### Brain Teasers

# Undiscovered Planet

You land on an unknown planet which has a radius of 10km and is completely round and smooth. You start from your ship and walk straight for 17.345 kilometers. You turn left and walk straight for 47.124 kilometers. How far are you from your ship?

### Answer

14.142135623730950488016887242097Or square root of 200!

If you imagine you are facing a globe head on, you have the north pole at the top of the globe and the south pole at the bottom. Imagine a "west pole" and "east pole" to the left and right of the globe.

If you are at the north pole and turn left, you will walk through the "west pole" (right and you go through the "east pole")

If you walk on an axis from the north pole towards the south pole and make a left or right turn you will always walk through these imaginary east and west poles. So in the question 17.345 kilometers is irrelevant, only the turn.

(It also doesn't matter where you start on the planet, the distance at the end will still be the same.)

47.124 is approximately 3/4 of the circumference of this planet, which will leave you directly on the imaginary east pole. The distance is now the hypotenuse of a right angle triangle of side 10km.

Answer: root 200 or approximately 14km!

(If you got the distance as 15.7km - the distance you would have to walk back, then that's ok too!)

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