From your camp, you walk one mile south, one mile east, and one mile
north. Then you are back in your camp from where you started. Where is
your camp?

Dear m00se,

The camp is located exactly on the (geographical) North Pole. Only
there, it is possible that following the directions you described
leads back to the starting point.

Regards,
Scriptor

I agree and i concur.

Actually there are other places your camp could be as well.  Your camp
could be anywhere on a circle 1 + 1/(2*pi*n) miles north of the south
pole, where n is any positive integer.

Hmmmmmmm

Sorry but I can't follow Racecar's logic.

If your camp is 1 mile north of the South Pole, a journey 1 mile South
will take you to the South Pole.

If you then walk 1 mile East, this must take you 1 mile away from the
South Pole and 1 mile North from there could then take you almost
anywhere!

Or am I missing something?

If you're already at the south pole, in which direction would you need
to go in order to walk one mile south?

Sorry, that should've read 'in which direction would you need to go in
order to walk one mile east'

If you were at the South Pole and you were to walk 1 mile East, you
would proceed Eastwards but the turn of the Earth would prevent you
from reaching an absolutely accurate position relative to the South
Pole.

You would proceed in a banana-like direction.

Hence when you then proceeded Southwards, you could finish up ANYWHERE.

Ergo ... This Riddle ONLY works for the North Pole.

I suspect that, unlike me, many folk who have left comments here have
never been to either the North Pole or the South Pole ...

So how could they possibly know what it's like up or down there?

Let me tell you ...

Standing atop of the World at the North Pole is truly a breathtaking
experience because you can feel the Earth pulsating beneath your feet;
it's impossible to stand upright as you are twirled round an round.

It's probably like poor Ginger felt when Fred danced around her.

Exhilirating yes but after a few twirls you soon lose track of day and
night. Or North and South. Or East and West.

And I defy anyone to WALK one mile in any fixed direction because sure
enough you'll meet a friendly polar bear, or a crevasse, or a yeti
blocking your path.

And, as for setting up camp ....

Just you try pitching a tent when the Earth is frigging around like a
wild Dervish.

And the South Pole is worse because then you have tp do it all upside down.

Believe me.

Racecar-ga is correct that there are a family of "extra" solutions.

Find a point just far enough from the South Pole that a circle of
latitude has circumference 1 mile.

Starting anywhere 1 mile north of this circle, walking one mile south
brings us there, walking one mile east circles the globe, and one mile
north takes us back to the original "camp".

regards, mathtalk-ga

In fact any circle which requires an exact number of reveolutions will
work. A 1/2 mile circumfernce traveled twice, a 1/3 mile three times
etc. So there is an infinite number of solutions

Theories? Bah!

Mathematicians? Bah!

These are the same guys who used to insist that the World was Flat!

(I kid you not.)

How on this Good Earth can anyone find a latitude of 1 mile from the South Pole?

Particularly when Magnetic North ain't even at the North Pole!

QED

Because of the curvature of the earth, there is actually a very slight
error in the 1 + 1/(2*pi*n) answer I posted above.  The exact
(assuming a spherical earth) solutions are 1 + R*arcsin(1/(2*pi*R*n)),
again for any positive integer n.  But the error is less than 3
millionths of an inch, which is negligible, so you may as well just
use the first formula.

there can never be a direct, definite answer to this question. Due
mainly to the generalisation of walking one mile south. Do we walk one
mile south in a straight line, or by following the natural curvature
of the earth. Are we talking about the map directions north south and
east, or the magnetic ones?

i agree, you are on the north pole, with that informatio but one
aditional question is this a conventional camp etc where a tent is
set. or is it a trick question