Not at sea, not using moving surfaces, not mixing magnetic and true north, etc. No tricks, honestly. You just have to think outside the box (just as you had to think outside the box to realize the north pole was the original answer).
Hint: all of the other locations where this can occur are near, but not at, the South Pole.
Originally posted by The PlumberAha! Very interesting.
Not at sea, not using moving surfaces, not mixing magnetic and true north, etc. No tricks, honestly. You just have to think outside the box (just as you had to think outside the box to realize the north pole was the original answer). ...[text shortened]... cations where this can occur are near, but not at, the South Pole.
If the bear is less than 1 km from the south pole, the bear can't travel 1 km south (because when you get to the south pole, you're done going south).
If the bear is exactly 1 km from the south pole, the bear can't travel west because there is no direction to go other than north.
However, if the bear is more than 1 km from the south pole, and is at such a distance that the circumference of the circle it travels on while travelling west is 1 km, then it will make a full circle and can travel north 1 km back to where it came from! Very interesting. Of course, it will probably freeze to death unless it cuts open the carcass of one of it's friends with a light saber and sleeps inside, but that a little bit outside the question, isn't it?
Originally posted by PBE6Well done....
Aha! Very interesting.
If the bear is less than 1 km from the south pole, the bear can't travel 1 km south (because when you get to the south pole, you're done going south).
If the bear is exactly 1 km from the south pole, the bear can't travel west because there is no direction to go other than north.
However, if the bear is more than 1 km from th ...[text shortened]... nds with a light saber and sleeps inside, but that a little bit outside the question, isn't it?
Originally posted by AThousandYoungOf course! (not!) 😀
Wow Plumber. Very smart. Did you come up with that yourself?
Ever heard of Piers Anthony? In the early 80s he wrote a trilogy called the Adept Series. It's in one of those books (Split Infinity, Blue Adept, Juxtaposition), I don't recall which one. In the late 80s he extended the series to a seven book series, but I never read the other four.
Piers Anthony has a habit of working little puzzles like that into his writing. Wish I could remember a few more....
Originally posted by The PlumberI loved that series. I don't remember that puzzle though. Wasn't it actually called the Apprentice Adept series though?
Of course! (not!) 😀
Ever heard of Piers Anthony? In the early 80s he wrote a trilogy called the Adept Series. It's in one of those books (Split Infinity, Blue Adept, Juxtaposition), I don't recall which one. In the late 80s he ...[text shortened]... like that into his writing. Wish I could remember a few more....
There are countably infinitely many latitudes where this works.
At the north pole, obviously it works.
You will also end up where you started if the latitude line 1 km S of where you start is x km long, where 1/x is an integer.
The length of the L° latitude line is EQ*cos(L°😉. (EQ = circumference of earth)
You have to start 1 km above one of those solutions.
The solutions in the northern hemisphere are less than 1 km from the pole, so they don't work.
There are infinitely many fitting latitude lines less than 1 km from the south pole, and you have to start 1 km above those.