20031014, 00:26  #1 
Jun 2003
The Texas Hill Country
2×541 Posts 
What colour is the bear?
Here is an old one 
A hunter leaves his base camp one morning and travels one mile due south. He then turns and travels one mile due east. At this point, he shoots a bear. Taking the direct route, he travels one mile due north and is back at the base camp. What color is the bear? (I expect many of you know the answer. Tune in tomorrow for the follow up question which is much more interesting) Richard 
20031014, 01:18  #2 
"Gang aft agley"
Sep 2002
3,581 Posts 
White. Perhaps he is holding a bottle of Coca Cola and wandering in the neighborhood of a post that reminds one of a barber shop.

20031014, 04:30  #3 
"Richard B. Woods"
Aug 2002
Wisconsin USA
7188_{10} Posts 
Is there evidence that a bear of any color has ever wandered to only one mile from the North Pole?

20031014, 06:18  #4  
"William"
May 2003
New Haven
2^{2}·3^{2}·5·13 Posts 
Quote:


20031014, 10:39  #5 
Jun 2003
The Texas Hill Country
43A_{16} Posts 
Well, wblipp spoiled the follow up ....

20031014, 10:49  #6  
"Mike"
Aug 2002
7,699 Posts 
Quote:
I think I understand the direction thing, but knowing you guys the obvious answer is never the real answer so I await your solution... 

20031014, 12:55  #7 
Jun 2003
The Texas Hill Country
2×541 Posts 
As only_human notes,
If the base camp is at the North Pole, the hunter travels south along a line of constant longitude for one mile. Then his easterly travel is at a constant latitude (he remains exactly one mile from the base camp at all times during this leg of the trip). After shooting the bear, he returns to the camp along that line of longitude. If a bear is near the North Pole, it must be a Polar Bear. Polar bears are White. For many years, this was the accepted answer. Then someone realized that there are other locations where a base camp can be located in such a manner that it is possible to travel the prescribed path and end up back at the base camp. Fortunately, these locations are remote from any location where a bear might be found. But, where are they? 
20031014, 19:11  #8  
"Gang aft agley"
Sep 2002
3,581 Posts 
Quote:
I liked your question; it put me in mind of an old joke about an engineer, a physicist and a mathematician on a train heading north into Scotland: The engineer looked out the window and said "Look! Scottish sheep are black! The physicist said, "No, no. Some Scottish sheep are black." The mathematician looked irritated. "There is at least one field, containing sheep, of which at least one side is black." 

20031015, 10:26  #9  
"Gang aft agley"
Sep 2002
3,581 Posts 
Quote:


20031015, 11:35  #10 
Jun 2003
The Texas Hill Country
2·541 Posts 
OK, let's discuss these points near the South Pole.
First, let's describe the travel in terms of latitude and longitude. Traveling South is to move along a line of constant longitude while increasing southern latitude. Traveling North is the same except that the southern latitude is decreasing. Traveling East or West is moving along a circle of constant latitude while changing the longitude. Now, I will reject the idea that any path which passes through the Pole is a proper path. I contend that although the path is a straight line, part of it is traveling south and part of it is traveling north. However, if you wish to allow such paths, that simply adds another family of possible camp locations. Back to the puzzle, If you pick any fixed latitude and travel due East, you will eventually circumnavigate the planet. The length of that trip depends on the latitude chosen. (Assuming a spherical planet) the distance is greatest at the Equator and steadily decreases (in proportion to the cosine of the latitude) as you near the Pole. Now, consider an arbirtary starting point anywhere on the planet. If you do a circumnavigation, you will have returned to the same starting point. If we pick our point near the South Pole, we won't have to travel very far. In particular, there is a small circle around the South Pole whose circumference is exactly one mile. It is located 1/ (2*pi) miles from the Pole. Now establish the base camp exactly one mile north of this circle. The hunter travels one mile south and arrives on this circle. Here let's assume he drops a pack for future reference. He then travels one mile east. This circumnavigation of the Pole returns him to the pack that we just had him drop. He then travels one mile north retracing the path back to his camp. Notice that there are an infinite number of base camp locations because the camp can be at any longitude. Now there is another circle of camp locations even nearer the Pole. From these camps, the hunter travels to a point that is midway between the Pole and the place where he dropped the pack. From that point he travels east 1/2 mile and is back to the start of his eastward journey. So he travels another 1/2 mile and completes a second circumnavigation of the Pole. Having completed the required one mile east, he returns north to the base camp. In fact, there is a whole series of latitudes which correspond to 1, 2, 3, etc. circumnavigations of the Pole while traveling one mile East. 
20031015, 15:01  #11 
Nov 2002
Vienna, Austria
51_{8} Posts 
I guess, there are fans of Martin Gardner somewhere around here

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