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The Safe (Posted on 2003-08-11) Difficulty: 2 of 5
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?

  Submitted by Lewis    
Rating: 2.7500 (4 votes)
Solution: (Hide)
The amount of possible combinations is 60*60*60*60*60, which is 777,600,000. There is an equal chance of getting it on the first go as there is getting it on the last go - which is 1 in 777,600,000. After trying half of that many times - 388,800,000 - there will be a 50% chance that they will have cracked the code and a 50% chance that they will not have cracked the code. So the average amount of tries it will take is 388,800,000.

If they get fined 1 million 388,800,000 times this will mean a total lose of 388,800,000,000,000. When they crack the safe they will get 100,000,000,000,000. Now take this money away from their losses and you get 288,800,000,000,000, which is the average amount of money that they will lose.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
QuestionSomething oddgabbo2004-09-16 00:06:15
my solution is redundantBart freeman2003-09-20 13:24:48
correct me if i'm wrongBart freeman2003-09-20 13:14:46
No SubjectDave Cheetham2003-08-17 13:12:19
Some Thoughtsre: solutionBrian Wainscott2003-08-12 15:22:15
Some Thoughtsre: daniel's solutionDaniel2003-08-11 17:25:09
solutionDaniel2003-08-11 17:13:20
code versus using it?Gamer2003-08-11 12:33:39
re: solutionSanjay2003-08-11 10:23:44
SolutionsolutionCharlie2003-08-11 09:43:59
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