A man walks 1 mile south, then 1 mile east, and finally 1 mile north to find himself in exactly the same position as he started. He is NOT at the north pole, nor does he shoot a bear.
Where is he?

Original Credit: Martin Gardner

The man could be on any point on the circle drawn 1 + 1/2pi miles from the south pole. (ignoring the curvature of the earth)

He walks 1 mile south, to get to 1/2pi miles from the south pole. From here, if he walks 1 mile east, he will complete a full circumference of a circle and get back to his original spot. Finally he walks 1 mile back up north to his starting location.