Choice of problem
Source: St Petersburg Olympiad 2009, Grade 9, P2
August 30, 2017
combinatorics
Problem Statement
There are members of jury, that want to choose problem for contest. There are list with problems. They want to find such problem, that can be solved at least half members , but not all. Every member solved problems, and every two members solved different sets of problems.
Prove, that they can find problem for contest.