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brain teaser, please help

 
 
Reply Wed 20 Jul, 2005 08:56 pm
Ok here goes:
>
>Somewhere on earth...
>
>you go on a hike following these directions:
>- first you hike 10 mikes due South
>-then you hike 10 miles due West
>-then you hike 10 miles due North, and stop
>
>to your amazement, at the end of your hike you find yourself back in
>the exact same spot you started.
>
>question 1: Where did you start your hike?
Question 2: Is there anywhere else on the planet that you can do this
>same hike ( and end up in the same place you started).
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yitwail
 
  1  
Reply Wed 20 Jul, 2005 10:07 pm
here's a clue: it's usually a bear that does the walking, and the question to be answered is "what color is the bear?"
0 Replies
 
markr
 
  1  
Reply Wed 20 Jul, 2005 10:13 pm
The bear clue provides one of infinitely many solutions.
0 Replies
 
raprap
 
  1  
Reply Wed 20 Jul, 2005 10:16 pm
North and south poles, except at the south pole you go 10km north, 10 km west and 10 km south and end up at the same place.

The trick, at the north pole all directions are south, east and west don't raise their ugly heads until you gat off of the north pole.
0 Replies
 
markr
 
  1  
Reply Wed 20 Jul, 2005 10:29 pm
Actually, there are infinitely many locations near the south pole, and you don't swap north for south and vice versa.
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nething1
 
  1  
Reply Wed 20 Jul, 2005 10:41 pm
The trick, at the north pole all directions are south, east and west don't raise their ugly heads until you gat off of the north pole.

Raprap.. what does that mean?

someone told me for the first question the answer is south pole and ur saying its not right?

what do u mean by at the north pole all directions are south, east and west dont raise their ugly heads ?? can u explain abit mroe please?
0 Replies
 
Grand Duke
 
  1  
Reply Wed 20 Jul, 2005 10:50 pm
Imagine you are standing at the very top of the torch of the Statue of Liberty. Which directions can you climb in? Down. You can only do down. Once yoou have gone down a little way, then you can go left, right, down and even back up, if you want.

The same is true at the exact North Pole. Everywhere is South. Once you've gone South (even a single metre) then you can go East, West, South and back North again.

The answer to the first question is the North Pole, and the answer to the second question appears to be the South Pole, but I'd like Markr to expand on his post a little, as I'm confused as well...
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nething1
 
  1  
Reply Wed 20 Jul, 2005 10:52 pm
Well I emailed dr. math and here is what he said for the 1st questionn...tell me if this makes sense? and then what u would think for the 2nd question.

Suppose you start out just a few feet more than 10 miles from the
south pole. You go 10 miles south. Now you're just a few feet away
from the pole. If you walk due west for 10 miles, you walk in a
little circle around the pole - kind of like walking around and around
a tree.

If you choose your original distance carefully, after you've circled
for 10 miles, you'll be right where you started circling. Then you
turn around and go due north for 10 miles, and you're back where you
started.
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markr
 
  1  
Reply Wed 20 Jul, 2005 10:56 pm
You can't go south from the south pole. Therefore, that can't be a solution.

If you head south from the north pole, you will end up at a latitude that is 10 miles south of the pole. This latitude runs in a circle around the pole. As you traverse any latitude, you are traveling east or west. Therefore, you never leave the latitude and are always 10 miles south of the pole. When you go 10 miles north, you're back at the pole.

It's a bit trickier, but not much, near the south pole. Here the key is to start at a point that is 10 miles north of a latitude that has a circumference that is an integral fraction (divide by 1, 2, 3, etc.) of 10 miles. When you go 10 miles south, you land on this latitude. You then make one or more trips around the pole and end up where you started on that latitude. Traveling 10 miles north takes you back to where you started.
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markr
 
  1  
Reply Wed 20 Jul, 2005 10:59 pm
I guess you found the answer while I was typing.
0 Replies
 
nething1
 
  1  
Reply Wed 20 Jul, 2005 10:59 pm
well technically u can...it says u start a few feet more than 10 miles from the south pole. ur not there yet..ur before it, then u go 10 miles south and ur a few feet away from the pole. Doesnt that make sense?
0 Replies
 
markr
 
  1  
Reply Wed 20 Jul, 2005 11:01 pm
Note: There are infinitely many latitudes from which you can start (near the south pole). And, of course, there are infinitely many starting points (all points on the circle) at each latitude. Pick how many trips you want to make around the pole and that determines your starting latitude.
0 Replies
 
markr
 
  1  
Reply Wed 20 Jul, 2005 11:04 pm
nething1 wrote:
well technically u can...it says u start a few feet more than 10 miles from the south pole. ur not there yet..ur before it, then u go 10 miles south and ur a few feet away from the pole. Doesnt that make sense?

But you're never at the pole. All directions from the south pole are north. You can get as close to the pole as you want on your trip, but you'll never quite be there.
0 Replies
 
nething1
 
  1  
Reply Wed 20 Jul, 2005 11:04 pm
what u said earlier about the north and south poles and how u think the 1st one is the north pole and the 2nd is the south pole, are you sure about that?
because i dont know which answer to use
A. 1- north pole
2- south pole

or

B. 1- south pole
2. north pole

pls let me know, thanx
0 Replies
 
markr
 
  1  
Reply Wed 20 Jul, 2005 11:10 pm
Just keep in mind that you can only go south from the north pole, and you can only go north from the south pole.

However, the south pole (as a point) isn't a solution for either.
0 Replies
 
nething1
 
  1  
Reply Wed 20 Jul, 2005 11:23 pm
Ok, thank you very much for you help, i really appreciate it.
0 Replies
 
 

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