We are a commune of inquiring, skeptical, politically centrist, capitalist, anglophile, traditionalist New England Yankee humans, humanoids, and animals with many interests beyond and above politics. Each of us has had a high-school education (or GED), but all had ADD so didn't pay attention very well, especially the dogs. Each one of us does "try my best to be just like I am," and none of us enjoys working for others, including for Maggie, from whom we receive neither a nickel nor a dime. Freedom from nags, cranks, government, do-gooders, control-freaks and idiots is all that we ask for.
At the North Pole you have to go South 1st (you can’t go north of the North Pole). Therefore there is actually only one place where you can go one mile north, then one mile east, then one mile south to end up where you started (the South Pole).
All the lines of longitude are meet at the poles so wherever any of us are, if we walked true north (not magnetic north), until we could walk north no more, we’d meet at the North Pole (vice-versa for the South Pole).
It’ll probably take me longer, but I’ll see you guys there in a few days.
I don't know that I buy your second answer - "Any point one mile south of a one-mile circumference around the North Pole."
One, I don't think spinning around in an anticlockwise direction at the North Pole would really constitute walking East. And if you aren't exactly on the North Pole when you walk North from the one-mile circumference you've walked less than one mile North, or you've overshot and gone slightly south. (To walk in an easterly direction - you'd actually have to be slightly south of the North Pole - say walking about a circle of radius 1-meter in an anticlockwise direction around the North Pole.)
Two, "Any point one mile south of a one-mile circumference around the North Pole any point South" means there are in infinite number of points - so more than two altogether.
Then again, rebutting my own rebuttal, maybe I'm being somewhat overzealous with my requirements for precision in the measurement of a mile, and if I allow a measurement of + or - ten feet or so, then the walking east thing (in an anticlockwise circle) is doable and fair enough. And maybe I'm being pedantic with my second point, as you did say "two locations", not "two points", and a one-mile circumference is a location, though not a particularly precise one.
But to if I'm brutally honest with myself, I'm just pissed I didn't get it… :)