Keys and a safe
Source: Finnish Mathematics Competition 1998, Final Round, Problem 2
November 14, 2011
combinatoricscombinatorics solved
Problem Statement
There are members in the competetion committee. The problem set is kept in a safe having several locks.
The committee members have been provided with keys in such a way that every six members can open the safe, but no fi ve members can do that.
What is the smallest possible number of locks, and how many keys are needed in that case?