With the Hogsmeade trip behind me, I turned my full attention back to the project I had been working on all year. The Firebolt spell, I was so close to completing the spell, I could almost taste it.

All I needed to do was find the perfect wand movement, and it would be finished. But, as I discovered, finding the right movement was just as if not more difficult as finding the right incantation.

I tried out hundreds of wand movements, each of them failures. Most fizzled out harmlessly, but others were a bit more dangerous. The worst nearly took my head off as it caused an old broom to explode violently.

I got so obsessed with wand movements that soon, it was all I could think about. I even started dreaming about them when I was sleeping.

"Alex," a voice hissed, bringing my thoughts back to the present.

Startled, I blinked rapidly and saw Jessica nodding toward the front of the classroom where Professor Sinistra was looking at me with an expectant expression on her pale face framed with long dark hair.

Having drifted off, I wasn't sure what she wanted. "Can you repeat the question?"

Professor Sinistra's expression morphed into displeasure as it became apparent I hadn't been paying attention. "Well, I originally wanted you to list how many moons Saturn has. But, now I think I will have you list them out. Oh, and just for fun. For every moon you miss, I want you to write an inch of parchment on Saturn's moons."

Jessica shot me a smug look as if she were sure I wouldn't be able to list them all. After all, there were eighty-two of them.

With a sly smile, Jessica covertly mouthed 'challenge' at me. Over the past couple of months, we had been challenging one another in a little game. The rules were relatively simple. Once a week, a challenge could be issued to the holder of a badge that displayed King or Queen, depending on who was holding it.

Jessica won the first challenge, using what I have decided to call unfair tactics. But, I claimed the badge the following week in a transfiguration challenge. Since then, I've only lost the badge once, and that was in a Herbology class, which didn't bother me, not one bit. Magical plants can suck it.

I slowly raised one eyebrow at her challenge, which made her grin more as she was positive she had me. I hid a grin. She still didn't understand that storing and retrieving information was a piece of cake for me.

Inside my mind palace, I retrieved the memory of when I read the chapter on Saturn's moon. I turned my back to Professor Sinistra and started counting off moons.

"Titan, Iapetus, Rhea…"

Around halfway through the moons, the smile had been gracing Jessica's face slowly slid off as worry began to replace it.

When I got down to the final ten, I turned to Jessica and gave her a toothy grin. I waggled my ten fingers at her and continued listing off moons while lowering a finger for each one I listed.

"Janus, Prometheus, Helene."

When I got down to the final four, I decided to play with Jessica and pretend to struggle to remember. When a glint of hope appeared in her blue eyes, I smirked and quickly listed the final four so she would know I was teasing her, "Dione, Hyperion, Calypso, and Pandora."

Jessica narrowed her eyes and glared at me when she realized what had happened.

At the front of the classroom, Professor Sinistra looked torn between being impressed and annoyed that I had slipped out of the punishment she had intended.

After class, Jessica caught up to me and gave me a nudge in the hall.

"You tricked me," she pouted.

I showed her my pearly whites, "You're gonna have to step your game up if you want the crown."

"I thought I had you," Jessica sighed. She gave me a sideways glance filled with concern, "What's up with you? Lately, you've been distracted."

I rubbed my eyes, "I'm fine. Just been burning the midnight oil on a little side project."

Jessica accepted my deflection and changed the subject. "Are you ready for Arithmancy? Professor Vector said she had a surprise for us in the next class."

"I hope so," I replied. "We haven't done much in her class other than having advanced calculations drilled into us. I'm looking forward to putting them to the test."

Jessica nodded in agreement, "Me too."

We ran into Cedric on our way to Arithmancy, and when we got to class, the other students were buzzing with excitement.

Our regular desks had been replaced with small round tables meant to seat three or four students. What had everyone interested were the four mysterious vials of liquid on each table. The vials themselves were made of darkened glass, which concealed what laid inside.

Cedric, Jessica, and I grabbed a table for ourselves. Before we could speculate on what the lesson would be. Professor Vector entered the class. She smiled at the sight of all the student's eager eyes.

