A man leaves his house, walks one mile south, one mile east, one mile north, and finds himself back at his house. Where is his house located?

You’ve probably seen this brainteaser before, and if so, you will be quick to identify the North Pole as the location of his home. Did you know there is more than one correct answer?

The most common answer focuses on the fact that if he walked only three straight lines in his journey, he must have started in the one place on earth where it would be south, no matter which way he set out.

Suppose, however, that he chose to build his home on the other side of the world. Perhaps he had a penchant for extreme climate, but he couldn’t quite handle the cold of the South Pole. Consequently, he opted for a place slightly less frigid: 1.8 miles away from the Pole.

Why is that location so significant? At that point, when he sets out from his house and heads south for one mile, he will find himself 0.8 miles from the South Pole. At that point, when he turns east, it will take him exactly one mile to circle the earth and return to that same point. (See the illustration below)

There are, of course, any number of correct solutions to the original problem. One option is to move the house even closer to the South Pole so that a one-mile journey to the east will cause the man to make two complete circles before ending up in the original position.

In short, there is an infinite number of solutions.