At which point(s) on Earth can you go one mile south, one mile east, and one mile north, and end up at the exact point you started? Assume the Earth is a perfect sphere. There is more than one answer.

But you wouldn't be at the north pole any more, since you have gone one mile south and one mile east. There are 3 more answers that I can think of: Equator Tropic of Cancer Tropic of Capricorn

There are infinite number of answers: 1) The circular area that is 1 mile north of a point that has factor of 1 mile circumference. 2) North Pole 1 mile north of the South Pole doesn't really count because you can't stand at the point that has 0 circumference and walk 1 mile east. The concept is valid but in reality it's not (mainly mathematically than physically, because you only get 0 circumference if South Pole is the tip of a perfectly levelled 3D round object -and Earth is not-). But if you are 1 mile north of a point that has 1 inch circumference, you CAN walk 1 mile east, that'd be hellota trips around the circle but still you can make it. I saw this question a few years ago and the question asked "which bear would you encounter in those areas?" It makes more sense because technically there are infinite number of answers to "where"

There is one more set of points that deathfisaro missed. I found out this stuff by myself, then was devastated to see that other people had already discovered it online.

Oh, your question specifically says "assume Earth is a perfect sphere" I didn't see that. There's too much alcohol in my system I miss things.