19 Mathematics Rules!

That afternoon, Hermione nervously made her way to Professor Vector's office. Rose was accompanying her, as per her parents' instructions that she not be alone.

Hermione kept trying to reassure herself that she had nothing to fear, but all she could think was that if she made a mess of this, then she blew her only chance at testing into Arithmancy next year.

Along with her wand, Hermione was carrying a notebook full of notes she had taken over the break. Before she had left, Professor Vector had lent her a spare Arithmancy textbook for Hermione to read while she was away from the castle. Using her bracelet, she had read it several times and taken thorough notes. In her other arm, Hermione carried the textbook itself.

"You know, if you want, I can just make you a sack to carry your things," Rose said.

"I'm fine," Hermione replied. "You've given me enough already."

"So? WBL is just a guideline! No one actually listens to it!"

"What's WBL?"

"Wealth by Level."

"What's that mean?"

"It's the wealth that a single character is expected to have once obtaining a given level. Some adventurers end up higher, some end up lower. I hear the Door Thieves cracked because they were always so far below it."

"Do I want to know?"

"The Door Thieves? They're wonderful! They go around stealing random doors, cackling like lunatics!"

Hermione blinked a few times, furled her brow, and widened her eyes. "What?! Why?!"

"Like I said, they went bananas," Rose replied. She tilted her head to the side and gazed off into space. "I like bananas."

Hermione opened her mouth to complain, but then realized that the "Door Thieves" either weren't real or weren't her problem. Either way, she didn't have to care.

"Me too, Rose," she replied.

"Just use the seashell when you're done," Rose told her when they reached the Professor Vector's office. "I'll be in the library researching Nicholas Flamel if you need anything."

"Thanks, Rose," Hermione replied, and entered the room.

She found Professor Vector sitting at her desk, looking over some papers. She looked up as Hermione entered her office.

"Good afternoon, Ms. Granger," Professor Vector greeted her. She motioned to the chair in front of her. "Please, have a seat."

Hermione nervously took her seat, still holding both her notebook and the Arithmancy textbook that Professor Vector had given her at the end of last term.

"How far are you in the textbook?" she asked the young Gryffindor, indicating the book in the girl's hand.

"I finished it, Ma'am," she replied.

"Well, that makes this a little easier. Did you have any questions?"

"A few," Hermione replied, pulling out her notebook. "But many…" Hermione hesitated for a moment, not wanting to admit that she didn't know something. "Many of them might just be me misunderstanding calculus."

Septima did a double-take. She couldn't have heard that correctly. This girl was 11 for Merlin's sake! She shouldn't even know the term calculus! "You've learned calculus?"

Hermione nodded. "My parents know this college professor, and he gives me some of his older textbooks. I spent a lot of my break reading all the books I could, since Rose gave me this bracelet that lets me read books quickly."

"Define 'quickly'."

"I can just touch a book, say… 'boop' (Hermione groaned. Why did Rose have to pick such ridiculous command words?), and it's as if I had read it once."

"That's… interesting. I'm not sure I've ever heard of a spell like that. There are charms to copy text, but none to speed read a textbook. Did she say how it works?"

"No, she just calls it scholar's touch," Hermione replied.

Hermione knew that her crimson-haired friend was a bit different, and she had magic of which Hermione hadn't heard, but she assumed that it was just a kind of magic that they hadn't learned yet. Hermione didn't realize that it was actually unheard of.

"Hmm," Professor Vector hmm'd. "Did she say anything more about it?"

"Not really, although it gave me a headache at first," Hermione admitted. "I used it to read all my maths books, my Arithmancy book, and any other books I could find. Also… if you don't mind, I'd rather not discuss Rose."

Professor Vector furled her brow. "Isn't she your friend?"

"She is, but… Everything just comes so easily to her!" Hermione blurted. With the dam finally broken, the water came gushing out. "It seems like everyone always talks about her, and she's perfect at everything she does, and I've always been the clever one, but no matter how hard I try, I can't match her level!"

Hermione's face began to turn red. She was shocked that she had finally expressed that out loud. Ever since the Arithmancy seminar in the fall, she had been harboring resentment towards Rose for being so much better than her at maths. Up until then, Hermione had kept her spirits high by telling herself that even if Rose was better than her at everything else, Hermione could still outdo her in maths. It had always been Hermione's favorite subject in school, but finding out that Rose could do complicated calculations in a matter of seconds had been devastating.

