Weeks of regular days passed without note, and with a start she realized it was almost time for the visiting schools to arrive.
Everywhere around the school, people were anxiously awaiting the arrival of Beauxbatons and Durmstrang, paying much less attention to learning magic than to the thousands of rumors circulating through the school.
While passing her fellow students, she heard such riveting news as, "I've heard that Beauxbatons and Durmstrang are the only magic schools on the continent, and Durmstrang requires all of their students to serve in a magical militia after graduation."
She was leaving potions class one afternoon, and overheard Daphne Greengrass say to Pansy Parkinson, "Did you know that Beauxbatons witches have an entire course dedicated to love potions and charms?"
Hermione snorted at that one, getting glares from the two witches. She hurried away, trying to avoid an altercation with Snape so close. She was still keeping her head down in that class, making sure Snape didn't catch her eye. He was probably infuriated that he had nothing to dock from her potions, for she never handed in an imperfect potion.
Another one she heard in the great hall. "Oh yeah, Durmstrang's in the middle of the black forest, and it led all the students to become dark magic practitioners."
Despite Hermione's resolve to stick by Harry during her first go-rounds, and trying to cement his friendships with his other year mates, Hermione found herself retreating more and more to the privacy of her "workroom."
Hermione had warded a nice little abandoned classroom for herself, where she could work on her potions and exercise without being interrupted. The age-altering potion had finally reached it's last stage of experimentation, and her arithmancy equations convinced her it was time to brew it.
She tried to tell herself she was using her time wisely, working on experimental potions to fool Poppy's inquisition, but she eventually had to admit that she was also creating the potion out of enjoyment. She had never had as much free time in her life to experiment and study; the possibilities were limitless. In her spare time, while brewing, sitting through classes, or between classes, she started running arithmancy equations in her head.
She couldn't actually cast the spells without writing it down, of course, but she could analyze all the elements and organize her thoughts so that when she did get ink to parchment, she would take less than a minute to have her answer.
And through these calculations, she started to realize a disturbing trend. It didn't matter what task she was analyzing (finding the cup, retrieving the locket, or even the confrontation with Voldemort) - her calculations were coming out wonky. One day her odds of success were in the eighties, and the next day they were so close to zero that she had to re-evaluate the equation several times before assuring herself that her math was correct.
She couldn't figure out, then, why her calculations weren't working. The only conclusion she could think of was a change in the data, but surely nothing had altered catastrophically. Hermione had worked hard to keep herself out of the big events, the events that could alter the timeline.
She eventually gave it up as a bad job; clearly there was something missing from her equations, and she would have to give it time before the new elements came to pass.
Her lack of success was made up for in other areas. Her age altering potion was a great success, and she had successfully gone to Poppy without the woman realizing her true age (she was almost sixteen and two months, now, although only one real month had passed), and she had a good stock of everything from Thanalos to Polyjuice.
She had enlisted Sirius and Dobby's help in locating Hufflepuff's cup, after some hesitation on Sirius's part. Hermione had briefly hoped Sirius would be able to check the Lestrange vault, but Sirius was less than confident.
"Oh yeah sure, Hermione. I'll just walk in, ask to go to the Black Vault, and hopefully they'll let me just nip over to the Lestrange vault to get dear cousin Bella's ancient magical artifact. And they'll overlook that I'm a fugitive, maybe they'll even crown me their king since they'll love me so much after that."
Hermione sighed, letting Sirius rant as she stirred a Wolfsbane potion idly. Remus had moved in with Sirius, after Hermione had remembered that he would still be living in relative poverty due to his Lycanthropy. When Remus replied saying he wouldn't endanger Sirius like that, Hermione demanded he go, and she'd make his Wolfsbane every month. "Listen, Sirius, I need that cup. I know it sounds ridiculous."
She paused, for Sirius had given a snort so loud it shook the mirror that was balanced on her worktable.
"It sounds ridiculous, but I have a really strong feeling that this is one of Voldemort's horcruxes. I have no idea where else it could be." She was starting to be very concerned about the whole thing. Even if it wasn't in the Lestrange Vault, how could she hope to find it?
Sirius rubbed his eyes, looking tired. "I can ask Kreacher to look into it, Merlin knows he saw more death eaters than I did. I think he might've even met Voldemort, once."
"Brilliant, Sirius. Thank you. I've already got Dobby looking for it, but Kreacher knows anything, that'd be quite helpful."
Her progress on the ring was similarly stalled, as was Nagini. And Hermione was still torn on how to deal with Harry's horcrux. She had a few ideas that she'd tried to run through her arithmancy equations, but they were still less than reliable.
The arrival of Beauxbatons and Durmstrang passed uneventfully, although Hermione did get to engage in conversation with the French speaking students, and Harry gave German a good try. Hermione was almost fluent in French, but the Beauxbatons students sitting at the Ravenclaw table still managed to find flaws in her grammar and pronunciation.
