Here’s an irritating little conundrum.
Imagine you are a student in a philosophy-of-logic class that meets five days a week. On Friday the teacher announces that there will be a surprise quiz one day next week. As you are leaving class it dawns on you that it can’t be next Friday, because if you get all the way to Thursday without having been given the quiz, you will know that it has to be coming on Friday, and therefore won’t be a surprise. So Friday’s definitely out. It has to be Monday, Tuesday, Wednesday, or Thursday. But, having realized that (and of course, your professor, being an expert logician, will have realized this as well), then if you get to the end of Wednesday without having had the quiz, you’re going to know that it has to be Thursday, because we’ve already conclusively established that you can’t give a surprise quiz on Friday. But this means you can’t give a surprise quiz on Thursday, either! So having ruled out Thursday and Friday, it’s got to be Monday, Tuesday, or Wednesday. But if Wednesday is the last possible day, then this really means it can’t be much of a surprise on Wednesday, either, by the same reasoning. So Monday or Tuesday, then. Actually, it’ll have to be Monday, because Tuesday is now the last available day, and if you haven’t had it Monday, you can expect it for sure on Tuesday. But if it has to be Monday, then it’s no surprise at all.
You are forced to conclude that your teacher simply cannot give a surprise quiz next week; he probably was just hoping that some of the students would see this elegant proof. So you don’t even bother to study, and are thoroughly shocked on Thursday when the quiz is presented.