"Today, we are going to do something different." Professor Vector explained. "For the last two months, we've gone over and over calculations used to predict future events. Now, it's time to put that knowledge to the test in a controlled environment."

She strode over to our table, plucked one of the darkened vials off the table, and held it up before the class.

"Before each of you sits four vials. One contains harmless water, but the other three have potions that cause relatively different effects. Identifying the water will net you a passing grade. But, if you can identify the effects of the other potions. I will give you extra credit."

Next to me, Jessica eagerly raised her hand. "How will we know if we picked the right vial?"

A gleam appeared in Professor Vector's brown eyes. "I'm glad you asked that. One of you will need to drink the vial to test it." With a terrible, sweet smile, she added in a sugary voice, "Make sure to double-check your calculations."

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Some of the class paled when they realized we would be testing the vials ourselves. As for me, I thought it was a great idea. It was a potent reminder to take the calculations seriously and to make sure we double-checked our work.

Amy, a bespectacled mousy, Hufflepuff raised her hand. Once Professor Vector gave her a nod, she asked, "Are we supposed to do these alone or as a group?"

Professor Vector gave a half-shrug. "How you handle your calculations is up to you. I don't care if you do it individually or as a group. But, keep in mind, someone from each table will be drinking a vial at the end of the class. And if they are incorrect, someone else will continue until each table has selected the right vial."

Seeing a lack of reaction among the class, Professor Vector said with a wave, "Well, you don't have all day. Chop, chop."

As everyone started discussing with their partners, I turned to Cedric and Jessica.

Always a team player, Cedric asked, "Should we do this as a group or individually?"

Jessica looked unsure and turned to me for an answer.

I shook my head, "I think we should do both. First, we do our separate calculations. Then we can compare our work at the end to see if we arrived at similar conclusions."

Seeing Cedric and Jessica nod in agreement, I pulled out some parchment and got started. The first thing I did was number the vial to keep track and not mix them up. I would need to put each vial into a set of calculations, and if I did everything right, the calculations should spit out a series of numbers that I can convert into a prediction.

Since I was trying to predict what would happen if I consumed a vial, I also needed to convert myself into a set number. This was the easy part. One of the first things we had done in class was to figure out our basic mathematical representation. All that was required was to convert each letter in my full name into numbers and add them together.

The conversion chart was fairly straightforward. It took the twenty-six English characters and assigned them numbers with A represented by one and Z, twenty-six.

What is interesting is this is just one way to determine your mathematical representation. There are many different ways for people to figure their representations.

My first name, Alexander, equaled out to eighty-four. Nicola, my middle name, fifty-four. Fawley, my last name was seventy-two for a total of two hundred and ten. This was my number, the one that represented me. It would stay the same for the rest of my life. The next step was to multiply it by my age, which was fourteen. My final number was currently two thousand, nine hundred, and forty.

Professor Vector had told us that there are other factors we can add as what we calculate becomes more complicated, but at this level, this was all we needed.

Since I had my starting point, I started to write out the magical formulas and started punching in the numbers. The formulas themselves were mentally draining to use. Professor Vector explained that muggles would be driven mad if they tried to use them as we did.

There was almost a mentally draining feeling as we used the formulas to predict the future. But, I'm not quite sure how much of it was caused by the sheer complexity or the inherent magic in the formulas themselves.

There are many tried and true formulas that we can use to predict specific general actions. Supposedly, a talented Arithmancer can craft unique formulas on the spot. But, being able to do so is far beyond my abilities at the moment.

As I scribbled page after page, my calculations eventually spit out the number fifty-five, which I had to put through another formula designed to break down that number into a series of numbers that would give me two, twenty-one, eighteen, and fourteen.

I mentally converted the numbers into letters, which translated as burn. If I did everything right, the vial's contents should have some burning effect. It could also mean fire, heat, or something similar. It's possible to come to a different number depending on the formulas. Arithmancy can be as much an art as a science.

Knowing I had three other vials to do, I rubbed my eyes and got back to it.

