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 re: ?!? Master Key
If the "Master Keys" scenario looks realistic to you then this will be even more realistic:
Only one lock that "senses" that 3 different keys have been used and opens the chest. Then 5 different keys will be distributed to each person. The lock might even have 5 holes that count the number of keys that have been used at once.
That solves it. Of course, but that was not the point of the exercise.