Consider a circular road that has n toll booths and n reward booths.At each toll both, you have to pay $1. If you have no money, you are stuck and cant go. However, at each reward booth, you collect $1. You start out with no money, but you decide where to start. You have no choice of direction: you must move clockwise. Prove by mathematical induction that for every n ? 0, no matter how the booths are arranged, there is always a starting point that will allow you to go all the way around. Hint: to prove the inductive case, remove two carefully chosen booths.