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[BillSL]

BillSL, When you say he didn't necessarily go the cardinal directions, then the guy also didn't necessarily go in straight lines, which is why I said it invalidated the premise. A person can walk in a circle with a 30 mile circumference in alot of different places.

Oh no. Even if he did walk in a circle, he would HAVE to be within a 10 miles radius of the MN. Which is all water.

If he walked 10 miles S, 10 miles W and 10 miles N (and, as the OP, he arrived at the campsite) while using a compass, it would be exactly the same thing as if he was using original cardinal directions, but the "North Pole" would actually be somewhere in the sea in northern Canada.

For clarity sake, lets just assume a couple of things here. The south, east, and north directions are astronomic. Magnetic north is only used as a reference to astronomic and as GPS is becoming more widespread, the use for magnetic becomes less (except in the case of emergency equipment or power failures). (Those of us in the geodesy and cartography business cringe at the use of the reference "True North"...call it what it is....astronomic, magnetic, or grid.) The fact that the area is over water is inconsequential. Provided that the scenario occurs with the man walking over the terrain, one can deduct that the event occurred during the winter in that particular hemisphere.

Where (or who, for that matter) does it say he "walks"? He "goes"!

OP's question is, evidently, True North.

My "twisted" version is Magnetic North, for he is using a compass.

(Your conclusion/post is, therefore, inconsequential.)

BillSL-
I'm not sure of what you are asking other than the fact that the designation of whether it is astronomic or magnetic north was left out....

If he used a compass, he used magnetic north, as you have eloquently explained. Question is at OP's.

You are correct in that it can originate at the North Pole, but there are an infinite number of places on the Earth's surface where this can originate other than the North Pole, so why is it a Polar Bear?

Name 1 besides N pole (S pole is impossible, because you cannot head "south" if you are already at the southmost part of the earth. If you claim you have "walked without moving" (if you know what I mean), it would've violated the data at the OP (you would've never walked back into your campsite)).

The fact that the S pole has no bears is off the point.
(

since there are no bears at the south pole, then it has to be at the north pole.....

.)

If instead you assume a great circle path starting in the given direction, then there is no solution. I cannot think of any other assumptions that would allow an infinite number of solutions as stated by evilleramsfan.

If the camper has started and ended in the same spot, and he has walked on 3 different directions, there are only 2 places on Earth. Just 1, actually, for the South Pole is negated for conflicting data.

OK, I suddenly recognized the other (infinite number of) solutions which occur when the westward leg results in a complete circle or multiple complete circles around the south pole. All such solutions have the initial starting point within approx 11.6 miles of the south pole.

Okay... Can someone please explain me how on EARTH (pwn semi-intended) will you get infinite possibilites, considering, as intended by the OP, that the camper has walked in 3 distinct directions and has arrived at the original spot?





Tone of this post is supposed to be light - it is hard to transmit a "peaceful" post in writing, normally.

As for the flag pole question. The wires cross at the same height regardless of the distance between the poles.

That's awesome to know! Thanks!

 

[oceanblue]

Okay... Can someone please explain me how on EARTH (pwn semi-intended) will you get infinite possibilites, considering, as intended by the OP, that the camper has walked in 3 distinct directions and has arrived at the original spot?

Since the earth is a sphere (approx.), the westward leg is a curve and not a straight line other than at the equator. Near the poles, that leg will be a tight circle around the pole. If the circumference of that circle is 10 miles, then a 10 mile walk to the west will return you to your starting point. If the hunter's cabin is 10 miles north of a point on this circle, his complete trip starting at the cabin will go 10 miles south to a point on this circle, 10 miles west - making one lap around the circle back to the starting point of this leg, then 10 miles north to the cabin. If the cabin is 10 miles north of any point (of an infinite number) on this circle, he will end up back at the cabin. There are infinitely more solutions for circles with a radius of 10/2, 10/3, 10/4 ... miles as well.

