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What Color Is the Bear?

A hunter leaves his campsite and travels one mile due south. He then travels one mile due east, where he shoots a bear. He drags the bear back to his campsite by traveling one mile due north. What color is the bear?
There are actually infinitely many campsite locations that satisfy this condition, but only one location has a bear population. The quarry at the other sites more typically would be birds in formal-looking attire.

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There is one campsite at the North Pole that satisfies the puzzle, but surprisingly, an infinity of sites near the South Pole. To understand this, just imagine that the eastward leg of the journey completes one (or more) complete circles around the South Pole.
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