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 Another way of looking at it. by Juggler)

I feel that I am somehow missing the point of this problem and so I'll post the solution that immediately came to mind when I read the problem. Please feel free to shoot holes in my solution or correct me if I'm not solving in the spirit of the problem.

There is one lock on the chest that can only be opened by the simultaneous turning of a key in each of its three keyholes. Distribute five keys that will turn in each keyhole, one to each person.

You can further adapt the lock and/or keys to suit yourself.

ie. Keys to cannot be copied or are destroyed in the process or a lock so big that one person cannot turn more than one key at a time.

I guess I'm under the mindset that you design the hardware to simply and fully meet the exact need instead of trying to adapt the hardware to fulfill the need. If a nuclear missile ignition sequence needs to two keys to be simultaneously turned, why can't a lock require three?

Posted by Charley on 2005-08-07 04:56:35