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This is a "Wild Mass Guess" entry, where we pull out all the sanity stops on theorizing. The regular entry on this topic is elsewhere. Please see this programme note.
The Night Circus
Wild Mass Guessing
The man in the grey suit (A.H) is actually Merlin when he meets with Widget at the end, Widget can see he has an extraordinarily long past and the man in the grey suit insinuates that he used to be a romantic but has lost interest in things hinting that it did not go well for him, which fits in the Merlin tree story. If he's been competing with Hector Bowen for a truly long time, that might place Hector as someone important too. They both founded their schools of magic/thought.
Alternatively, A.H is Slenderman . After all, The only things noted about him are that he's outlandishly tall and wears a dark suit.
Alternatively, maybe Hector really is Prospero and A. H. is Ariel, considering that the story makes frequent references to Shakespeare and the power of storytelling, and even quotes Prospero's final monologue.
Alternatively, A.H. is Andrew Hussie's Author Avatar, AH. He's mysterious and, though he seems detached from the rest of the cast, is the one responsible for the story's existence and more integral to its events than many of the characters will ever know.
I've been wondering about Hector's age. We know that he's one of A. H.'s first pupils, but that doesn't neccessarily SAY much - after all, who knows when A. H. actually started teaching? So, time for some wild-assed assumptions!
Lower bound: There have to have been at least three previous challenges because A. H.'s last student won, but the overall record leans in Hector's favour. We also know that A. H.'s teaching takes until just before a pupil turns 19 and that the challenges have become steadily more complex. The 4th challenge takes 10 years, if you disregard the initial teaching. Assuming that each challenge doubled in length and that finding a new student only takes a year, that means they would have been at this for ((10+19)+1+(5+19)+1+(2+19)+1+(1+19)+1) = 98 years; further assuming that Hector broke with A. H. immediately after his own schooling was over, that would give 117 years as a semi-reasonable lower bound for his age.
Upper bound: A. H. had to derive his entire system first before he could begin teaching, but let's assume he's an incredible prodigy and/or had earlier sources to work from, such as they were. Hector wasn't his first pupil, but he could've been the second one - that would make Hector's age roughly Alexander's age minus 45 or 50 years.
So, all in all, we have a range from 117 to millenia. ... any thoughts?
The lower bound is much higher than that: When A. H. and Hector speak on the night Theissen was killed A. H. says that seven of Hector's students have chosen to kill themselves to end the game in the past, and with the odds leaning in Hector's favor overall that means that the challenge must have occurred at least fifteen times before The Night Circus.
Also, the previous challenge ended eighty-three years, six months, and twenty-one days before Celia and Marco's did—a bit more than one year between them.
Also also, it's stated that the previous challenge lasted for 37 years.