"Hermione, I had a student a while back when I had just started teaching called Lily Evans. She was in Gryffindor, and exceptionally talented. She remains one of my top students, even now, and while she was here, she was made Head Girl in her seventh year."

Hermione nodded her understanding.

"I always assumed that everything was fine with her, since she came to class everyday looking cheerful and eager to learn. I later found out that she had all but lost touch with her family while she was here, as the First Wizarding War had just begun, and she was a Muggle-born. Ms. Evans felt that she couldn't possibly explain to them what was happening in our world. She was also being harassed by an awful group of Gryffindor boys, and her best friend, one of the Slytherins, had completely stopped talking to her after they had a falling out."

"That's awful!" Hermione exclaimed.

"Yes, but still, there she was, smiling away as if nothing had happened. My point, Hermione, is that you can't always tell by looking at someone how they're doing. Ms. Peta-Lorrum could be working just as hard as you, or could have already done the hard work that you're now doing. Considering that she was orphaned at the age of nine, and has apparently been living on her own thus far, I can imagine that she's got plenty of troubles of her own."

Hermione nodded. Truth be told, she was a little worried about ending up like this Lily girl. She was harassed by a group of Slytherins on a fairly regular basis, and she had found it difficult to explain to her parents about the troll and dragon. She hadn't told them about Professor Quirrell trying to kill Harry, assuming that it was Professor Quirrell, and she still wasn't sure about that. What would happen if she lost touch with them completely? She couldn't bear the thought of not talking with her family.

On the bright side, Hermione was pretty sure that she had some good friends here. She was worried about getting angry at Rose, but she knew from watching Professor Snape that it would take more than getting angry at the pale girl to drive her away.

"And besides, you've got two things that Ms. Peta-Lorrum lacks."

"What's that?"

"The first is discipline. Not only are you leaps and bounds ahead of Ms. Peta-Lorrum, but you've got far more discipline than almost any other student your age, which is quite impressive on its own."

"Thank you," Hermione said. Most of the older students had warned her that Professor Vector was strict, nearly as much so as Professor McGonagall, but Hermione was finding that the older witch was kind to her. "What's the second?"

"You're here, aren't you? Of the hundreds of students to pass through the castle, you are one of the few that I thought had the talent necessary to even consider testing in early."

"You offered it to Rose, too."

"I was bluffing," Professor Vector replied, traces of a smile coming across her face. "I was assuming that your friends, being Gryffindors, wouldn't want the extra work."

"Ronald still can't understand why I'd want to do more work than I've got," Hermione muttered.

"Ms. Peta-Lorrum may be talented, but I saw passion in you, Hermione. Maths isn't just something at which you excel, it's something you love. I haven't seen someone so enthusiastic about Arithmancy in many years."

Hermione smiled. "Thank you, Professor."

As the lesson continued, Septima continued to be astounded by the first-year's understanding of Arithmancy. Not only did she reference several sections of the book, reciting a few of them from the top of her head, she was doing computations much faster than she had a few months ago during the seminar.

"I've been working on memorizing my multiplication tables since the start of winter break," Hermione explained when Professor Vector asked her about it.

"And integrals, apparently," the Arithmancy Professor remarked. "I think you know these better than some of my third-year students."

Something occurred to the older witch. It was a little unorthodox, not to mention premature, but given the girl's current progress, Septima had confidence that it was a good decision. It was one of those decisions that she was certain she'd look back upon and be glad that she'd made it.

"Hermione, how would you like to sit in on my third-year Arithmancy class Monday afternoon?"

"Erm… I've got Herbology right after lunch."

"I'm sure if I ask Pomona, she won't mind if you miss just the one class, and your friends can inform you of whatever you miss."

"Rose does take an awful lot of notes," Hermione said.

Hermione knew that Rose kept her wand in her glove, as she had mentioned that before. What Hermione didn't know was what was stored in the other glove, although she suspected that it was that weapon her pale friend had used to kill a dragon on Hallowe'en. If that was the case, then Hermione had no clue where the girl kept that notebook of hers. It was as if it just popped into existence when Rose needed it and vanished when she didn't.

"I'd love to, so long as it's alright with Professor Sprout."

"I doubt it will be a problem," Professor Vector replied. "Pomona's quite understanding. I'll talk with her tonight about it."

"Thank you, Professor," Hermione said, smiling. "Thank you so much."

"I look forward to seeing you in Arithmancy, Ms. Granger."

As she left the class, she took a hold of the seashell, and sent a message to Rose.

<We're all finished here.>

"Did you have fun?"

Hermione jumped as her friend appeared next to her.

