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Suppose there are n positive real numbers such that their sum is 20
and the product is strictly greater than 1. What is the maximum possible
value of n?

(A) 18 (B) 19 (C) 20 (D) 21
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If x<1, then (1-x)(1+x)<1

We will want to keep number as small as possible, but when choose a number less than 1 we have to choose another number much greater than 1 to compensate, ex. for 0.5 we have to choose >2,  0.1 we have choose >10. So for optimal solution we end up choosing 1.

But all can not be 1, so we end up choosing 18 1s and 1 2.

It needs more rigorous proof though.

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