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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 Another way of looking at it. | Comment 43 of 45 |

I have a solution that can work, but another item is required, A second smaller chest to house 3 keys.

there will only be one lock on the smaller chest and three keys will be distributed to 3 of the 5 people.

inside the chest there is another set of 3 keys, one for each lock that needs to be on the chest.

the locks on the main chest are distributed such that one person can reach only one lock at a time and the lock is not a standard padlock, it is the type that once the key is removed or even let go of, the lock will close itself, in the UK we call these Yale locks, as a result of this 3 people need to operate the locks simultaneously.

therefore 4 locks are required and 6 keys.

Edited on March 11, 2004, 11:42 am
  Posted by Juggler on 2004-03-11 11:40:17

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