MathDB

Suppose that you are standing in the middle of a

100

meter long bridge. You take a random sequence of steps either

1

meter forward or

1

meter backwards each iteration. At each step, if you are currently at meter

n

, you have a

\tfrac{n}{100}

probability of

1

meter forward, to meter

n+1

, and a

\tfrac{100-n}{100}

of going

1

meter backward, to meter

n-1

. What is the expected value of the number of steps it takes for you to step off the bridge (i.e., to get to meter

0

100

)?
Let

C

be the actual answer and

A

be the answer you will submit. Your score will be given by

\max\{0,\lceil25-25|\log_6(\tfrac{A-C/2}{C/2})|^{0.8}\rceil\}

Problem Statement