An interesting “Puzzle”

puzzleOne Friday a professor announced to her class that on one of their five meeting days during the next week, she would administer to them a surprise quiz. The class would not know which of the five days it would take place until the morning in which it was actually to be given. One of her students argued as follows: “You cannot give the quiz on Friday, for if it had not taken place on one of the four earlier days, we would know on Thursday night that it was to be given on Friday and it would not be a surprise. Similarly, it cannot be given on Thursday. Friday is out, so if it had not been given on one of the first three days, we would know on Wednesday night that it was due on Thursday. Again it would not be a surprise. Obviously, the same sort of argument applies to Wednesday, Tuesday, and Monday. It follows that you cannot give a surprise quiz at all.” The professor was puzzled. She had decided to give the quiz on Wednesday, and she was quite sure that the students did not know that. But she found the student’s argument convincing, so she cancelled the quiz. Should she have?