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.

All you can do with your scales is: divide by $2$; add two numbers; and subtract two numbers. And you can't get to $\frac13$ from $1$ with a finite sequence of these operations, because all numbers created by them have a denominator that is a power of $2$.
