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The Second Level (Posted on 2005-04-26) Difficulty: 1 of 5
You are on the first level of a steel platform, and you must get to the second level immediately.

On your right, there is a ladder that leads to the second level with rotten wood steps. There are 11 steps to the top, and each step fails 8% of the time when stepped on in this weathered condition. If the step breaks, so does your leg that's on it. These steps are too steep to take more than one at a time. You can grab the sides of the ladder with your hands, but cannot pull yourself up without stepping on the ladder's steps.

On your left there is set of stairs that has 15 steps on it which are slightly more weathered. The stairs are at such an incline that you can skip over one of these steps to get to the next. However, the odd numbered steps fail 10.5% of the time, and the even number of steps fail 12% of the time. As you might have guessed, if the steps break, then so does your leg.

What is the best route to take to avoid breaking your leg?

  Submitted by Michael Cottle    
Rating: 1.6000 (10 votes)
Solution: (Hide)
The ladder on the right has a fail rate of 8%, so the success rate of 1 step is 92%. The probability of success all the way to the top is therefore.

(0.92)^11 = 39.96%

For the stairs on the left, if you take the even number of steps, you must step on 7 steps. The success rate of 1 step is 88%. So the probability of success all the way to the top is

(0.88)^7 = 40.87%

If you take the odd number of steps, you must step on 8 steps. The success rate of 1 step is 89.5%. So the probability of success all the way to the top is

(0.895)^8 = 41.17%

So take the odd number of steps on the stairs to your left and prepare to get your leg broke!

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle SolutionK Sengupta2008-12-21 02:31:11
AnswerK Sengupta2008-12-17 06:15:28
No SubjectRachael2006-05-18 09:56:10
No SubjectSean2005-10-26 13:25:32
SolutionNo SubjectDominique2005-05-18 01:54:47
easydqbombo2005-05-02 22:20:11
re: Cheating solutionLeming2005-04-26 21:01:31
Cheating solutionJer2005-04-26 18:15:49
SolutionEric2005-04-26 17:30:58
SolutionTake the elevator - spoilerLeming2005-04-26 12:41:09
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