No one has yet found the new "possible but very expensive" solution to the travel problem (go south 1 mile, east 1mile, then north 1 mile to return to your starting point.)
Hint 1 was "Space Ship." Hint 2 was "Celestial Coordinates." Hint three, now given, is "Year Long."
These three hints help overcome the following three self-imposed limits: (1) Travel must be typical of that people often do. (2) Coordinate system (in which South, East and North are well defined) is the one with origin at the center of the Earth, not one with the sun at the origin. (3) Trip can not last slightly more than one Earth year.
If one understands why these three "breakouts from the box" are still not sufficient, surely some member of this list can escape from the remaining self-imposed limitation and tell me what my final "TF" hint stands for when it is also expanded to two words.
My other two new solutions, already posted, were called the "roll-a-coaster" and "tunnel" solutions. Both were trivial extensions of the South Pole circumnavigation solution, but the first had the advantage of permitting a large area near the South Pole for the departure point rather than a set of points with zero measure. The second "tunnel" solution is technologically possible only near the North Pole, but conceptually extended the solution to the entire Earth, if one accepted either (1) my claim that the problem statement does not forbid more than three miles of travel. (Only westward travel is implicitly disallowed, but problem statement permits unlimited purely radial travel.) or (2) I may start my trip deep inside the Earth.
I am also surprised that no one has pointed out the flaw (hidden "Easter Egg") in my very detailed description of a "solution" that permits the departure point to be anywhere within the Tropics, which I called the "Tropics solution."
I will not repost the Tropics solution, as planed, but refer you to the slightly changed version given with my August 28 post that gave Hint 2. Only change was that "cone" replaced "plane" as suggested by Leigh.
Doesn’t anybody out there like to solve problems? – Bill Powell
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