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 Open By Majority (Posted on 2004-03-03)
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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 Revision to revised solution to revised puzzle | Comment 35 of 45 |
(In reply to Revised solution to revised puzzle by Penny)

I came to this conclusion before looking at Brian Smith's latest  post (about redundant locks).

10 locks, 30 keys.

A[1,2,3,4,8,10]
B[1,3,4,5,6,9]
C[2,4,5,7,9,10]
D[1,5,6,7,8,10]
E[2,3,6,7,8,9]

Explanation:

Starting with the previous post result:

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]

A+B lack 8 and 9. A+C lack 6. A+D lack 11. A+E lack 5.
B+C lack 10. B+D lack 2. B+E lack 12. C+D lack 3.
C+E lack 1. D+E lack 4 and 7.

So I guess we can eliminate locks 8 and 7. And then we just renumber ... 9-->7  10-->8 11-->9 12-->10

A[1,2,3,4,8,10]
B[1,3,4,5,6,9]
C[2,4,5,7,9,10]
D[1,5,6,7,8,10]
E[2,3,6,7,8,9]

Edited on March 4, 2004, 12:32 pm
 Posted by Penny on 2004-03-04 12:29:40

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