0, 1 and Infinity

Quiz - "Can you walk 1 mile south, then walk 1 mile east and finally walk 1 mile north to end up where you started?"

Answers:
1. No. We need to walk 1 mile west to come back to where we started.
    Begin from the starting point A, walk 1 mile south to point P. Then walk 1 mile east to point Q. Finally, walk 1 mile north to point B. We are still 1 mile east of A where we started.

2. Yes, when we are at North Pole.
     At North Pole N, any direction will head south. So just choose one and walk 1 mile to get to point P. Then walk 1 mile east to get to point Q. Finally, walk 1 mile north to get back to North Pole N where we started.

3. Yes, there are infinitely many places we can do so.
    There is a circle with circumference of 1 mile around the South Pole S. From any point Q on this circle, we can walk east for 1 mile encircling the South Pole S once to get back to Q. 1 mile north of Q, we can find a place P.
    Now, starting from place P, walk 1 mile south to get to point Q. Then walk 1 mile east encircling the South Pole S once to get back to Q. Finally, walk 1 mile north to get back to P where we started. Since Q is an arbitrary point on the circle, P is also arbitrary. Hence there are infinitely many places of P we can do so.

   

        Furthermore, we can find a circle with circumference of 1/2 mile around the South Pole S. From any point Q on this circle, we can walk 1 mile east encircling the South Pole twice to get back to Q. From Q, find place P as above. Likewise, we can find circles of circumferences of 1/3 mile, 1/4 mile and 1/5 mile etc. around the South Pole S and from any point Q on the circles, walk 1 mile east encircling the South Pole S 3 times, 4 times and 5 times etc respectively to get back to Q. Thus theoretically, we have infinitely many circles and infinitely many points Q, and hence infinitely many places of P we can do so.