Round: 83

The Scorchio Thief was tired of the small change he was getting from the cashiers at the Neopian National 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.



Answer: 4,575 Days

The first number in the combination can be any one of 60 numbers (0 through 59). Same with the other numbers in the combination. So there are a total of 60 x 60 x 60 3-number combinations and 60 x 60 x 60 x 60 4-number combinations. But since he didn't know which way to turn the dial, he needs to double that number, because the 3-number combination could be either right-left-right or left-right-left, and the 4-number combination could be either right-left-right-left or left-right-left-right.

So, the total number of combinations is [(60x60x60) + (60x60x60x60)] x 2 = (216,000 + 12,960,000) x 2 = 26,350,000 combinations. With 15 seconds per combinations, it'll take 395,280,000 seconds, divide by 60 to get 6,588,000 minutes, divide by 60 again to get 109,800 hours, and divide by 24 to get 4,575 days.

If you go even further, that works out to 12.5 years! I think the Scorchio Thief would be better off investing in the Neopets Stock Market!



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