First, weigh A+B against C+D. If one side is lighter, then the side is guaranteed to have the fake coin. If not, then we know the chameleon was behaving as a fake coin, and it’s not on the same side as the fake coin.

Then, weigh A against B. We know at least one of them is real. If one side is lighter, then we have found the fake coin. Otherwise, the other has to be the chameleon, and we know the fake coin is either C or D. ]]>

I like Puzzle 2. I won’t spoil it for others, but in my solution you ask the same question twice. Getting the same answer each time means it’s a knight or a knave and the answer tells you which. Getting a different answer means it’s an alternator.

]]>Is a scale actually random in a probabilistic sense and “asymptotically better” means involving terms like expectation?

Or does the solution you mentioned give a worst-case estimate for any sequence of results from that scale?

For example, we can choose the pair on each step. If each weighting is truly random, the probability of not discovering faulty scales till the last step goes to 0 very fast. Are you expecting an answer like this? ]]>