A math teacher tells her class on Friday that they will have a surprise quiz one day next week. She tells them they will have no way to predict which day of the week it will be on, and that they won't know its coming until she tells them to clear their desks for the quiz.
The students reason as follows: the quiz can't be next Friday because that wouldn't be a surprise. Since we didn't have a quiz on monday->
thursday, we would be able to deduce on Thursday night that the quiz would be on Friday.
Which means that it can't be on Thursday since we know its not going to be on Friday, if we haven't taken the quiz by Wednesday, we'll know that the quiz is coming on Thursday. Of course, that means that it can't be on Wednesday either since if we haven't taken the quiz by Tuesday, we'll know its coming on Wednesday. So it can't be on Tuesday either (we'll know its coming on Tuesday by Monday evening), but that means it will be on Monday. So it can't be a surprise. Therefore, there can't be a surprise quiz.
The week came and went, and the teacher's prediction came true. How did she do it?
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