A group of crazy bank robbers try to crack a safe, even though they don't have a clue what the code is. The code has 5 numbers in, and the numbers on the dial range from 1 to 60. If they crack the safe, they get £100 billion.(That's a British billion - a million million). If they get the code wrong, they get caught and fined £1 million.

Assuming the bank robbers don't enter the same code twice, if they keep trying and re-trying until they crack the safe, are they more likely to have lost or gained money? If so, how much would they probably gain/lose?

Well if they got it wrong, and get caught, means if on the first try they get it wrong then they get caught.

Im assuming the code allows repeated entries which makes a  1 / 777600000 chance of winning.

Which i think gives an expected payoff of;

-871399.18 rounded to a penny

100000000000000/777600000 - 1000000*777599999/777600000

Which isnt good (although my math maybe flawed in the payoff thing).

But if Im right, it could eventually payoff if the bank was stupid and never changed its passcode,  and you kept at it knowing your previous codes wont work, you would eventually get to a point where your getting caught is less costly relative to your ''earnings'' :)  [imagine the years you would wait in jail waiting to get out and try again (is this another puzzle maybe? :P )]

how did i go from 3rd to 2nd person?

anyway, i think a minimum wage job at McDonalds would be a better course of action.  

Edited on September 16, 2004, 12:07 am

Posted by gabbo on 2004-09-16 00:06:15