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Problem 1.3.
Albert announces that he plans a surprise 6.042 quiz next week. His students wonder if the quiz could be next Friday. The students realize that it obviously cannot, because if it hadn’t been given before Friday, everyone would know that there was only Friday left on which to give it, so it wouldn’t be a surprise any more.
So the students ask whether Albert could give the surprise quiz Thursday? They observe that if the quiz wasn’t given before Thursday, it would have to be given on the Thursday, since they already know it can’t be given on Friday. But having figured that out, it wouldn’t be a surprise if the quiz was on Thursday either. Similarly, the students reason that the quiz can’t be on Wednesday, Tuesday, or Monday. Namely, it’s impossible for Albert to give a surprise quiz next week. All the students now relax, having concluded that Albert must have been bluffing.
And since no one expects the quiz, that’s why, when Albert gives it on Tuesday next week, it really is a surprise!
What do you think is wrong with the students’ reasoning?
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