 

[BillSL]

Since the earth is a sphere (approx.), the westward leg is a curve and not a straight line other than at the equator. Near the poles, that leg will be a tight circle around the pole. If the circumference of that circle is 10 miles, then a 10 mile walk to the west will return you to your starting point. If the hunter's cabin is 10 miles north of a point on this circle, his complete trip starting at the cabin will go 10 miles south to a point on this circle, 10 miles west - making one lap around the circle back to the starting point of this leg, then 10 miles north to the cabin. If the cabin is 10 miles north of any point (of an infinite number) on this circle, he will end up back at the cabin. There are infinitely more solutions for circles with a radius of 10/2, 10/3, 10/4 ... miles as well.

Exactly.

All the infinite solutions , as you say, point to the North Pole (or anything within a FEW miles from it).

The bear will be polar, no matter what.

 

[evilleramsfan]

No..... Look at a globe and specifically at the South Pole straight on from the axis. Now, if you were to find a parallel of latitude which has a circumference of 10 miles and travels around the pole. Any point 10 miles north from this circle would meet this requirement. The person would walk 10 miles south to that circle, east or west around that circle for 1 lap, and then north 10 miles to the point of beginning. There are an infinite number of solutions near the South Pole, but since there are no bears there, it must be at the North Pole and thence white.....

Look, this is all in fun, and in case any of my questions or comments are taken as otherwise, that was not the intent. You are right in that it works for magnetic as well as astronomic, but are there not times where the magnetic north pole freezes over? (Same goes for the magnetic south pole) I have told a variation of this riddle for years, but used the term "walk". I had not gone back to check the original wording.....walk, boats, goes, mushes....the way he does it matters not.

 

[BillSL]

No..... Look at a globe and specifically at the South Pole straight on from the axis. Now, if you were to find a parallel of latitude which has a circumference of 10 miles and travels around the pole. Any point 10 miles north from this circle would meet this requirement. The person would walk 10 miles south to that circle, east or west around that circle for 1 lap, and then north 10 miles to the point of beginning. There are an infinite number of solutions near the South Pole, but since there are no bears there, it must be at the North Pole and thence white.....

Yes I got that. But the fact is that he would still be within 10 miles of the S Pole, which, given the conditions, is negligible. But I got what you meant by "infinte possibilities" when oceanblue explained. I'll be honest, I did NOT think of that. But the answer would still be 1, practically speaking.

Look, this is all in fun, and in case any of my questions or comments are taken as otherwise, that was not the intent. You are right in that it works for magnetic as well as astronomic, but are there not times where the magnetic north pole freezes over? (Same goes for the magnetic south pole) I have told a variation of this riddle for years, but used the term "walk". I had not gone back to check the original wording.....walk, boats, goes, mushes....the way he does it matters not.

By no means I took your posting as, well, "not fun". I had my share of experience with wrong transmission of feelins over a Forum...

I did not know about the magnetic poles "freezing over"! That's good to know. What I DID know is that the MP DO move every year.

Oh, and if the wording was otherwise, a "troll twist" would've never been possible

 

[evilleramsfan]

As a land surveyor who specializes in geodesy and cartography, problems like these hold special meaning.....lol....
Now on to one that is really fun...

If you have a sphere and drill a hole through the center of it so what remains is a ring. The distance of the inside of the ring is 2 inches. (Meaning measuring the inside of the ring from where the edge of the bit entered the surface of the sphere to where said bit exited the surface of the sphere. What is the radius of the sphere?
Have fun! (The answer will blow you away....)

 

[BillSL]

evill, I was actually rethinking that problem.

There is really just 1 solution - there is no way you can move 10 miles in a direction and have a 10 mile circumference.

 

[evilleramsfan]

Sure you can! You can move in an east or west direction along the equator a distance of the circumference of the Earth and end up where you started. Same goes with any parallels of latitude....(even if that parallel only has a circumference of 10 miles....)

 

[cisco]

Fine, I'll explain. At the north pole, you can ONLY go south. Once there, going east or west follows the lines of longitude which is perfectly perpendicular to the north south line. Once at the next point, a path straight north leads back to the pole. Is it really necessary to do the geometry? The intuition is readily apparent with the answer.

