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 No Subject by brianjn)

Brianjn wrote: "Solution:  9 keys, 4 people get 2 but one soul gets 1 such the table distribution is obeyed."

If you think about it for a while, you realize that you don't need more keys than there are people: 5. Because the multiple keys that a given person possesses can be replaced by one key that unlocks all the locks that each of the multiple keys unlocks.  

Posted by Penny on 2004-03-04 04:28:52