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 Solution by Penny)

Any two of these people must lack a key to at least one lock. But then the other three must all have a key to that lock; otherwise there would be three people who couldn't unlock it. There are 10 groups of 2 people among 5.

Therefore 10 is the minimum number of locks, and 5 the minimum number of keys (one per person).

 

 

Posted by Penny on 2004-03-03 18:35:54