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 The Second Level (Posted on 2005-04-26)
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?

 See The Solution Submitted by Michael Cottle Rating: 1.6000 (10 votes)

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 Puzzle Solution Comment 10 of 10 |

Let f and s respectively denote the probability of failure and success in one trial. We know that s=1-f, and:
probability of succcess in n trials = s^n = (1-f)^n

Case I: taking the ladder to the right

Here (f,n)= (0.08, 11)

-> s^n = (1-0.08)^11
= 0.399637 (correct to six places)

Case II: Taking an even number of steps for the left ladder

Here (f,n)= (0.12, 7)

-> s^n = (1-0.12)^7
= 0.408676 (correct to six places)

Case II: Taking an odd number of steps for the left ladder

Here (f,n)= (0.105, 8)

-> s^n = (1-0.105)^8
= 0.411703 (correct to six places)

Consequently, the best route to take is to go for the odd number of steps for the left ladder.

 Posted by K Sengupta on 2008-12-21 02:31:11

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