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The numbers $1,$ $2,$ $\dots,$ $10$ are to be entered into the 10 boxes shown below, so that each number is used exactly once: \[P = (\square + \square + \square + \square + \square)(\square + \square + \square + \square + \square).\]What is the maximum value of $P$? What is the minimum value of $P$?

 Jul 17, 2020
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Hint: Use AM-GM inequality. which states that \(\frac{x+y}{2}\geq\sqrt{xy}\). (You can prove this with the trivial inequality. )

 Aug 7, 2020

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