^Correct

No..... Look at a globe and specifically at the South Pole straight on from the axis. Now, if you were to find a parallel of latitude which has a circumference of 10 miles and travels around the pole. Any point 10 miles north from this circle would meet this requirement. The person would walk 10 miles south to that circle, east or west around that circle for 1 lap, and then north 10 miles to the point of beginning. There are an infinite number of solutions near the South Pole, but since there are no bears there, it must be at the North Pole and thence white.....

Look, this is all in fun, and in case any of my questions or comments are taken as otherwise, that was not the intent. You are right in that it works for magnetic as well as astronomic, but are there not times where the magnetic north pole freezes over? (Same goes for the magnetic south pole) I have told a variation of this riddle for years, but used the term "walk". I had not gone back to check the original wording.....walk, boats, goes, mushes....the way he does it matters not.

^ Like you said, look at the globe...
Since the question states your going South, it can't be the South Pole.

Now, looking at the globe, it should have the Long and Lat lines, look closely at all of them and you'll see they all make squares, but only in 1 other place does it not, the North (or South, but we ruled that out) Pole. Going in the stated places the question said he went, everywhere else would be a square except for the NP.

 

[BillSL]

Sure you can! You can move in an east or west direction along the equator a distance of the circumference of the Earth and end up where you started. Same goes with any parallels of latitude....(even if that parallel only has a circumference of 10 miles....)

You're saying -- You start at point A (MUST be at south pole).

Point A must be within "exactly" 11.59 (rounded up, evidently) miles from the S Pole (actual "dot", extreme SP). He will move S for 10 miles. Radius will be 1.59, so circumference will be almost 10 miles long. No other place on Earth has that property (besides perfect NP...).

Therefore, there is just 1 solution to the case - as stated, SP does not have bears. SO, as there are "infinite" (by infinite I mean any point in the 11.59-radius circumeference N of the SP) possibilites near the SP, which are all inviable. Solution can only be NP.


Is that what you are telling me, evill? If not, I must analyze a drawing.

 

[evilleramsfan]

First of all to those who assume i am saying you start at the south pole, you misunderstand. Read it again.

Bill...you now have the idea. The point of origin can be any point 10 miles north of that circle. Since there are an infinite number of points along a circle, there are an infinite number of points of origin.
As though that wasnt enough, there are an infinite number of circles. What if the circumference was 5 miles. He could travel east or west for 10 miles and do 2 laps. A circumference of 10/3 would yield 3 laps, etc.

 

[BillSL]

Oh, I got what you said that the S Pole is impossible.

The truth is, however, that, considering the data:

10 miles S
10 miles W
10 miles N
Back at campsite
Tent destroyed by BEAR

There is just 1 answer (start point is necessarily NP, exactly).

Now I got what you meant by the SP circumferences. I feel stupid now, but thanks for the explanation.

 

[evilleramsfan]

Exactly. Now if the cabin had been destroyed by a flock of emperor penguins, then that would be another answer (one that couldn't be derived based on the info provided). But since it was a bear, that rules out all of the other possibilities.....

 

[BillSL]

Hm. Simple answer is simple.

Thanks a lot, I hope I wasn't too much of a bore.

 

[evilleramsfan]

No problem....still waiting on an answer to the sphere problem.....

 

[HueyNation]

Here's the visual solution to the 'sphere' problem - its simply a case of non-Euclidean geometry:

Starting from the top, you head down (south), to the left (west) then back up (north) - as you're back up on the North Pole we assume that the most likely type of bear we'll come across would be the Ursus maritimus aka Polar Bear.


.....guys, its just a joke! I've never come cross such in-depth analysis of a simple joke before

 

[BillSL]

If you have a sphere and drill a hole through the center of it so what remains is a ring. The distance of the inside of the ring is 2 inches. (Meaning measuring the inside of the ring from where the edge of the bit entered the surface of the sphere to where said bit exited the surface of the sphere. What is the radius of the sphere?
Have fun! (The answer will blow you away....)

... 1 inch? (If I got what you meant by "distance"...)

