2013 UNCO Math Contest II Problems/Problem 5
If the sum of distinct positive integers is , find the largest possible value of their product. Give both a set of positive integers and their product. Remember to consider only sums of distinct numbers, and not or , etc., which have repeated terms. You need not justify your answer on this question.
Intuitively, we want all the numbers to be as close as possible to , or . Thus, we get the numbers , , , and . These multiply up to .
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