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HOW DID IT HAPPEN???


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

How did it happen?

The North Pole

The Obvious Answer was the north pole, if you looked. Duh. Who knows how many times this problem has been redone.

But the real riddle is...

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

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I think this answer doesn't work: when you get to the South pole, how do you run West? But this answer: does: for example, any point on the circle (1 + 1/2pi) miles from the South Pole. After go

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I think this answer

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?

But this answer:

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

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Easy with the bumpin'.

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

Pardon me but after traveling 1 mile south and arriving at the South Pole, there is no way the runner could have chosen a westerly direction for the 2nd leg of the run since you can only leave the South Pole in a NORTHERLY direction.

There is only one answer to this puzzle: The North Pole is the point of origin. Start going south, turn west and then when you turn north again you will arrive at your point origin.

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I think this answer

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?

But this answer:

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-inch 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

You allow 1 lap around a 1 mile circumference circle to serve as the westerly leg of the journey when in fact the direction of the run is changing from the moment the 2nd lap begins. It may start westerly but gradualy changes to NW, NNW, N, NNE, NE,ENE, E... etc.

Only the North Pole truly satisfies the constraints of this riddle.

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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-inch 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

Because if N is negative, when trying to run 1 mile south you will at some point reach the south pole and cannot move the rest of the distance let alone run another mile west...

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You allow 1 lap around a 1 mile circumference circle to serve as the westerly leg of the journey

when in fact the direction of the run is changing from the moment the 2nd lap begins.

It may start westerly but gradualy changes to NW, NNW, N, NNE, NE,ENE, E... etc.

Only the North Pole truly satisfies the constraints of this riddle.

Why would you change directions? Your compass stop working or something? :P

Starting from any point on earth other than the NP or SP, you can walk as far as you wish in a westerly direction.

The circular route in the answer is a path of constant latitude.

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You allow 1 lap around a 1 mile circumference circle to serve as the westerly leg of the journey when in fact the direction of the run is changing from the moment the 2nd lap begins. It may start westerly but gradualy changes to NW, NNW, N, NNE, NE,ENE, E... etc.

Only the North Pole truly satisfies the constraints of this riddle.

I think I see what you mean here, but look at it this way:

If you're inside a helicopter about 50m from the ground and hovering just over the South pole.

If you are watching this guy trying to run 1 mile west at about 1/2pi miles from the south pole, you will see him go in a circle and would easilly feel he is moving from NW, NNW, N, NNE, NE,ENE, E... etc. just like you posted.

However, this is merely an illusion, in fact HIS compass will assure him he is going West all the time, no matter how many laps he ran...

In fact any perpendicular direction to any line issued from the south pole to any point on the globe is a EAST or WEST direction...

And he will be running in circle(s) around the north pole...

As for Bonanova's formula 1 + 1/2Npi it is a approximation (a very close one to reality), since he is assuming the small distance of 1 + 1/2Pi is too small to consider the earth's curvature. You can reach the same answer with a simple figure on a plane (piece of paper), and the rest is simple geometry...

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Bonanova,

I'm afraid you are inconrrect in your (1+1/2pi) miles. The circumferance of a circle is ∏D (Pi * the diameter of a circle).

After you walked south for one mile, then you would be 1/2∏ miles from the South Pole. This would leave a circle with a cicumfernce of 9.86miles. (1/2∏ = 1.57. 1.57*2 = 3.14. 3.14 * ∏ = 9.86.) You obviously can't walk 1 mile of your 9.86 mile circle and then go one mile north and end up back where you started. I would assume that you meant you need to start (1+ ((1/2)/∏)) miles from the south pole. After you walked one mile south, you would be left with a circle that has a circumference of 1 mile.

Adding your unknown interger (N) into the equation would only work if the circle your are left with, after walkgin south one mile, had a circumference of 1 mile or a non-complex, fraction of a mile with 1 as the numerator; i.e. 1/2 mile circumference, you would walk 2 laps to go one mile west. 1/3 mile you would walk 3 laps. 1/4 mile, 4 laps, etc...

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Why would you change directions? Your compass stop working or something? :P

Starting from any point on earth other than the NP or SP, you can walk as far as you wish in a westerly direction.

The circular route in the answer is a path of constant latitude.

Well its obviously the north pole if he was running around the world-u see he runs south(south pole) runs west(pointless info.) and runs north(north pole) :D

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Bonanova,

I'm afraid you are inconrrect in your (1+1/2pi) miles. The circumferance of a circle is ∏D (Pi * the diameter of a circle).

After you walked south for one mile, then you would be 1/2∏ miles from the South Pole. This would leave a circle with a cicumfernce of 9.86miles. (1/2∏ = 1.57. 1.57*2 = 3.14. 3.14 * ∏ = 9.86.) You obviously can't walk 1 mile of your 9.86 mile circle and then go one mile north and end up back where you started. I would assume that you meant you need to start (1+ ((1/2)/∏)) miles from the south pole. After you walked one mile south, you would be left with a circle that has a circumference of 1 mile.

Adding your unknown interger (N) into the equation would only work if the circle your are left with, after walkgin south one mile, had a circumference of 1 mile or a non-complex, fraction of a mile with 1 as the numerator; i.e. 1/2 mile circumference, you would walk 2 laps to go one mile west. 1/3 mile you would walk 3 laps. 1/4 mile, 4 laps, etc...

Hint: Take a long look at the number 9.86 - you'll recognize it as pi2.

Put pi [and N] into the denominator of my fraction.

OK now? http://brainden.com/forum/public/style_emoticons/#EMO_DIR#/wink.gif

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He could be on a treadmill with the treadmill oriented south, he runs a mile, gets off, turns the treadmill, runs a mile, turns the treadmill, runs a mile.

the treadmill is a possibility,all though im not so sure its that easy to move a treadmill, or he could have started at a bus stop, gotten on the bus, rode the bus for one mile east, gotten off, then ran 1 mile south, 1mile west, and 1 mile north.

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

How did it happen?

The North Pole

The Obvious Answer was the north pole, if you looked. Duh. Who knows how many times this problem has been redone.

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

How did it happen?

The North Pole

The Obvious Answer was the north pole, if you looked. Duh. Who knows how many times this problem has been redone.

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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