There are n identically looking coins one of which is fake. There is a balance scale, but there are no weights. The scale can tell whether two sets of coins weigh the same and, if not, which of the...

There are n identically looking coins one of which is fake. There is a balance scale, but there are no weights. The scale can tell whether two sets of coins weigh the same and, if not, which of the two sets is heavier. Assume that the fake coin is heavier than the genuine ones. Please design an algorithm to detect the fake coin.