tough logic problem for math Wizard!

[heisrisen287]

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

[pinus]

He won't get the chance, as the staff will be in in the morning.

[DOB]

I reckon 4,135 days which is worked out as follows: Four Number combos 60x59x58x57 = 11,730,240 x 2 (directions) = 23,406,480 combos Three Number combos 60x59x58 = 205,320 x 2 (directions) = 410,640 combos Total combos = 23,817,120 @ 15 secs each = 357,256,800 seconds which equates to 4,134.9 days which is 4,135 rounded

[DOB]

An alternative is to only use the Four number combos on the assumption that every 3 number combo will be contained in a four number combo. This would then mean 23,406,480 total combos which would take 351,097,200 seconds which equates to 4063.63 days which is 4,064 days rounded

[tomd]

I got same as your first answer (didn't think of the three numbered combinations being covered by four number ones, very clever) but took 60*59*59*59 and 60*59*59, as the same number could be used twice within the combination, (ie. 40 50 30 40) but obviously not consecutively (ie. 40 50 50 30) http://www.theanswerbank.co.uk/How-it-Works/Question61690.ht ml

[pinus]

A four number combination wouldn't cover a three number combination, as putting the fourth number in would effectively be the start of another three digit setting.

[pinus]

There are 60 ways of choosing the first number The second number must be different from the first number, but could be reached either way, so there are (59*2) ways of choosing the second number The third number must be different from the second number (but could be the same as the first) but could be reached either way, so there are (59*2) ways of choosing the third number Similarly for the fourth number So there are 60*(59*2)*(59*2)*(59*2) ways of choosing four numbers that�s 98581920 ways There are 60*(59*2)*(59*2) ways of choosing three numbers that�s 835440 ways Total 99417360 at 15 seconds per go 24854340 minutes 414239 hours 17259.9 days 47 years

[tomd]

Does it not matter which way you turn to the first number? On my Permuatation padlock it does, you have to turn it round twice & then approach the first number.

[pinus]

Probably - so double the figures

[bernardo]

I don't know enough about how such locks work, otherwise it would be easy to work out. Is the direction of rotation something which only works in the "correct" direction? Or is the direction of turning the wheel just a matter of going either way to the next number according to which is nearest? After each number do you have to return the dial to a neutral position before doing the next number?