How many points are there on the earth where, by walking one mile south, then one mile east and then one mile north, you would reach the place where you started?
Solution: The first idea you might have is to say that there is only one point, namely, the North Pole. However, this is not the only point there is. In fact, there are an infinity of such points. Consider a circle of circumference 1 mile around the south pole and another circle which is concentric with this one but one mile north of each point on the first circle. Any point on the second circle can be a starting point. Since the number of points on a circle is infinite, the number of solutions is infinity. Can you find even more solutions? Hint: Consider circles of smaller circumference around the south pole.