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Somewhere on a sphere

What is the mean distance between two randomly choosen points within a sphere of radius 1?

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Pay problem

Bob buys two things in a shop. With his pocket calculator he calculates in advance what he has to pay: 5.25 dollars. But what he does not notice is that he pressed the division instead of the addition button. At the desk he is not surprised if he hears that he has to pay 5.25 dollars. What is the price of the two things Bob has bought?

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Milk bottles

Suppose you have two bottles with equal perimeter, thickness and height. One bottle is cilindrically shaped, the other one has the shape of a rectangular box with a square shaped bottom. In which of the bottles fits more milk?

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 Last changed 16-01-2010
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