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?
The keys are simple keys which open exactly one lock. The locks are simple locks which can be opened only by keys made for the lock. Multiple keys can be made for any lock.