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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 = (\squar

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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\$?

May 4, 2020