Let set {X1,X2, . . . ,Xn} be such that. X1+X2+ . . . +Xn = X1 * X2 * . . . * Xn..

then maximum possible value of max{...} will be n.

The Sum = Product = 2 * n.... The set would be {1,1, . . . 1, 2 , n } with (n-2) 1's

( Note:-If order matters we can find by permutation. )

First all are 1's, since last two ones are covered by the 2, and 1's are added to each location by last n. Thus the sum is 2n, and multiplication is also 2n.

If we had 3 as a member, product > addition for a set of maximums. Thus this is only the solution.

I have not studied Number theory. Is there some thing like this there??

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