safe is protected with a number of locks
Source: Polish MO Finals 1971 p3
August 22, 2024
combinatorics
Problem Statement
A safe is protected with a number of locks. Eleven members of the committee have keys for some of the locks. What is the smallest number of locks necessary so that every six members of the committee can open the safe, but no five members can do it? How should the keys be distributed among the committee members if the number of locks is the smallest?