You’re asking for an example of details that aren’t those of the other guard. If they give you a non-working example, then the lying guard has been truthful. Which is a contradiction.
Consider the question ‘what is an example of something that is not a cat?’. Any answer that is not a cat is truthful; therefore the lying guard must give an example of a cat.
Ah, ok, so to clarity, you could also ask, “tell me anything that isn’t the other guard’s number,” and they have to tell you exactly the other guard’s number.
You’re asking for an example of details that aren’t those of the other guard. If they give you a non-working example, then the lying guard has been truthful. Which is a contradiction.
Consider the question ‘what is an example of something that is not a cat?’. Any answer that is not a cat is truthful; therefore the lying guard must give an example of a cat.
Ah, ok, so to clarity, you could also ask, “tell me anything that isn’t the other guard’s number,” and they have to tell you exactly the other guard’s number.