When a thieft comes to the bank he finds a combination lock on the vault, with the dial numbers going from 0 to 59. Unfortunately, he isn't sure whether there are 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?

2287.5

are you sure??have you considered "or even which direction to turn the wheel!
"?

Is this a question you don't know the answer to? Because if you do it really should go in the Challenges Forum...

The question is taken off of neopets.com, and is part of a contest there, so I'm going to hold off until the contest is finished

In the interim, a question:

do you always change to the opposite direction each time you stop at a number, or can you continue in the same direction, to the next number?

I really have no idea, which is rather unfortunate since the answer depends rather heavily on that. I assumed it not to be the case, but thinking about it afterwards it seems more likely that you do switch every time.

I'm running out of fingers, but does this sound right -- if you can go in either direction every time you stop at a number then, for each 4 number-answer, there'd be 16 different ways of getting to that sequence, e.g. if the answer is 24-11-36-17, the 16 alternatives are these:

L 24, L 11, L 36, L 7
L 24, L 11, L 36, R 7
L 24, L 11, R 36, L 7
L 24, L 11, R 36, R 7
L 24, R 11, L 36, L 7
L 24, R 11, L 36, R 7
L 24, R 11, R 36, R 7
L 24, R 11, R 36, L 7

and then redo the above 8, starting with R 24. If you need to change direction when you arrive at each number, then there are just 2 sequences: L 24, R 11, L 36, R 7 and R 24, L 11, R 36, L 7. That makes one heck of a difference to the answer.

I'd say about 11.3 years (four thousand and something days).