33. 

Suppose A makes the statement: "I am a liar, and B is not a liar."

Who among the islanders A and B is a knight and who is a liar?
33. First, note that A cannot be a knight. Indeed, if A were a knight, his statement would be true, but in it, he claims that A is a liar. Therefore, A is a liar, and his statement is false. If B were a knight, then A's statement would be true. Therefore, B is also a liar. Thus, A and B are liars.