Logic riddles

[Alpha]

I have some logic riddles.
Lets start with a nice one, that starts like this:
Two hunters Mr. A and Mr. B meet in Mr. A's house.
Mr. B: Oh, what a beautiful carpet you have.
Mr. A: Yeah, it is made of bear's fur.
Mr. B: How did you hunt the bear?
Mr. A: Well, (Light his pipe ), I started from the camp, and went 1 mile to the south, There I saw the bear.
I followed him exactly 1 mile to the east. There I shot him. From this point I returned to the camp, exactly 1 mile to the north.
The question is what is the color of the bear?

[blinc]

ummm... erm... uhh

Are you by chance a friend of Thespians?

*grumble*
Need me a Big bottle of aspirin.
Big, big bottle yep.
These young whippersnappers tormenting us poor old fogeys
*mumble*

Will you give us clues? Like was it wintertime? or does it matter if it was winter or not?

By the way Alpha, it's nice to meet you and glad to see you're posting already!

[KatCo]

I believe the bear would be white as in a Polar Bear, to go in a circle and end up back where you were would mean that you would have to be at the pole. Just a guess....

[Alpha]

Excellent KatCo!
The Answer is correct.
The only place on earth in which one can go south, east and then north and return to his starting position is the North Pole, because the longitudes meet there.
So this is the only answer, or is it?
Ignore the bear in the story, is there another place on earth where it is possible to go the same path and return to the starting position?
Be careful this is a very difficult question!

[KatCo]

humm....other than the south pole I would assume???
the "same path" has me thinking.....no answers as of yet.
tis a tough one......I'll keep a pondering.

[Alpha]

The South Pole can't be the answer, because you cannot go southward from it (In the story he went 1 mile south, east and then north).
As a matter of fact if you are standing exactly on the South Pole you can go only northward (At least in your first step...)
There is a solution, but it is quite hard to come up with it.

[blinc]

South, then east and then North... the equator could be the other answer couldn't it?

You know if you traveled at angles you could always end up back at the same point. Head S at an angle like this / then straight east _ and then the reverse angle back north again... you could make a giant triangle... but I assume you mean straight south, huh? If it's not the equator, I'm really stumped over here! Great logic riddle Alpha!

[Alpha]

The equator is not the answer.
As a matter of fact, the equator is where the coordinates are nearest to cartesian coordinates (where the axis are straight and in 90 degrees) and therefore the hunter would finish his journy in the farthest point from his origin. That distance would be of course exactly 1 mile.

As I told you, this is a tough question.
If nobody solves it I will give the answer in few days.
Good luck.

[blinc]

Arrgh! You've stumped me Alpha - thought the equator would work because if you were standing at the very edge of the equator "line" and tried it, was thinking you would end up back on the equator line, but of course, one mile to the west of where you started... back on the line? well dang, I sure've mulled this one over - haven't given up though!

[blinc]

*pulls out tufts of hair in frustration*

AAAARRRGGGGH!!

[Alpha]

The question was really hard.
As a matter of fact there is not only 1 place like this, but infinite number of places.

Before I reveal the solution I will remind you what does going south, east, north and south mean:
Going north and south is simply going up and down on the longitudes. Going west and east is going right or left on the latitudes.

The longitudes are going from the South Pole up to the North Pole.
The latitudes are parallel to each other and go around the globe in circles that are small around the poles and largest near the equator.

Since the latitudes are small near the poles, one can find a latitude near the South Pole that is 1 mile long in circumference. This latitude would be about 250 yards from the pole (1 mile/2/Pi).

If one stands on this latitude and walks 1 mile to the east, he will go around the globe (that is easy near the poles) and return to his starting position.

If one stands 1 mile to the north of that latitude he would be able to go 1 mile to the south, 1 mile to the east, and then 1 mile to the north and return to his starting position.

The solution, therefore, is all the places on the latitude that is about 1 mile and 250 yards north of the South Pole.

Of course he won't find any polar bears there. The polar bears are only in the North Pole. In the South Pole there are penguins, and not so far inland ...

This was a long explanation, but not the end of the logic riddle.
The next part of the riddle, as you could guess is...
Find another point on the globe that one can go fron it 1 mile south, east, and north and return to his starting position.

[blinc]

*stares*
*twitch*
*stares some more*
*drool*
*twitch*

[Anat]

He is wicked isn't he?

That's okay blinc, I can NEVER find the answer to his logic riddles. My poor little brain is not up to it.

In fact I couldn't follow the explanation very well and he had to show me (we used an orange as a model of the earth - then we ate the whole planet ). I finally got it, but I couldn't repeat the explanation myself

[thespian]

"Okay - Lights! Camera! Action!"

The thespian has arrived!

Listen Alpha all this talk about longitude and latitude has got me going round in circles ( Ha! Circles - get it? )

I know of another place where I walk a lot more than a mile in the same direction and always end off at the same place I started from. It's at the Gym around the corner.
"Okay everybody, let's get those Treadmills fired up. Come on, all together now - We're on the Road to Nowhere ..."

[Anat]

He's not home yet, but does all that song and dance means you're actually trying to solve this?

Just curious...