Suppose a Professor announces that he will take a surprise quiz next week. If he has to follow his exact wordings then the paradox is he can’t take the quiz.
Reason goes like this=>
He surely can’t take a surprise quiz on Friday since it is last day and if he has not taken the quiz till Thursday then everyone knows that he will be taking it on Friday so it can’t be surprise.
Now based on above correct assumption let us say that everyone knows that Professor can’t take quiz on Friday. So he can also not take a surprise quiz on Thursday since everyone knows that it can’t be on Friday and if he has not taken it till end of Wednesday class then it must be on Thursday known to all. So, Thursday is also ruled out everyone knows about it.
Now we know that professor can’t take quiz on Thursday also because if he has not taken the quiz till Wednesday then it surely will be held on Thursday. Hence let us consider about Wednesday. Can he take a Surprise quiz on Wednesday given that he can’t take a surprise Quiz on Thursday or on Friday. No! If he has not done till Tuesday then he can’t do it on Wednesday everyone will know.
In same way we can rule out every day of the week and he will not bale to take quiz in that week.
But he can surely take the quiz on any day of the week except Friday. Like if he takes the quiz on Tuesday it will be surprise.
Another example of surprise paradox is
Let us say Professor announces that “you will have a Quiz in tomorrow’s class and it will be a surprise”
You presume that you can’t be surprised since they already told you, so there is a contradiction in what they’ve said. Therefore, you conclude that there will not be any quiz tomorrow. But next day Professor comes with the quiz and you are Surprised !!! :).
But if you know about this paradox or is intelligent logically then you will not be relaxed and prepare for Quiz. In tomorrow’s class you are fully prepared waiting for Quiz. If the Quiz will be taken you will not be surprised. So Quiz can’t be held. Situation is dependent on what you choose to belief.