"Everything alright?" Professor Vector called from the classroom.

"Rose just startled me," came the reply.

"Salutations, Professor Vector!" came an additional reply. The crimson-haired girl subsequently poked her head in the door.

"Good afternoon, Ms. Peta-Lorrum," Professor Vector said politely.

"I'll see you Monday, Professor," Hermione called as the two girls left Professor Vector's office.

"So, how'd your lesson go?" Rose asked.

"It went great!" Hermione exclaimed. "She's even invited me to sit in on her class on Monday. Which reminds me, would you mind walking me there? I know it's a long way from the Arithmancy classroom to the greenhouses, but–"

"No problem!" exclaimed Rose. "I can just dim door!"

"That's what I thought," Hermione said.

Dim door, which Hermione had learned was short for dimension door, was Rose's transportation spell of choice. As far as Hermione could tell, the spell could transport Rose to any point on the grounds. Hermione had heard of apparition, which was similar to what Rose did, but it didn't work inside the castle. How Rose managed to get around that was beyond Hermione.

"Did you find anything in the library?" Hermione asked.

"No, Madame Pince made me leave," Rose pouted. "I don't think she likes it when I send a bunch of prying eyes around the library."

Hermione nodded. As much as she loved the library, the Librarian scared her. Not only was Madame Pince was strict, she didn't seem to like people actually using her library. It seemed like an odd trait for a librarian to possess, but it certainly wouldn't be the first odd thing at Hogwarts.

Not to mention Rose's tendency to get on peoples' nerves without trying.

As they walked off, Hermione realized that that was the second time she had heard about Lily Evans. Professor McGonagall had mentioned something about her back in October.

"Hey, Rose?"

"Yeah, Hermione?"

"Have you ever heard of a girl called 'Lily Evans'?"

"I think Professor McGonagall mentioned her."

"Yeah, she did. I was just asking because Professor Vector mentioned her too."

Rose pulled out her notebook and wrote down "Lily Evans". "Thanks for letting me know, Hermione. Any character mentioned more than once is probably important."

"You're welcome, Rose."

Rose watched as Hermione paced back and forth across the Room of Requirement. It was early Monday morning, so early in fact that the sun wasn't up yet. Hermione had been so stressed out that she couldn't lie still in her bed after she had woken up.

Rose, being a responsible and caring friend, had suggested that they go hang out in the Room of Requirement. Because she thought her friend could use additional support, she had set it to become her crafting room so Inar could keep them company.

"Just to recap," the crimson-haired girl said. "Professor Vector is letting you sit in on her third-year Arithmancy class this afternoon, and you feel like you're going to make a fool of yourself."

"That about sums it up, yeah," Hermione said frantically.

"Okay," Rose said, getting up. Serendipity appeared in her hand. "I can fix that."

"I don't think any of your tricks are going to help."

"Of course they will!" Rose cried defensively. "I can fix anything!"

Serendipity vanished into Rose's glove as an idea popped into her head.

"You know what always calms me down?" Rose asked.

"I'm not sure I want to know," Hermione muttered.

"Dancing," Rose said, extending her hand to Hermione.

Hermione looked from Rose to the girl's hand, and back again. "Seriously?"

"Yup!" Rose exclaimed, cheerful as ever. "My parents taught me how to dance, and it reminds me that they're always watching over me. Carolina says it keeps my mind and body focused on one nondestructive task so I can't think about whatever it is that's bothering me!"

Hermione considered this for a moment, taking note of the word "nondestructive", then decided she might as well. Hermione hesitantly took Rose's hand, and the crimson-haired girl began to lead her bushy-haired friend in a waltz.

"Wow," Hermione said. "I'm not sure why, but I wouldn't think that you'd be a dancer."

"Loved it since I was a little girl," Rose replied. "Intradora."

"What's that mean?"

"It's Illumian for intelligence. Intradora."

Hermione began to feel funny. Her head was starting to tingle. The feeling was familiar somehow.

"Intradora."

Hermione remembered when she had felt this way. It was when she had first attached the hair clip to her hair, or when Rose had used that spell back in December.

"Rose, what are you doing?"

"Dancing!"

"No, every time you say 'Intradora', my head tingles."

"Oh," Rose replied. "I'm using Serendipity to grant you an inherent bonus to your Intelligence. Intradora."

"What does that mean?" Hermione was starting to feel dizzy. It didn't help that she was moving around while this was going on.

"Feeling faint?"

"Yeah; how'd you know?"

"It's a side effect of a sudden increase in Intelligence," Rose replied. "Just focus on me and where your feet are supposed to move next."

