"Well, for this to make sense, since there are only three moves involved here, the geometrical shape of the route taken cannot possibly be a square. So to have done so in three moves and end up where they started, it would have to be a triangle. So for that to be the case, where on Earth would they have to be if they were to end up where they started in three moves like that? It would have to be a fixed point on the planet. The planet is spherical, but if they are walking one mile south, and then one mile west, and then one mile north, those are fixed directions that cannot be altered, so that would mean it was a direction that is fixed, so I guess they started and ended their three-mile walk at The North Pole."