Question 5
Suppose $n$ is a positive integer and 3 arbitrary numbers are choosen from the set $\{1,2,3,\ldots,3n+1\}$ with their sum equal to $3n+1$. What is the largest possible product of those 3 numbers?
Editorial convention for this imported question: the three values may repeat. This is an editor-selected interpretation, not a condition confirmed in the source. The distinct-elements interpretation is also proved in the solution.
Editorial convention for this imported question: the three values may repeat. This is an editor-selected interpretation, not a condition confirmed in the source. The distinct-elements interpretation is also proved in the solution.