by Tigerlady

Combinatorics: Relating to or involving combinations.

A derangement of n ordered objects, denoted !n, is a permutation in which none of the objects appear in their "natural" (i.e., ordered) place.

Hermione watched him from across the room, an empty plate and a full glass of pumpkin punch mostly forgotten in her hand. His eyes were just a little bit wild, but he smiled and nodded as he was supposed. She had socialized earlier, but now her corner was a refuge from the sea of ecstatic well-wishers, the faces from her youth crowded into the small living room. She didn't begrudge Harry the party; she could understand his desire to share his joy with the world. After all, not everyone's godfather got to come back from the dead.

Hermione sighed. It was a miracle indeed when Sirius Black had stumbled into this very room, wide-eyed and trembling, mouth gaping slightly as he appeared out of nowhere. The three of them had been laughing over a bottle of wine; Hermione tucked into the lounger while Ron and Harry shared the couch. She had probably drunk most of the wine herself (as neither of the boys had very refined tastes), which explained why her memories of the event itself were blurred and confused. Ron had knocked over his glass when he jumped up to catch Sirius as he collapsed. The edges of the stain still marked the carpet; not even a good Scourgify could completely defeat Merlot on wool.

A roar of laughter pulled her attention to the group once more. Sirius smiled jaggedly, cradling his glass of scotch, while everyone else chuckled at something Dumbledore had done. The old wizard was as resplendent as always in shimmering purple dress robes highlighted with the faintest touch of silvery green. Harry and a gaggle of Weasleys were hanging on his words, Harry occasionally glancing back at Sirius as if to make sure he was still there. Sirius hadn't aged since that day he fell through the veil, not physically anyway. He was a good looking man, though you had to look to past the lines on the face and the tightness around those pale, pale blue eyes to see it.

She'd had such a crush on him back when she was still a school girl, after his rescue and before the Department of Mysteries. Even now she could remember the heat of his strong hands across her hip bones, the barest brush of his thighs next to hers on that glorious ride on Buckbeak. That feeling had fueled her fantasies, incomplete and immature though they were, for a guilty year and a half.

That had been the first night she had ever seen him, in person anyway. His hair was longer then, filthy and ragged from being on the lam. Thinking back Hermione was amazed at how quickly her feelings had changed, how all of their feelings had changed, in that brief encounter in the shack. From hate and dread and fear of him to love and dread and fear for him. Then again, they had been very much children then, given to the fast-paced illogic of childish emotion. She smirked and reassessed; adult emotion rarely held with logic either.

Sirius seemed to be holding his own. He still nursed the small tumbler of scotch in one hand while nodding politely at the throng surrounding him. All of the remaining Order was here. Well, all except Remus Lupin. That surprised her almost as much as the fact that Severus Snape was in attendance, though not in the same room. Hermione wondered whether it was entirely Dumbledore's doing that the potions master was here. Perhaps some bit of regard for Black lurked beneath those scornful eyes? She thought it more likely that Snape had a morbid curiosity.

She scanned the rest of the room. Molly Weasley was slowly but steadily drinking herself into a stupor on the edge of the sofa. Hermione supposed she should do something about that, but she had little energy to apply to other people's problems lately. Let Harry deal with the fallout from this brilliant little party. Perhaps the task should fall to Ron, but she knew he hadn't been able to deal with his mother with more than stilted politeness since the end. Since the end, when Arthur and Percy fell to either side of Voldemort's stupid war.

Suddenly the dishes in her hands were more than annoying. She threaded her way into the kitchen, nodding politely but keeping her distance from her guests. She poured the punch down the stainless steel sink and then dumped the plastic-ware into the large rubbish bin by the back door. Harry had been fascinated by all contrivances Muggle since graduation. Hermione found this slightly disturbing considering his upbringing, but she didn't argue the practice. It was simple enough to transfigure the waste after it was in the black plastic sack as it was before. She brushed invisible crumbs off her hands as debated returning to her corner. Instead she decided that a spot of air would do her good.

She leaned against the porch railing, drawing in a deep breath of the cool night air. The smell of tobacco alerted her to another's presence. She searched the dark, but it was a heavy exhale followed by a deep chuckle that pinpointed the who and where. Severus Snape was sitting on the wide rail to her left, visible only by the pale gleam of his hands and face and the dull glow of a cigarette.

"What's the matter, Miss Granger? Smoke bothering you?"

His voice was slyly amused, hard but not caustic. Her former professor almost sounded mellow.

"Not at all," she replied primly. Try as she might to change her demeanor, everything she said came out prim. "Though it surprises me that you indulge in the habit, as it dulls the sense of smell."

She didn't add that a good sense of smell was a necessary quality for a potions master, as that was an obvious statement. He had always been excellent at calling her out when she stated the obvious. Instead of rebuking her, he just exhaled a steady stream of smoke like a lazing dragon. She was turning back to study the stars when his deep bass caught her.

"Perhaps that's why I do it."

Her eyebrows shot up, though she was sure the light was too low for them to have an effect. The statement was an oddity anyway she looked at it: too civil, too intimate, too obscure, too revealing. She had no reply, only questions and curiosity, but she didn't think he would stand for her probing. She took a different route.

"Don't suppose you'd share a ciggie?" she asked without much hope. A slight rustling was all the warning she got before something came flying at her face. She fumbled around rather foolishly as she tried not to drop the pack. She slipped one of the cancer sticks out of the plastic wrapped box, surprised to realize it was Muggle. How strange. She stuck it between her lips and reached for her wand. Before she got it out Snape murmured something. The tip glowed cherry-orange. She tossed the package back his direction, spitefully hoping he would make as much a fool out of himself as she did. The light smack of plastic against flesh told her he had no such difficulty.

Hermione adjusted the fag to take a pull, preparing herself as she did so. It had been months since she last smoked, so the first breath burned down her throat and across her chest like acid on fingertips. She tightened her ribs and opened her throat, not giving in to her body's urge to choke. The next drag was much easier, and in moments the light bliss of nicotine enveloped her.

"I'm amazed to see you here tonight, Professor," she said before she examined the logic of trying to converse with him. She attributed such foolishness to the nicotine.

That deep chuckle confounded her again.

"I suppose you are, Miss Granger."

Snape seemed amazingly calm, especially considering that his childhood nemesis was being feted not twenty feet away. Perhaps his nasty demeanor stemmed from nicotine withdrawal. If she were feeling especially generous towards future Hogwarts students, she might introduce him to the lovely Muggle invention called the patch. The thought made her giggle a little.

"Something amusing?"

She sighed, mirth dying a merciless death.

"No, not particularly."

They shared the silence for a few minutes longer. Hermione saw the soft glow of his cigarette drop to the porch floor, then die under his boot. Her eyes narrowed; he didn't bother to pick it up. Stupid git was a Wizard after all, it didn't take much to clean up after himself.

"So why are you here?" she prodded.

Snape sighed, a deeper and wider sound than when he had exhaled smoke.

"I don't suppose that boundless curiosity will leave me alone if I say that it is none of your business. Very well, Miss Granger. I am here as a favor to someone."

Before she formed another question he was on his feet and brushing past her.

"And as that favor has been carried out, I see no further reason for my presence at this lackluster soiree. Good evening, Miss Granger."

With that he swooped out into the back yard, not pausing in his stride before he disapparated with a small pop. He hadn't even bothered to say goodbye to anyone inside. Severus Snape was still a loner, no matter that he was as much a hero as anyone in the other room. She felt a bit of empathetic solidarity before she remembered she hadn't really been alone since the troll incident in the middle of her fist year. She smiled a little at that feeling of acceptance. Despite her occasional solitary tendencies, her boys would always love her, and that was a very good thing.

She ground out the butt of her cigarette under the toes of her trainers and left it on the ground. She would have to find Snape's rubbish tomorrow; she could pick up her own then as well.

Inside the party was wrapping up. Ginny tiredly smiled at Hermione as she dumped a stack of plates into the bin. She didn't bother to say anything as Hermione passed through the kitchen. In the living room Dumbledore was shaking hands with Harry. Most of the professors and older members of the order had gone after the meal was served. Professor McGonagall was still here, edging towards the door while keeping an eye on the headmaster. Ron was fidgeting with hands tucked under his pits as he watched Fred and George approach his mother. The twins seemed to be on Molly duty tonight. Bill and Fleur were already gone by an hour, after a strained conversation that gave the impression that all was not well in that household. Charlie had begged off before that, saying he had to get back to monitor some eggs. So now the identical pair coaxed Molly off the couch, one of the two passing over a small vial. Normally Hermione would have stopped anyone from ingesting something that came from the pair, but she knew that they didn't play pranks on Molly, not anymore. Maybe they should have done.

Just then a gaggle of her former classmates got stuck in the door, but Dumbledore wandered up behind and everyone pushed through. She hoped they remembered to look for nosy neighbors before Apparating. Some of them were a bit dense when it came to Muggle civilization.

Finally the room was empty except for Hermione, the three men, and party remains. She raised her wand, and with an extended swish and flick, banished all of the plates, glasses, and silverware to the kitchen. Another sequence saw the buffet table emptied, folded, and stored in the hall closet. That was quite good enough. She would take care of the rest tomorrow.

