The problem is stated as follows:

With a balance scale and six given weights; 1g, 2g, 3g, 4g, 5g and 6g, is it possible to make sure the labels on the weights are put on correctly only using the scale twice? Assume there is no way to identify weights by apperance, and that only the labels might have gotten in the wrong place (ie there is exactly one of each). 

I've come as far as realizing a good way to start would be to balance 6g towards 1+2+3g. If balanced, the 6g weight must be correct, and 1g, 2g, 3g can only have switched labels with each other. It gives no direct info on 4g and 5g, but they can only have switched with each other.

With that in mind, the next step must include exactly 2 out of 1g, 2g, 3g but not both on the same side of the scale (as we still wouldn't know if they have each other's labels in that case), and atleast one of 4g, 5g. Furthermore, if we choose 1g and 2g we might confuse ourself and not realizing that the switch 1g->2g->3g->1g has been made, and same thing with 2g+3g, therefore the weight labeled 1g on one side and and 3g on the other is the best option. But where do I go from here? I've tried so many things but always end up with some sort of ambiguity. That is not a solid proof that it is not possible, however. Do anyone have a way of succeeding in two uses of the scale, or a way of *prooving* that it is not possible?