"I'm not even sure how I know what to do," Hermione said.

"You've probably seen it once or twice," Rose said. "Information doesn't leave the brain, it just becomes harder to get at, and I've just made it easier for you to recall it."

Hermione's head was starting to feel better as she adjusted to her now increased intellect. It still hurt a little as information flowed through her mind seamlessly.

"I used wish to give you a +4 inherent bonus to Intelligence. It means that you are now permanently smarter, which will make it easier for you to not make a fool of yourself in Arithmancy today."

"How is it scaled? What does +4 mean?"

"If I had to take a guess, I'd say you started this year with about a 14 in Intelligence. That's a +2 modifier. On average, a Human has a 10, which is +0. With the hair clip, your score was increased to a 16, giving you a +3 modifier. I just increased your score to a 20, giving you a +5 modifier."

Hermione thought about that for a second, then nodded. "I guess that makes sense." Many ideas occurred to Hermione, although one in particular held her attention.

Ms. Peta-Lorrum could be working just as hard as you, or could have already done the hard work that you're now doing.

"Is this what it's like for you all the time?"

"I've got a 40 in Intelligence," Rose replied. "Artificers need it for our infusions, so it determines how often I can use Serendipity. At Character Creation, I put an 18 into Intelligence. I get +10 from my circlet, +5 inherent, +5 from levels, and +2 from Greater Visage of the Deity."

The numbers worked themselves out in Hermione's head with almost no effort on her part. She began the computation with what she knew: 10 was +0, 14 was + 2, and 20 was +5. That meant the modifier increased every two steps, starting from ten. Rose had a 40, which meant it would be (40 - 10) ÷ 2, or 15.

"So you're three times as smart as me," Hermione said, astounded by how effortlessly her mind had just run the computation. "If the modifier is the important part, then you've got a +15, and I've got a +5."

Hermione typically took everything Rose said with a grain of salt, but Rose had just used magic to make Hermione cleverer. She wasn't sure if, or when, it would wear off, but for the moment, it had actually worked. Hermione was able to think faster, and ideas of which she wouldn't have otherwise thought were popping into her head. She realized that Rose had said "permanently", so it probably wouldn't be wearing off.

"Try not to think anything of it," Rose said. "My circlet is a workaround, or in some circles, a cheap trick, to get around the inability to craft anything with higher than a +6 enhancement bonus. The standard technique for crafting an item with an enhancement bonus becomes unstable if you try to craft anything above a +6. It might work, but it will most likely collapse if you try."

"With you so far," Hermione said.

"To get around this, I convinced my brother to research the spell divine agility, which gives the target a +10 enhancement bonus to Dexterity. He created divine enlightenment, which gives a +10 enhancement bonus to Intelligence. It costs about twice as much to enchant an item with it continuously rather than using the standard method, but as previously stated, the standard method doesn't work for that high of a bonus."

"Makes sense."

"I'm also level 20, which is the absolute maximum of the official scale set forth by the Personnel Handling Bureau, or PHB, so I've got high scores to begin with. They're the ones that invented the entire scale I just explained to you. The idea was to standardize equipment and make rating adventurers easier." Her face lit up. "If you want, I can give you bonuses to your other scores too!"

"Thank you," Hermione said, "but not just now."

Hermione didn't even want to think about what would happen if Rose did that. Of course, given her now improved mental capabilities, she was thinking about it anyway.

As the girls continued dancing, Hermione was finding it easier to concentrate her thoughts. Rose had been right; it was calming her down to dance, thus occupying both her mind and body.

With Rose accompanying her, Hermione made her way to Classroom 7A later that day and took a seat in the front of the class. She was 20 minutes early, and there was no sign of Professor Vector yet, so she sat down and began to go over her notes one more time. Not that she needed to, of course, as she had already memorized them all. Despite the feeling of dizziness she had had all day, Hermione was feeling wonderful. In Transfigurations class that morning she had managed to use Avifors to turn the block of wood they had received into an entire flock of birds on her first try, receiving 10 house points for her work. Ron had glared at her, but Rose and Sally-Anne had both complemented her, not to mention the look of pride that Professor McGonagall had given her.

Rose's spell had worked, and it hadn't worn off after a few minutes like the last one. As the day progressed, Hermione remembered more information from books she had read over the break. She could recall nearly all the information from her calculus book, and she could recite entire chapters out of her Arithmancy book. Maybe Rose was right; maybe she could fix anything.

"Excuse me?"

