Suppose you have a balance scale such as the one shown which can be used to compare the weights of two objects (the heavier object goes closer to the ground). Someone gives you 9 coins that look identical, but one of the coins is fake. Using only the scale, what is the minimum number of weighings required to definitively identify the fake coin in each of the following cases: 1) You know the fake coin is lighter than the real coins. 2) You know that the fake does not have the same mass as a real coin, but you don’t know whether it is heavier or lighter. *
