# Color of Bear Puzzle

1. Jun 16, 2004

### Gokul43201

Staff Emeritus
Okay, so a hunter gets out of his cabin on morning and gets into his jet powered surface cruiser. He travels 4000 miles south; turns eastward and travels 4000 miles and finally turns north and cruises for 4000 miles, at the end of which he is back outside his cabin. Now he sees a bear standing outside his kitchen window and eyeing the pie he had left to cool.

What is the color of the bear ?

Give complete solution, with reasoning !

eg : if x^2 = 4 then solutions are x=2, and x=-2 because 2^2 = 4 = (-2)^4

I know, I know...enough crap already.

2. Jun 16, 2004

### AKG

First, where is the hunter? Either at the North pole, or at any line of latitude such that, if you go 4000 miles south, you reach a line of latitude whose length times some natural number is 4000 miles. And when I talk about the length of the line of latitude, I mean the circumference of the cross-section of the Earth at that latitude.

If the hunter's at the north pole, the bear is probably white-looking (a polar bear). If that's not where he is, then the bear might be brownish, blackish, or greyish; those are the only other colours I can think that bears are found in, and I think there are enough places in the world that the hunter could be so that the bear might be any one of those colours.

3. Jun 16, 2004

### Gokul43201

Staff Emeritus
Not very many places, really !

4. Jun 16, 2004

### Njorl

If you travel 4000 miles south you are down around the 60 degree north line of latitude. The length of this line is about 12000 miles. The line of latitude that is 4000 miles is about 80 degrees north. Since this is well within 4000 miles of the north pole, you can't go 4000 miles south to get to it. This means that the cabin is at the north pole.

This makes the bear orange. Since no polar bears live that far north, and, as I recall, a wealthy prankster who hated this joke mounted an expedition to the pole to place the orange-dyed, frozen carcass of a bear at the exact pole.

Njorl

5. Jun 16, 2004

### Njorl

Ah.

A south american speckled black bear living at about 50 degrees south is one solution.

Njorl

6. Jun 16, 2004

### Njorl

cos(x)=1/(2pim)

yields how far south (x in radians) the cottage is, with m=to an integer

As you get to near 4000 miles from the south pole, you get an infinite number of discrete solutions, though exactly 4000 miles from the south pole is not a solution. The north pole is a solution.

Njorl

Last edited: Jun 16, 2004
7. Jun 16, 2004

### Njorl

Oops.

I misread my table. I thought the Earth had an 8000 mile radius, it is an 8000 mile diameter.

I'll change my equation.

Njorl

8. Jun 16, 2004

### Gokul43201

Staff Emeritus
Yes, please. 50 S was different from what I intended, but ...

9. Jun 16, 2004

### Gokul43201

Staff Emeritus
You don't find the speckled bear that far south..only in Venezuela, Colombia, northern Brazil, and a few in Peru and Bolivia.

10. Jun 16, 2004

### Njorl

I also screwed up the algebra. Hehe

11. Jun 16, 2004

### Njorl

The allowable latitudes for the eastward movement are defined by

cosx=1/(2pim)

cos-1(2pim)=x

For m=1, you get about 10 degrees from the pole (80 degrees south)

the cottage will be 4000 miles north of this, or about 57 degrees north of this at 22-23 degrees south.

For higher values of m, the cottage will move no more than 10 more degrees southward, to about 33 degrees south.

Njorl

12. Jun 16, 2004

### Gokul43201

Staff Emeritus
Good, so what's the answer ?

13. Jun 17, 2004

### Njorl

Koala bears are tan!

Njorl

14. Jun 17, 2004

### Gokul43201

Staff Emeritus
Hah, what I've been waiting for !

Koala bears are not bears. In fact, they're not even related to bears ! But this is what I've been hoping someone would say, and my patience has been rewarded.

Your previous guess of the speckled bear is the correct answer. They are dark brown, with yellow speckles.

AKG & Njorl share the pie !

15. Jun 17, 2004

### Njorl

Mmmm...pi/2....orthoganalicious.

Njorl

16. Jun 18, 2004

### hemmul

Black & White! Like Pandas, i bet!
You see - after such a long trip, in polar conditions, surface cruisers start malfunctioning: oil starts leaking, the ice underneath is melted due to the overheated engine ... the hunter repairs it in the "yard" (just outside the kitchen) so there are too many oil spots on the earth... that's why the poor bear is partially black :rofl: