Also, I just realized what makes the envelope example particularly clear. If I say "even if you open four envelopes first and find them empty" (I still guarant

Also, I just realized what makes the envelope example particularly clear. If I say "even if you open four envelopes first and find them empty" (I still guarantee you will be surprised on the fifth) I'm in a way implying that that has a non-zero probability. The way to formalize this is to say so. "This is a stochastic process, there is a non-zero chance that you will go through four days without a test (have it on the fifth day". Obviously, you cannot make this guarantee, while guaranteeing surprise in 100% of cases. So basically, the only intuitive problem this puzzle poses is that it sounds like the teacher is giving you some kind of guarantee that there is a case where you open four empty envelopes before opening the fifth with the heart in it. In fact there is no such guarantee. So, really, my cases A and B can be summarized as follows. A) In case the teacher makes any guarantee that there is a non-zero chance of a test on Friday and that this chance is assured by a stochastic process, he CANNOT 100% guarantee surprise. This was my original, knee-jerk interpretation. Of course, the teacher does not ACTUALLY make any such guarantee!!! By saying "test-day = Monday" he has gone back on his word that there is a non-zero chance the test is on Friday: in fact there is a zero chance of that. Version B, in which he does not guaranteee a non-zero chance on any day of the week, leaves the teacher able to fulfill both his obligations (surprise and test on a weekday) without a paradox. Really, this is INSANELY clear and simple when you view it clearly. We think he's giving a guarantee that there's a chance the test will be on Friday and a stochastic process determines this. But he's giving no such guarantee.