2013 UNCO Math Contest II Problems/Problem 5

Problem

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.

$\begin{tabular}{|c|c|c|c|} \hline EXAMPLE: & Distinct Integers: {2, 3, 4, 8} & Their Sum: 2+3+4+8=17 & Their Product: 2 \times 3\times 4\times 8=192 \\ \hline \end{tabular}$ (Error compiling LaTeX. Unknown error_msg)