Consider the following popular riddle:
“An explorer walks one mile due south,
turns and walks one mile due west, turns again and walks one mile due
north. He finds himself back where he started. He shoots a bear, what
color is the bear?”
The answer found in most puzzle books is “White” since he must have started at the North Pole.
But in fact, he could have started in other place(s). Another possible starting location is 1+1/(2pi) miles north from the south pole. In this solution, he walks 1 mile south to be 1/(2pi) miles north of the south pole, then walks due west in a circle of circumference 1, and then north to his original starting location.
See if you can figure out every possible solution (assuming the Earth is a perfect sphere).