant. Prove that it is possible to choose of inhabitants so, that if you tell them a news simultaneously, it will be known to everybody in days.