An old riddle runs as follows. An explorer walks one mile due south, turns and walks one mile due east, turns again and walks one mile due north. He find himself back where he started. He shoots a bear. What color is the bear? The time-honoured answer is: "White," because the explorer must have started at the North Pole. But not long ago someone made the discovery that the North pole is not the only starting point that satisfies the given conditions! Can you think of any other spot on the globe from which one could walk a mil south, a mile east, a mile north and find himself back at his original location?(source: My Best Mathematical and Logic Puzzles By Martin Gardner)
Solution:
Us there any other point on the globe, besides the North Pole, from which you could walk a mile south, a mile east, and a mile north and find yourself back at the starting point? Yes indeed; not just one point but an infinite number of them! You could start from any point on a circle drawn around the south pole at a distance slightly more than 1 + 1/2Pi miles ( 1.16 miles ) from the Pole, the distance is "slightly more" to take into account the curvature of the earth. After walking a mile south, your next walk of one mile east will take you on a complete circle around the Pole, and the walk one mile north from there will then return you to the starting point. Thus your starting point could be any one of the infinite points on the circle with a radius of about 1.16 miles from south pole. You could also start at points close to the Pole, so that the walk east woule carry you just twice around the Pole, or three time, and so on.
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