It was good that I learned about Percy's crush, because Tuesday worked out to us spending a ton of time in classes with her. Charms and transfiguration in the morning both happened to be the classes Gryffindor shared with Ravenclaw, arithmancy after lunch, and then the Gryffindors in arithmancy missed the normal history class that was up against arithmancy, so sat it with Ravenclaw and Hufflepuff. The only class of the day where we wouldn't see Penelope was mid-afternoon herbology with the Hufflepuffs.

I was honestly surprised I hadn't noticed the crush before, and maybe I was imagining things but I thought both that it was reciprocated and that their respective heads of house thought it was a good match. I definitely thought I was sending pretty definite looks at Flitwick and McGonagall that said, "Look at these two, aren't they so adorable and we should make sure they get together?" Maybe they thought I was just being weird, rather than giving me tacit permission to overcompensate for stealing Percy's dating mojo the day before.

When McGonagall set up the lesson for the day, I certainly thought she was sending me signals. "As a bit of a first-day review for OWL year, let's think back to one of the first transfigurations you accomplished as first years, where you transformed a matchstick into a needle. The reverse is actually far more complicated, if your changes are more than cosmetic. I'd like you all to turn a needle into a matchstick, which is capable of being struck to produce flame."

"Professor," I began, barely able to control my smirk, "I didn't actually cover this as a first year, so I may need some extra help. Can I partner with Percy and… maybe, Ms. Clearwater so I get a cross-house understanding of how this works?"

"If they're amenable," she allowed.

As we gathered around a desk, Penelope asked, "Why ask to work with me, Dresden?"

I shrugged, trying to look like it was no big deal, "Percy mentioned you were brilliant."

"He did?" she said, suddenly paying attention to Percy, who shrugged and was trying to keep from turning as red as his hair.

"Well you are, Ms. Clearwater," he said, without any sense that he was being anything but forthright. "Though I suspect Harry does not actually need much help from me."

I gave him a frown for being overly self-deprecating, even though he wasn't wrong, but said, "I assume you know way more about Gamp's laws than I do, after you were just rattling them off for our thought exercise last night. Transfiguring an inert object to a chemically complex one interacts with those, right?"

"Actually, yes," he admitted, suddenly off in magical wonk theory land. "In this kind of transfiguration, you are changing the iron of the needle into the carbon of the match, but the remaining chemistry is essentially conjured from raw magic. Otherwise, cancelling the transformation after the match burned could cause gaseous particles to change back into iron in a chemical configuration that does not make sense."

Penelope interjected, "But doesn't the smoke contain some of the carbon from the match? Wouldn't that part still change back to iron and cause similar problems?"

He lit up, "If it was a pure iron needle, certainly. I think that is why we use steel needles for the process, because the steel contains trace amounts of carbon in its structure. I would wager, if fully tested under controlled conditions, any carbon turned into smoke is either pure magic or the carbon contained in the steel of the needle."

"Which we could test by reverting the ashes of the match and seeing if they're pure iron!" said Penelope, excited.

I just grinned at the two nerds and mentioned, "Then let's figure out how to get the transfiguration to work, so you can move on to the fun, sciency part."

The process did prove to be somewhat tricky, with all three of us getting matches that wouldn't light the first couple of times, but each succeeding to McGonagall's delight by the end of class. Both of my lab partners were very intrigued by my practice of using chalk circles for transfiguration instead of a focus. Both also seemed delighted when, as they'd hypothesized, the ashes of the burnt matches reverted back to pure iron once de-transfigured.

After a quick lunch, the first arithmancy class was the most intimate teaching experience so far, much more similar to my previous schooling since there were only six students in the class. In addition to Percy, Penelope, and me, the other Gryffindor prefect, Alexis, and two Ravenclaw students were present. None of the other three were also taking runes, which I figured was a mistake because the classes were very complimentary. There were a small number of Hufflepuffs and a Slytherin taking the class as well, but they weren't there on Tuesdays due to a conflict with another class.

Professor Vector was a formidable, dark-haired woman who favored crimson robes. She had an edge of foreign pronunciation to her English accent, as if she'd been born elsewhere, maybe Russia. Her introductory speech was succinct, "Arithmancy OWLs are about the basics, so this year we will perfect them. You will prove that you are competent in algebra, geometry, and basic trigonometric functions that translate one into the other. You will diagram the spell matrices for the signature charms and curses taught in your other classes. You will be able to translate Latin with high proficiency, as well as some Ancient Greek. You will be able to hear the incantation and see the motions for an unfamiliar spell, and use that to estimate the likely results of casting the spell. Conversely, you will be given the desired effects of an unfamiliar spell and suggest the necessary gestures and cadence of the spoken spell phrase.

"This has all been a warm-up. While I want you to prioritize getting high marks on your OWLs, never forget that the first three years of this class are just to give you the tools you need for your real purpose. Next year, we start in earnest learning to improve and spontaneously adapt existing spells, as well as to create new spells entirely. If you're feeling confident and keeping up with your homework, I'm happy to help you get a head start on that process this year. It's the real fun of arithmancy, and I'm excited to get us there.

"But, for now, let's start our review of algebra."

As we were packing up, it was Penelope that approached Percy and mentioned, "I'm really looking forward to actually making spells. I may take the professor up on the offer to start early."

"Sounds like a really cool extracurricular project," I said, raising an eyebrow at Percy.

Percy looked like he was going to be stubborn, but accepted the hint after a moment and said, "What Harry is saying, is that we were talking last night about possible student projects that would look good on an application for something like the Department of Mysteries after Hogwarts. You would be more than welcome to be involved, if you have the time."

She bit her lip in worry, and said, "Do you think I'd actually have a shot?"

I was confused, but Percy seemed to understand, and said, "While their hiring practices and alumni are largely unknown, as I understand it, the Unspeakables are much more meritocratic than most of the other departments. Most of the jobs at the Ministry, as Harry bluntly brought to my attention, do not actually use much magic, so they tend to go to the better-connected. But as far as I know, everyone in Mysteries is extremely competent, so that makes it harder to get in just based on a family name."

That was a relief for the the apparently non-pureblood Ms. Clearwater, so she nodded, "I'm definitely up for discussing it. Let me know. I better get to creatures class, though!"

"We have to go to the greenhouses. Can we walk you out of the castle?" asked Percy, puffling up a little as he found the courage to be gallant.

"Why thank you, Mr. Weasley," she grinned.