This Question was originally posted Here, where I'm more interested in the methods for manual solutions yielding $n$ or less moves on average.
I wanted to post it here as well, to see what the people of mathoverflow think about it.
I think we are familiar with the classic problem where we need to find one heavier ball among the rest identical lighter $n$ amount of balls using a scale and the minimum number of weightings.
But I'm interested in a variation of this problem.
You have an even number of balls, $2n$ identical balls.
Half of them, $n$ amount of balls, are "Heavy Balls" and the other half are "Light Balls".
Find a method to separate the balls into the "Heavy" and the "Light" box with the least weightings as possible; Using a scale instrument, which from you can read exact difference between the total weight of the right and the left side of the scale.
What is the minimum number of weightings required if we are given $2n$ balls?
What is the optimal method we can use for any case of $n$ to separate the balls with the least weightings as possible?
For my progress on the specific cases of $n$ so far, check the original question linked Here.