E. Suppose that you have a two pan balance scale which you use by putting things into both pans, and then seeing which way the balance tips to see which pan is heavier (or if they are equal if the balance does not tip). You are given a set of n coins and told that exactly one of them is counterfeit. You are also told that the counterfeit coin will be the one of them which is heavier than the others. Examine the algorithm FindCounterfeit, presented on the next page. Explain why this algorithm will determine where the counterfeit coin is. (It may help to try it out on an example problem with three or four coins, and where the counterfeit coin is in various spots.)