## Problem of the Day #98: A Serpent with Regenerating Heads
*June 25, 2011*

*Posted by Alex in : potd , trackback*

There exists a magical serpent with a single head of size $234$. Saketh the Valiant and Sreenath the Troll wish to slay this magical serpent. They know that when they pulverize a head of size $n$, there is a $\frac{2}{3}$ chance that the head will regenerate into two new heads, each of size $m$, where $m$ is a random integer between $0$ and $n$, inclusive (the two new heads may have different sizes). To slay the magical serpent, they must pulverize all of its heads. What is the expected value of the total size of all the heads that Saketh the Valiant and Sreenath the Troll will have to pulverize in order to slay the serpent?

## Comments»

I don’t approve of that epithet.

It is clearly entirely appropriate.

What are you talking about im not a troll

shut up sreenath.

You guys are so mean to me