[0xfaded]

This puzzle is used to inrto entropy in "Information Theory, Inference, and Learning Algorithms".

Basically there are log2(12) + 1 bits or log2(24) of information (which ball and heavier or lighter). Any solution must reveal all information.

For example, a first weighing with an initial (4,4,4) split has three possible outcomes with equal probability (left, even, right), so reveals log2(3) bits. 3 independent weighings with equal outcomes would reveal 3*log2(3) bits, or log2(27). Of course the weighings cannot be independent since 27 > 24.

The trick is to design a scheme which reveals all 24 bits. With the static solutions this is trickier since all bits need to be revealed in all 27 possible outcomes, but if you work through them it should reveal why the solution works.