# 163 geometry/bear.p

## Description

This article is from the Puzzles FAQ,
by Chris Cole chris@questrel.questrel.com and Matthew Daly
mwdaly@pobox.com with numerous contributions by others.

# 163 geometry/bear.p

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?

geometry/bear.s

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

integer n.

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.

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