### Not about polar bears

There's a well-known puzzle which is :- 'A bear hunter walks one mile south, one mile east, and one mile north, only to find himself back at his starting point. What colour is the bear he's hunting?'

The traditional answer is 'white' because with a starting point of the North Pole, someone walking one mile south, one mile east, and one mile north will find themselves back at the North Pole. Therefore the bear he's hunting must be a polar bear.

There are, however, a number of other points on the Earth's surface from where someone walking one mile south, one mile east, and one mile north will find themselves back at their starting point. Where are they?

## 3 Comments:

On a tradmill which is being rotated to face the direction of supposed travel.

You could also be at a number of distances of greater than 1 mile away from the South Pole. The condition would be such that after you travel the initial 1 mile south toward the South Pole, you make full circle(s) around the South Pole by traveling east for 1 mile. Thusly, when you travel north for 1 mile, you end up at the same point you started.

Unfortunately, there are no naturally occurring bears on or near the South Pole.

Yep, you've got it.

So an example would be if he travels one mile 'around the South Pole'. A circumference of 1 gives a radius of 1 / (2 * pi). So any point at a distance of 1 + (1 / (2 * pi) ) miles from the Pole would fit the criteria.

Another example would be if he circles the South Pole twice, i.e. the circumference around the Pole is 1 / 2 mile. That gives a 'radius' of 1 / (4 * pi). So any point at a distance of 1 + (1 / (4 * pi) ) miles from the Pole also fits the criteria.

As an aside, the traditional answer must be wrong anyway because polar bears actually have pale yellow fur (at least that's what I'm told).

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