Spoiler for perhaps

the audience is a red herring. Assuming a single audience member who can be truthteller, liar or undecided/human , a single question that uses the truth value of the answer inside the question might do the trick for going away with the whole prize all the time. Higher order logic though, bu then so are the axioms about the three types of people.

If I would ask you if the prize is behind door #1 and your answer would be as truthful as the answer you're gonna give me now, would your answer be yes?

Truth teller says yes/no equivalent to prize being behind door 1/ being before door 2

Liar would give opposite answer to what he would normally evaluate the expression. If a and b then c.

If prize is behind door one and he would lie his answer would be no. So trying to lie about the outcome pf the hypothetical question, he says yes. Similar argument for the other case.

Undecided person is forced by the paradox of the question to evaluate the trith value of the actual answer before evaluating the answer itself. A machine might get syntactically stuck but a person shoul be able to evaluate/decide the truth value / context before evaluating the question itself. Therefore after he/she does that, the evaluation goes a deterministic path. Hence his/her answer would match the same equivalence as the other types discussed above.

Key here is if this is allowed by the OP.

The wording I intepreted would suggest this apparent paradox would qualify.

Then again, I've already decided if I'm gonna lie or tell the truth in this post

If I would ask you if the prize is behind door #1 and your answer would be as truthful as the answer you're gonna give me now, would your answer be yes?

Truth teller says yes/no equivalent to prize being behind door 1/ being before door 2

Liar would give opposite answer to what he would normally evaluate the expression. If a and b then c.

If prize is behind door one and he would lie his answer would be no. So trying to lie about the outcome pf the hypothetical question, he says yes. Similar argument for the other case.

Undecided person is forced by the paradox of the question to evaluate the trith value of the actual answer before evaluating the answer itself. A machine might get syntactically stuck but a person shoul be able to evaluate/decide the truth value / context before evaluating the question itself. Therefore after he/she does that, the evaluation goes a deterministic path. Hence his/her answer would match the same equivalence as the other types discussed above.

Key here is if this is allowed by the OP.

The wording I intepreted would suggest this apparent paradox would qualify.

Then again, I've already decided if I'm gonna lie or tell the truth in this post

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