1. It is known that in a set of five coins three are genuine (and have the same weight) while two coins are fakes, each of which has a different weight from a genuine coin. What is the smallest number of weighings on a scale with two cups that is needed to locate one genuine coin?
1. It is easy to see that no single weighing gives the result. However 2 weighings would be enough. We compare weights of coins 1 and 2 and coins 3 and 4 . If weights are equal both times, then coin 5 is genuine. If both unequal, then coin 5 is genuine again. If one is equal and another is not, then both coins in the equal weighing are genuine.