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The complete question is that at the end of the three journeys you are back at your start. There is a common fallacy that there is only one starting point - the North Pole which satisfies the route. In fact, there are an infinite number of points.

Select a point, near the North Pole such that, after you've walked 1 mile south, the radius of that latitude is 1 mile. So your 1 mile east takes you once around the world, and then the northward mile takes you back to your starting point. Clearly, the starting point can be on any longitude so there are an infinite number of starting points.

Then consider similar points where the 1 mile east takes you twice round the globe at that latitude. Those points will do. As will points where the eastward leg takes you any integral number of times round the earth at that latitude.

But that is not all. You can start near the South Pole where the 1 mile south brings you to a latitude where you can walk round the world in 1 mile east. And so on.

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Q: How many points are there on the globe where by walkng one mile south one mile east and one mile north?
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