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Open By Majority (Posted on 2004-03-03) Difficulty: 3 of 5
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?

See The Solution Submitted by Brian Smith    
Rating: 4.1429 (7 votes)

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Solution Revised solution to revised puzzle | Comment 30 of 45 |
(In reply to Solution to revised puzzle by Penny)

12 locks, 36 keys.
 
We can distribute 30 keys to 10 locks among the 5 people as follows:  
  
A[1,2,3,4,7,10]
B[1,3,4,5,6,7]
C[2,4,5,7,8,9]
D[1,5,6,8,9,10]
E[2,3,6,8,9,10]
 
But now A+D and B+E can open the chest.
 
Add locks 11 and 12. Give B,C and E a key to 11. Give A,C and D a key to 12.  
 
A[1,2,3,4,7,10,12]
B[1,3,4,5,6,7,11]
C[2,4,5,7,8,9,11,12]
D[1,5,6,8,9,10,12]
E[2,3,6,8,9,10,11] 

  Posted by Penny on 2004-03-04 11:54:41
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