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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»

1. Jonathan - November 2, 2011

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

2. Jonathan - November 2, 2011

nm, got one