"Well, I'm knackered. Think I'll off to bed, then," Ron said quickly, and headed up the stairs. Harry's concerned eyes followed him all the way up. She wondered if they talked about it, Ron's grief. They'd all mostly recovered from the losses from the war, but Sirius' return had brought up the emotions again. Most of the lost would never return.

The three of them stared at each other for a weighty moment, after Ron drifted out of sight. Harry finally broke the silence.

"So, did you have a good time tonight, Sirius?"

Sirius smiled. It looked a bit unnatural, a bit brittle, as if his lined face might crack from the movement of his lips.

"As good as you can ever have at one of these things, hey."

Harry laughed a little, and Hermione even smiled.

"Think I'm going to duck out back for a bit, catch some fresh air," he continued.

Harry's face wrinkled up in that cute little way he got whenever he was concerned. "Is everything...I mean, do you want some company?"

Sirius smiled again, more relaxed this time. "Don't worry, Harry. I just want to take a look at the stars, maybe spend some time as Snuffles."

Harry nodded slowly, and then he gave Sirius a quick hug. Hermione was somewhat surprised when one of Sirius' warm hands caught her shoulder and squeezed. Then he passed on out of the room, heading into the night.

"You okay, Harry?"

Harry nodded again. "Yeah. I just worry about him, you know? He's had such a hard life."

Hermione didn't say the things that sprang to mind, that Harry'd had a hard life also, that she was more than worried about Sirius, that they should be worried about their friend upstairs. Instead she reached out and pulled him in close. They held onto each other for minutes, neither wanting to give up the comfort of physical contact. Finally Harry pulled back. She was happy to see those pretty green eyes a little less troubled.

"I think I'll go up, too. Ron tends to take up the whole bed if I'm not there to stake my space."

She laughed at that. The boys had been sharing since Sirius arrived, Ron's small bed transfigured into a king-sized. It was a hazard to walk into the room these days, and she didn't envy having to share with Ron. His clothes were always everywhere, and he had a tendency to snore.

"All right, then. I've got a spot of light reading to finish up myself." As she had predicted, Harry groaned.

"Geez, Hermione. It's a party night, can't you give it a rest for once? Have a good time?"

She responded in her most uptight voice. "That is my idea of a good time, Mr. Potter."

Harry laughed and punched her lightly on the shoulder. They started up the stairs, Harry mimicking her in a merciless falsetto from behind. Her heart felt lighter than it had all evening. At least she still knew how to get a laugh out of her friend.

Later she lay in bed, her journal article fallen to her lap. It had only held her attention through the introductory remarks before her mind drifted back to the party. Everyone there seemed overjoyed to see Sirius. Well, except Snape, of course. She wondered again why Remus wasn't there.

Those two had seemed so close back before. Remus had been devastated after Sirius disappeared, when they thought he had died. Oh, he had hidden it, burying himself in work for the Order, always being supportive to the three of them. But Remus had looked so broken to her; his cheekbones sharper in his thin face, his hair a little more grey, the scars appearing more frequently on his face and arms. She wondered if it was because he didn't have someone to keep him company during the transformations, though he had surely gone through them alone while Sirius was in Azkaban.

She thought that must be part of the reason he hadn't come tonight. It must have been very strange to have someone that close to you back from the dead. Hermione had trouble with the concept herself, and she never knew Sirius that well in the first place. Really, just that short time the summer before fifth term, and he was often eccentric and angry then. Now she found herself wondering if he was real at the strangest times. Yesterday she had found him drinking milk from the carton while the refrigerator door stood wide open. She had been seriously contemplating whether he was a variety of Boggart when he smiled cheekily and asked if everything was ok.

Hermione called off the light and tossed the journal onto her bedside table. As she snuggled under the quilt she pondered the situation. How did one ungrieve?

A few minutes of thought proved fruitless. She decided to go to the library tomorrow. Perhaps there were Muggle psychology texts that addressed the topic. After all, dead people reappeared on her mum's soap operas all the time.


A mathematical expression can also be said to be indeterminate if it is not definitively or precisely determined.

Hermione frumped down the staircase, still in nightgown and floppy slippers. She had slept in later than usual on a Sunday, due to the late party last night and the knowledge that she would have the house to herself. The boys were taking Sirius to a Quidditch match–the Cannons, she thought. She could never keep track of all of the Quidditch information that flowed through this house. Well, she could have if she wanted to, but she didn't.

She was surprised that the noise of them leaving at dawn hadn't woken her. They must have been trying especially hard not to wake her despite their typical enthusiasm. The thought gave her warm tingles. Harry in particular had been excited about the game. She thought he wanted to show off Sirius to the world, to parade around the fact that his godfather was not a murderer. Harry had fought hard after Voldemort's defeat to get Sirius pardoned posthumously. She thought he had never truly given up hope that Sirius would pass back through the veil. Maybe that was why he took to it so naturally when it actually happened.

She was walking through the kitchen doorway when she smacked into something. Hermione shrieked a little; the something was human. She fumbled for her wand even as rationality set in.

Sirius had his hands on her shoulders to steady her, a look of concern in those pretty blue eyes. "Sorry, sweets. Didn't mean to run you down like that."

She put a hand to her chest, feeling her heart race beneath it. Sirius let go of her shoulders and stepped back.

"What are you doing here? I thought you were with Harry and Ron? Are they here, too?"

Sirius smiled at her barrage of questions. He held a finger up to her lips. "One at a time, please. Harry and Ron are at the game. I decided to stay home."

He didn't explain any more, just stepped around her.

"How come?"

He shrugged without turning back towards her.

"Didn't feel like being the main attraction. Thought the crowds would be more interested in the serial killer from beyond than a little old Quidditch match."

By the time she thought of anything to say he was already in his room, the door shut behind him.

She sighed and collected a bowl of cold cereal from the kitchen. It was pink and sugary and completely bad for her, something her parents would have banned from their house. Of course it was her favorite. As she sat and chewed, she thought about Sirius. He would have caused quite a stir at the match. He was the first ever to escape from Azkaban, he was pardoned for the most shocking murders of the century after a mysterious death, and then he came back from the dead to top it all off. Yes, Sirius would create a stir wherever he went for quite some time.

Hermione didn't think he would handle the attention with the same equanimity Harry managed. She herself had wanted to hex various gossip mongers and peeping toms at times, and she didn't garner near the attention that Harry did. Knowing Sirius, he might very well shoot off several hexes before anyone could stop him.

She finished her breakfast with an inelegant slurp. Sirius might gather a lot of gawkers in the Wizarding world, but he would be just another face in the crowd in the Muggle world. She headed up to the shower with a sense of purpose. She needed to go the library today, and Sirius needed to get out of the house.


An expression is said to be ambiguous (or poorly defined) if its definition does not assign it a unique interpretation or value. An expression which is not ambiguous is said to be well defined.

The library was quiet of course, not crowded but still busy. There were mothers with young children flocking to the special programs section, while other adults of all shapes and sizes flitted about the building like heavy ghosts. The computer section was overflowing, those without the technology at home taking advantage of the end of the work week to do whatever it was they did. Hermione paid no attention to the crowded electronic card catalogues. She was used to finding things by hand. Years of wading through oddly organized volumes at Hogwarts had only sharpened her analytical senses. The smell here was a little different–less dusty leather and more stale plastic–but the rows of books felt the same.

She headed deeper into the building, pulling Sirius in her wake like an obedient puppy. His eyes were wide and his shoulders hunched, but she thought he was enjoying the experience. He had barely protested the idea earlier, simply saying he didn't know what to wear to a Muggle library. She'd rolled her eyes and pulled a few things out of his chest of drawers. He'd added the black leather jacket himself, the one Harry had bought shortly after Sirius' return. Harry said it went with the bike. It looked good on Sirius, making him look like the bad boy he had been in his youth, all dark and scruffy. Hermione bet he was very conscious of its effect.

She stopped suddenly as she realized that Sirius might have interests other than her own. He didn't quite knock into her from behind, but she could feel the brush of his heat as he was forced to a stop. She knew he liked Quidditch, and motorcycles, and that was about the extent of her Sirius knowledge. Deplorable, really.

"What would you like to see?" she asked as she spun around.

Sirius looked at her like she was speaking a foreign language. "Do they have something beside books?"

She opened her mouth to explain about computers and video libraries when it struck her that she simply needed to clarify her original question.

"I meant what types of books interest you? They won't have anything on Quidditch, but there's sure to be a section on Muggle sports. And periodicals if you'd prefer something up to date."

Sirius smiled, teeth showing just a little. She couldn't help but smile back.

"Oh right," he said. "Do they have fiction? I used to fancy the ones with space ships."

She laughed a little at the thought of this pure-blooded wizard enjoying scifi, but she just led him towards the stacks.

"Where'd you pick up an interest in science fiction?" she asked as they walked. Silence was the only response. She turned to make sure he was still there. He was studying the floor, but he soon looked up with a pale imitation of his earlier smile.

"Remus," he said with no further explanation.

She nodded. It must be a sore point that his friend didn't show last night. She turned back to her task; led him to the back wall. She debated instructing him on the card catalogue, but decided that browsing would suit his magic-trained mind better. She pointed out her own destination and left him to it.

