I was thinking about the Earth on the way to work today. Here are a few puzzles I compiled on the way:

- you are standing an the north pole. you travel 8000 miles south, then 8000 miles east, then 8000 miles south again. How far are you from the north pole?
- you are standing on the north pole. you travel 3 miles east, then 4 miles south. how far are you from the north pole?
- you are standing on the north pole. you travel 3 miles south, then 4 miles east. how far are you from the north pole?

try to guess the answers – they’re not as obvious as they seem.

of course, I suspect that anyone that reads my blog has already guessed the answers…

you probably think it’s very easy, don’t you!

here’re the answers for those people that didn’t figure them out:

- trick question. you cannot travel 16000 miles south because the circumference of the earth between the two poles is only 24860 miles, meaning that the maximum distance you can travel south 12430 miles.
- trick question. when standing on the north pole, you cannot travel east or west, as they’re one dimensional at that point (no, turning around is not traveling).
- not a trick question, but also not obvious. the first answer to pop into someone’s head would be 5 miles (via Pythagoras), but you need to remember that the Earth is not flat – if you are 3 miles south, you could travel a million miles east and still be 3 miles south. The answer is 3 miles.

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Another one:

How many distinct points are there on the surface of the Earth from which you can walk one mile due South, then one mile due East, and then one mile due North, and end up at the same exact spot from which you started?Possible answers for the last one are given at:

http://blogs.sun.com/dcb/entry/microsoft_s_puzzle_a_challenge

very good! I looked at your first comment and wondered if you’d read the third puzzle above at all, but of course, you were well ahead of me – the “just north of the south pole” answer eluded me.

Hear’s an old puzzle. You have to allow some license, otherwise it’s good.

You’re standing in the wilderness. You set a marker on the ground. You walk one mile south. You turn and walk one mile east. You turn and walk one mile north and arrive back at your marker.

You see a bear. What color is it?

I got the first answer wrong (due to the fact that I was changing miles to kilometers in my head with a direct substitution of 1 mile = 1 km, which is wrong on so many levels).

Also, I got the third answer “wrong”, since I was thinking of Pythagoras, but applying it to a spherical surface with a circumference of distance stated above, which gives the answer not three miles but slightly less (as that is how far I am from the pole at that time; the question didn’t state that I was supposed to go back on the surface:)