In answer to Callaway's question. Here are the answers:
First is the North Pole (assuming the Earth is a perfect sphere).
Second copy/pasted from my PM exchange with Callaway):
Somewhere near the South Pole there is a horizontal circle circling the sphere with a circumference of 1 mile. If you go east 1 mile at any point X on the circle, you end up back to the same point X. This means that going north 1 mile from that point X is the same as going south 1 mile to that point X.
So any point that's 1 mile north of X is the answer.
After much struggles, I finally got the third answer:
You know how there are circles near the South Pole that are (in circumference) half a mile, quarter a mile, eighth a mile, and so on. Every point X that is 1 mile north of any of the points Y on any of such circles is the answer.
The key is that you have to go around each circle more than once before you can safely say you walked 1 mile east for each scenario. So, for example, on the half a mile circumference circle, you have to go around it twice. For the quarter mile, 4 times. And so on.
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There you go, folks. I'm now officially a math geek.