These are the problems I found in a book. I hope someone can help me with this:
1. In an island there are two types of people: liars and truth tellers. When asked a yes/no question, a truth teller always tells the truth and a liar always lies. Then how to ask a single question, that would distinguish between them?
The answer given was ask a question:
"If you are a truth teller than how would you answer the question, 'Are you a liar'?"
The truthful will answer no. And as the truthful has replied yes the liar would reply yes.
My question, independent of the answer of truthful, how does the liar think? What is the response of 'If you are a truth teller' to him ie how does he take the 'if' part into account?
2. Suppose two person - a liar and a truthful - comes to you. Say 1 is A and another is B. Then how to ask a single yes/no question to A to determine whether B is a liar or truthful?
3. Now there are 3 sorts of people: liars, truthful and semi-truthful (part time liar). How to ask a single question to find the type of person?