Allan writes down n positive integers so that the sum of those numbers is 23. When he multiples those numbers, he gets the maximum result. List all of the n positive integers that Allan has written.

Step-by-step explanation:

To get maximum product we need to optimize how we break down the numbers

Its obvious we don't want number 1 to be used as it won't change the product

Also we don't want to use big numbers, we can have four 5's instead of two 10's as it would give greater product, 5*5 > 10

What is best number?

So the best is to break the number down to 2's and 3's

As we see the maximum product we can get is 4374 with seven 3's and one 2.

Hence the numbers are:

astronomers is your final answer! : )