She looked behind her and saw a boy walking in the classroom. He wore a Hufflepuff crest on his robes, and reminded Hermione a little of Percy, in that he was in the 99th percentile among the boys in the school in terms of how well kept he was. He had brown hair, slightly darker than her own, and a kind smile. Everything about him was neat and tidy, but it was different to how Percy always looked. Percy walked around with an air of arrogance, while this boy had a more kindly manner.

"I hate to bother you," the boy said politely, "but we've got class in here soon. If you need a classroom, I think 7C is unused this time of day."

"I'm…" Hermione hesitated, a little nervous around the older student.

It's alright, Hermione, they're students too. They're only two years older than you. There's nothing to be worried about.

"I'm here for Arithmancy."

"I'm sorry?" the boy asked.

"Professor Vector invited me to sit in on the class today."

"Oh," the boy replied.

He looked shocked at first, but it faded quickly. He sat down next to her and extended his hand.

"I'm Cedric, by the way. Cedric Diggory."

"Hermione Granger," Hermione replied, shaking his hand. "I'm a first-year."

"Wow," Cedric replied. "I didn't think Professor Vector let anyone in early, especially not two years early."

"Oh no, I'm not in the class. I've been taking an independent study with her this term, and she wanted me to sit in on an actual class."

"Still, you must be something special for her to let you sit in on a class."

"I'm–"

"Ms. Granger, good to see you were able to make it," Professor Vector said as she entered the room. "And Mr. Diggory has naturally introduced himself already."

"Good afternoon, Professor," Cedric said. "How was your weekend?"

"Filled with excitement and maths, just the way I like it," the professor replied. She spread out some papers on her desk, and began to write a problem on the chalkboard as more students filed in.

"Good afternoon, class," Professor Vector said once the rest of the class arrived. "As many of you have noticed, we have a student sitting in on our lecture today. Everyone, this is Hermione Granger. She's currently undertaking an independent study with me, and I have asked her to sit in on our class."

As Professor Vector began her lecture, Hermione regretted her position in the front of the classroom. She hadn't thought about it when she had taken her seat, instead acting on instinct and taking a seat in the first row. Now she heard whispering behind her, and began to lose confidence in her decision to sit in on class. There she was, alone with a bunch of third-year students, and attention had already been drawn to her.

Despite her initially not wanting her friend to be there, Hermione now found herself wishing that Rose were there with her. She was no longer worried about Rose being more clever than her, because Professor Vector had been right; Rose had already done all the work with magic, and now it was Hermione's turn to excel.

Rose had a tendency to draw attention to herself, which meant it was off other people. Hermione found herself wondering if that was part of the reason that Harry hung out with them. After all, so long as he was around Rose, people paid less attention to him, which seemed to make him happier.

Professor Vector began the lecture, which, as Hermione had been forewarned, focused on the study of polynomials.

"To start us off, can anyone tell me what a polynomial is?" Professor Vector asked.

Hermione flinched, nearly raising her hand, but reminded herself not to speak up. She was just here to watch, and… wait, why was she there, exactly? What purpose did her being there serve? Was it just to experience a lecture? If she sat there like a wallflower, what did she gain?

Hermione didn't really want to speak up, but she also didn't want to waste Professor Vector's time.

While Hermione was preoccupied with questioning her purpose in the classroom, another student had raised her hand.

"Ms. Gamp, no doubt you've got an answer for us."

"A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents."

"Well done, Ms. Gamp."

Hermione had heard that name before. It took her a second to remember, but then she realized: Gamp's Law of Elemental Transfiguration. Hermione didn't realize that a member of the Gamp family was in Hogwarts, much less the third-year Arithmancy class.

Hermione's hand slipped inside her pocket, and she grasped the blue seashell that never left her person.

<Rose, there's a Ravenclaw student with the surname 'Gamp'. Do you know her first name?>

There was a pause, during which Hermione swore she heard pages turning, then, <Rebecca.>

Hermione didn't bother asking how Rose knew the girl's first name; most likely, she had heard it by chance, or Reflectesalon had gleamed it from someone's mind.

<Thank you.>

Rebecca Gamp. It was good to know her name. Maybe they could be friends.

"Now, one of the important parts about polynomials is finding their roots, that is, the solutions of the polynomial when set to zero." Professor Vector wrote "x2 - x - 20 = 0" on the board, and turned to face the class. "Ms. Granger, why don't you give this a shot?"

Hermione paled. Now not only was she being given a problem, it was presumably one that they hadn't worked on yet.

