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

I think this answer

doesn't work: when you get to the South pole, how do you run West?Yep. I presume you mean 1 mile north of south pole?

But this answer:

does: for example, any point on the circle (1 + 1/2pi) miles from the South Pole.There's an infinite number of circles around the South Pole where he could have started.

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