Horcrux Math

Draco

For the first time in a while, there was peace in Draco's life. His classes passed in routine. In between homework and Quidditch, he worked on the vanishing cabinet, which he'd hauled into the shared room, and played games with Rosalie. Ron's birthday passed and Harry and Hermione gifted him his own Wizarding version of Dungeons and Dragons. Fred and George were helping to copy and distribute their version of the game and so far had ten boxes on order from different students.

The ministry was quiet. They got their warrant and came and looked through Umbridge's office and decrees without comment. Gathered a few statements. But something funny happened. Whenever someone attempted to mention the resorting, they would stutter and their words would fail them. Pansy Parkinson tried and tried and ended up with her tongue hanging out of her mouth like a dog's, lax with exertion.

Hermione left the hospital wing and began taking up a corner of the room with an array of items dedicated to her personal war. They had, without fanfare, decided that each person got a slice of the room. Draco's was filled with wood shavings. Hermione's was filled with Horcrux maps and diagrams and a funny machine that Rosalie had said could detect radiation.

Harry was still not entirely sure how to fight his war, so he sat in his slice and did his homework and fumed to himself.

And Rosalie finally got her computer to charge.

They were all in the room when she did. Hermione had three layers of black rubber gloves on and was bent over the diadem, squinting. Nagini was feasting on a few rats that the house elves had delivered to her. Draco was sanding the new inside panel of the cabinet. And then Rosalie had said, very calmly, "I've got it."

Slowly, Hermione had set the diadem down. Draco had put down the sandpaper. Harry had set aside his quill. To Draco, Rosalie's system looked perfectly normal. Just her laptop sitting on a wooden table at standing height. She waited for their attention and then pointed to the cord plugged into the side. A white light was on, indicating a charge. They traced the cord to the wall, where the house elves had installed three electrical outlets in every slice – twelve total.

A tear ran down Rosalie's face. "I got it," she said again. "It's charging – I've got it!" She hopped on one foot, then leaped towards him. He couldn't help but give her a congratulatory hug and kiss. She squeezed him so tightly that his ribs ached, then went to hug Hermione and Harry as well.

That same day, the electric lights came on, and they stopped using the magical lights. At that point, Rosalie desperately needed to show off, so they disguised Nagini's cage and put the diadem away and opened the room for Ravenclaw, Gryffindor, and Slytherin houses to come see. And it was quite interesting, but Rosalie's laptop seemed to glitch less often as they all celebrated the new accomplishment.

And that was when Draco learned that not all the holes he'd drilled in the ceiling were for lights.

"Hang on, now," Rosalie said, holding up a hand for quiet. "Everyone focus. Have we got Hufflepuff in here? Can Hufflepuff come in through Slytherin? They're closest, aren't they?" Everyone looked to Draco, but Draco looked to Hermione and saw her already on her way out. Still favouring her hurt arm, but on the move. "Right, I really hope these work," Rosalie said. She took out her Muggle cell phone and began hitting buttons.

The Muggle-born students all whispered excitedly in the quiet, but many Pureblood and Half-blood students looked lost. Then a beep echoed around the room. And then music began quietly playing.

"What's this sound?" Pansy Parkinson asked with a wrinkled nose.

"This is Firework, by Katy Perry," Rosalie said. "And you are going to love my playlist."

"Oh my gosh!" A voice came from the Slytherin door. It was the first of the Hufflepuffs. Draco recognised a Muggle-Born student bearing food and drink in her arms. "I love this song!" she exclaimed.

Draco couldn't remember a party where the Muggle-Borns were more comfortable than the Purebloods. But this was that party. It was a mess of jumping around, fighting over the phone, and groaning when certain songs weren't downloaded to play.

Draco knew ten Taylor Swift songs. One started playing and another Muggle-Born girl hit her knees and began crying almost immediately. "Oh my goodness!" she sobbed. "I've missed her so much!"

"Do you know her?" Draco asked, confused at the over-emotional response.

"I grew up with her!" the girl cried through actual tears. "I can't believe I'm missing her new album release…"

Fred and George Weasley somehow ended up in the middle of a crowd of people singing at the top of their voices, even though it was clear they knew none of the words. It wasn't too hard to learn, though.

