56. 

Suppose the brother Alice met said: "I am lying today or I am Trulala." Could it be determined in this case which of the brothers it was?
56. It is possible. If the brother Alice met that day was lying, then the first statement in the disjunction would be true, which would make the entire complex statement true as well, leading to a contradiction. Therefore, on the day of the meeting with Alice, the brother was telling the truth, and his statement is true: either he is lying, or his name is Trulala. Since the brother was not lying on the day of the meeting, his name was Trulala.