I honestly can't see how you're supposed to isolate the odd coin from the other eleven whilst determining whether the coin is heavier or lighter, even through deductive reasoning. Looking at the probability of choosing the odd one out from the process of elimination, this impractical puzzle leaves no room for error. You'd need to conduct six measurements, not just three; under either presumption said odd coin is heavier or lighter.
I think I'll go and punish myself with a Rubik's cube now.
I think I'll go and punish myself with a Rubik's cube now.