This Question was originally posted [Here](https://math.stackexchange.com/questions/1762437/separating-heavier-from-the-lighter-balls), 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](https://math.stackexchange.com/questions/1762437/separating-heavier-from-the-lighter-balls).