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You have $n$ rectangles of area $1$ and variable height. Pack as many as possible in a semicircle of area $n$. How many leftovers will there be?

You have $n$ rectangles of area $1$ and variable height. Pack as many of these rectangles as possible in a semicircle of area $n$. How many leftover rectangles will there be, in terms of $n$? How to ...