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 Is the impediment that there are no polar bears in
 Antarctica?:) Whatever, I was interested in what John said
 about how we know when we have the whole solution set when a
 problem may not easily reduce to a mathematically solvable
 form. Like he said when setting the riddle, you have to think
 outside the square, then maybe think outside the square beyond that.

For me, the impediment is partially that; but more so that I've heard
this one since I was a kid and was always told the answer was the North
Pole (combined probably with a northern hemisphere prejudice) all of
this combines in my head to provide a powerful disinclination to search
for other answers beyond the one given.
As an aside, both answers provide a nice example of how geometry on S2
(surface of a 3dim sphere) is different from geometry on R2 (Euclidean
plane).