## Task B-2.4.

Pinocchio tells the truth on Mondays and Tuesdays, always lies on Saturdays, and on the other days of the week, he either tells the truth or lies. In response to the question "What is your favorite subject at school?" over six consecutive days of the week, he gave the following answers in order: "History", "Mathematics", "Geography", "Physics", "Chemistry", "Physics". What subject does Pinocchio like the most? Explain your answer.
## Solution.

If among those six consecutive days during which Pinocchio gave us the known answers there were both Monday and Tuesday, we would have to have two consecutive identical answers (since Pinocchio speaks the truth both on Monday and Tuesday), which we do not have, so the only two possibilities that remain are that the series of questions started on Tuesday (and the sixth answer we received was on Sunday), as well as the possibility that the series of questions started on Wednesday (and the sixth answer we received was on Monday). If the series of questions started on Wednesday, then we received the answer "Physics" on Saturday, as well as on Monday, which is impossible since Pinocchio always lies on Saturday, and always tells the truth on Monday. Therefore, the only remaining possibility is that the series of questions started on Tuesday. In that case, Pinocchio gave the answer "History" on Tuesday. Since Pinocchio always tells the truth on Tuesday, we conclude that "History" is his favorite subject.