Qiaochu_Yuan comments on Harry Potter and the Methods of Rationality discussion thread, part 19, chapter 88-89 - Less Wrong
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When I first read the end of the chapter, my thought was that Quirrell hadn't arranged the incident; he had thought it was a "surprisingly good day" which suggested to me that he hadn't expected the troll.
After reading comments, I became less sure about that; someone suggested that Quirrell might have simply not intended for Harry to be at the scene and in danger. This seems plausible, but one thing still makes it difficult for me to believe it was Quirrell.
The troll had been enchanted against sunlight:
And Harry transfigured part of the troll:
But before, it was stated that Quirrell could not charm something that Harry had Transfigured:
For Quirrell to have been behind this, I can see only two possibilities: 1) Harry can transfigure something Professor Quirrell has cast spells on, even though Professor Quirrell can't cast spells on something Harry has transfigured, or 2) Quirrell had a confederate (or imperiused lackey) cast the appropriate spells.
If you go with option 2, the increased complexity makes it less likely that it happened (though not necessarily less likely than a given alternative).
Harry transfigured the inside of the troll. Maybe Quirrell only needed to enchant the outside?
Or that the enchantment is somewhat less fixed to the body of the troll?
Or Harry and Quirrel might be wrong about how their magic can touch? Harry never exactly knew the boundaries. He has only the sense of doom and the resonance from the Avadakedvra - Patronus interaction.
He touched it. In chapter 56 or 55, I forget which, Harry had to wear a glove to ride the room that Quirrell enchanted. In chapter 89, he picks up the troll by the ear.
I don't think that Harry actually knows for sure that he couldn't touch the broom.
Good point, I missed the picking the troll up by the ear entirely.