This is a solution to problem 10 on the hard interview questions node. There are infinite points where walking one mile south, one mile east and one mile north you reach the place where you started. - The North Pole. Walk a mile south (i.e. any direction), then one mile east (an arc of 1 rad around the pole), then walk back north one mile. - Exactly 1 + 1/(2π) miles from the South Pole. You walk south one mile, ending up exact 1/(2π) miles from the South Pole. You walk east one mile, around the South Pole and back (drawing a circunference of radius of 1/(2π) miles and length of 1 mile). Walk north one mile, and you're back where you started. - Exactly 1 + 1/(4π) miles from the South Pole. Just as above, except you go around the South Pole two times. - Exactly 1 + 1/(2xπ) miles from the South Pole, where x is a natural number, nonzero. You got the idea. This, of course, assuming both poles can be walked and circled around at will.