In the game of Cootie, players race to construct a "cootie bug" by rolling a die to collect component parts. Each cootie bug is composed of a body, a head, two eyes, one nose, two antennae, and six legs. Players must first acquire the body of the bug by rolling a 1. Next, they must roll a 2 to add the head to the body. Once the body and head are both in place, the remaining body parts can be obtained in any order by rolling two 3s for the eyes, one 4 for the nose, two 5s for the antennae, and six 6s for the legs. This game raises the question:
If the game lasts for T turns, what is E[T], the theoretical expected value of the number of rolls required to make a cootie?
© 1999 Consortium for Mathematics and Its Applications (COMAP, Inc.)
Benjamin, A.T, & Fluet, M.T. (1999). Bounds on a Bug. Journal for Undergraduate Mathematics and Its Applications, 20(1): 5-9.