This article is from the Puzzles FAQ, by Chris Cole firstname.lastname@example.org and Matthew Daly email@example.com with numerous contributions by others.
If a hunter goes out his front door, goes 50 miles south, then goes 50
miles west, shoots a bear, goes 50 miles north and ends up in front of
his house. What color was the bear?
The hunter's door is in one of two locations. One is a foot or so from the
North Pole, facing north, such that his position in front of the door is
precisely upon the North Pole. Since that's a ridiculous place to build a
house and since bears do not roam within fifty miles of the pole, the bear
is either imaginary or imported, and there is no telling what color it is.
There is another place (actually a whole set) on earth from which one
can go fifty miles south, fifty miles west, and fifty miles north and
end up where one started. Consider the parallel of latitude close
enough to the South Pole that its length is 50/n miles, for some
Take any point on that parallel of latitude and pick the point fifty miles
north of it. Situate the hunter's front porch there. The hunter goes fifty
miles south from his porch and is at a point we'll call A. He travels fifty
miles west, circling the South Pole n times, and is at A again, where he shoots
the bear. Fifty miles north from A he is back home. Since bears are not
indigenous to the Antarctic, again the bear is either imaginary or imported
and there is no telling what color it might be.