"one mile south" answer
I don't think the answer to "one mile south" at http://techinterview.org/Solutions/fog0000000127.html is completely correct. It is not possible to walk one mile south from the north pole. To do so would be walking "into" the earth, which is not possible.
This depends very much on what your definition of south is. If you're standing at the equator, the shortest line to the south pole also goes through the earth. This is true for any point on the surface of a sphere, apart from the south pole itself. If you define south as something like 'walking along a geodesic line joining this point and the south pole' there's no problem. This definition also works at the north pole - it just isn't unique.
you start about 117 meters from the pole: go 100m south so your 17m away, at that point, when you go east, the circumfrence of the globe around the pole is 100m, so you end up back on the same spot, then you go the 100m north, back to where you started
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