Problem of the Day #226: Halloween MadnessOctober 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?