I see that this is getting upvoted. * Guys, I made a logical mistake here. I said "this is because if it hasn't happened by the last day it can happen"... Bu

I see that this is getting upvoted. * Guys, I made a logical mistake here. I said "this is because if it hasn't happened by the last day it can happen"... But this supposes the students know what day it can happen. They might not. For example, the Teacher might give the test on Monday every year. Assuming the students have no contact with last year's students (or didn't bother to ask) they would not know that the space of possible days is Monday. Therefore, the teacher can make a guarantee that the test is on Monday through Friday, while saying that the students will be surprised. The students, thinking that the test may be Monday through Friday, would assume that the last day the test 'can happen' is Friday. But that's not a possibility at all. So this assumption would be a mistake. In fact, if the teacher is completely hiding his algorithm, then the students can be surprised. They don't know if the space of possible days is "only Monday", "only Tuesday", or "Monday, Tuesday, or Thursday", or whatever. Each of these spaces fulfills the requirement of some day monday thru friday next week: however, if the teacher keeps the space of possibilities quite secret, then the students cannot make their FIRST step of assumption, which is the last day that the thing "could" happen. So, I have two answers: 1) If the students know 100% of the teacher's ALGORITHM (how the teacher chooses days) -- even if it is random -- then the teacher cannot 100% guarantee them that they will be surprised. Namely, on the last day of the space the teacher chooses from, they would not be surprised. if, however, the teachers know NOTHING about the algorithm the teacher uses to determine the day, the teacher is indeed able to make his guarantee. In other words, if I am the teacher and I am trying to make this guarantee, I can do so, provided that instead of choosing a day randomly from monday through friday, I hard-code the day Monday, while keeping this algorithm secret from the students. TL;DR: if the teacher tells them only something ABOUT the day (that it is next week, and a monday or a tuesday or a wednesday or a thursday or a friday) then there is no paradox and he can guarantee that they will not know for sure of the day it is happening). If, however, they also know HOW the teacher chose the day (even if the algorithm includes randomness! i.e. 'a random day monday to friday') than the teacher may be unable to make his guarantee.