Alice, Bob and Charlie are one of each type:
- a truth teller (always tells the truth)
- a liar (always lies)
- and a spy (can lie or tell the truth)
They make the following statements:
Alice: I am not a truth teller.
Bob: I am not a spy.
Charlie: I am not a liar.
What type is Charlie?
(A) Truth teller
(D) There is not enough information
Charlie is a liar.
If Alice is a truth-teller, she cannot state that she is not a truth-teller. If Alice is a liar, then she would always lie but saying she is not a truth teller will be true. Therefore Alice has to be a spy.
If Bob is a liar, he would always lie, but saying he is not spy would be true. Since Bob cannot be the spy, he has to be the truth teller.
This means Charlie has to be a liar.