Math Problem

[Todd Bardoni]

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

 

[Legacy 21301]

=ROUND((PERMUT(60,4)+PERMUT(60,3))*15/86400,0)

 

[Todd Bardoni]

Impressive.

I've never seen PERMUT used before and I'm not sure what the 86400 is for. Please explain at your convenience...

Actually, I get the 86400...

 

[Legacy 21301]

Have a look at PERMUT in Excel Help.

 

[Todd Bardoni]

Thanks...

 

[Zack Barresse]

The number of seconds in a day ..

 

[litrelord]

=ROUND((PERMUT(60,4)+PERMUT(60,3))*15/86400,0)

Nice. Always good to see a function that I'd never even noticed before.

Only thing is, doesn't this result need to be doubled to account for not knowing which way to turn the wheel? Maybe I got the wrong end of the stick though.

Also, by trying every 4 number combination you've also covered every 3 number combination although maybe I'm just being picky.

Bored
Nick

 

[Todd Bardoni]

You make a good point about not knowing which way to turn the wheel.

Hmm, intriguing about covering every 3 number combination....

If both of these points are correct, then the answer given by Ponsy would still reamin true since one would cancel out the other.

 

[Legacy 21301]

It is quite true that all 3 number combinations would be covered by the 4 number combinations.

The 3 number combinations can therefore be eliminated.

I had assumed that the wheel could not be rotated more than 360 degrees from 0 so that the numbers themselves would dictate which way the wheel needed to be rotated.
I don't think that can assumed. The effect is to increase the combinations of the 4 numbers by 8 times (I think). So the formula would become :-

=ROUND(PERMUT(60,4)*8*15/86400,0)

 

[Ken Puls]

Hey guys,

Just a note that on any combination safe I've ever used, you have to clear the dial (usually a few rotations in the opposite direction you want to start in) before you dial the combination. This clears the previous combination used in the lock.

If you dial a four number combination, where you need three, it won't open, as the previous dial wouldn't be cleared first.