Several hours later she was surrounded by psychology texts, more befuddled than before she had began. She'd skimmed through theories of Freud and Jung, Skinner and Pavlov, and it felt like she was further from understanding the human mind than she had been this morning. Penis envy, of all the mad things.

She sat back with a crack of release in her back, only to find Sirius watching her. She didn't jump, though her heart did speed up from the surprise.

"Are you ready to go?" she asked after she recovered herself.

Sirius nodded, then held up a couple of thick novels. "Can I get these?"

She held out her hand. "I'll check them out on my account. Do you want anything else?

He shook his head, so she stacked his books with the two she was planning on taking home. The psychology section had been frustratingly silent on the subject of recovered loss, but there were a couple book from the metaphysics section that looked interesting. She dropped the textbooks into the return cart, and then sped through the checkout.

Sirius quite gallantly offered to carry the books after they get outside. She suspected he just wanted to hold his books. He looked quite pleased with himself, and the feeling was shared. It might not have been the triumphant return to Wizarding society that Harry was hoping for, but it was a return to society all the same.

"What're you smiling at?"

She smiled wider at the question, enjoying the brisk air and the setting sun.

"Good books and good company, what could be better?"

Sirius smiled back, but after a moment his gaze fell to the pavement. He was quiet the rest of the way back to the house. Hermione wasn't sure what she had done wrong. She would have to puzzle it out some other time, because Harry and Ron were back. They pulled Sirius inside with laughter and exuberant tales of the match. She sighed at their antics and went to put on the kettle.


A variable that may assume complex values.

They settled into a routine over the next few weeks. They four shared a quiet breakfast each morning, taking turns at cooking. Harry always made a full hot breakfast, saying that at least the Dursleys had taught him something useful. He never said that where Sirius could hear, though. Ron managed a new mish-mash every time, somehow combining his mother's domesticity with the twins' ingenuity. His meals were usually edible and often good, though there had been notable and memorable exceptions–the egg scramble with olives and pineapple never should have seen the light of day. Hermione herself usually forced them to subsist on whatever looked good at the bakery the night before and some fresh fruit. Sirius had cooked a few times, bland food like porridge that filled them up and didn't actually taste bad.

Usually they shared quick goodbyes and then three of them split off to their daily tasks; Harry and Ron to work and Hermione to her assistantship. She didn't know what Sirius did during the day. She had assumed he tinkered with the monstrous bike that took up most of their garage, but when she had looked in the other day it still had been covered by a dusty tarp. Maybe he read books and took walks. She was starting to think she should worry.

Today she was enjoying a late morning at home since the university was on holiday. Harry and Ron had sped off just moments ago, hurried and disorganized as usual. Sirius was puttering around in the kitchen while she skimmed the Daily Prophet over the remains of her tea. She had never been able to give up the habit, despite the paper's tendency towards gossip and hatefulness. Occasionally an informative tidbit snuck through, so it was a habit she didn't bother to fight.

She was on the last pages when the doorbell buzzed. Whoever was ringing was rude enough to leave his finger on for a good thirty seconds. She sighed and rose, thinking dark thoughts about door to door salesmen that would probably get her sent to Azkaban if she acted them out.

She jerked the door open, `we don't want any' ready on her lips. Instead, she was shocked to silence. Severus Snape stood in her entryway, black robes and glowering look in full force. It took her a moment to remember that he had no authority over her.

"Yes?" she asked, disregarding conventions of politeness because she could.

He raised an eyebrow at her tone. "May I come in, or would you prefer to conduct our business in full view of your neighbors?"

Hermione wrinkled her nose but stepped back to let him walk through the door.

"I wasn't aware we had business," she said after closing the door behind her.

Snape towered in the middle of their living room, peering at its nooks and crannies like they might have been harboring gremlins. Or possibly Neville Longbottom. That puzzled her a little, since he had been here recently, and frankly the room wasn't that interesting. But before she could ask, he turned to her, producing a stack of parchment scrolls from somewhere in his robes.

"The Headmaster requested that I bring these to you. As always, I find myself at his bidding."

That quirked a smile out of her. They were all subject to Dumbledore's whims, even as proud a man as Snape. Snape more than any of them actually, considering his history and convenient proximity.

Hermione took the scrolls. They must have been from the Headmaster's personal collection. She had requested a peek for her current research, but she hadn't expected him to actually send them to her.

"Why didn't he just owl?" she asked, but before he could reply there was a loud thump. She looked behind her to find Sirius looming over a fallen dining chair, a dangerous look on his face.

"What's the greasy git doing here?"

She closed her eyes for a half second.

"I fail to see how that is any of your business, Black," Snape snapped out.

"Please, Sirius, he's just bringing me some-"

"It's very much my business when you're standing in my living room!" Sirius rode over her plea. Loudly.

"Your living room, is it? So you have actually taken to paying rent now? And here I thought you were the same lazy roustabout as at Grimmauld Place."

Hermione knew that Snape had gone too far. She stepped forward into the line between them just as Sirius got his wand up. His face was flushed an unhealthy dusk rose, and his normally pale eyes were dark little pinpoints.

"Sirius! For God's sake, put down your wand!"

His eyes flicked to her face and then past again. She chanced a glance back at Snape. He had his own wand out, but it wasn't leveled in threat. Instead he seemed to be studying Sirius, eyes moving as if cataloguing traits for later recitation. She turned back to Sirius. His wand was still out but no longer tensed to attack.

"Sirius," she said again, her voice thin and pleading.

Without a word he turned and stormed to his bedroom, slamming the door behind him.

Hermione sighed in relief and annoyance. "I'm sorry about that," she told Snape. "He's still a bit on edge these days."

"As if that miserable excuse for a Wizard was ever less than unhinged," he replied softly. His eyes, dark and unreadable, were locked on the door where Sirius had retreated.

She sighed again, drawing his eyes back to her. He started to say something, then paused as if changing his mind. Hermione raised her own eyebrow at this unusual behavior.

"I hope you find the scrolls useful, as Professor Dumbledore saw fit to make me his pack animal for your pleasure. Good day, Miss Granger."

Then he turned and stormed out her front door, not giving her the chance to usher him out or to thank him. Still, the whole encounter had been rather tactful. On Snape's end of things, at least.

She turned towards Sirius' door, intent on giving him a piece of her mind. She burst in without knocking. He was staring morosely at the floor, a faded Quidditch pennant in hand.

"Why do you do that?" she asked, softer than she originally had intended.

"Do what?" He didn't look up.

"Always goad Snape, treat him that way," she clarified.

"`Cause he's a nasty git, that's why," he said flatly. He was much calmer than she expected, almost as if the fight was just habitual action with no fire behind it.

"He might not be perfect, but he is a human being, and you should treat him with respect," Hermione chided.

That made him look up. "He was a Death Eater, for Merlin's sake! You can't trust him, the smelly, oily git."

"Was a Death Eater, was! He's a hero of the war, just as much as me or Ron, almost as much as Harry." She pinked a little as she realized she had raised her voice. "And he's not smelly," she added, more softly.

Sirius laughed, low and rueful.

"Not smelly, huh? Well, I suppose I've never been close enough to find out, thank goodness." He tossed the pennant aside. "Ah, Hermione. You're such a good soul."

She wasn't sure if she had made her point, but he was looking at her with a half smile and soft eyes, and that made her all warm inside. She shrugged.

"I just think, whatever it is between you two is in the past, and it should be left in the past. It won't kill you to be civil."

"It might," he muttered.

"Sirius! Don't even joke about that."

He didn't say anything, just stood and gathered her into a hug. It surprised her a little, because while Sirius and Harry frequently shared such affection, he'd been a little distant from her and Ron. She accepted his warmth gladly, once again realizing that he was really back from the dead. He let go eventually and smiled at her.

"So what're the plans for today?"


Triad: A set with three elements.

It was the three of them that evening, Ron and Harry watching the footy match on the telly while she curled up with her latest research journals. Sirius had locked himself up in his room after being silent and sullen at dinner. Through experience she had learned to leave men alone when they got in that mood. Something about Mars and caves that she vaguely remembered, something that had sounded like a load of Trelawney's drivel the first time she had heard it.

The match was apparently a dull one, the boys' team having gained a large lead early on. Their usual jumping and shouting was muted to occasional mutters and good-natured ribbing. She judged it safe to uncurl and plopped her feet in Ron's lap without a by-your-leave. After a minute of continued watching, Ron finally noticed.

"Oi Hermione! Get your stinky toes out of my face!"

She smiled sweetly and waved one foot closer to his nose in threat. He batted at it, but then returned to watching the game. After a while his hands came to rest on her feet. He started to rub without thinking, just as she had known he would. That had been their habit for years, one that had outlasted the war and countless skirmishes of their own making.

She was deep into her article, contentedly relaxed by the attention to her feet, when Harry's face appeared in front of hers. Her eyes crossed from his proximity.

"Harry!" she shrieked as she struggled to sit up. Ron still had her feet in his grip, so it was a losing battle.

"Hermione," he sing-songed back with a grin. "Match's over. We're bored."

"Well get out of my face, you big lout," she said, pushing him back to the best of her ability. He collapsed across her legs, though he was careful not to overextend her knees. Hermione was well and truly trapped by the two of them.