Draco found Harry and Hermione moments before the song ended. "Isn't this great?" he asked.

"Absolutely!" Hermione agreed. "But I was telling Harry – this room will never be quiet again."

"They'll leave eventually," Draco said.

"No, no, I meant Rosalie. There will always be music playing now. And it's only a matter of time before she fixes the rest of the school."

"This song," Harry announced to Hermione. "I know this one. You have to dance to this one with me. Come on…" He pulled her away and she went, laughing, as he sang badly, "Will your eyes still smile from your cheeks?"

"Anyone heard of Griff?" Rosalie called from the table her phone was set on. "Right, we're ending the night with Vertigo, then. Five more songs, everyone!" Everyone groaned in disappointment.

Draco examined the ceiling. Electric lights had been installed, yes, but also grey fabric-covered units that the sound was coming from. Speakers, if he remembered the word correctly. But they don't really speak to you. They just amplify what sound is already coming through them.

His phone was plugged into the wall. He was so excited to have it back, even if it didn't really work that well, or work anywhere outside this room. Three weeks last December had changed his whole life.

He made it to Rosalie, but she was too near the crowd of chanting people to be able to talk to. Draco hadn't realised just how many people were Muggle Born at the school. There were a handful of Half-bloods as well, but since "Half Blood" also accounted for people raised by Muggle-born witches and Pureblood wizards (like Harry, actually), most of them hadn't been raised with Muggle media. But everyone was getting caught up in the beats and by the end of the last chorus, there were Purebloods and Half Bloods singing along.

Draco tried to raise his voice so Rosalie could hear him. The song was ending and he thought it'd be a good moment. But then the Muggle Borns exploded into celebratory cheers at the next song. "What?" Rosalie hollered.

"Can you play Top Gun before we go?" He shouted.

"I can't hear you!" she laughed, then waved him over to the phone. "Are you asking about a song?" He looked at the up next list. Levitating by Dua Lipa was playing. Scheduled was Good For You by Olivia Rodrigo, Shut Up and Dance by WALK THE MOON, followed by I Ain't Worried from Top Gun and Vertigo by Griff. Draco shook his head with a smile and gave Rosalie a thumbs-up. Then he leaned in to kiss her. She seemed happier than she'd been since she'd first seen him in Hogsmeade.

Someone tapped Draco's arm. To his surprise, it was Crabbe, who he'd not spoken to in about a month. "Can you open the door?" He asked over the screaming in the room. "I want to go get more food!"

Draco shook his head. "No!" he called back.

Maybe his voice was lost in the crowd, but the shaking of his head was a good enough signal.

"Why?" Crabbe shouted at him.

"We're ending soon!" Draco yelled. "No more food!"

"But it's faster to go back!"

Still, Draco shook his head and realised that that would probably become a hot topic here pretty quick if he didn't dip out. But he didn't want to miss Top Gun. So he gestured for Rosalie's phone and moved it up in the que. Just in time too – the whistling began almost immediately after he'd moved it.

Fred and George Weasley had managed to form a gap in the middle of everyone and people were taking turns dancing in the middle of the circle. Draco had never seen dancing like this before. They got on their knees and pretended at playing guitars, banging their heads back and forth. They shuffled their feet. One short Hufflepuff boy crouched down, put his hands on the ground, and then began rotating one of his legs underneath him like a ceiling fan. The crowds went wild.

Rosalie gestured him back to her with a finger. He leaned forward and she cupped her hands right up next to his ear. "The first time I heard this song," she yelled, "I was in Brazil! I learned every word!"

Brazil. The word meant something, Draco was sure, but he couldn't place it. "Where?" he yelled.

"Brazil!" Rosalie shouted again. Then, seeing his mystified expression, smiled and said, "South America!"

That rang a bell. But that was on a different continent! He wasn't sure why that surprised him… Rosalie was American. She was already from a different continent. But in Draco's mind, nothing truly existed outside of the European Wizarding World except trees and dirt.

He cupped his hands around her ear. "How did you hear it?" he asked.

