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

(In reply to Solution by ananth)

I liked your method for the no duplicates case.
Had you used it for the duplicates allowed case, you would have gotten the correct answer.

22=11+11
11=5+6
5=2+3 and 6=3+3
((2*3)*(3*3))*((2*3)*(3*3))=2916

Note:2*2*2=8, but 3*3=9, so 3's are better
2*2*2*2=16 and 4*4=16 so 2's and 4's are equally good.

For _any_ sum, where you want the maximum product, pick as many 3's as you can and then one or two 2's if needed.

Posted by Jer on 2003-03-28 08:08:11