[unreality]

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:

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.

[unreality]

Need a hint?

[unreality]

Nobody knows?

[Martini]

Easy with the bumpin'.

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

[unreality]

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

[bonanova]

I think this answer

Quote

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:

Quote

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

[deartous]

Martini, on Sep 23 2007, 07:06 PM, said:

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.

[deartous]

bonanova, on Sep 23 2007, 09:12 PM, said:

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.

[roolstar]

bonanova, on Sep 24 2007, 04:12 AM, said:

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...

[bonanova]

deartous, on Jan 29 2008, 09:50 AM, said:

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?

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.