"Let me up," she panted after she tried to squirm free. It was all but impossible to even breathe, let alone free herself. Harry giggled like a little boy and she heard one or two of Ron's deeper chuckles. Finally she stilled, nearly exhausted.

"See Ron, told you I could get her nose out of her stupid book," Harry taunted.

That did it. She bucked wildly, catching them by surprise. Harry tumbled onto the floor while Ron hastily guarded his family jewels from stray kicks. She stood quickly, then took a pose with her hand on her hip.

"What was that, Mr. Potter?"

Ron snickered while Harry looked rather sheepish. His glasses were skewed and his hair was even crazier than usual, full of static.

"Uh, nothing, Hermione. You feel like playing a game? We're bored," he added with a pout.

Ron stuck his face down next to Harry's, looking up at her with sad eyes and a matching pout. She huffed, but gave in. Such was her life with the two of them.

"Fine. But no exploding snap."

Harry climbed to his feet and headed for the stash of cards in the entertainment center, pulling out one of the Muggle packs. She had just never got used to having cards explode in her face. The boys were good about conceding to her whim. She played with Wizard cards on occasion to share the compromise.

"Should we ask Sirius?" she asked.

Ron looked at the closed door behind them. He shrugged uneasily.

"Uh," Harry stumbled. He had been so happy to have Sirius back, but Hermione thought the honeymoon glow was starting to fade. The other two were noticing that Sirius was not the perfect example of humanity that they had made him into after his disappearance. That didn't lessen their love for Sirius, of course. Now they were starting to think about how to handle his moods, rather than simply glossing over them.

"I'm sure he'd prefer a Wizarding game," Harry finally said. "We'll play with him some other time."

Hermione smiled at him, hoping he knew that he wasn't alone. Harry was used to taking on the problems of the world; sometimes he forgot that others were willing to help shoulder his burdens.

"Sounds good," she agreed. "So, poker?"


A hypothesis is a proposition that is consistent with known data, but has been neither verified nor shown to be false.

The owl had taken her by surprise, the letter more so, though after his visit not as much as it once would have. The contents were short and expressed his personality so well that she had looked for a charm hidden in the ink.

"Miss Granger," it read, and how did one convey a sneering drawl just through penmanship? "We have items of mutual interest to discuss. Meet me tomorrow at sunset, your choice of location. S. Snape." There was an addendum, so slashing in style she could barely read it, but she finally puzzled out the word "Please". It had made her laugh, that irritated condescension to civility. She had sobered when she realized it must be a serious matter for him to make it a request rather than a demand. So she had owled back right away, a simple address all the note had contained. Out of spite she had chosen a Muggle café, sure to be crowded at the appointed time of day.

She hadn't a reply, so here she was, waiting nervously for him to show. Half of her was certain he would stand her up, the other half sure that he would show despite her fervent wishes. She was settled into a comfortable chair in the far corner of the shop, where she could theoretically watch the door. Unfortunately there was so much traffic from the wait staff and customers that she could only see across the room about fifty percent of the time.

And so she was yet again taken by surprise when he appeared in front of her. He was not quite so imposing as usual; it must have been his normal billowing robes that made him so much larger than life. Now he was wearing black trousers and a black button-up shirt with long sleeves. The top button was missing, showing a bit of pale throat, and she caught sight of greying at the elbows. She wondered if he had got the set from a thrift shop.

He just stood there, looking at her, looking around at the store, so she pushed a chair out with her foot and waved at it with her cup of tea. He raised an eyebrow, but sat. Still he didn't speak, so she huffed and rolled her eyes.

"Honestly. You were the one who wanted to meet. You can at least say hello."

Snape nodded in acknowledgment. She wondered if he had been testing her in some way.

"Hello, Miss Granger. I trust you are well?"

"As well as I can be, considering the mysterious nature of your owl. What's going on?" She almost called him Severus, but she didn't quite have the spine. Damn her authority issues, anyway.

He ignored her question and signaled the waiter with a sharp wave. Looking all the world like he did it every day, he ordered a pot of tea and a sandwich. So much for hoping to discomfort him with Muggle surroundings. He turned back after the waiter left, fussing with his napkin and silverware, and then leaning his elbows on the table so he could steeple his fingers. Perhaps he was uncomfortable after all.

"I wish to discuss that man living in your house."

As there were three such individuals, it took Hermione a bit to decide which he was talking about. She discarded Ron right away, because although Snape disliked him, Ron had never rated that particularly enthusiastic level of hatred which infused Snape's words. Harry used to generate that much heat, but since the war Snape's attitude toward him had mellowed to active dislike. Besides, she doubted that Severus Snape would ever refer to a former student by any term other than boy.

"Sirius," she ventured after a moment.

"Yes, Black," he spat.

She almost bit back at him but then decided that mutual provocation did little to progress a conversation. She took a deep breath, wishing she had thought to bring a pack of cigarettes.

"All right, then. What do you want to talk about?"

Snape let out a slow breath, too measured and soft to really qualify as a sigh. "Has he been behaving out of the ordinary? Is he healthy? What does he do with his time?"

The questions puzzled her, concerned her. She got a little knot in her belly at the thought that something might be wrong with Sirius.

"He's fine as far as I know, but I'm not sure what he does with himself. Why? Do you know something? Is he in danger?"

Snape snorted. "I should be so fortunate. No, I am merely trying to assess his well being. Does he ever mention Lupin?"

"Prof-I mean Remus? No, not really, but he rarely talks about anyone. He hasn't had much interest in socializing–not that I blame him. And Remus hasn't bothered to show up for a simple hello, glad you're not dead, so I hardly think Sirius would dwell on him."

Snape gave her a cold look, enough to make her want to cower in her seat like a first year.

"Obviously I was mistaken about your intelligence, Miss Granger. Perhaps I should forget this whole venture." He tossed his napkin on the table, obviously preparing to leave.

"Wait! What do you mean? Is there something going on with Remus and Sirius? I didn't mean to be flip, but it irritates me that he hasn't even asked about Sirius."

Snape settled back in his chair, holding her eyes for a long measuring moment before breaking away to reach for his teacup.

"Remus Lupin," he drawled in that gravelly voice, "has gone on a bender."

She felt her eyes widen and her jaw loosen, and she knew she must have looked a fool. Surely not! Not Remus, one of the most controlled, calm people she had ever met. She was forming a protest when Snape continued.

"Oh, yes." There was a light in his eyes, but it was not glee. He took no pleasure from Lupin's state. "When I looked in before I came here, he was in the process of remedying a hangover by the simple expedient of imbibing most of a bottle of Old Ogden's. All because that imbecile Black didn't have the decency to stay dead!"

He had leaned forward in his tirade, staring deep into her eyes, and Hermione found herself unable to respond. Responses flew about her brain like crazed pixies. Anger at his disregard for Sirius. Anger at his presence in her personal space. Surprise that his eyes were a dark brown rather than the demonic black they had always assumed them to be. Concern for Remus.

Poor, poor Remus.

"Oh," she breathed finally, and found that said it all.

"Oh," he agreed, and then slumped back into his chair, one large hand coming up to cover his eyes.

"I don't understand," she said finally. "What's happened? Why isn't he happy to have Sirius back?"

Snape pinched the bridge of his nose with his thumb and index finger, rubbing like he had a headache.

"I am far from an expert in matters of emotion," and Hermione was slapping a hand over her mouth and nose, but the snort had already escaped. He merely glared while he continued. "As I was saying, I believe that he never really allowed himself to grieve. He simply buried himself in work for the Order and concern for you three."

Hermione nodded along with his words, his ideas echoing her own from the night of the party.

"And now it's all hitting him," she said, guessing at his conclusions. "He's going through the stages of grief, even though the reason is gone."

She looked up into dark eyes, eyes that almost seemed to soften in shared sympathy. But then they looked away and she was pulled back to the problem.

"I understand more of what is going on now, but why did you tell me this? What do you want from me?"

Snape took a sip from his tea, and then stared into the cup as he replied.

"I don't know. I thought you might have some...insight into the problem. After all you are living with the root cause," he finished with a curled lip. The way he had said `insight', as if it were a dirty word, made it clear that he had a very difficult time admitting to his own shortcomings.

She sighed. This was not an area she was good at. Emotions were too volatile, too illogical, and even the psychology books she had studied had little in the way of practical application.

"Not particularly," she confessed, expecting him to find great satisfaction in that. When he just continued staring at his cup she decided to say more. "I'll think on it. Maybe I'll manage to pull something out of Sirius one of these days."

Finally he looked up.

"Very well. Anything you can think of should be reported to me as soon as you can." He paused with a little frown, as if realizing she was no longer his student. "It will be appreciated."

She smiled. "Perhaps we could meet again and discuss some strategy." For some reason she felt like they were gearing up for another war, back to the days of gathering intelligence and waiting for the opposition to make their move. Her body thrummed with the same anticipation as in the old days, even as she told herself she was being ridiculous.

"That would be acceptable. Good day." He was standing to leave when a thought occurred to her.

"Professor, if I may ask, why is this so important to you? I thought you didn't like Remus."

He was silent long enough that she thought he wasn't going to answer.

"I have found Lupin's company tolerable since sometime before the end of the war."