Forty minutes later, I found myself staring at four different words with a slight headache forming behind my eyes.

Burn, freeze, heave, and water. I was quite sure that I had figured out each of the effects of the vials. I wasn't sure how they would cause these effects, but I was positive that I was right.

I was the first of my friends to be finished, and seeing the looks of concentration on their faces as they scribbled their feathered quills, it may be some time before they were finished.

Jessica finished next, and I wasn't too surprised by that. She had a good head for numbers. Cedric quickly followed, and for a moment, I considered that it might be a little unfair to the other students that all of us were at the same table.

Hiding her work beneath her arm, Jessica challenged me, "Since you were first, I think you should go first."

I reached out and slid my work to the center of the table. "For the first vial, I predicted a burning effect."

I alternated between Jessica and Cedric. "What about you?"

Cedric nodded, "I got heat."

We both looked at Jessica, "Fire," she simply said.

It wasn't too surprising that we all ended up with different words. Not including the changes that vary from person to person, you can use different calculations, or go about the formulas differently. The end results may slightly change, but they all should describe something similar.

I set the first vial off to the side. "Alright, I think we can all agree that none of us want to drink whatever is in that particular vial."

We had similar results for the following three options, with all of us identifying the final one containing the water.

Not long after, Professor Vector spoke, "All right, we are just about out of time."

Looking around the room, she asked, "Now, who is feeling confident they identified the vial containing water.

Everyone at our table raised their hand. I looked around the room and noticed that only about a third of the students raised their hands. The remaining two-thirds looked decidedly nervous.

Professor Vector pointed at our table. "Since you were done first, I think you should go first."

As I turned to Jessica and Cedric to see who would be volunteering, I found someone had scooted the vial of water into my area of the table.

I figured Cedric wouldn't do such a thing, so I turned my suspicious gaze towards Jessica.

"What?" she said innocently. "You were so confident that you were right, I figured you wouldn't mind testing the vial.

"Uh-huh," I sarcastically remarked.

"I don't mind drinking it," Cedric offered.

I held up a hand to stop him. "Oh no. I've got this."

Even though I was mostly confident, I still felt a sigh of relief when I tasted the cool, refreshing water running down my throat.

I turned back to Professor Vector and triumphantly showed her the empty vial.

"Excellent," She remarked with a pleased smile. "Mr. Fawley, Mr. Diggory, and Miss. Brooks have successfully used Arithmancy to predict which vial was harmless."

The students at the next table also found the correct vial on the first try. It wasn't until the third table that there was a mishap. A bespectacled, brown-haired girl from Hufflepuff drank the vial and shrieked seconds after finishing it. She quickly turned into a frozen block of ice. There was a flash of amusement from everyone as we recognized what she had drunk.

It was a prank potion from Zonko's joke shop, the flash-frozen solution. She would thaw out in about two minutes, and other than some embarrassment, she would be fine.

By the time every table had tested their vials, the last two options were made clear. They were from Zonko's as well. One was the gaging solution, which made a person gag and throw-up for a few minutes, and the other was the fire-breathing solution. While it didn't let a person breathe fire, it sure felt like it. One interesting effect was that if you opened your mouth, smoke would pour out like a chimney.

If the usefulness of Arithmancy wasn't apparent before this class, it sure was now. I can imagine how useful pioneers in the art of potion-making and Alchemy find Arithmancy to be life-saving. Even curse breakers can use Arithmancy to discover curses and avoid traps as they move through ancient tombs.

However, Arithmancy does have limits, and it's best to use it in controlled environments. I am looking forward to seeing how far I can push Arithmancy in the future.

As November passed by, I continued to experiment with my spell. It wasn't until the last Saturday in November that something finally changed.

Pointing my wand at an old dusty broom on my workbench, and spun the tip of my wand in a circle. As I completed the loop, I flicked it up and down at an angle like I was about to write an A.

"Nullaresistentia."

I felt something within me click. Like I had just put in the final piece of a really complicated puzzle.

The old broom I had pointed my wand at shuddered for a moment, then fell still.