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### Contest problems with connections to deeper mathematics

I already posted this on math.stackexchange, but I'm also posting it here because I think that it might get more and better answers here! Hope this is okay. We all know that problems from, for ...
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### Fast removal of weighted edges in a graph in a way such that all shortest paths are preserved

This problem is analogous to fast removal of the minimum number of edges in a weighted graph such that if the graph were to be drawn on paper with edge lengths linear in proportion to their weights, ...
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### Elementary mathematical books

I understand that this is a bit of offtopic but mathoverflow is my last resort, as google did not help. I am about to publish an English translation of my Russian book for high school students. The ...
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### Question about Banach's matchbox problem.

Hi, I've been struggling with this for awhile ( http://en.wikipedia.org/wiki/Banach%27s_matchbox_problem) and I put together this little bit of Python code ...
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### Examples of using physical intuition to solve math problems

For the purposes of this question let a "physical intuition" be an intuition that is derived from your everyday experience of physical reality. Your intuitions about how the spin of a ball affects ...
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### Math Puzzle: calculating the dimensions of variable rectangles in a fixed square

I've got the following problem, I've got a fixed size square and within there are a fixed number of rectangles to be contained within it. I want the rectangles to cover the maximum amount of space ...