Here's the visual solution to the 'sphere' problem - its simply a case of non-Euclidean geometry:

Starting from the top, you head down (south), to the left (west) then back up (north) - as you're back up on the North Pole we assume that the most likely type of bear we'll come across would be the Ursus maritimus aka Polar Bear.


.....guys, its just a joke! I've never come cross such in-depth analysis of a simple joke before

Check quote from above, that's the polar bear problem, not the sphere problem.

The Polar Bear problem, in short terms is: You can start EXACTLY at the NP, or you can start NEAR the SP (for explanation, read above ). For there are no bears in the SP, the only answer is NP.

Quite a complex joke, isn't it?

 

[hornetguy]

I can't help but be reminded of a funny joke I once heard (attached with another variation) when I see the arguments:

"A physicist, an engineer and a mathematician were all in a hotel sleeping when a fire broke out in their respective rooms.
The physicist woke up, saw the fire, ran over to her desk, pulled out her CRC, and began working out all sorts of fluid dynamics equations. After a couple minutes, she threw down her pencil, got a graduated cylinder out of his suitcase, and measured out a precise amount of water. She threw it on the fire, extinguishing it, with not a drop wasted, and went back to sleep.
The engineer woke up, saw the fire, ran into the bathroom, turned on the faucets full-blast, flooding out the entire apartment, which put out the fire, and went back to sleep. The mathematician woke up, saw the fire, ran over to his desk, began working through theorems, lemmas, hypotheses , you-name-it, and after a few minutes, put down his pencil triumphantly and exclaimed, "I have *proven* that I *can* put the fire out!" He then went back to sleep.

Three employees (an engineer, a physicist and a mathematician) are staying in a hotel while attending a technical seminar.
The engineer wakes up and smells smoke. He goes out into the hallway and sees a fire, so he fills a trashcan from his room with water and douses the fire. He goes back to bed.
Later, the physicist wakes up and smells smoke. He opens his door and sees a fire in the hallway. He walks down the hall to a fire hose and after calculating the flame velocity, distance, water pressure, trajectory, etc. extinguishes the fire with the minimum amount of water and energy needed.
Later, the mathematician wakes up and smells smoke. She goes to the hall, sees the fire and then the fire hose. She thinks for a moment and then exclaims, 'Ah, a solution exists!' and then goes back to bed. "

 

[BillSL]

I can't help but be reminded of a funny joke I once heard (attached with another variation) when I see the arguments:

"A physicist, an engineer and a mathematician were all in a hotel sleeping when a fire broke out in their respective rooms.
The physicist woke up, saw the fire, ran over to her desk, pulled out her CRC, and began working out all sorts of fluid dynamics equations. After a couple minutes, she threw down her pencil, got a graduated cylinder out of his suitcase, and measured out a precise amount of water. She threw it on the fire, extinguishing it, with not a drop wasted, and went back to sleep.
The engineer woke up, saw the fire, ran into the bathroom, turned on the faucets full-blast, flooding out the entire apartment, which put out the fire, and went back to sleep. The mathematician woke up, saw the fire, ran over to his desk, began working through theorems, lemmas, hypotheses , you-name-it, and after a few minutes, put down his pencil triumphantly and exclaimed, "I have *proven* that I *can* put the fire out!" He then went back to sleep.

Three employees (an engineer, a physicist and a mathematician) are staying in a hotel while attending a technical seminar.
The engineer wakes up and smells smoke. He goes out into the hallway and sees a fire, so he fills a trashcan from his room with water and douses the fire. He goes back to bed.
Later, the physicist wakes up and smells smoke. He opens his door and sees a fire in the hallway. He walks down the hall to a fire hose and after calculating the flame velocity, distance, water pressure, trajectory, etc. extinguishes the fire with the minimum amount of water and energy needed.
Later, the mathematician wakes up and smells smoke. She goes to the hall, sees the fire and then the fire hose. She thinks for a moment and then exclaims, 'Ah, a solution exists!' and then goes back to bed. "

That was HILARIOUS>!>!!!>!