Tony Mountifield wrote:

Guy Macon http://www.guymacon.com/ wrote:

[21] A man travels due south for one kilometer. He turns left
90 degrees and travels due east for one kilometer, at
which point he shoots a bear. He then turns left 90
degrees and travels due north for one kilometer, returning
to the exact spot he left from.
[21a] What color is the bear?
[21b] What direction is the wind blowing from at the
starting/ending point?

The man starts at the North Pole, from which all directions are
south. The bear is a white polar bear. The described itinerary is also
possible starting from a point very near the South Pole, but there are
no bears there.

Correct! (And very few get that second location, or incorrectly
miss the lack of bears there.)

BTW, There are an infinite number of possible starting points near
the south pole, and not just then obvious case of different places
on a circle that is 1 kilometer + 1/Pi kilometers from the pole.

That circle won't work - you only go half way round and end ups
180 degrees out.

The obvious case is 1 + 1/(2*Pi) km from the S pole.

Of course. Silly bonehead error on my part. Sorry about that.

Where are they?

Concentric circles of radius 1 + 1/(2*Pi*N) kilometers for all positive
integers N

N is the number of times walking round the pole while travelling 1km east.

Correct. BTW, it took me two days before I had the "Aha!"
thought that the hunter could circle two or more times.

And strictly speaking, the radii quoted above are as measured along the
curved surface of the earth, rather than in a true straight-line between
the pole and the start point.

Indeed. That's (and the fact that lines of lattitude are highly
curved sideways near the poles) why in the original question I used
language like "walked due east." I should have done so above as
well.

--
Guy Macon
http://www.guymacon.com/