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: 2 for all but 1 by SilverKnight)

SK, I had a trip through the day.  Whilst travelling I reflected that my solution may have been flawed.  On arrival home I found that only 2 persons would be need in some instances, so I revise my solution somewhat upwards.

I was suggesting that 4 locks are therefore the minimum and with 10 keys distributed in pairs to each person such that each has a unique pair.

eg
                               Person
Lock     A      B      C      D      E
 1         x                      x
 2         x               x               x
 3                  x      x      x     
 4                  x                       x

I note however that  B, C and E could not open the chest.
Back to the drawing board!

Edited on March 5, 2004, 1:07 am

Posted by brianjn on 2004-03-05 01:00:56