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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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re(2): Solution (Penny's) | Comment 15 of 45 |
(In reply to re: Solution by Penny)

"Therefore 10 is the minimum number of locks, and 5 the minimum number of keys (one per person)."

I'm wondering how anyone can open 10 unique locks with 5 keys.

The minimum of keys is 30 because at least 3 of the people have to have the key for any of these ten locks.

Edit: I see what you meant now, but I don't think that you could have five keys that each open a different set of locks.

Edited on March 3, 2004, 8:31 pm
  Posted by Tristan on 2004-03-03 20:26:49

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