"What?" She yelled.

"How did you hear it? Do they have phones too?"

She squinted at him with that expression of, "Are you joking?" Then put her mouth back up by his ear. "I was in the city. It's like London, but hot!"

Then she drew back and laughed at his expression. He was sure he looked quite stupid, but he hadn't ever heard of cities in South America. And cities as big as London? "Did you apparate?" He yelled.

"You can't apparate that far! It's got to be five thousand miles away!"

"How'd you get there?"

"Airplane!"

And she did the funniest thing – put her arms straight out from her shoulders and moved as if she were soaring. And without thinking, Draco put his arms out and mirrored her. The motion reminded him of flying no hands. He smiled.

I want to go.

He pictured himself sitting on top of an airplane that resembled the spaceship he'd seen in the muggle children's books. He pictured waving to people on the ground as he skimmed mere feet over their heads. The rocket boosters blasting him across the ocean. How long would it take? A minute? Two?

He imagined the warm air as he looked down at the vast ocean. It would be hot, wouldn't it? Not like the air in Scotland when he was flying. Rosalie had said like London, but hot. How hot was hot? And he imagined, as the airplane drew close to South America, that he could leap off the top of the airplane with his broom and fall down, down towards the city.

"I want to go," he told Rosalie. "One day." The room was still a million units too loud, but somehow she heard him.

"Oh, if we get married, you're going everywhere!" Rosalie said. "You're going to Paris and New York and China – we need to see what real Chinese food is!"

"And Brazil?" Draco said. "And London?"

"You've not been to London?"

"Never needed to!" London was a Muggle city and the Malfoys were rich enough to have anything they needed popped to them.

"You're such a sheltered rich kid!" But it didn't pass for an insult when she was laughing so hard.

"Do you want to go with me?"

Rosalie looked at him like he was crazy. "Hell yes!" She shouted.

Draco laughed and grabbed Harry's arm as he passed by. "Harry, I'm going to go to London! And Brazil!"

"When?"

"I don't know! One day!"

Harry stared, then smiled. "Glad you're excited, mate. You've just got to win your war first."

The speakers and the phone turning on were a big step, but there was no service to Hogwarts still. Rosalie was going crazy trying to get this gadget called a router to work. Draco didn't understand exactly what she meant until he tried to text her and got an error message. None of the videos on his phone would work. Only the music he'd downloaded would play.

Then he really wanted the router to work as well.

The house elves put dark grey carpet down and then brought in a table and some chairs for the very centre of the room, and some other chairs to line the room. They each got a filing cabinet, and Dumbledore loaned Hermione some gadgets to help with the Horcrux Hunt.

March passed without much success, though Hermione made several small break-throughs on her Horcrux tracker and confirmed that Nagini was, in fact, one of the horcruxes. "It would be great," she said one day, making another rat appear in the cage for Nagini, "If I could figure out a way to determine when each horcrux was made and how much of his soul he had. Then we could confirm whether it really is seven."

Harry had looked up from his homework to Rosalie, as if she'd have the answer, but Draco had pulled a whiteboard marker from his blue jeans and stood. "Well, in Arithmancy, you have the ability to track how long a spell has existed using Merlin's Method, so if you can figure out a way to guess at the original size of the soul-"

"Does the soul affect magical power?" Hermione asked. "Would his power diminish as he makes these?"

Rosalie had mounted a whiteboard on the wall. Now, whiteboards were simply wonderful. They were like chalkboards, but without the screeching, and with more colours. He went to the one mounted near Hermione's workstation and wrote out the formula for her. "Possibly, but he has done other rituals to make himself more powerful," Draco said. "You've seen this, right?"

"Well, that's unfortunate. And yes, I have."

"Is there a way to measure a soul in the first place?" Rosalie asked. "I mean… can a person have more soul than another? And if so, they ought to be normally distributed statistically, right? Like IQ."

A loud knock came from the Gryffindor room. All four inner doors were propped open for this purpose. Harry got up and went to open the Gryffindor Common Room door. "Ron!" Draco heard off in the distance. "Come on in… all these brainiacs are killing me."

