The evil professor says to the students: you are going to have an exam next week. I’m not telling you which day, but I am telling you that it will be unexpected (i.e., the day of the exam you won’t be sure whether the exam is that day or not). I’m assuming that the week starts on Monday and ends on Friday.
So this is what the students think:
Okay, it can’t be on Friday, because if Friday comes and we haven’t had the test yet, then in the morning we’ll surely know it’s that day. So it will be a day from Monday to Thursday. After pondering a bit, they realise that it can’t be Thursday either, for the same reason: If Thursday comes and they haven’t had the exam they’ll think “we know it’s not Friday, therefore it has to be today”. So Thursday wouldn’t be a surprise either. Similarly (by induction), all days are eliminated !
Then they are happy and think the evil professor made a promise he couldn’t hold, and don’t prepare for the test. However, the next week, on Wednesday, they have the exam. And all are surprised.
Where is the flaw in the logic ?
Hover to show the answer.
There is no answer to this… I will try to explain later.