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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?

 Jun 13, 2023
 #1
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its 756 man

 Jun 13, 2023
 #2
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Set 1: {1, 3, 4, 9, 10} (sum = 27)

Set 2: {2, 5, 6, 7, 8} (sum = 28)

 

27 * 28 = 756 - the greatest product possible.

 Jun 13, 2023

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