Then he spun and headed towards the door, the effect slightly spoiled by the lack of robes. She was so flummoxed by that declaration of friendship that it took her a moment to realize he had stuck her with the bill.


A group of four elements, also called a quadruplet or tetrad.

Another lazy Sunday found them at home, Harry and Ron enjoying their day by comparing the merits of football to Quidditch. Ron, surprisingly enough, one was the one who had the love affair with the Muggle sport. It was hard to draw him away from the television set sometimes. Harry enjoyed them both, but Quidditch had given him his first sense of identity, so it would always reign supreme in his heart. She wasn't sure if he understood that himself, but Hermione's favorite sport had always been Harry and Ron watching. In it, she was a master. She knew more about her boys than they knew about themselves. Ron, for instance, pulled on his left ear whenever he was trying to work out the best way to spring a new idea on her or Harry. He always ordered pepperoni on his pizza and then picked most of it off, and his driving ambition to be wealthy and famous had faded away with the losses of the war. He still worked hard, but his heart was no longer focused on riches. Rather, like Harry, he was happy with the little things in life.

Hermione uncurled her legs and shifted around in the big stuffed arm chair, rearranging the text book so it didn't dig into her leg. It was another psychology book, this one focused on mental illnesses. She had given up on the ones on grief. They were too general for her needs, and she still had no idea how to help Remus. So instead she focused on Sirius. She was worried that the veil might have had some effect on him, that it might have scrambled his brains, as Ron would say. Luckily Sirius hadn't exhibited any of the signs of the scarier ones, like dissociation or sociopathic personalities.

"Oi! Hermione, are you ever going to relax?"

That was Ron, of course. Even after all those years together, he and Harry still didn't quite understand how much she loved books. The idea was anathema to them. Strangely enough, Sirius shared her passion. She wondered if he was always that way, or whether the years of deprivation had increased his appreciation.

"It's a lost cause, Ron. You know she'll be buried in that thing till it's done," Harry said.

"Yeah, and then tomorrow she'll be complaining that we never do anything together anymore. Women. Can't live with them, can't hex them."

"Hey," she yelled, and then tossed a cushion at his head. He barely deflected it, and then grabbed for it as it fell.

With a shriek she was out of her chair, running for the opposite side of the couch where she thought she could get another weapon. Unfortunately she was ambushed by Harry, the little turncoat, tossing his own cushion straight at her head. It hit the floor and she grabbed it, just as Ron thumped her in the arse with his pillow. The fight was on in earnest, Ron and Harry briefly ganging up on her before deciding to make it a free for all.

There was a reason she didn't keep bric-a-brac in the living room.

Hermione retreated for a breather as Harry and Ron escalated the attacks on each other. She was panting in the corner when an arm snuck around her waist. She wondered what Sirius was up to.

"Boys! You're missing out over here!"

The betrayal hit hard. She squirmed and aimed her pillow at whatever she could reach. Sirius was laughing just a little, something new, so she didn't try too hard to get away. Then Harry and Ron were there, beating both her and Sirius with the fluffy pillows. She got her pillow up over her face. Finally she couldn't take anymore.

"Truce! Truce!" she yelled, and eventually they settled down, all of them laughing. Sirius still had her pinned against him, and it felt nice. Warm and safe and loving.

"That was bloody brilliant, Sirius," Ron said with a big grin.

"We don't get her cornered very often," Harry agreed.

"You two ought to be ashamed of yourselves, picking on a girl like that," Sirius replied.

She opened her mouth to defend her feminist perspective when suddenly Sirius dropped her like a log. While Harry and Ron were busy laughing, Sirius scooped up two of the cushions. She grabbed the third, next to her foot, and together they evened the score on the boys.


Conjecture: A proposition which is consistent with known data, but has neither been verified nor shown to be false.

They met at the same café, though today she was running late from class and he was the one waiting for her. Hermione fully expected him to strip skin off her back for being late, but he simply pushed out a chair with a subtle wave of his hand. She was impressed despite herself; wandless magic was a tricky thing.

"Good afternoon," she greeted.

Snape glanced pointedly at the bay window behind her, where the setting sun was sparking an artist's pallette of orange and purple-pink.

"Good evening," he replied after a moment. Well, it was a far more pleasant rebuke than what she had expected.

A waiter wove through the filled tables to take her order. Despite her best intentions, she ordered a sweet scone and a pot of tea. It would spoil dinner, but it had been a hard day. The clink of silver and the hum of conversation all around was nearly overwhelming; she really should have chosen their meeting place more carefully.

"Well?" he prompted without further polite chatter.

She rubbed her temples, wishing for a Pepper Up Potion. Or even aspirin. One should never have to deal with Severus Snape whilst in the throes of caffeine and sleep depravation. She tried to gather her thoughts to present her deep cunning and sparkling insight, but found that all she had to give were meaningless book reports.

"I've been studying Muggle psychology texts, but nothing really leaps out at me. Nothing terribly disturbing, anyway. We studied practically everything known about the veil after the incident, but I found nothing when I reviewed my notes on itl. Perhaps if we had access to an Unspeakable..." She trailed off, knowing that was an impossibility.

"Bloody waste of gold," Severus muttered.

She kept her opinion to herself, though she suspected it matched his own. Fudge might no longer be Minister of Magic, but the bumbling bureaucracy he was so well known for lived on in his stead. Her tea and scone arrived during their mutual contemplation of idiots the world over. She took a minute to pour and to sample the cinnamony treat, feeling her headache lift at just the scent of caffeine. He passed her the pitcher of milk, apparently remembering her preference from their last meeting.

"And Black? How does he fit in with all of your newfound knowledge?"

She took a moment to savor the hot liquid, barely cool enough to drink without scalding her throat. Through the steamy haze she noticed that an empty plate rested by his elbow. A stray crumb was brave enough to muss his shirtfront; the white speck a fleck of snow against the black night of his cotton shirt.

"I don't know, Severus," she paused to gage his reaction, but he simply raised an eyebrow and waited for her to continue. "I think he's just depressed. He doesn't do anything during the day, as far as I can tell, and he doesn't seem to have any drive to make anything of his life. He interacts with us well, but sometimes he gets quiet, or acts tired too soon. But who knows what effect the veil had on him? It just spit him out, and he claims not to remember any of it."

Severus had his left hand up, thumb stroking his lips. She didn't remember the gesture from her youth. Perhaps he was more given to expressiveness now that he wasn't being watched every hour of the day. For the thousandth time she wondered how he did it, how he had borne the pressure of being a spy against the most feared wizard of the century.

"It's entirely possible, of course. But I would think it would have had more effect than a bad mood."

"Depression is more than a bad mood, Severus."

He waved his hand sharply, as if dismissing class.

"Yes, I know that, Hermione." He drew her name out in a long sneer. She took it as permission to continue using his given name. "But it can be dealt with, over time at least. He's not suicidal, is he?"

"I don't believe so, though it's hard to gage his moods. I've tried to talk to him, but he's very good at turning the subject."

"Perhaps you should try harder," he said quietly.

"Perhaps I will." It somehow felt like a dare, a challenge to her own abilities rather than concern for someone she cared about. She pushed down the unworthy impulse and concentrated on being a good friend. "How is Remus doing?"

He sighed. "Better, actually. He's stopped drinking quite so much, though he's still angry and depressed. He worries about Black whenever he's not cursing his existence. I had hoped that bastard you live with might actually have shown some concern about Lupin."

"Well, Sirius hasn't talked about him, but that doesn't mean he's not concerned," she defended.

"Wrapped up in his own little world, you mean."

She rolled her eyes. "You know, I get really sick of hearing this childish squabbling between the two of you. Why can't you leave it in the past? You're both grown men, you should act like it."

Predictably, Severus drew himself up, folding his arms across his middle in a gesture that would have had more meaning with a volume of black cloth.

"You know nothing of what is between us," he said in a cold voice.

She knew she had pushed him to his limits of civility, but the feud annoyed her like little else these days. "Oh really? I know that this probably started because of a snub or a prank by one of you, just like little boys do, especially when they've been taught to behave badly by their parents. And instead of rolling with it, the other returned the favor, over and over in pointless escalation. You both got your feelings hurt, and neither of you were willing to forgive."

Snape just looked back at her, eyes black and reflective, his whole posture as still as a Petrificus Totalis.

"I suppose you probably got picked on a lot when you were younger, for stupid reasons, like wealth and family and looks and intelligence, and it made you sad and bitter. Maybe that's even why you became a Death Eater. Well, I'm sorry that you had to go through that, but get over it! Make a different life for yourself. You're not eleven anymore."

She was almost panting by the end, and amazement was setting in that she'd had the balls to actually say that to his face. Amazement, and a little fear. He was still cold and controlled, and she wondered what was to come.

"Are you through?"

She nodded, because there was a nervous lump in her throat that she couldn't vocalize around.

"I am very impressed, Miss Granger. You have obviously been doing your reading, because that is the largest bunch of Muggle psychotripe I have ever heard in one sitting. If you applied your talents to something worthwhile, such as reading the Quibbler, perhaps you might have a future as a first-class charlatan of Trelawney's ilk."

Snape stood, walked around the table to lean over her. He was much taller than she when they were both standing, and now he made her feel like a mouse. He leaned forward, bracing his hands against the table. His breath seared against her ear, and a length of his hair whipped against her cheek.

