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?

Since locks are expensive and keys are cheaper, i believe i have come up with a better solution,

5 Locks and 10 Keys.

call the locks A, B, C, D, E.
call the Keys 1, 2, 3, 4, 5.

Albert holds lock A and key 1 + a copy of Key 3
Brenda holds lock B and Key 2  + a copy of Key 4
Charlie holds lock C and Keys 3 + a copy of Key 5
David holds lock D and Keys 4 + a copy of Key 1
Eileen holds lock E and keys 5 + a copy of Key 2

This way only three people ever need to be at the chest to open it but 2 people cannot

Edited on March 3, 2004, 7:45 pm

Posted by Juggler on 2004-03-03 19:40:55