## Problem of the Day #98: A Serpent with Regenerating HeadsJune 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?

1. Sreenath - June 25, 2011

I don’t approve of that epithet.

2. Saketh - June 25, 2011

It is clearly entirely appropriate.

3. Sreenath - June 25, 2011

What are you talking about im not a troll

4. Will Ashe - June 26, 2011

shut up sreenath.

5. Sreenath - June 26, 2011

You guys are so mean to me