Hermione picked up a marker and began rewriting the formula Draco had written on the board with the variables they knew. She put "s" in place of soul energy and then leaned back to peer at their work. "Reckon we could win an Order of Merlin for this if we can figure it out?"

"You're such a Slytherin," Draco replied, circling the 's' she'd written and drawing an arrow to a blank space so he could begin listing ideas to quantify the totality of a soul.

"Well, you're such a Hufflepuff for helping me," Hermione replied. "What's in it for you, Mr. Former Slytherin?"

Draco glared at Hermione as Ron and Harry chuckled and came to sit in the middle of the room. Draco noticed Ron had his Dungeons and Dragons kit and a large collection of letters. "Maybe I'll just leave you to it?" he asked. "Weasley looks like he's hauled in a much more interesting opportunity."

"I have," Weasley said. "I'll show you just as soon as Harry's seen it."

"No, no, please stay here," Hermione said. "Listen to me think out loud for just a second, alright?" She drew a circle on the board and said, "We know when a soul is split it causes a physical difference. So perhaps… there's a way to determine based on the portion of the soul in a horcrux…" she sectioned out her circle and shaded it. "…the state of the soul when it was split off?"

Draco sighed. It wasn't that he didn't want to solve this issue. On the contrary, it was interesting and Hermione was talented and it directly related to his personal decision to double-cross Lord Voldemort. But it was also a crazy idea that was going to take a lot more than a whiteboard to mess with.

He began to plot points on the board and fill in the formula. Hermione did the same thing, but attempting to solve for s. Working with her was quite swell. He had one side and she had the other and when he hit a dead end, he moved it to the middle and she moved it to her side. Then, he noticed she wasn't redrawing anything he put in the middle, but flicking her wand at it and moving it like a magnet.

"Wot spell are you using?" he asked.

"Hover spell, actually. Just push from the side so you don't erase the marker."

"Potter, your girlfriend is a genius." Draco pulled his wand out of his pocket and moved some of Hermione's notes to his side. "They'll have to rename the Order of Merlin after her."

"Hell yeah," Hermione said with a smile. Her ears had started to glow bright green as she worked, and she seemed to be writing faster than a person should be able to.

Rosalie paused in her work to come and put her arm around Draco's waist as he wrote. He felt a little more pressure to not screw up with her looking over his shoulder. But she just watched and then leaned her head on his arm. "Couldn't you cast it on the whole board?" she asked.

"No, because then you couldn't write on the board," Draco replied. "But good idea!"

Rosalie nodded. "I think you could have passed for a Ravenclaw," she said.

"Why is Malfoy a Hufflepuff?" Weasley asked from the centre of the room. "He was always so… proud? Yeah, proud works. Anyway, Malfoy fit right in with the Slytherins."

"Draco fit in with all the Slytherins when all the Slytherins should have been Hufflepuffs," Hermione said.

"I look at it as a measure of what brings a person comfort and joy in their lives," Rosalie said. "Draco is happy when people are proud of him, when they trust him to do things that are important to them, and when he's included."

Draco didn't say anything as he continued working on the formula he was on. Their words kind of bit at him. He didn't like that he was a Hufflepuff and all the things he'd said about the house were still surfacing. And Hufflepuff didn't like that he was Hufflepuff either. And that kinda sucked… for the exact reasons that Rosalie had just listed.

"Draco." Hermione tapped a formula on the board. "Do you reckon… I could use part of a joining rune? Because the Joining Spell senses when something used to belong together… perhaps if we substitute s in this arithmancy for a portion of that rune…"

"You could be here all night guessing what that part of the rune would be," Draco said. "But… assuming you could find it… that would create an entirely different spell. And if you could somehow move the piece of the soul in that horcrux into your detector and put that rune on it…"

"It would sense whether what we've got our hands on is a horcrux," Hermione said, "But would it direct us towards it?"

"Put a prototype together," Rosalie said. "Because I've been experimenting with how a horcrux is made and I think I've got an answer for how we can move the one in the diadem to the radiation detector." She pulled on one of Hermione's thick pairs of gloves. The diadem began to rattle in its case.

