Maximizing the Product: A Problem

This week I offer a problem:

What is the largest possible product you can make with a group of positive integers if the sum of those integers is 2017?

Here we do not assume that the integers are distinct from each other in any way, so repetition is allowed. For example, you could use the numbers 1000, 1000, and 17 to get a product of 17,000,000. You could also use 2017 1s if you wanted to, but that would be inadvisable. It is possible for the product to exceed 17 million, but I’m not going to tell you how just yet.

If you’re feeling a bit overwhelmed by the possibilities that 2017 present, try a more manageable version of the problem where the integers add up to 10 instead. Then, maybe try 20. You should find some helpful insights that way.

Good luck!

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