"Never presume, Miss Granger, to analyze my motivations. Not about Black, and certainly not about the Death Eaters."

Then he spun away and left the restaurant, trademark exit perfection.

Hermione blinked away the dampness in her eyes, proud that she didn't cry but frustrated that she had come close. It made her mad that his opinion of her had any weight on her self-image. She sipped her cold tea, thinking that yet again he had stuck her with the bill. Stupid git.

Then she smiled. Even Trelawney had moments of insight. Hermione thought her own was pretty close to the mark. Severus would have laughed at her otherwise.


The term asymptotic means approaching a value or curve arbitrarily closely (i.e., as some sort of limit is taken).

She tucked the note in her pocket, then set about finding the owl treats. Hermione hummed in disgust as she noticed they were almost out; Harry was supposed to pick up more the last time he went into Hogsmeade. Of all the people to forget.


She turned and smiled at Ron, then scattered the remaining treats in front of the Great Horned owl perched on the window sill.

"Just something I'm working on," she told him. It wasn't a lie, not really. More like an oversimplification of a problem for someone who couldn't grasp the entirety of the equation. "Were you expecting something?"

Ron shrugged, then walked to the refrigerator. He stood with the door open, staring at the contents like an exhibit at an art gallery. "No, not really."

She frowned. "Not really?"

He sighed, then slammed the door shut. He turned to her with a wry smile. "I was hoping to hear from my mum."

"Oh," she said, a bit stupidly. Her own relationship with Molly hadn't been stellar since the war. Hermione had always felt like Molly held the breakup against her. "Something up?"

Ron dropped onto the kitchen stool. "No, nothing more than usual. I just wish..."


"I don't know," he sighed. "This whole thing with Sirius has really turned her upside down, you know? I don't think she ever really liked him very much."

Hermione snorted. "He does seem to inspire either love or hate rather strongly, doesn't he?"

Ron smiled. "He claims it's a Black thing." His smile fell, his eyes turning thoughtful. "She's been so resentful lately. I mean, I wish Dad were alive, too, but that doesn't mean I'm not glad Sirius came back."

She nodded. She noticed he didn't mention Percy, but decided to leave that untouched. "You shouldn't feel bad about that," she told him.

"I don't," Ron assured her. "I just wish she could be happy. That she..."

He trailed off again, and this time Hermione had a guess to where his thoughts led. "That she remembered she has six wonderful children still alive?"

He nodded slowly, eyes on the floor. She reached across the table for his hand.

"She's nutters, but I still love her. I don't know what to do."

"I don't either," she told him. "Maybe with time. I don't think there's anything you can do, though."

He sighed again, then squeezed her hand. "I know." He smiled up at her, a very Weasley grin that never failed to make her wary. "We could get married, that would make her happy."

She snatched her hand back and smacked him on the nose. "What did you put in the coffee this morning, Ronald? Or has Harry driven you round the bend?"

He laughed, and something relaxed inside that she hadn't known was tense. It was a very good thing that they were at a point in their lives where they could joke about their failed relationship. They were much better friends, and that was that.

"Just the beans," he said as he rose from the table. He pressed a kiss to her forehead, then walked toward the door. "And a bit of something the twins sent me," he called as he ducked through the doorway.

She tossed off a mild hex at his retreating back, but she was laughing too hard for it to take. She giggled for a bit longer, leaving her feeling rather peaceful afterward. She did wish she could help Molly in some way, but she thought the problem was beyond her amateur skills. Besides, she was already busy enough with Sirius and Remus.

Speaking of which. Hermione pulled the flattened note from her back pocket and unrolled it.

Miss Granger, and they were back to formalities again, were they? As you so eloquently stated recently, the past is in the past. At the present I find it necessary to look to the future. She blinked, trying to untangle the meaning in that before reading on. As such, will it suit to continue our meetings as before? I am still engaged in finding a resolution to the situation in question. It was signed simply Severus, which confused her to no end.

After a minute of pondering, she sat back with a contented smile. Perhaps it was too much to hope he had taken her words to heart, but at least he was ready to move beyond his anger. Her impudence was forgotten, if not forgiven.

Well. She had work to do. Severus would be expecting her report.


A proof or demonstration is said to be rigorous if the validity of each step and the connections between the steps is explicitly made clear in such a way that the result follows with certainty.

Hermione sighed as she saw a form stir on the back porch. She had come down for a midnight snack, bored with her current article. The sloppiness of some people! It made her angry just to think that those conclusions were published. Peer review, indeed. She shook her head, aware that her frustration accomplished nothing. Instead, she forwent her snack and decided to brave the man sulking in her darkened yard.

Sirius was in human form, leaning against the porch rail as he studied the stars. He looked at her with a sad smile, light from the crescent moon glinting off the whites of his eyes. She walked to his side, trying to figure out what he was so interested in.

"There's me," he said, the line of his arm and finger as sharp and sure as any pointer.

The star blinked brightly. It was one she knew well from her very first astronomy lessons, back when her father had introduced her to his passion for the night sky. She smiled at the memory, then turned to study Sirius the man.

His shoulders were rolled inward, giving him a hunched and defeated look that she only remembered from that summer at Grimmauld Place. Before, though he was starved and ragged and nearly mad, he had been filled with the fire of righteousness. Now he only looked empty, as if his whole reason for existing had been sucked out of him.

"What are you doing out here?" she asked.

He shrugged.

"Sirius, why don't you tell me what's going on? Maybe I can help."

He turned to her with that sad little smile again. "What's going on? I'm just looking at the stars, Hermione."

She huffed in exasperation. "You know very well what I mean." She calmed herself, and then tried again in a softer, gentler tone. "Why are you so...down?"

She elided the other d-words: depressed and desperate and dark and maybe even delusional. The crickets chirped as she waited for an answer, hoping that for once the direct approach would serve her purpose.

"Oh, Hermione," he sighed. "It's so very much to put on your shoulders."

"I'm stronger than I look, Sirius. And who better? Harry?"

She knew that would prick his conscience, because the one thing they very much had in common was their desire to protect Harry from all the ills the world might yet provide.

"You learned how to fight dirty," he said, admiration in his tone. There was much about him that could be Slytherin. Then a breeze gusted around them, lifting the curls of his hair like a wild mane, and she remembered his wild, impulsive bravery. He took a deep breath, and that courage came through. "It's just so much, Hermione. The world is so different, and I don't know who I am."

Finally. She felt a small burst of triumph before panic took over. She had no idea what to say, how to draw him out further. So instead she stepped forward, brushing his hand with her own, hoping the physical contact would urge him onward. He took her hand, lacing their fingers together loosely.

"When I first got out of Azkaban," he started quietly, "I was more than a little insane. They take so much, you know. You lot should have done away with me then for your own good."

"No, Sirius, no," she protested.

He smiled and brought her hand up to brush with his lips. "Too bloody Gryffindor, all of you."

He returned to watching the stars, and she wondered what to say. She snuggled in closer to his side, thinking that Sirius responded well to affection.

"There was so much of me missing when I got out, but I didn't even realize it. I was so focused on revenge, on protecting Harry, that nothing else really mattered. And then I just kept thinking about keeping Harry safe and staying alive."

She made a small noise of understanding, not wanting to interrupt his flow of words.

"Then I had that awful idea. I was so intent on making sure he stayed safe, finding a way to end the war as soon as possible, that I didn't even think about how it would be, locked up in that place again."

"I'm so sorry," she murmured. "None of us really understood, back then."

Sirius shrugged. "Well, it's not like I wanted you to understand. You had so much more on your minds than young people should have. And I behaved like a terrible lout."

He turned towards her, bringing up a hand to pull at one of the curls that had sprung loose from where it was piled on top of her head. Then he stepped away, fading into the shadows of the night.

"Now, I can see everything. My whole life is meaningless. All I've done is hurt people with my very existence."

"Sirius! That's not true–we,"

"Don't, Hermione. Don't coddle me. I'm a failure as a human being, that much I know. And really, the only thing I really ever tried at, being a godfather for Harry, well I failed at that worse than anything else."

Tears were starting to prick her eyes, and she wasn't sure how to argue with him. She tried anyway.

"Harry loves you very much-"

"Because that's Harry's nature. But what have I done for him? Scared the bejeezus out of you lot third year? Gave him a bunch of bollocksy advice a few other times? The biggest way I affected his life was by dying. I'm sure that did wonders for his psyche."

Hermione sniffed as a few tears escape, her heart tugged by the despair in his voice more than his self-pitying words. She gathered her composure and her thoughts, then stepped close to him once again.

"Sirius. You may not have been with him for long, but you gave Harry so very much. You gave him love and support, something he needed so very badly then. And he loves you for you, Sirius. Not because he owes you something, or because he's supposed to, or because it's just his nature. Because he finds you worthy of love."

Sirius cleared his throat, the sound loud and rough amongst the soft creak of insects beyond them.

"I just feel so dead inside," he whispered hoarsely. "Like the man is gone, and I'm just a hunk of rotting skin."

