Problem - 4687
$\textbf{Interesting Locations}$
How many points are there on the earth such that after walking one mile south, then one mile east and finally one mile north, one will return to the original departure point?$\textbf{Answer}$
Infinite.
$\textbf{Analysis}$
While the North Pole is an obvious place satisfying the given condition, it is not the only qualified location. In fact, answering "one" falls into the trap.
Consider the ring which centered at the South Pole and has a circumference of $1$ mile. Then any point $1$ mile north of the ring meets the requirement: walking south for $1$ mile will reach this ring, walking east for $1$ mile along the ring will lead to the same spot on the ring, and finally walking north for $1$ mile will return to the departure place.