Wandering The Earth
Thanks John E
Answers:
#1.
White
bear.
Explanation:
starting at the North Pole will return you to
the North Pole after the 3 manoeuvres (south along a line of longitude,
east along a line of latitude and north again along a line of
longitude).
#2
You
can start anywhere on
a line of latitude (which is a circle) which
is 1 mile north of the point where the circumference of the earth is 1
mile.
You
will see that this is
very close to the South Pole.
So
you start by
travelling 1 mile south, 1 mile east  a circle which
brings you back to the "1 mile south position"  then travel back 1 mile
north.
The
sketch is below
(when
last discussed with
a friend, we were talking in kilometres, so
you have the option of changing the sketch or rewriting the question in
kilometres).
The
fact you can start
anywhere on the circle of latitude gives you an
infinite number of equal solutions.
Further,
you can get
another infinite set of solutions by moving
towards the South Pole so that the "eastward mile" is 1 loop, 2 loops,
3 loops, etc., each of these solutions bringing you closer to the South
Pole.
In
the limit, of course,
the starting
point is within a hair of 1 mile north of the South Pole.