"Oh, Sirius," she soothed, pulling him into a hug. He clung to her tightly, and she knew that he was more than he thought himself. She just didn't know how to convince him. She pulled back just a little, studying his face. His eyes were closed, damp streaks shining along the valleys of his cheeks, glittering in drops on his trimmed beard.

Struck with a sudden impulse, she leaned up against his chest and kissed him.

His eyes flew open, pale, pale blue almost swallowed by the black of his pupils, and she thought she had made a mistake. But instead of pushing her away, he reached up and brushed her cheek.

"Sweet Hermione," he murmured. "You have no idea what you do."

She swallowed, weighing her options in the length of a breath. Yes, this was a mistake, a terribly bad idea, but she thought it might be the best bad idea she'd ever had. She leaned forward again, lingering against the softness of his lips.

His hand curled around the base of her skull, pulling her deeper into him. Sirius Black might have spent most of his life in desperate isolation, but his kissing skills didn't lack because of it. She moaned deeply as his tongue licked at her lips, as his teeth nibbled her neck and ear lobe. She returned the favor, burying her face against his neck, just inhaling his scent. She had noticed it before, but now it was nearly overwhelming, salty and sweet with a hint of patchouli and rose. She nipped just below the edge of his beard, and he growled out a moan.

She was intent on producing that sound again when he grabbed her shoulders and pushed her back. She blinked, trying to regain her equilibrium.

"Hermione...I. What?" He stopped and took a deep breath. "Are you sure?"

She smiled, slow and seductive and sultry, the confidant woman inside her coming to the fore. This might be a very bad idea in the larger scheme of things, but she'd always had a thing for Sirius Black. Hermione had got very good at holding onto the things she wanted.

"Oh, I'm very, very sure," she purred, and part of her was rejoicing in the fact that she didn't sound ridiculous doing so. The other part was taking his hand and leading him inside, leading him to his own bedroom.

There was an awkward moment after he closed the door. She cast a silencing charm, then slid off her slippers. For a moment she wished she was wearing one of her sexy teddies, but he'd seen her worse than this. Thank God she had shaved her legs that morning.

Sirius was completely intent on her, his eyes bright in the shadowed room as she slipped her nightgown off her shoulders. She had a little pooch at the middle, a result of too many sweets and books, but she felt comfortable with her body. Sirius caught his breath, and that made her last little bit of nerves fall away. She swept the clip out of her hair, letting it tumble down in a dramatic gesture, and stepped forward.

He sank both hands into her hair, capturing her mouth in a kiss that went on and on, leaving her panting and wobbly when he broke away. She clung to him, then started to unbutton his shirt once she calmed a little. She paused as she saw the faded tattoos. The runes made little sense to her. She simply traced them with her tongue as her fingers continued their task. He had good muscles on his chest, though she could tell he used to have more. His skin was smooth except for the soft black line of hair that started at his belly. She brushed over it, almost compulsively, and his skin twitched under her hand.

Sirius took control then, kissing her quickly before leading her to the bed. He gently nudged her to lie down, then slipped his pants off. He was hard, and she tried to touch him as he crawled towards her, but he caught her hand and urged her to lie back down.

"It's been a long time, sweets. Let me see if I remember the basic steps first," he said with a wink.

Hermione smiled back at him, then caught her breath as he captured her nipple between his teeth. He moved on to her belly, nipping and licking as his hands crept up to her breasts. He barely brushed her nipples with the pads of his fingers, setting her on fire. She arched her back, silently begging for more.

He left her stomach alone, looking up with a gleam in his eye. Suddenly he started kneading both of her breasts, thumbs circling her nipples as he gently squeezed and massaged the surrounding flesh. She felt wild, uninhibited, energy zinging through her skin and making her want to thrash and moan. Incredibly, she thought she might have an orgasm from this alone, but then he let go and backed down her body. She whimpered.

Then his tongue was on her, warm and wonderfully wet, circling and stroking and pulling her tighter and tighter. She was getting closer and closer, and then he dipped down to thrust his tongue inside her. It was too much and not enough and she was panting wildly.

"Sirius," she moaned, begging him for something to finish her off. He returned to her clit, his tongue flicking strongly over and over and then the rhythm started, shivers quaking at her center, pulling and tightening and moving outward as she came and came. He slowed down just a little, letting her peak fade naturally into something soothing and satisfying.

She was still coming down when he moved up her body and entered her.

She couldn't breathe for a moment as she clenched around him, feeling both stretched and on the edge once again. Hermione looked up into his face, hovering close to her own. His eyes were nearly translucent, and they were focused on her like she was the only thing in the universe. As she relaxed, Sirius started to move, small little thrusts that spark all over her body, building and building and building and she just wanted more.

"Sirius," she moaned again.

He picked up the pace, withdrawing and then pushing in fast and hard. She tilted her hips and wrapped her legs around his back, and it was enough to set her off. Her body convulsed, lifting her head off the mattress as she lost all control. His arms scooped under her shoulders and he thrust one last time, deep, holding her close as they ground into each other. She felt him pulse inside as he groaned.

Slowly they relaxed against each other, regaining their breath. Their bodies were slick with sweat and the semen between her thighs. She felt glorious, the weight of Sirius on top of her real and warm. Eventually he shifted to the side, but stayed close, playing with her hair.

"I'd say you remembered the steps quite well," she said with a satisfied grin.

Sirius laughed. "Hmm. I'm glad you thought so. I had forgotten how enjoyable sex is, though."

"We shall have to remedy that," she flirted.

Sirius smiled at her, then a concerned look crossed his face. His eyes flicked away, then returned to hers. "Hermione, you know I care about you right?"

Ah. She knew how to handle that concern. "Sirius, don't worry about it. We're just having fun, right?"

Such a look of relief crossed his face that she couldn't help but feel a little hurt. She might not have been in love with Sirius, but every girl had a part that wanted all the men in the world to be madly in love with her.

"You don't have to be such a man about it," she muttered, feeling some of the glow fade.

Sirius pushed away the strands of hair that were stuck to her face. "Hey. Hermione, you are a very beautiful woman, and I had a wonderful time. I just want to make sure I don't hurt you."

She rolled her eyes at her own fragility. "I know, you just managed to step on my delicate ego. But you don't have to call me beautiful to make up for it." That was one thing she had always known for certain. She wasn't ugly, and she wasn't beautiful. She was just somewhere in between.

Sirius shook his head. "Good lord, woman. You may not be the best looking woman in the world, but you are beautiful. And besides that, you have such a beautiful spirit, all this confidence and intelligence that shines through, like a diamond reflecting the sun in a thousand facets."

She had ought to laugh at his hyperbole, but instead she was blushing at the compliment. She rolled towards him, idly tracing the tattoos on his chest.

"Thank you," she murmured.

Sirius puffed out his chest comically. "I aim to please."

She smiled, but shook her head a little. "No, that's not what I meant. I just realized how dead I've been myself these past few years. I wasn't down or anything, but I wasn't living either. Tonight, you made me feel alive again."

Sirius caught her wandering hand in his own, then scooted down so he can look her in the eyes. "No, thank you. You've made me feel alive, and I thought that would take a miracle."

They shared a moment of mutual admiration, before Hermione blushed and sat up. Then a devilish idea entered her head. She hovered above Sirius, ready to move downwards.

"So, do you remember fellatio?" she asked with a grin.


An identity is a mathematical relationship equating one quantity to another (which may initially appear to be different).

Nervousness had made her more than early this time, and so the minutes ticked by with agonizingly fast-slowness. She'd already finished a sandwich (smoked turkey on rye with a bit of cheese and avocado), and now she was picking at the edges of a scone. She felt like a therapist who had overstepped the bounds of propriety, waiting for the world to read her disgrace from the big scarlet stamp on her face. Hermione knew it was ridiculous, that she hadn't really done anything wrong, but it ate at her all the same. She told herself to get it together; Severus was the most observant man she knew. He'd spot her anxiety a mile away.

Really, it was the best resolution to sexual intimacy she'd ever experienced. Sirius had been warm and friendly to her, almost grateful, without any sense of expectation. It was almost like it was just a normal aspect to their friendship. Hermione smiled. A really, really good aspect.

"Swallowed the cream, Miss Granger?"

Hermione jumped, images of doing just that leaping to mind and staining her face crimson. Severus had his head tilted, eyebrow raised in that condescending curiosity he'd perfected. Sometimes she thought he affected a sour disposition simply because it suited his features so well.

"Severus! You startled me. I was deep in thought," she rambled, and then stopped herself. There was no use in looking a complete idiot. "Have a seat, why don't you."

He did so without comment, which was a great relief to her. She took advantage of his inattention while he was ordering to remind herself of why she was here. She had plenty to tell him about Sirius' mindset. She just didn't have to tell him everything.

"So, how are you doing?" she ventured when the waiter had left.

The unusual politeness of her greeting caught him off guard, and he didn't reply immediately.

"Well," he answered simply. "And you?'

"Fine," she said with a wide smile. "And Remus?"

Severus unfolded his napkin with a flourish, settling it on his lap. "Better, I suppose. I haven't seen him drink in quite some time, thank Merlin. He's still reluctant to see Black, however."

"Hmm," she pondered. "Sirius opened up to me some the other night. We were right, it's pretty much depression associated with all the years he's lost."

