The only information that the students are given is, "There is going to be a surprise quiz next week." They don't know anything else. Therefore, I think the students got it wrong from the beginning by thinking that it can't be on Friday. I don't see any logical reason on why it can't be on Friday (or any other day). The quiz will be a surprise to them as long as there is no way of knowing exactly what day it will be given, and given the information they know about the quiz, I think it's impossible to know that. So, the quiz can be given on any day the Professor wants and it will still be a surprise quiz (even though it's not much of a surprise if they're already told that it's going to be on some day during the week).
However, if the students come to the conclusion that there is going to be no surprise quiz at all, then, of course, the Professor can just surprise them by giving the quiz on any day.
However, if the students come to the conclusion that there is going to be no surprise quiz at all, then, of course, the Professor can just surprise them by giving the quiz on any day.
