A group of five people want to put a set of locks on a chest and distribute keys to the locks amongst themselves in such a way that all the locks on the chest could be opened only when at least three of them were present to open it.

How many locks would be needed, and how many keys?

(In reply to Poor Solution by DJ)

A better poor solution is to have locks and keys 1,2,3 assigned to people A,B,C,D,E according to A1,B2,C3,D1,D2 so that 3 people are required (one of whom must be C, and one must be either A or D, and the other either B or E). The problem is clearly asking for the least number of locks, which is not 5. There must be at least 3 locks, however. Now let's concentrate on the real problem of finding what the minimum number of locks is that permits any majority to open the chest.

Posted by Richard on 2004-03-03 16:49:38