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