I've become a connoisseur of hard paradoxes and riddles, because I've found that resolving them always teaches me something new about rationalism. Here's the toughest beast I've yet encountered, not as an exercise for solving but as an illustration of just how much brutal trickiness can be hidden in a simple-looking situation, especially when semantics, human knowledge, and time structure are at play (which happens to be the case with many common LW discussions).

A teacher announces that there will be a surprise test next week. A student objects that this is impossible: "The class meets on Monday, Wednesday, and Friday. If the test is given on Friday, then on Thursday I would be able to predict that the test is on Friday. It would not be a surprise. Can the test be given on Wednesday? No, because on Tuesday I would know that the test will not be on Friday (thanks to the previous reasoning) and know that the test was not on Monday (thanks to memory). Therefore, on Tuesday I could foresee that the test will be on Wednesday. A test on Wednesday would not be a surprise. Could the surprise test be on Monday? On Sunday, the previous two eliminations would be available to me. Consequently, I would know that the test must be on Monday. So a Monday test would also fail to be a surprise. Therefore, it is impossible for there to be a surprise test.”

Can the teacher fulfill his announcement?

Extensive treatment and relation to other epistemic paradoxes here.