Non-Euclidean Geometries . He first walked 10 mi South, then 10 mi West, and then 10 mi North. It so happened that he found himself back at his house door.
Most people react with disbelief on hearing that the problem has solutions.
Here's one solution. Consider the North Pole. South from the Pole brings one on a parallel each point of which is located 10 mi South from the North Pole. Walking straight West one stays on the same parallel and, therefore, at the same distance from the Pole. To get there, just stroll 10 mi North.