"Ron, I'm sorry, I'm excited about all this, but I just can't focus with all this going on," Harry said. "It's giving me a headache." He set down what looked like a letter on top of a massive stack.

"Got yourself some fanmail, Potter?"

"Yeah." Harry replied. "Ron says that the Prophet's response to the Quibbler article was delivered after we left breakfast."

"Oh really?" Draco put the whiteboard marker in his pocket and wandered over to where Harry and Ron were sat. The stack was impressive – Draco couldn't lie. "And Professor Umbridge isn't here to ban it. What a shame."

"I wonder," Hermione called from the whiteboard, where she was scribbling rune variations and tapping on them with varying successes, "if she can still issue Educational Decrees from the ministry?"

"I bet I could sue her for banning reading material." Rosalie cracked her knuckles. "The ministry too. Now, Harry or Draco, if you don't mind?"

Harry got to his feet, but Draco beat him over to where Rosalie was setting the diadem on a side table. She got the radiation detector and broke open the back and pointed out a metal box inside it. "I believe the horcrux has to go there. Now… from my research… the separating spell won't cut it. The idea is that as long as the container is intact, it lives in the container. So I've created a new spell, which will work a little like a confundus, a little like a severing spell, and a little like the Killing Curse."

"Do tell," Draco whispered, studying the little metal box. Rosalie followed his gaze and began to pry open the back of the box. She pulled a rock out of her pocket. A simple, small one from the lake that she must have gotten for this purpose. It was purple and had little freckles in the stone face and was smooth to the touch. She put it inside the metal box.

"The Killing Curse severs a soul from a body. The confundus charm will hopefully confuse the horcrux into believing the container has been damaged. But if this doesn't work, I've got nine others."

Hermione finished her whiteboard scribbling but did not announce a conclusion. Her hands were, however, bright green. She wandered over to the table and Harry and Weasley also joined the circle. Hermione held out a hand to Rosalie and Rosalie reached into a different pocket and pulled out a paper list. Hermione unfolded the list and began to skim it.

"The spell is Vehecrima." Rosalie said. "Ve-hec-rima."

"Vehecrima," Draco said. It did not feel like a real spell, but he wasn't the creator. He pulled his wand out of his pocket. "Before I cast this, what do you expect it to look like?"

"Hold your wand tip above the horcrux, as if you're pulling a memory out of it for a pensive," Rosalie said. "I'm hoping it'll stick to your wand and you can place it on the rock instead."

"Why don't you do it?" Draco asked.

"You've got a steadier hand," Rosalie replied.

Draco almost went to try and roll up his sleeves before he remembered that he had none. Merlin's beard, he loved Muggle clothes. He readied his wand, focusing on the wrist movement Professor Flitwick had lectured them about countless times, and then said, "Vehecrima." A slash left his wand and hit the diadem face on. It dinged and the diadem fell to the floor, no one was touching it.

Rosalie picked it back up with her gloved hand. "No dings," she said.

"Draco," Hermione said, "Try Secrevementi instead."

"I didn't come up with that one," Rosalie said.

"No," Hermione agreed, showing her the list. "Your spells all work, per se, but you put the power statement prior to the directional statement."

Rosalie looked quite stunned. Her bottom lip swung for a moment, then she shut her mouth. "Right," she said. "Okay." She shrugged and gestured for Draco to continue.

He looked to Hermione. "One more time?"

"Secre-vementi."

Draco flicked his wrist and let the wand stop parallel to the diadem's arc. The tip of his wand was touching the sapphire. Then he raised his hand slowly and felt as if a twenty-pound weight was on the tip of his wand.

The air around the horcrux grew dark. It was absorbing the light energy from right out of the air. Draco lifted and a green, mossy-coloured substance clung to the end of his wand as he pulled. And then the horcrux began to scream.

Across from Draco, Harry's eyes rolled into the back of his head, and he collapsed with a thump. Ron and Hermione both jumped to try and help him, but Rosalie put her hand on Draco's arm to help him lift up. "Focus!" she called.

Nagini was writhing miserably in her cage. She thrashed about and then curled into a ball and shivered.

