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?
I am working on the assumption that one lock can be opened with one key or its copies and there is no masterkey to open 6 or more locks.
That is the point of the problem as I see it. As simple and realistic as it can be. How realistic is it that a key opens 6 different locks and another key opens the same 5 locks as the previous one but not the 6-th...?