Ah, the great Quagmire mystery.
I agree with Foxy that the Q's can't have been at Prufrock before the fire, because of the orphans' shack; I also think you can't really solve it by changing the length of semesters, because semester by definition means half a year. You can have more than two academic terms in a year, but wouldn't be semesters. (I mean, Prufrock Prep is so odd that if they decided a semester was three weeks we couldn't stop them; but I don't think we should go for such extreme solutions if we can avoid them.)
If Quigley were lying one would expect this to be revealed at some point. The real-world explanation is no doubt to suppose that DH changed his mind; how to work out an in-story explanation I'm not sure.
Hermes! Thank you!!!! I think that too! I'm going to look for the semester definition on M-W and I'll be right back.
Definition of semester:
1: either of the two usually 18-week periods of instruction into which an academic year is often divided
2: a period of six months.
In Lemony's letter to the editor at the end of TMM, Lemony states that the Baudelaires spent half a year in Prufrock Prep. If Hermes is right, the history of TAA happened between 63 to 90 days.
I've never spent a lot of neurons thinking about when the Ququimire fire happened ... But I'll try to write now, to see if it's possible that both the Q mansion fire happened before the B mansion fire and what Quigley said is true. (You will witness my way of thinking about something.)
So for all the facts to be true, the fire of mansion Q must have happened before the fire of mansion B. Let's consider this to be true.
We need to consider that Quigley stated that he spent an unknown period of time inside the tunnel before finding Uncle Monty's house. By the time Quigley arrived at Uncle Monty's house, the Baudelaires had already left.
For what Quigley said to be true, it must be that the length of time that Quiglhey spent inside the tunnel had been considerably long for the following facts to happen: the time between the Q mansion fire and the B mansion fire itself fire of mansion B, the time the Baudelaires spent Mr. Poe, the time the Baudelaires spent with Olaf, the time they spent with Olaf, the time they spent with Uncle Monty.
The question is, did Quigley have water and food inside the tunnel? I don't know I'll look and come back. I returned. There is no indication that Quigley had food or water inside the tunnel. Unless he's lying about the origin of the backpack he has. But we are considering the hypothesis in which Quigley spoke the truth. So the conclusion is that for Quigley to be telling the truth, and the fire had to have happened after the Baudelaire Mansion fire. Then comes the chance that he was lying about the chronology, or the way he survived the fire. But we have reached a dead end: there is no reason for Quigley to lie so specifically. Quigley's account is detailed, and he even reports on physical evidence of where he had been. So honestly speaking, Quigley doesn't seem to be lying.
If Quigley is not lying, then the Q mansion fire happened at the time of the events recorded in TRR or shortly thereafter.
So we need to check because we believe the fire might have happened before the B-mansion fire. Maybe we just misunderstood what was written.
1 - The Q's were at Prufrock Prep for three semesters; "Is it possible that part of that time they spent in normal dorms, and they went to specially designed facilities to accommodate orphans after they actually became orphans?" Answer: No. They said that they spent three semesters in the referred facility for orphans.
A hypothesis arises: and I will resort again to an outlet that I have frequently resorted to.
Daniel Handler duplicates events to confuse you. Q's parents died twice. Once a lie, when they faked their own death or were presumed dead. Anyway, the death was not real.
At this time Ducan and Isadora went to Prufrock Prep. The Q's parents' first "death" was the Quaquimire case to which Lemony's illustrator referred, and it must have been when Olaf tried to steal the emeralds earlier. Later, when their parents revealed they were alive, Ducan and Isadora returned home.
The fire happened, and the parents died again, this time for real. Isadora and Ducan returned to Prufrock Prep again. I think this is the best explanation so far. Interestingly, Daniel Handler must have thought of something like this when he published LSTUA. It was not just a careless change of mind. He actually thought of something, as he put the remark made by Lemony's illustrator when he published LSTUA, which was close to the time he published TSS. Then that's it.