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 The Safe (Posted on 2003-08-11)
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?

 See The Solution Submitted by Lewis Rating: 2.7500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: solution | Comment 6 of 10 |
(In reply to solution by Daniel)

Sorry Daniel, but I think you missed a couple of points:

1 - for opening a safe, order matters. The combination 1-2-3-4-5 is NOT the same as the combination 1-2-3-5-4. In this sense it is really a permutation that opens the safe, not a combination (hence, I think, the use of the word "code" in the puzzle, instead of "combination"). This would increase the number of codes from 60 choose 5 to 60!/55!

2 - There is not necessarily a restriction that the numbers in the code be distinct, so the true number of codes is more likely 60^5, giving you Charlie's answer.

 Posted by Brian Wainscott on 2003-08-12 15:22:15

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