How to find a fake coin

Abstract

There are n coins, all identical in appearance, one of which may be fake. The fake coin, if it exists, is either lighter or heavier than the fair coins, but it is not known which, nor by how much. Given is a balance with two pans but no weights. Equal number of coins can be placed on each pan and weighed. There are three possible outcomes: the left-hand pan may be lighter than the right-hand pan, or of equal weight, or heavier. Design a recipe for determining the minimum number of weighings guaranteed to determine the fake coin, if it exists, and whether it is lighter or heavier than the others.