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The numbers  1, 2, 3, ... 10    are to be entered into the 10 boxes shown below, so that each number is used exactly once:

 

(_+_+_+_+_)(_+_+_+_+_)=A
What is the maximum value of  A? What is the minimum value of  A?

 Jan 27, 2020
 #1
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By AM-GM, the maximum is (45/2)^2 = 506.25, and there is no minimum.

 Jan 27, 2020

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