## Problem of the Day #160: Ladder Climbing
*August 26, 2011*

*Posted by Alex in : potd , trackback*

There are $160$ kids, each next to an infinitely tall ladder. Each kid starts at height $0$, and rungs on the ladder differ by height $1$. Every second, each kid flips a fair coin. If the coin lands heads, the kid climbs up one step. Else, the kid stops climbing forever. Find the expected value of the average height of the kids after each one of them as finished climbing.

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