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?
By AM-GM, the maximum is (45/2)^2 = 506.25, and there is no minimum.
