Originally posted by SuzianneI believe it was the Plumber who dropped the science on me with this one on another thread a few months back. I don't want to give it away outright, but imagine this: at most points south of the north pole, if the bear walks east 1 mile, it ends up 1 mile east of where it started - does this ever change? Try moving the bear south and see what happens...BTW, the south pole won't be a starting/stopping point for the bear because walking "east" at the south pole doesn't mean anything (unless you're syphilitic or clinically insane!).
What word? I see a collection of letters that *looks* like it might be the word color, only misspelled.
Originally posted by PBE6I was imprecise. It would be a mile north of the circle which was on the surface of the Earth, was centered on the north/south axis and had a circumferance of exactly one mile and was south of the Equator.
I believe it was the Plumber who dropped the science on me with this one on another thread a few months back. I don't want to give it away outright, but imagine this: at most points south of the north pole, if the bear walks east 1 mile, it ends up 1 mile east of where it started - does this ever change? Try moving the bear south and see what happens...BTW, ...[text shortened]... st" at the south pole doesn't mean anything (unless you're syphilitic or clinically insane!).
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Originally posted by LordOfTheChessboardI never answered about the color.
This still does not say anything about its collor. But why can a bear not walk like that here in holland?
Get a compass, a large field, and try it.
Walk long EQUAL distances SOUTH, EAST, then NORTH.
you will not return to the same spot with out going Northwest.
Your path would be like an open box.
The closer to the north pole, the closer you will return to you original position in this manner.
Unless you were at the north pole, this would not work.
Think about it.
Only at the Northpole will that work. because of the position of the poles.
Also think of this if you are at the North-Pole, you cannot go in any direction with out going a southernly direction.
You cannot go East or West from the North or South poles.
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Originally posted by AThousandYoungHow would that work out?
Or a mile from the South pole.
If the bear were one mile from the SouthPole, there is no way it could follow the same path as in the question.
After the first mile south the bear would be at the south pole. After that he could not go in any other direction except a Northernly direction.
You cannot go East or West from the North or South poles.
Originally posted by SuzianneYes, the places where one can go 1 mile south, 1 mile east and 1 mile back north to arrive back at the starting point are:
An infinite number of spots? On *this* planet? Please explain.
1) the north pole
2) Near the south pole, all the points on the parallel which is one mile above the parallel that has a circumference of 1 mile
3) As in 2, but every parallel one mile above parallels with a circumference of a whole fraction (1/2, 1/3, 1/4, .....) of one mile.
Originally posted by LordOfTheChessboardThe bear could be any colour that bears come in - providing that the den was more than a mile wide and the bear left it from the west wing.
A bear left her den, moved 1 mile southword, then 1 mile eastword, turned north and, after another mile, got back into her den.
What is the color of the bear?
Originally posted by Mephisto2That is so clever. I never thought about 2 and 3. Very nice.
Yes, the places where one can go 1 mile south, 1 mile east and 1 mile back north to arrive back at the starting point are:
1) the north pole
2) Near the south pole, all the points on the parallel which is one mile above the parallel that has a circumference of 1 mile
3) As in 2, but every parallel one mile above parallels with a circumference of a whole fraction (1/2, 1/3, 1/4, .....) of one mile.
Originally posted by Mephisto2This is indeed an elegant solution and not immediately grasped by many.
Yes, the places where one can go 1 mile south, 1 mile east and 1 mile back north to arrive back at the starting point are:
1) the north pole
2) Near the south pole, all the points on the parallel which is one mile above the parallel that has a circumference of 1 mile
3) As in 2, but every parallel one mile above parallels with a circumference of a whole fraction (1/2, 1/3, 1/4, .....) of one mile.
Except for one thing.
The first stipulation is that a bear left her den and walked this route.
There are no bears of any kind living on Antarctica.
Originally posted by SuzianneAn excellent point, lost on none save the stupidest bear south of the equator.
This is indeed an elegant solution and not immediately grasped by many.
Except for one thing.
The first stipulation is that a bear left her den and walked this route.
There are no bears of any kind living on Antarctica.
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Originally posted by Mephisto2Clever indeed!
Yes, the places where one can go 1 mile south, 1 mile east and 1 mile back north to arrive back at the starting point are:
1) the north pole
2) Near the south pole, all the points on the parallel which is one mile above the parallel that has a circumference of 1 mile
3) As in 2, but every parallel one mile above parallels with a circumference of a whole fraction (1/2, 1/3, 1/4, .....) of one mile.
1. easy enough
2. Very clever
3. Pure genius.
Same idea as 2 I get, but I am still processing it.
So you would be making multiple trips round the smaller
circumference parallels, ending once again directly south of the
origin. The smaller the circumference(thus the closer to the
South pole, the more trips you make round!
That is my understanding sans math.
In answers 2 and 3, the path is no longer triangular.
So much for that puzzle.
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Originally posted by PBE6That is correct. Therefor my initial answer above was: "White, if it is an aboriginal bear. Although I am doubtful that there is a bear den exactly on the north pole. Making abstraction of that requirement, it could be any colour (you can find or make a bear of), and there are an infinite number of spots where this 'bear' could have a den, the northpole being just one of them."
An excellent point, lost on none save the stupidest bear south of the equator.
edit. That 'bear' would have a unique opportunity to meet his antipole 'friend' the pinguin, something which normally is possible only in a zoo.
Originally posted by Mephisto2Yeah, there's probably no den there, just a bunch of American and British flags. Lousy patriots.
That is correct. Therefor my initial answer above was: "White, if it is an aboriginal bear. Although I am doubtful that there is a bear den exactly on the north pole. Making abstraction of that requirement, it could be any colour (you can find or make a bear of), and there are an infinite number of spots where this 'bear' could have a den, the northpole ...[text shortened]... to meet his antipole 'friend' the pinguin, something which normally is possible only in a zoo.
Originally posted by Mephisto2I say Brooklyn that can be done, yes Brooklyn.
Yes, the places where one can go 1 mile south, 1 mile east and 1 mile back north to arrive back at the starting point are:
1) the north pole
2) Near the south pole, all the points on the parallel which is one mile above the parallel that has a circumference of 1 mile
3) As in 2, but every parallel one mile above parallels with a circumference of a whole fraction (1/2, 1/3, 1/4, .....) of one mile.