The bear is white. Only at the North Pole can the
conditions of the above puzzle be satisfied. Here is the hunter's map of his
journey. Return to my Puzzle pages
Go to my home page
© Copyright 2001, Jim Loy
I'll repeat the puzzle:
A hunter walked one kilometer south from his camp. Then he walked one kilometer west. There he shot a bear. Then he walked one kilometer north, and found that he was back at his camp. What color was the bear?
Answer:
The bear is white. Only at the North Pole can the
conditions of the above puzzle be satisfied. Here is the hunter's map of his
journey.
All of the conditions of the puzzle, except one, can also be met near the South Pole. There are no bears in Antarctica. But our hunter could follow a path as described above. Camp is 1+1/(2pi) kilometers from the South Pole. The hunter walks one kilometer south, and then one kilometer west, completely around the Pole, and then walks one kilometer north to his camp. There are actually other distances that our hunter's camp can be from the South Pole, and still satisfy the terms of the problem (except for the bear). Before reading the next paragraph, can you imagine how that is possible?
The other solutions (without the bear) are to position the camp so that the westward journey of one kilometer, goes twice around the pole (1+1/(4pi) km), or three times around the pole (1+1/(6pi) km), or four times, etc. There are infinitely many such situations.
This problem is somewhat similar to H. E. Dudeney's question about how a rectangular house can be built so that the windows on all four sides are facing south. The house happens to be at the North Pole.
Return to the original problem.