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Intrism comments on Harry Potter and the Methods of Rationality discussion thread, part 20, chapter 90 - Less Wrong Discussion
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That solution has the disadvantage of requiring the students to move through the halls, which is extremely hazardous. The Great Hall has its own risks, but the seventh year armies should be sufficient to secure it.
According to the Harry Potter wiki, the Great Hall is located off the Entrance Hall, which suggests that leaving the castle from it should be fairly trivial.
The professors are mostly there, which is a sufficiently powerful bundle of combat magic to handle a troll. If you don't need to split them into four groups, then there's plenty of leftover firepower.