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# HOW DID IT HAPPEN???

Best Answer bonanova, 24 September 2007 - 03:12 AM

Yep. I presume you mean 1 mile north of south pole?

doesn't work: when you get to the South pole, how do you run West?

There's an infinite number of circles around the South Pole where he could have started.

does: for example, any point on the circle (1 + 1/2pi) miles from the South Pole.

After going South 1 mile, you're (1/2pi) miles from the Pole,
which allows you to run West 1 mile [1 lap of a 1-mile circumference circle]
and be able to go a mile North to the starting point.

As Martini noted, there is an infinite number of starting distances:
1 + 1/2Npi miles North of the South pole where N is any positive integer.
N is then the number of circular laps in your westerly mile.

e.g. N=5280 - you'd run 5280 laps around a 1-foot circumference circle.

Here's a counter question - why can't N be negative?
i.e. start closer than a mile - you could still do N laps Go to the full post

70 replies to this topic

### #21 miya

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Posted 06 March 2008 - 04:12 AM

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### #22 mmaa

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Posted 10 March 2008 - 12:33 PM

He sterted from the equater, runs mile south then a mile then a mile north backing to the equater.
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### #23 horia

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Posted 10 March 2008 - 08:53 PM

A man runs a mile south, a mile west, and a mile north... and ends up back where he started!

How did it happen?

Spoiler for Solution

But the real riddle is...

There are actually an infinite number of answers for where the man could have started from.Explain.

North Pole on an infinite number of planets! - Ha!
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Posted 13 March 2008 - 12:24 AM

A man runs a mile south, a mile west, and a mile north... and ends up back where he started!

How did it happen?

Spoiler for Solution

But the real riddle is...

There are actually an infinite number of answers for where the man could have started from.Explain.

He is on the North/South Pole
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### #25 Jordanmax

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Posted 13 March 2008 - 04:18 AM

North Pole
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### #26 Jordanmax

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Posted 13 March 2008 - 04:19 AM

He is on the North/South Pole

How do you run south from the South Pole????????????????
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### #27 new guest

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Posted 16 March 2008 - 11:24 PM

You dont, but here is an answer. Try being who knows what distance from the south pole, run south 1 mi, and then run west 1 mi, in a circle around the south pole, and run north back to where you started!
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Edited by new guest, 16 March 2008 - 11:26 PM.

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### #28 jword

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Posted 17 March 2008 - 12:48 AM

well, north pole did not come to mind, but i thought of an island 1mile in diameter

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### #29 unreality

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Posted 17 March 2008 - 01:05 AM

For the south pole solution:

Let's say there's a latitude (a circle around the earth running east-west) that's exactly 1 mile in circumference. In other words, a point shortly north of the south pole that is 1 mile around the earth. If you start on any of the infinite points that are 1 mile north of that special latitude, then you can go 1 mile south and then 1 mile west to go all the way around the earth, then 1 mile north to be back where you started ;D
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### #30 jword

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Posted 17 March 2008 - 01:33 AM

For the south pole solution:

Let's say there's a latitude (a circle around the earth running east-west) that's exactly 1 mile in circumference. In other words, a point shortly north of the south pole that is 1 mile around the earth. If you start on any of the infinite points that are 1 mile north of that special latitude, then you can go 1 mile south and then 1 mile west to go all the way around the earth, then 1 mile north to be back where you started ;D

The latitude is 89º 59.68´ . and of course 1 mile north of that is 89º 58.68´ south
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