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Topic: How Long to Crack The Vault? (Read 1235 times) |
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Sarah
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How Long to Crack The Vault?
« on: Sep 9th, 2004, 1:22pm » |
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I found this riddle I cannot solve, and it's driving me crazy. If anyone here could solve it, they would have my gratitude:
A thief was tired of the small change he was getting from robbing cashiers, so he broke in one night to raid the local bank's vault. When he got to the vault, he came to a combination lock on the vault, with the dial numbers going from 0 to 59. Unfortunately, he wasn't sure whether there were three or four numbers in the combination, or even which direction to turn the wheel.
If it takes him 15 seconds to try a single combination, how many days will it take him to to try every possible combination? Round to the nearest day if needed.
So...
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rmsgrey
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Re: How Long to Crack The Vault?
« Reply #1 on: Sep 9th, 2004, 1:55pm » |
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The easiest way to do it would be to assume that each attempt at a combination is distinct, work out how many combinations there are, and multiply by 15 seconds to get a large number of days ::4575::
Then you can start getting clever, and notice, for instance, that each 4-number combination starting with a turn to the right ends with a 3-number combination to the left, so you only need to worry about the ::2*604:: 4-number combinations, which, at 15 seconds each take ::4500:: days
and then you start being even cleverer and finding sequences or turns so that each turn starts a different 4-number sequence, meaning that, if it's possible to find such a sequence (which I suspect but don't know to be true), you can try all possible combinations in a mere 2*604+3 twists, though since we don't know how long each twist takes (presumably not long since the time given is the same for 3 or 4 twist combinations) it's hard to say how much time is gained by compressing things this far...
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| « Last Edit: Sep 9th, 2004, 1:57pm by rmsgrey » |
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Sarah
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Re: How Long to Crack The Vault?
« Reply #2 on: Sep 9th, 2004, 2:05pm » |
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Hmmmm....I see where I goofed. Thanks so much for the help! 
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Grimbal
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Re: How Long to Crack The Vault?
« Reply #3 on: Sep 9th, 2004, 4:37pm » |
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Just a side note.
In "Surely You're Joking, Mr Feynman!", Richard Feynman wrote a chapter about these kinds of locks. He had such a lock on a safe in his office. He took it apart and studied it. He could find a way to speed up the cracking of such a lock. He even did it as a hobby.
The trick is that such a lock is made of a number of disks that have to be aligned. When you move the button, you move the last disk. After almost one turn, that disk starts to move the previous disk, and so on. When you turn enough, you move the first disk that needs to be set with the first code number. Then you move the other way round, less than before, and set the second disk, and so on until the last number, which you position with the button, that turns with the last disk.
So, after entering 3 numbers of the code, you can try all values for the last number. If it fails, you can turn back just enough to move the previous disk and proceed trying all the last numbers. And so on. You save a lot of time.
Feynman also discovered that the locks were tolerant, the code can be offset by 1 or 2, the lock still opened.
And by the way, on such a lock, every combination that starts right has a dual combination that starts left. The numbers are just offset by as much as a disk can move relative to the previous one.
As I said, just a side note. The problem stated that the thief needs 15 seconds for one combination.
Maybe it is better explained at
http://www.totse.com/en/bad_ideas/locks_and_security/166220.html
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| « Last Edit: Sep 9th, 2004, 5:01pm by Grimbal » |
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John_Gaughan
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Re: How Long to Crack The Vault?
« Reply #4 on: Sep 10th, 2004, 1:18pm » |
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This is true, but modern combination locks (the good ones) minimize or eliminate these attacks. For example, I used to break into lockers back in middle school by listening for the click of the disk. On some models if you turn the dial while trying to open it, it would "stick" in the correct location. Ah, the good old days... Oh, by the way, I did not break in and steal stuff, I was just curious. Yes, that is it. That is my excuse 
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Grimbal
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Re: How Long to Crack The Vault?
« Reply #5 on: Sep 10th, 2004, 4:03pm » |
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You didn't even steal the lock, to play with it at home?
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Icarus
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Re: How Long to Crack The Vault?
« Reply #6 on: Sep 17th, 2004, 6:23pm » |
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Another factor is that for cheaper dial locks - such as you common combination lock as used on a locker - you don't have to get exactly the right number at top. The locks Feynman studied (on filing cabinets at Los Alamos during the Manhattan project) allowed you to be off by 2 either way. As a result, instead of needing to try out 60 values, he only needed to try 12 for each entry. Of course, one would hope that bank vaults have more exacting requirements.
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