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 2 for all but 1
How is distribution obeyed?
Many pairs, together, have all three keys. So if I remove (as you
suggest) E1, then Person A and B (or B&C, or C&D, or B&D,
etc.) together have all three keys and can open the chest.
But the problem says only when at least three are present.