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.