The sum of the elements of a set of positive integers is 22.
What is the greatest possible product of the integers in this set if:

A Duplicates are allowed?
B Duplicates are not allowed?

Problem modified from UNL Math Day with help from friedlinguini

calculus tells us that the max will be reached when the numbers are as close to each other as possible, which greatly reduces the number of situations that need be checked - just one configuration for each number of elements in possibility a and 2 or 3 for each number of elements in possibility b.

I got the max for "A" with 7 or 8 elements to be 2916, and the max for "B" with 5 elements to be 1008.

It could be shown using calculus that these are the (well, at least the "a") maximums possible despite my numerical approach.

Posted by Cory Taylor on 2002-12-24 04:00:55