I can't see how it's possible to deduce such things, in the sense of obtaining an answer associated with high degree of confidence. It seems to be hindsight bias on your part to assume it's deducible, and similarly for some of the other hidden "facts" (or, alternatively, you meant to say something else, and didn't mean to imply high degree of confidence being obtainable, but I can't imagine what).
(Imagination allows noticing promising hypotheses, where a person lacking said imagination would need to learn that hypothesis from someone else. But it doesn't allow making confident conclusions despite lack of information, where uncertainty is appropriate. So there could be hypotheses which are better than any other possible hypothesis, but none of them would be "the deduced answer". If you argue that imagination is the problem, you need to be able to argue for your conclusion in a way that fends off other possible conclusions, and not just consistently determine your conclusion as an author by adding more facts to the story.)
What if: a) Quirrell and Harry's actions in ch 51 only make sense in light of their planning to do something in particular, and b) doing that thing requires a charm not to be in place? I think that counts as a correct deduction.
[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.