You live in a strange town where there are only two groups of people: the ones who always tell the truth (Truth-tellers) and those who always lie (Liars). You are accused of a crime and brought before the judge, where you are allowed to speak only one sentence in your defence. The judge does not know which group you belong to.
For questions 1 to 5, what could you say in order to convince the Judge to let you off?
1. You are a Liar and you are innocent. The Judge believes that the crime was committed by a Liar.
(1) “I am not a Liar.”
(2) “I did it.”
(3) Either (1) or (2) would work
(4) None of the above
2. You are a Liar and you are guilty. The Judge believes that the crime was committed by a Liar.
(1) “I am not a Liar.”
(2) “I did not do it.”
(3) Either (1) or (2) would work
(4) None of the above
3. You are a Truth-teller and you are innocent. The Judge believes that the crime was committed by a Truth-teller.
(1) “I am innocent.”
(2) “I am not a Liar.”
(3) Either (1) or (2) would work
(4) None of the above
4. You are a Truth-teller and you are guilty. The Judge believes that the crime was committed by a Truth-teller.
(1) “I am guilty.”
(2) “I am not a Liar.”
(3) Either (1) or (2) would work
(4) None of the above
5. You are innocent and it is an established fact that the crime was not committed by a “Normal” person. “Normal” people are a new immigrant group who sometimes lie and sometimes speak the truth. What sentence, no matter whether you are a Truth-teller, Liar, or Normal person, can convince the Judge to let you off?
(1) “Either I am a Normal person and guilty, or I am a Liar and innocent.”
(2) “Either I am a Truth-teller and innocent, or I am a Liar and guilty.”
(3) “Either I am a Normal person and innocent, or I am a Truth-teller and guilty.”
(4) “Either I am a Truth-teller and innocent, or I am a Liar and innocent.”
(5) None of the Above
