[Update: and now there's a fifth discussion thread, which you should probably use in preference to this one. Later update: and a sixth -- in the discussion section, which is where these threads are living for now on. Also: tag for HP threads in the main section, and tag for HP threads in the discussion section.]
The third discussion thread is above 500 comments now, just like the others, so it's time for a new one. Predecessors: one, two, three. For anyone who's been on Mars and doesn't know what this is about: it's Eliezer's remarkable Harry Potter fanfic.
Spoiler warning and helpful suggestion (copied from those in the earlier threads):
Spoiler Warning: this thread contains unrot13'd spoilers for Harry Potter and the Methods of Rationality up to the current chapter and for the original Harry Potter series. Please continue to use rot13 for spoilers to other works of fiction, or if you have insider knowledge of future chapters of Harry Potter and the Methods of Rationality.
A suggestion: mention at the top of your comment which chapter you're commenting on, or what chapter you're up to, so that people can understand the context of your comment even after more chapters have been posted. This can also help people avoid reading spoilers for a new chapter before they realize that there is a new chapter.
Do what? Confidently name the "official" hypothesis, guess teacher's password? There certainly are good hypotheses, possibly one hypothesis significantly better than any other, which makes the probability of privileging the one you had in mind non-trivial and thus explains your observations. It doesn't follow that it's correct to assign high level of certainty to that hypothesis (as a within-world event, not prediction about what you had in mind, as the latter would be biased towards the best guess and away from the long tail).
(My best guess in this particular case is "enable time turners (in some sense)", but I won't be confident it's indeed so, it could be something else. ETA: On reflection, "revealing if someone is already in the room" is a better guess, although one could sidestep the defenses by entering from the future as well as from the past, and so not be present at the time of the casting.)