### Brain Teasers

# Where Am I?

I start at point X. I walk one mile south, one mile East and then one mile North and arrive back at point X. Where, besides the North Pole, could point X be?

### Hint

There are an infinite number of points X.### Answer

I am just so far north of the South pole that after travelling the mile south, my mile East takes me on one complete circumference of the pole. Then my mile north will take me back to point X. There are an infinite number of points X on this line of latitude.Hide Hint Show Hint Hide Answer Show Answer

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## Comments

Where exactly is "just so far north" ? this is the real question.

You would be 1 mile from a small circle of radius 1 divided by 2 Pi, or about one sixth of a mile. Since for such a small distance the horizontal distance would be approximately the same as the distance across the surface of the Earth, you would be about 1 mile plus 300 yards (about 2000 yards)from the South Pole! Great teaser!

I thought it was the equator! Would this work?

The equator wouldn't work, but there may also be infinite of these lines. If you walk 1 mile south and then walk east, circling the pole more than once and ending up where you were, such as if you would walk around half a mile and be back where you were, then another half mile you'll be back again, and then walk the mile back north. Same with a third of a mile, fourth of a mile, etc.

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