Difference between revisions of "2013 UNCO Math Contest II Problems/Problem 5"

Problem

If the sum of distinct positive integers is $17$, 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 $3+7+7$ or $2+3+4+4+4$, etc., which have repeated terms. You need not justify your answer on this question.

$\begin{array}{|c|c|c|c|} \hline \text{EXAMPLE: }& \text{Distinct Integers: }{2, 3, 4, 8} & \text{Their Sum: }2+3+4+8=17 & \text{Their Product: }2 \times 3\times 4\times 8=192 \\ \hline \end{array}$