In Prisoner of Azkaban, Hermione is known to take all 12 subjects that are proposed to students (among which 7 compulsory classes, and 5 optional classes, which are : Arithmancy, Ancient Runes, Care of Magical Creatures, Divination, and Muggle Studies). We learn at the end of the book that she has been using a Time-Turner to get to all of her classes simultaneously. Up until that point, it all adds up.
What doesn't make sense, though, is that at several points during the book, we see her having compulsory classes at the same time as optional classes. For example, at around page 135 (depending on the edition), Hermione disappears after a Potion class (during which she has helped Neville with his Shrinking Solution). :
"Five points from Gryffindor because the potion was all right ! Why didn't you lie, Hermione ? You should've said Neville did it all by himself !"
Hermione didn't answer.
Ron looked around.
"Where is she?"
Here, we can confidently assume that she turned back time in order to attend one of her optional classes. But that seems very unlikely, because it would mean that no other Gryffindor or Slytherin took that same optional subject. Indeed, students from the same Houses and same year always share their 7 compulsory classes (DADA, History of Magic, Astronomy, Potions, Charms, Transfiguration and Herbology), and sometimes share them with another House (for example, the Gryffindors share their Potions and Care of Magical Creatures courses with the Slytherins) - at least until year 6 (when they can drop core subjects). Which is why a mandatory class being at the same time as an optional one means that only Hermione takes this optional class. Which could maybe be true, although it seems far-fetched.
However, we come across other examples like this one on the following pages. On the next page, which is page 136 of the same edition (the current Bloomsbury one), and after exiting the Potions class, Hermione splits her bag because it is overloaded with too many books - books of subjects she can't have today - Ron assumes, because their only classes this day are Potions, in the morning, and Defence Against the Dark Arts, in the afternoon :
"Why are you carrying all these around with you?" Ron asked her.
"You know how many subjects I'm taking, said Hermione breathlessly. Couldn't hold these for me, could you?"
"But-" Ron was turning over the books she had handed him, looking at the covers "-you haven't got any of these subjects today. It's only Defence Against the Dark Arts this afternoon."
"Oh, yes," said Hermione vaguely, but she packed all the books back into her bag all the same.
So there again, it seems she has another optional course (that neither Harry nor Ron take) at the same time as a compulsory/core course (Defence Against the Dark Arts). Which would mean that she is the only one of the Gryffindor 3rd years taking that subject (whichever it is, Muggle Studies, Arithmancy or Ancient Runes). Which would mean that, in total, she is the only Gryffindor to take 2 of the 3 subjects that she takes without Ron and Harry. A bit more unlikely.
Again, at page 313, she misses Charms because - here we can only assume - she wanted to go to one of these 3 optional classes.
We know that she has Arithmancy and Muggle Studies on Monday, as we learn on pages 117 and 281 (respectively), and one of these 3 classes on Thursday (which is the day they have Potions in the morning and DADA in the afternoon) - just for reference.
And then, on page 335, we see Hermione's time-table for her exams, which says :
MONDAY
9 o'clock, Arithmancy
9 o'clock, Transfiguration
Lunch
1 o'clock, Charms
1 o'clock, Ancient Runes
(We can note that this time-table doesn't reflect on their regular time-table because they have Care of Magical Creatures on Monday afternoon and that course isn't in her time-table here, however they do have Transfiguration in the morning).
So yet again, we are proved that she is the only 3rd year Gryffindor student to take Arithmancy and Ancient Runes, because otherwise it would mean that other Gryffindors would need a time-turner in order to get to these classes, as they take place at the same time as compulsory classes (Transfiguration and Charms).
It tells us so because the fact that the exams of compulsory and optional classes are at the same time means that this schedule fits everybody's time-tables, except Hermione's (but as she can use a Time-Turner, that doesn't matter for the making of the exam time-tables), otherwise and again it would mean that she isn't the only one allowed a Time-Turner, which seems very unlikely as they can be so dangerous. AND it makes us assume that exams are taken by Houses separately (instead of all 3rd years of all 4 Houses taking the Transfiguration exam at the same time, for example), otherwise it would mean that she is the only 3rd year student to take Arithmancy and Ancient Runes, and as this would therefore mean she is the only student in the class, that seems most unlikely. But according to JK's descriptions in all the books, it seems that exams are taken at the same time by all Houses/students that took part in a particular class simultaneously (except for OWLs, as they're a bit more specific). So for example, the Potions exam for 3rd years is taken simultaneously by 3rd year Gryffindor students and 3rd year Slytherin students, as they attend that same class together during the year.
But in any case, even if exams are taken by 1 to 2 Houses at a time per subject, that doesn't explain why Hermione has compulsory classes (and exams) set up at the same time as optional classes, because again it would mean she is the only one in the House to take at least 2 of them, and the only one in the Gryffindor and Slytherin Houses to take 1 subject (which we can assume is the 3rd one, and which we could also assume is Muggle Studies, although that might be a prejudice against Slytherins).
So, does anyone know how to explain the simultaneity of compulsory classes and optional classes? Do you know if any of this already got addressed somewhere, by JK or someone else? I am very curious as to how it can be explained - or not.