The screaming only lasted another few seconds. Draco continued pulling upwards until a thick goop, probably about a fourth of a cup in totality, was oozing and squirming on the end of his wand. It looked smooth, though Draco wouldn't risk touching it. It actually reminded him of boogies, though this one definitely came with a life of its own.

Rosalie released his forearm and Draco slowly brought the goopy mess to hover over the stone in the box. Then he slowly lowered it down and the horcrux melted into the freckles of the stone as easily as water could melt through sand and leave it looking dry in seconds. Rosalie picked up the case to the metal box and snapped it into place. Then, she put on the plastic backing of the detector and looked over the table, where Ron and Hermione were trying to revive Harry. "Did he hit his head?" she asked.

Draco examined the end of his wand, then pointed it to Harry and cast the feather light charm. Coming around the table, he budged Granger away with his feet. "Right, Weasley, you got his shoulders? Let's take him to the cushions in the centre of the room. He'll come back around soon."

They carried him away and set him on the new cushions to rest. Hermione hovered over Draco's shoulder as they went. Draco used a quick diagnostic charm to double check he really was fine. The charm indicated a headache, but nothing else wrong with him. Still, Hermione fussed for a moment, removing his glasses, taking off his shoes, and then conjuring a cool cloth to put on his head.

Rosalie had continued to mess with the detector and now had it powered on. But she was frowning by the time they'd all put their attention onto her again. "Nothing," she said. "Nothing detected."

"Hand it here," Hermione said. "I think I know how to get it to match up."

Rosalie handed the detector to Hermione without complaint. Hermione picked up her wand and lit the tip up blue with a wandless charm that Draco did not recognise. She turned the detector over and, in the plastic removable case, etched two triangles, one smaller than the other, and a balance beam between the two. Then she finished the spell and prodded the rune with her wand. It lit up white and the machine began to squeak and squeal.

"How'd you do that?" Draco asked.

Hermione pointed back towards the board. "I found that rune. It didn't take me all night." She almost looked as if she was blushing green.

When she turned the box back over, there was a dot in the bottom middle of the screen. A pulsing ray was directing her forward. A very shrill beeping noise repeated itself very fast, as if it were anxious for them to listen. As a group, Weasley, Rosalie, Hermione and Draco followed the path with their eyes and saw that it indicated to Nagini's enclosure. Nagini did not seem to be in any more pain.

Hermione walked forward and back, to the left and to the right, and then all around Nagini's enclosure twice. The first time was turning towards it every single corner. The second time was facing forward the entire time to see if the pulsing ray would rotate around to continue indicating her. It did. She laughed in triumph and Rosalie cheered. Draco felt a smile coming on until Weasley elbowed him. Then he scowled and shoved back.

"It's marvellous – it works!" Hermione said. "I'm not sure for how far. But when Nagini is behind me, it moves the dot to indicate I need to look behind me, and it works in 360 degrees!"

"That's wonderful!" Rosalie said. "Once we kill Nagini, we can begin testing for distance amplification."

"Right," Hermione agreed. She began to walk back to her station, to glance at her notes. "We only need one horcrux to be the source. And-" She paused suddenly, staring at the markings on the detector. It was still making that infernal noise, and Draco hoped she was looking for the volume buttons.

Then Hermione took a step to the left, towards the middle of the room, and a step to the right, towards Nagini's cage. Her triumphant smile fell. "It's giving me another direction," she said. "But I don't get how it could pick up anything with Nagini so close. She should be the primary target."

"Follow it," Ron said. "The more we have, the closer we are, right?"

Hermione followed the beam across her section and towards the Slytherin door. Then she backtracked and headed to Hufflepuff. Then she angled herself to the centre of the room and walked around it before turning to the cushions where Harry was still out cold. Nagini was uncurling in her enclosure.

Hermione let the hand holding the detector fall to the side. Draco finally grew impatient with the beeping. "Granger," he said. "Can you shut that sound off?"

Hermione turned the whole machine off. "Don't kill Nagini yet," she said. "Either the horcrux is buried in the middle of the room… or we've got one big problem."

The next chapter will be called Salazar Slytherin's Visit. I'll post it early if I get five reviews.