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        riddles >> easy >> 6 locks
        
(Message started by: Christine on Nov 22^nd, 2013, 2:24pm)

Title: 6 locks
Post by Christine on Nov 22^nd, 2013, 2:24pm

If you have 6 locks on your door, and lock only 3 of them.

That way, if a thief tries to pick the locks, he'll always be locking 3 of them no matter how he does it.

Would that be true? Is it something you would do? If not, can you suggest a better way?

Title: Re: 6 locks
Post by 0.999... on Nov 22^nd, 2013, 7:19pm

In my experience you turn the key in a different directions to lock it and unlock it. However, I would imagine there do exist locks which have to be turned in the opposite direction from other locks allowing the intended setup.

Given that to unlock the three locked ones, you turn in the same direction as you do to lock the three unlocked ones, the thief can always undo what he or she tries. Provided with enough time, he/she will be able to try all configurations and eventually be able to open the door.

Title: Re: 6 locks
Post by rmsgrey on Nov 23^rd, 2013, 8:56am

on 11/22/13 at 19:19:10, 0.999... wrote:

I've come across a lock that's "backwards" - it's even on a door with two locks, the other one turning the other way.

Title: Re: 6 locks
Post by Grimbal on Nov 23^rd, 2013, 12:54pm

It took you longer to break in heh? ;D

Title: Re: 6 locks
Post by riddler358 on Feb 20^th, 2014, 2:27pm

i think he would need pick lock at most 41 times in such case

Title: Re: 6 locks
Post by rmsgrey on Feb 21^st, 2014, 5:33am

If the thief knows that there are exactly 3 locks actually locked, then he has to try 20 combinations, and transitioning between two "adjacent" combinations takes 2 picks (one lock; one unlock).

Assuming there's a sequence that traverses all 20 combinations by two-pick transitions without repeating a combination (which seems probable - each combination has 9 neighbours, 9 two hops away and only 1 at distance three, with a lot of symmetry) then it's 38 picks to traverse the sequence, and 3 picks to reach the first one, so, yeah, 41 picks for that worst case if the assumption holds.

On the other hand, if the thief doesn't know how many of the locks are actually locked to start with, then there are 64 possibilities and it takes 63 picks to check them all.