You find yourself in the usual situation with three locals whose answering is highly restricted. First, they can only answer yes or no questions. Second, one will always answer truthfully, one will always lie (answer the opposite of the truth), and one gives answers that are completely unconstrained - might be random, always yes, alternate truth and lie, alternate yes and no, or anything else (with one exception, below.)
Unlike other KKJ scenarios, these three are teenagers and as such lack true self awareness or awareness of the inner nature or motivations of others. Simply put, you cannot ask them questions about the structure of the puzzle (their life) such as "does Steve ever lie?" or "are you the one who always tells the truth?" These questions are unanswerable for them, and as such will gain you only a sulky teenage stare, from which you learn nothing. Asking the truth teller "will you answer this question Yes?" gets you the same sulky stare as the paradoxical "will you answer this question No?" even through the first should be answerable. They can't answer anything about how the others will answer a hypothetical future question, or how they themselves will answer, and they are unaware of the labels Knight, Knave, and Joker, or even of these categories of behaviour.
They can answer questions about past events: "when I asked you how many red balls I had in my hand, did you reply truthfully?" or "Has Steve ever lied to me?"
Since they don't know the labels, there is no difference between a "Joker whose strategy is to always respond truthfully" and a Knight, nor between a "Joker whose strategy is to always respond with a lie" and a Knave, therefore this Joker will not choose either of those strategies. However, Jokers won't sulk at a question that Knight or Knave would answer, or answer one they would sulk at.
Is there a way, given any number of questions, the usual props of the genre (coloured balls, coins, scales etc) about which you can ask questions, and plenty of time, for you to establish conclusively who is Knight, Knave, and Joker? What strategy does so in the fewest questions?
Edit: split the scenarios into two:
- the teenagers have been answering questions from other visitors before your arrival and have learned enough information that if they provided all the information to you, you would be able to label them, even though it doesn't occur to them to label each other
- the teenagers have never heard each other answer any questions yet, or have heard only questions in which the Joker happens to have always answered the truth or always a lie, and therefore cannot yet be distinguished from whoever they are agreeing with.
In the first scenario you can distinguish them quickly, without waiting for the Joker to diverge from a pattern. In the second, is there any strategy other than waiting while asking questions with known answers?