"Roots at negative four and five, Ma'am."

That was a mistake. Even Professor Vector looked astounded at how fast she had done that. Several of the students behind her started whispering to themselves, and shortly after that, Cedric raised her hand.

Oh no, Hermione thought, shrinking a little in her seat.

"Yes, Mr. Diggory?"

"I think it's going to be hard to hear you with everyone else talking."

This time, it was Hermione's turn to stare at someone in astonishment. She hadn't been expecting any of the other students to actually take it easy on her, much less stand up for her.

"Quite right, Mr. Diggory," Professor Vector said, glaring at the other students.

The whispering faded, and Hermione realized that she was still staring at Cedric. She quickly turned her head down, her face turning red.

"Thanks," she whispered.

"Don't mention it," he replied. "Hufflepuffs stand up for everyone, not just each other."

"Ms. Granger, would you please walk us through how you did that?" Professor Vector requested.

"It's the quadratic formula," Hermione explained. "X equals the opposite of B, plus or minus the square root of B squared minus 4AC, all over 2A, where, in this case, A is 1, B is -1, and C is -20. After that, you just have to solve it."

"Excellent," Professor Vector said. She began to write out the formula on the chalkboard.

"Did you do that in your head?" whispered Cedric.

"Yeah," replied Hermione, realizing that she really had done it in her head. The computation had been so seamless that she hardly noticed that she did anything. Upon looking at the equation, she had called up the formula, plugged in the variables, and her brain proceeded to solve it practically on its own.

"Wow. You really are something special."

Hermione was thankful that Professor Vector hardly called on her the rest of the class, saving her from having more attention drawn to her.

After the class was over, Professor Vector asked Hermione to stay after for a few minutes.

"I take it Ms. Peta-Lorrum has taught you a few of her tricks?" she asked the first-year.

"Sort of," Hermione replied evasively. She wasn't sure if it was alright that she was using magic to make herself smarter. "You were right, Professor. She's spent a lot of time working on being that clever."

"There's always more to learn, even about people," Professor Vector agreed. "Well, whatever the case, I'm quite impressed with your performance today. I can safely say at this moment that you should be looking forward to taking Arithmancy next year."

Hermione's eyes grew wide. "Really?"

"Absolutely," Professor Vector replied, smiling. "I'll see you Saturday."

Hermione left the room, and was ambushed by Cedric and two of the other students.

"That was amazing!" a boy called 'Davies' exclaimed. "How'd you do those problems so fast?!"

"It's cos my Hermione's the smartest in the land!"

"Ah!"

The three older students jumped back as Rose appeared, putting her arm around Hermione, who had just about grown accustomed to Rose popping up at random.

"Hey, Rose, how was Herbology?"

"Meh. Plants. How was Arithmancy?"

"Wonderful!"

Rose beamed.

"Who are you?" asked Davies.

Rose turned to face the other students. "Salutations! I'm Rose! Rose Peta-Lorrum!"

As always when introducing herself, she curtsied.

"Cedric Diggory," Cedric said, extending his hand to her. Rose shook it, and turned to the others.

"Roger Davies," Davies said, waving casually.

"Rebecca Gamp."

Rose noted that there was a look of slight contempt on Rebecca's face. Rose knew that look; it was the "You're threatening my position in class" look. She made a note to watch this Rebecca girl.

"We've all got to get going," Cedric said. "It was nice meeting you both. Hope to see you soon!"

"Bye!" Hermione called back as Rose waved.

Hermione walked quickly back to Gryffindor Tower. Now, she had a lot about which to tell her parents.

Dear Mum and Dad,

I'm so sorry for not writing you yesterday, but you won't believe what's happened! The start of the term has been going alright. I found out that Ron's really good at chess, and Rose gave Professor Snape an amulet that makes him scarier (I don't know why).

But most importantly is my progress with Arithmancy. On Saturday I had my lesson with Professor Vector (Rose walked me there, don't worry), and she was impressed by how well I've been doing over the winter. She even invited me to sit in on class today!

This morning, Rose and I went to the Room of Requirement, since I was really nervous, and Rose was trying to help. Apart from the hair clip, Rose can actually make people smarter with magic! I felt faint at first, sort of like when I attached the clip, but after my head started to clear, I was able to remember random things that I had only ever learned once!

Professor Vector was really impressed with how well I did in an actual class. I kept up with her during the lecture, and answered questions that even some of the other students didn't know. Afterwards, she said she would allow me to test into Arithmancy next year! I can't wait!

Lots of Love,

Hermione