9. (a) You are given 3 seemingly identical rings, supposedly made of gold. One of them is fake: it is made of copper and thus weighs less than a gold ring. You have access to a simple balance that you can use to compare the weights of objects. Using only a single weighing (you get to use the balance once) how would you detect the fake ring? (b) Given 9 rings (exactly one is fake), how would you detect the fake one if you are allowed to do only two weighings? (c) Generalize and prove by induction that it is possible to detect the one fake ring from 3" rings with only n weighings, n > 0