## Problem of the Day #226: Halloween Madness
*October 31, 2011*

*Posted by Billy in : potd , trackback*

It’s Halloween, and after Albert finishes his college apps he wants to go trick-or-treating. Albert’s neighborhood consists of 6 houses equally spaced around a circle of radius $1$ kilometer. He starts from his own house, visits the rest of the houses exactly once in a random order, and returns back to his house. What is the expected length of Albert’s trick-or-treating path?

## Comments»

I get ~8.9569 kilometers numerically. Do you have an elegant solution?

nm, got one