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?
Put 10 locks on the chest, and distribute the five keys to persons A,B,C,D,E as follows:
A's key unlocks [1 2 7 8 9 10]
B's [1 2 4 5 6 10]
C's [1 3 5 6 8 9]
D's [2 3 4 6 7 9]
E's [3 4 5 7 8 10]
Any three of them together will unlock all 10 locks.
A and B will not unlock 3
A and C will not unlock 4
A and D will not unlock 5
A and E will not unlock 6
B and C will not unlock 7
B and D will not unlock 8
B and E will not unlock 9
C and D will not unlock 10
C and E will not unlock 2
D and E will not unlock 1
Edited on March 3, 2004, 6:51 pm
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Posted by Penny
on 2004-03-03 18:13:37 |
Solution
