🚀 go-pugleaf

Sorry to have "ruined" it for you. I didn't know for sure I had all the
solutions (and I won't be surprised if someone comes up with
other solutions that I haven't thought of). The sequence of arriving
at the solutions that you described is the same pattern I followed
in solving it. I saw the North Pole right away and then focused
on the South Pole, because it seemed clear that (a) there must
be more solutions or you wouldn't have posed the problem and
(b) its the only place on the globe other than the North Pole
where the definitions of west and east get screwed up. I saw
solution b after about 5 minutes.  Solution c came to me
as I was typing up the reply. There are lots of "quantized"
phenomena in physics. I guess thats why it seemed obvious that
if you could walk around the world once, twice wouldn't be
much more difficult.

Jeff

P.S.  I "cheated". I'm actually a materials scientist, not a physicist
per se. Do you think that matters?