The problem of dividing 3kg flour to three 1kg parts using a balance Suppose you have 3kg flour, and you are asked to divide it to three 1kg parts using a balance scale. 
It seems to me that it's impossible to do with a finite number of weighing, but I can't see how to prove it. Is this a known problem? Any hint is appreciated. 
Please comment if the question is vague or needs further clarification.
Edit: I'd appreciate it if you formulate this problem with reasonable assumptions into a pure math problem.

Theoretically, assuming it is possible to use the balance scale to divide any flour quantity to two equal parts. Make a continuous sets of two half dividing rounds. At end of each set, sum one side and use the other side to continue the two dividing rounds sets. This shloud give you the sum:
$$ \color{red}{S} =\frac{3}{4}+\frac{3}{16}+\frac{3}{64}+\cdots =\sum_{n=1}^{\infty}\frac{3}{4^n} =\color{red}{1} $$
