# Math Problem



## Todd Bardoni (Sep 11, 2004)

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.


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## Legacy 21301 (Sep 11, 2004)

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


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## Todd Bardoni (Sep 11, 2004)

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...


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## Legacy 21301 (Sep 12, 2004)

Have a look at PERMUT in Excel Help.


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## Todd Bardoni (Sep 12, 2004)

Thanks...


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## Zack Barresse (Sep 12, 2004)

The number of seconds in a day ..


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## litrelord (Sep 13, 2004)

> =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


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## Todd Bardoni (Sep 13, 2004)

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.


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## Legacy 21301 (Sep 13, 2004)

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)


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## Ken Puls (Sep 13, 2004)

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.


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## Greg Truby (Sep 13, 2004)

I think you could try to open after each 3# combo as you worked your way through each 4# combo, so I agree that you could probably ignore them in the answer.  Since combination locks would go CW,CCW,CW,CCW or vice-versa I'd think it would be * 2, not * 8.  The Permut() formula is for sampling without replacement.  However I would expect that numbers could be repeated, so wouldn't the answer be:

=Round(15*2*60^4/86400)


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## Ken Puls (Sep 13, 2004)

Greg Truby said:
			
		

> I think you could try to open after each 3# combo as you worked your way through each 4# combo, so I agree that you could probably ignore them in the answer.



Just tried it to satisfy my curiosity (we have both here).

I took a legitimate 3 number combination, added a bogus first number, and dialed it as I would a 4 number combination safe, and it did work.  Go figure.  My understanding was that they were designed not to do that.    

So, I guess I'm saying that you could _definately_ ignore them in the answer... providing that all safes work the same, of course.


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## Legacy 21301 (Sep 13, 2004)

Greg Truby said:
			
		

> Since combination locks would go CW,CCW,CW,CCW or vice-versa I'd think it would be * 2, not * 8.
> 
> The Permut() formula is for sampling without replacement.  However I would expect that numbers could be repeated, so wouldn't the answer be:
> 
> =Round(15*2*60^4/86400)



Agreed (both points and the formula).


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## PaddyD (Sep 13, 2004)

{snip}
=Round(15*2*60^4/86400) 
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Agreed (both points and the formula).
{snip}

disagree - formula is missing an argument 

=Round(15*2*60^4/86400,0) 

...& at 4,500 days, I'd probably opt for explosives.


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## Legacy 21301 (Sep 14, 2004)

PaddyD said:
			
		

> disagree - formula is missing an argument



Picky.


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## Greg Truby (Sep 14, 2004)

PaddyD said:
			
		

> ...formula is missing an argument  ...


Guilty as charged.  The only defense I can offer is that I'd stopped by the Lounge while I was waiting for Outlook to shutdown (which takes _way_ too long IMHO) and had not planned to write anything, but got "drawn in".  By the time I'd drafted my answer, Outlook had actually finished "synchronizing with the server", so I was in a toot to post, shut down and get home to some roasted chicken 'n' taters.


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