## 14. The Bear Problem.

This problem has an intriguing feature: many people have heard it and know the answer, but the reasoning they use to justify it is entirely unsatisfactory. Therefore, even if you think you know the answer to the problem, check yourself by looking at the solution.

A hunter is 100 meters south of a bear, walks 100 meters east, turns to face north, aims, and shoots the bear in the northward direction, killing it. What color is the bear's fur?

## B. SILLY STUFF

I long hesitated, unsure what to call this book. I tried numerous titles like "Entertaining Logic," "Logical Amusements and Games," but couldn't decide on a suitable one. Then I decided to look in the Great Encyclopedic Dictionary. Opening it to the entry "Amusements," I read: "See Entertainment." Following the advice, I learned a wealth of useful information about buffoonery, games, amusements, entertaining pastimes, pranks, diversions, jokes, jesting, and humor. I discovered that one could play a trick on someone, stage a prank, start a commotion, create a ruckus, raise a dust, and even a cloud of smoke, and that there are antics, capers, antics, and even "silly stuff." Upon reaching this expression, I laughed and told my wife: "You know, I think 'Silly Stuff' is a wonderful title for my book." However, as expressive as such a title might be, it could give the reader a wrong impression of the book's overall content, as many of its sections hardly fit it. Nevertheless, you will soon see that the title "Silly Stuff" fits this section perfectly.
14. The fur must be white, as it belongs to a polar bear inhabiting the Arctic - near the North Pole. Usually, the answer is supported by the fact that the bear in the problem's conditions must be standing at the North Pole. If you step in any direction from the North Pole, you will always be moving south. Therefore, if the bear is at the North Pole and the hunter is 100 meters south of it, then, after walking 100 meters east and turning north, the hunter will face the North Pole. This is true, but as I have already said, the given solution is not the only one. Indeed, there are infinitely many solutions. For example, the hunter could be on a parallel 100 meters long, and the bear 100 meters north of him. Walking 100 meters east, the hunter will complete a full circle around the pole and return to the starting point. This is the second solution to the problem. But the hunter could be even closer to the pole on a parallel 50 meters long. Walking 100 meters, he will circle the pole twice and return to the starting point. But this is not all. The hunter could be on a parallel 1/3 of 100 meters long. Circling the pole three times along the parallel, he will also return to the starting point. Since a similar solution can be constructed for any positive integer \( n \), there are infinitely many places on Earth where the scenario described in the problem could have taken place.

Of course, in all these solutions, it is assumed that a bear located close enough to the North Pole must necessarily be a polar bear. However, there is another possibility, albeit a very unlikely one: some malicious individual deliberately transported a brown bear to the North Pole to "spite" the author of the problem.