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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?

Submitted by Brian Smith

Rating: 4.1429 (7 votes)

Solution: (Hide)

Ten locks and thirty keys are needed. Each lock would have three keys made to unlock it. Each person would get six different keys. Call the locks 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. Each person would get their keys following the table below.
A:1 3 5 78 0 B:1 456 89 C:123 6 90 D: 2 4567 0 E: 234 789

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Answer	K Sengupta	2008-03-21 13:02:56
One Lock to rule all locks.	Charley	2005-08-07 04:56:35
Another way of looking at it.	Juggler	2004-03-11 11:40:17
re(3): 2 for all but 1	Penny	2004-03-05 07:45:12
re(2): 2 for all but 1	brianjn	2004-03-05 01:00:56
"Open by Majority" was a great puzzle	Penny	2004-03-04 21:33:18
re(2): Revised solution to revised puzzle	Penny	2004-03-04 21:16:52
re: 2 for all but 1	SilverKnight	2004-03-04 17:15:58
2 for all but 1	brianjn	2004-03-04 17:07:27
re: Really Simple	Penny	2004-03-04 12:47:17
Revision to revised solution to revised puzzle	Penny	2004-03-04 12:29:40
Really Simple	DJ	2004-03-04 12:19:42
re: Revised solution to revised puzzle	Charlie	2004-03-04 12:04:18
re(4): About the keys and locks	Brian Smith	2004-03-04 12:04:14
re: Revised solution to revised puzzle	Brian Smith	2004-03-04 12:03:20
Revised solution to revised puzzle	Penny	2004-03-04 11:54:41
Solution to revised puzzle	Penny	2004-03-04 11:32:23
re(3): About the keys and locks	Stelian Trandafir	2004-03-04 10:50:45
re(2): About the keys and locks	Brian Smith	2004-03-04 10:32:10
re: About the keys and locks	Penny	2004-03-04 10:28:43
re(3): ?!? Master Key	Penny	2004-03-04 10:22:34
About the keys and locks	Brian Smith	2004-03-04 10:19:39
re(2): ?!? Master Key	Stelian Trandafir	2004-03-04 10:12:24
re: ?!? Master Key	Penny	2004-03-04 09:58:57
?!? Master Key	Stelian Trandafir	2004-03-04 09:29:22
re: Possible Solution	Penny	2004-03-04 07:58:55
Possible Solution	Stelian Trandafir	2004-03-04 07:28:29
re: No Subject	Penny	2004-03-04 04:28:52
No Subject	brianjn	2004-03-04 02:05:51
re(3): Solution (Penny's)	Penny	2004-03-03 22:18:47
re(2): Solution (Penny's)	Tristan	2004-03-03 20:26:49
re(2): Cost effective solution	Juggler	2004-03-03 20:00:16
re: Cost effective solution	Penny	2004-03-03 19:54:15
re: Explanations	SilverKnight	2004-03-03 19:53:15
Cost effective solution	Juggler	2004-03-03 19:40:55
Explanations	Gamer	2004-03-03 19:26:50
re: Solution	Penny	2004-03-03 18:35:54
re(3): key answer +an EXTRA key for GAMER	SilverKnight	2004-03-03 18:17:24
re(2): key answer +an EXTRA key for GAMER	Ady TZIDON	2004-03-03 18:15:00
Solution	Penny	2004-03-03 18:13:37
re: key answer	Gamer	2004-03-03 17:57:39
Why 'how many keys'?	George	2004-03-03 17:56:20
key answer	Ady TZIDON	2004-03-03 17:44:54
re: Poor Solution	Richard	2004-03-03 16:49:38
Poor Solution	DJ	2004-03-03 16:31:15

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