I don't follow the other list you mentioned, so I don't know what the actual problem to solve is - my guess is that this is an anti-bot protection measure, intended to make sure that only human participants can engage in a conversation.

If that's the problem - or if it's similar - you'll also need to make the puzzle difficult enough that it's hard to brute-force or solve statistically - let's say you provide

Yep, that's it. the

other party with 20 images, 19 cats and 1 dog, and ask them to identify the dog.

What keeps a bot from answering the question 20 times? Let's assume the first arms-race countermeasure prevents answering the question more than once by generating puzzles on-the-fly from known cat and dog images - so the bot just picks an answer randomly, and keeps doing that until they hit.

Oops... never thought of that.

Can God create a rock so big he can't lift it?

No, just as he can't create round squares. What's that got to do with anything?

This sounds like maybe it's essentially a credentialling/ID problem, where you're generating credentials on the fly based on a short-form Turing test. Can you restate the problem so that instead of a Turing test it's a more familiar multi-channel authentication process? (e.g., require new participants to have "introductions" from existing participants, track introductions, and remove the access for accounts found to be bots, or found to have introduced bots .. or similar.)

Well... one of the points of Freenet is to have anonymity (even if not cryptographically strong, just statistical anonimity). I don't know how well that can work with "introductions". [Maybe the public / private key proposals - which I haven't followed up closely - could me modified to be used as some sort of a pseudonym.] Mark