## Friday, November 11, 2005

### A strange place for a walk

A man goes out for a walk. He walks south one mile, east one mile, and north one mile, and ends up in the same place he started. He didn't start out at the north pole -- so where did he?

1. The South Pole?

2. A triangle-shaped island?

3. on a floating glacier?

4. Nice tries, but no. The south pole doesn't work.
There are two possible solutions:

Solution #1

Assuming a perfectly spherical Earth, somewhere one mile north of the latitude (in the southern hemisphere) that is one mile in circumference. The man walks south one mile to this latitude and walks one mile east, which takes him all the way around and back to where he started. The last step (one mile north) retraces the first step he took (one mile south).

Solution #2

The man could also be one mile north of the latitude that is one half mile in circumference -- on second leg of the journey, he'd go around twice instead of once. He could also be one mile north of the latitude that is one third of a mile in circumference, or one mile north of the latitude that is one quarter of a mile in circumference, and so on.

5. I was also going to guess the magnetic north pole too but i think that would not work.

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