TITLE: Separating Heavier from the Lighter Balls
QUESTION [5 upvotes]: 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.

REPLY [7 votes]: The answer is indeed asymptotic to $4n/\log(n)$, but I don't know of an elementary or easy construction for this upper bound. I believe simple probabilistic-method type constructions do not work.
This is also phrased as a "coin-weighing" problem. One point to keep in mind is that we can think of each weighing of $k$ balls as simply learning how many of the $k$ are light versus heavy. Thus you can rephrase your problem as follows: There is a special unknown subset $S$ of $\{1,\dots,2n\}$, where $|S| = n$, and we wish to determine $S$. At each step, we can query any $T \subseteq \{1,\dots,2n\}$ and learn $|S \cap T|$.
I find these references in the tutorial/lecture by Galvin[1], where he attributes the upper bound to (independently) [2,3] and the lower bound to (independently) [4,5]. Note that in his formulation there are only $n$ coins rather than $2n$ (hence the bound is $2n/\log n$), and it is not promised how many are heavy or light (so in particular the  upper bound holds for the case where half are promised to be heavy).
This is also addressed in this MO question[6], but I'm not sure where a factor $2$ has gone missing in that answer.

[1] http://arxiv.org/abs/1406.7872
[2]  D. Cantor and W. Mills, Determination of a subset from certain combinatorial properties, Can. J. Math. 18 (1966), 42–48
[3] B. Lindstr¨om, On a combinatorial problem in number theory, Can. Math. Bull. 8 (1965), 477-490.
[4] P. Erd˝os and A. R´enyi, On two problems of information theory, Publ. Hung. Acad. Sci. 8 (1963), 241–254.
[5]  L. Moser, The second moment method in combinatorial analysis, in “Combinatorial Structures and Their Applications”, 283–384, Gordon and Breach, New York, 1970.
[6] Guessing a subset of {1,...,N}