Cracking the Vault: How Long Will it Take to Try Every Combination?

[TKL]

The thief was tired of the small change he was getting from the cashiers at the bank, so he broke in one night to raid the vault. When he got there, 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? Please round to the nearest day.

I did this and got 1 Day. I want to make sure I got it right though. Can someone please check this, tell me if it's wrong, and explain how to do it? Here's my work...

3(First set of numbers) x 4(Second Set of Numbers) x 60 (0-59) x 8(# of possible turn cominations)=5760
=> 5760 x 15(Sec per Combination)=86400

Seconds per Day
60
x 60
----
3600
x 24
-----
86400

 

[rgoudie]

The number of three-digit combinations is 60^3 = 216,000.
At 15 seconds per combination, the time required would be:

216,000 * 15 / 60 / 60 / 24 = 38 days.


The number of four-digit combinations is 60^4 = 12,960,000.
At 15 seconds per combination, the time required would be:

12,960,000 * 15 / 60 / 60 / 24 = 2250 days = 6.16 years.

-Ray.

 

[TKL]

But What about the Different Turning Directions?

 

[rgoudie]

Almost everyone knows how to open a combination lock. :)

-Ray.

 

[Gokul43201]

But What about the Different Turning Directions?

Yes you have to multiply the first number by 2^3 = 8 and the second number by 2^4 = 16 to get the correct numbers, and then add these up.

 

[Tide]

Yes you have to multiply the first number by 2^3 = 8 and the second number by 2^4 = 16 to get the correct numbers, and then add these up.

Once you've decided on which direction to turn for the first number the direction for the remaining numbers is fixed so there's only two choices - clockwise or counterclockwise. You'll multiply by 2.