You are at a point on Earth. You travel exactly 100 miles due south. You turn and travel exactly 100 miles due west. You then turn and travel exactly 100 miles due north. You notice that you are now exactly at the point from which you started. Where are you at the beginning and the end of the trip? Are there any other points on Earth where this can happen? If so, where are they?

This standard brainteaser has a simple answer: you are on the North Pole. Because "north" is measured relative to the North Pole—and because traveling east and west preserves your distance from the North Pole—following the instructions in the prompt will put you right back where you started.
More interesting is figuring out whether there is anyplace else where the same principle holds. In fact, there is a band around the South Pole where the same steps will also bring you to the same place.
Because the Earth is (roughly) spherical, its circumference narrows as you approach the poles. That means there is a ring in Antarctica where an east-west circumnavigation of the globe takes exactly 100 miles. At any point on that ring, if you walk 100 miles west, you will end up completing a perfect circle and you will finish exactly at your starting point. So, if you begin the instructions in the prompt precisely 100 miles north of that ring, walk south toward the ring, travel the ring, and walk back north, you will finish right where you began, fulfilling the prompt's requirements.