A twist on a common riddle

alex12345

So a lot of people have heard this riddle.

A hunter goes 1 mile south, kills a bear and walks 1 mile east, then 1 mile north and ends up back where he started. What colour is the bear?

This isn't my question *riddle spoilers*







The answer is the bear is white because the hunter is at the north pole. Remember that the earth is a sphere when trying to visualize this. Now, a while ago it was discovered that there was another answer(not strictly about the bear but for the walking anyway). If you started 1 mile above where the lattitude of the earth was 1 mile long (right above the south pole) you would be able to recreate the scenario. Now my calculus teacher has proposed the question: Where else is this possible? Is this a trick or is there another answer (besides everywhere on the latitude of the above point). I have reason to believe this will be a bonus question on an exam.
 
There are an infinite number of answers involving the south pole. Any position in which walking 1 mile south puts you at a point in which the latitude divides evenly into 1 mile allows you to walk around the Earth at least one time and end up in the exact same spot, and then walk back north. For instance, if you walk south to the point at which the distance around the Earth is 1/2 mile, you will walk east around the Earth twice, and end up right back where you started. The same is true at the 1/3, 1/4, 1/5... parts.

Depending on your definition of "walking East", you could even count being 1 mile above the south pole. You walk one mile south, then rotate in place, then walk one mile north. Of course, this is an indeterminate solution because you have no way of saying you'll be facing the same way, or really any way to say "OK, I've walked a mile.", so I would avoid mentioning this 'solution'.
 
I was going to mention what Obi said about being one mile north of the south pole, but it wouldn't work due to the rotation deal.

The bear is Chaotic Neutral, by the way.
 
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