Still, they seemed to respect her more than they had last time, and Hermione wasn't about to turn away any potential allies. The two students she spoke with most, twins named Margot and Anton, were very skeptical of Hogwarts, judging by their disapproval of its visual appeal.
"It was a castle built for defense, first and foremost," Hermione explained in French, "and rooted in tradition. We did not have a taste for finery, like how you describe Beauxbatons."
Margot gave a very delicate snort. "That is evident. It does explain the differences, however. We have our traditions too, but unneeded things should be disposed of. Like this ugly metal," she gestured at a suit of armor that had clearly seen better days.
"Oui, we would tear that down and make something beautiful. Give it new life." Added Anton.
Hermione gave a tight smile, deciding their slights to Hogwarts were superficial; not worth arguing. It was a lesson she definitely hadn't learned when she was actually fifteen years old.
She headed to Arithmancy with their words swirling around in her mind. They made her think of something, but she couldn't quite figure it out. Give it new life, they had said. It was a loaded phrase, considering the proximity to Voldemort's rebirth. It was troubling. Her mind stayed fixed on the phrase throughout Arithmancy, where they were incorporating tables with three known elements and one unknown variable. Child's play, for Hermione, but she was used to setting webs with twenty or more variables.
She found herself returning to the same variables she had been dealing with all year: her odds of survival in retrieving the cup and the ring, balanced against any variables that could stand in her way. Before she knew it, she had listed out ten or more "obstacle" variables, including Snape (if he read her mind), Dumbledore (if he disagreed with her choice of action), the Ministry (if they caught her for underage magic), the horcruxes themselves… the list went on.
In a short time, she had reconstructed the exact same schema she had been writing for months, and was still getting uncertain answers. It was infuriating.
She sat back, glaring at the parchment as if it had caused the problem. The words of the twins, Margot and Anton, returned to her: Unneeded things should be disposed of.
Hermione suddenly saw her schema in a new light. Maybe it didn't need to be so complex, so filled with potential obstacles. In fact, maybe there were more allies than obstacles.
Getting a fresh piece of parchment, she started making much simpler schemas. Her survival rate, against the horcrux itself and its compulsions – that little equation gave her a 40% chance. But her survival rate, paired with her occlumency skills, against the horcrux- that gave her a fifty. So if she was occluding, she would be 10% more likely to beat the ring.
And as a test, she threw in the other "obstacles," but stacked them on her side instead of the horcrux's. Dumbledore as an ally gave her a sad 33% (but he had trouble with the ring on his own), Sirius a 60%, Draco 65%. Dobby's aid raised it to a surprising 70% - her best yet. She cast the spell again, the simplified situation with her and Dobby as a team, and got 70% once more. This was brilliant! Better luck than she had in the last month with her Arithmancy.
With this in mind, she balanced the full equation once more, adding Dobby as her ally and the rest as obstacles – 69%. She cast it again, just to see if it would waver again – 55%. Dammit, she was hoping this was the solution. Apparently she was missing a variable still, or she would have a consistent number. A third cast (just in case) returned her to 69%. What was she missing?
The class ended, and Hermione was left thoroughly unsatisfied with her arithmancy equations. She looked at Septima Vector, who was dismissing the class and collecting their work (Hermione had finished it in the first ten minutes). Vector had a brilliant mind for this sort of thing, and while she clearly couldn't share the context of her question, she might get some insight from it. None of her classmates were surprised when she walked up to the professor's desk.
"Professor Vector?" Hermione asked, grabbing her attention. "I was wondering if you could help me with a bit of extracurricular research."
Vector smiled kindly, used to Hermione's questions by now. "Of course, dear. What are you working on?"
"Well, I know we haven't started doing analysis on personal situations yet, but I was wondering if you know why a problem would have different percentages when casting."
Vector looked surprised. "Miss Granger, we won't be covering personal likelihood equations until sixth year, as you very well know. How much have you been working outside of class?"
Hermione blushed. "It's my favorite subject, Professor. I just can't keep myself from trying everything."
"I felt quite the same, when I was here. It's a powerful subject. So I'll give you a bit of advice, Hermione. Arithmancy can only take you so far. It relies on your knowledge of the world around you, and especially in a personal schema, you can't ever be certain of the outcomes. It's much easier to define the variables when you are aware of the scope, which is hard to tell when other people are involved. It's even harder to tell if they're someone you don't know very well. The different percentage could be a misjudgment of character on your part, a missed variable, or even a whole concept you're missing."
She gathered the papers on her desk, and they made a loud thunk when she hit them against the table to align them. "Don't live in equations, Miss Granger, and ignore the world around you. Sometimes the answer is outside."
AN: I didn't mean for Vector to get so philosophical, but there you go. Hope you enjoyed this chapter! In the next chapter, a lot of things are about to change.