Path on the Surface of the Earth


I got this problem from Rustan Leino, who says he must have heard this problem ages ago, but as he remembered it, one was always satisfied after finding just one solution. It was a math professor at the Kaiserslautern Technical University who brought asking for all solutions to his attention.

I solved it and wrote up my solution.


Initially, you're somewhere on the surface of the Earth. You travel one kilometer south, then one kilometer east, then one kilometer north. You then find yourself back at the initial position. Describe all initial locations from which this is possible.

Solution     Reveal