She looked up as she finished pouring another cup of tea, and she thought there was a glimpse of pity in his eyes. It disappeared as soon as he noticed her gaze.

"I suppose that's understandable, though it couldn't have happened to a better person." She opened her mouth to protest, though she wasn't sure what to say, but he hurried on. "All the same, with time he will recover. As will Remus, if his current arc of progression is an accurate predictor. Has Black discussed Lupin at all?"

She shook her head. "No, which I think is strange. I think he's avoiding the topic completely."

The waiter arrived with Severus' sandwich. They were silent as he spread a thin layer of Dijon across the bread, then carefully rearranged the ham, tomato, and lettuce to his exacting standards. He wiped his hands carefully, then caught her watching him.

"I think it is important that they do see each other again, though I'm not sure how soon it should occur."

She nodded her agreement. She picked at her scone as he started to eat.

"What I don't understand," she pondered aloud, "is why they are taking it to this extreme. I mean, if I lost Harry or Ron, I'd be torn up, but I'd heal eventually. And to get them back would be the greatest gift ever."

Severus was looking at her with a strange expression, sandwich poised in mid-air. "Perhaps. Though if you had lost Ron in the middle of the war, you may have felt the same way," he said after a moment.

She thought back to that time, when the two of them had been so wrapped up in each other, seeking solace in the best avenue open to them. Harry had held himself apart, though they tried to reach him, to support him in whatever way he needed. To lose Harry would have been horrible, though they had more than half expected to. To lose Ron would have torn her world apart.

"Wait," she said as the comparison dawned on her. "Do you mean Sirius and Remus..."

He actually laughed as she trailed off. "Do you honestly mean to tell me that you didn't know? That the great brain of Hermione Granger, smartest witch of her age, didn't figure out that Lupin and Black were lovers?"

A flush rose to her cheeks in the face of his disdain, then all the blood rushed away, leaving her skin cold and goosepimpled as she realized the implications. That night...

"Oh God," she gasped in horror.

Severus frowned at her. "I agree that Remus has execrable taste, but your reaction seems a bit extreme. Are you averse to such relationships, perhaps?"

His question pulled her from the laborious process of self-recrimination. "What?' she asked hazily.

"Are you homophobic, as I believe is the Muggle term?"

"Oh! No, not at all," she stated, falling back to her thoughts. Hermione felt like she had betrayed Remus somehow, though she knew it wasn't her fault. She wondered what Sirius had been thinking; whether he truly believed that Remus would never return to him, or perhaps it didn't matter to their relationship in the long run.

She looked up to find Severus studying her, puzzlement on his face. She almost blurted a confession, but stopped herself just in time. She would never regain whatever respect he held for her if he knew she had shagged Sirius Black.

Very carefully, she set her scone onto the plate and brushed the crumbs from her fingers. Then she stood, still feeling like she was caught in a slow motion video.

"I have to go," she said, then fled the shop. Vaguely, she realized that she had left Severus with the bill. It was really a shame she was too caught up in her thoughts to enjoy the moment.


Permutation: A linear arrangement of elements for which the order of the elements must be taken into account.

When Harry gave her an odd look on his way to the kitchen, Hermione finally realized she was being ridiculous. She'd been standing in front of the door for a good half hour, occasionally pacing as she sorted through her thoughts. She didn't feel guilty anymore, but she was puzzled by the problem. It was possible that Sirius didn't feel anything for Remus after all this time, but she suspected otherwise.

Hermione squared her shoulders and knocked sharply on the door, once. A vague noise sounded from inside; she took it as an invitation. Sirius was sitting beside the window. He didn't look surprised to see her.

She closed the door behind her, noticing a distinctly nervous look on his face. Perhaps things would be awkward between them despite their earlier ease. She sat in the small desk chair beside the bed, watching as he shifted against the sill.

"Sirius," she started softly, "why don't you ever talk about Remus?"

He looked up in surprise. She thought hurt and anger flitted through his eyes before he looked down with a shrug.

"There's not much to talk about, is there? Don't ever see the bloke."

He was making this difficult deliberately, and it made her want to yell and throw things. Preferably breakable things. But she knew that getting him to open up would take a more subtle touch.

"Don't you miss him?" she tried again.

He turned to face the window.

"I supposes," he said in a thready voice, then cleared his throat. "We grew up together, and he's a good sort to have around."

Better, but she thought he was just saying what she wanted to hear. "I've always admired him terribly. He was the best professor we ever had, and so brave too."

Sirius nodded his head slightly, but he still wasn't engaged in the conversation.

"And really, very handsome. Do you suppose he'd ever be interested in a former student?"

He whipped around, eyes widened in shock. His face started to color and she could tell he was searching for some protest.

It would have been flattering if it were for her benefit.

"Sirius," she said, her tone firm but gentle. "I know."

"Know?" he asked, voice barely above a whisper.

She nodded, feeling like she had started to torture a kitten. His face displayed the most emotion she'd seen since he'd been back, even in their night together. He looked lost, devastated and hopeful at the same time, like he couldn't decide whether he was being crushed by the weight of a mountain or someone had lifted it off of his back.

"That you and Remus," she paused, gathered her courage, "that you were lovers."

He sank down on the edge of the mattress, one hand shakily bracing himself. "Oh," he said. Finally he looked up, eyes crystalline and shimmery. "Oh."

"Sirius, it's okay. I'm not going to freak out or anything. I just want to know why you haven't tried to contact him. Don't you miss him?"

He shook his head slowly, as if trying to defend himself from her words. She scooted over to the bed to sit beside him, wrapped an arm around his shoulders.

"More than anything," he said hoarsely.

She hugged him to herself, and waited.

"He doesn't want anything to do with me," he continued, and she could hear how it hurt, tears in the edges of his voice.

She shook her head. "That's not true. He's just having a hard time right now, trying to cope with the idea of you being back." She wished she could say more, but she didn't want to betray Remus' confidence, as well as Severus'.

"Yes, because he feels guilty for not wanting me. Just like Moony, to feel a sense of obligation to this old bag of bones. I'm nothing but a failure, nothing to show for my life than being in the wrong place far too many times."

"Haven't we been over this before? You're not a failure. You've had a hard life, yes, not had a chance to do much with it. But that's not your fault, and I'm sure Remus loves you no matter what."

He was rocking slightly, hunched in on himself, and Hermione moved with him.

"How can you think that? I'm nothing, I have nothing. What can I give him but an old man's body with a teenager's stupid impulses?"

Hermione's arm was starting to get tired, so she let it drop to his waist as she pondered her words. She blushed a little, but she pressed ahead.

"Sirius, I've seen you, inside and out, and I think you're beautiful. You have charm and spirit and love, and that's all that anyone could ask for. If Remus doesn't want that, doesn't still love you, then he's a fool."

Sirius shuddered. A tear splashed on his hands clasped on his lap.

"Have you ever known Remus be a fool, Sirius?"

There was a long moment, and finally he shook his head sharply. "No," he whispered.

"Neither have I. That settles it, doesn't it. We'll work it out, you'll see."

He leaned into her shoulder, and she pulled him down against her neck, letting him cry silent tears against her as she held him. It wasn't the solution, but she thought the fever might have been finally lanced. She hoped that Severus was making progress on his end.


An equation is said to be a closed-form solution if it solves a given problem in terms of functions and mathematical operations from a given generally accepted set.

Severus entered the shop a few minutes after she did, looking a bit harried. Wisps of hair stuck out in a few places, giving lie to his greasy image. She waved the waiter over.

"Hello Severus."

"Hermione," he said with a tight smile, then ordered a cup of coffee. "I'm afraid I don't have much time. The Headmaster has decided that he most imperatively needs my assistance in a project involving the reorganization of the castle's larder. Why he can't get the House Elves to do it, I'll never know."

She laughed at the disgust in his tone, though she suspected the Headmaster's whim was inspired by some research she had shown him during her seventh year, regarding the welfare of the Elves. Severus smiled back at her, his face softened immensely by the expression.

"Merlin forbid I inconvenience the Headmaster," she teased. "I won't take too long."

"If you'd rather have a most horrible emergency that only a highly skilled potions master can attend to, I promise I won't complain," he returned, then muttered, "much."

She was filled with lightness, realizing through the course of this she had made a very unlikely friend. More importantly, she thought they were on the right path to helping two other friends. Hermione launched into her news with eagerness.

"Sirius and I had quite the discussion the other night. He misses Remus very much, and would like nothing more than to see him again. He's convinced that Remus feels otherwise, though."

Severus nodded. "Very well. I spoke with Remus earlier in the week. He would be interested in hosting you at his home for tea, and would not be opposed to you bringing a guest."

The wording was positively Slytherin, and she had no doubt that Severus was the one who had suggested it to Remus. She wouldn't protest though, if that was what it took to get the two of them together.

"All right. Will Saturday afternoon do?"

"That's what he suggested," Severus said. "Don't invite Potter," he added darkly.

"Of course not. I do have some sense of delicacy, you know," she replied. She wouldn't admit it, but she felt a need to keep this project to herself. Harry already had enough of a claim on Sirius.

Severus nodded. "Now, if you'll excuse me?"

He made a slight bow after he rose, then stalked to the door. Of course he'd left her to deal with the bill. She supposed he'd only had coffee, and only a few sips at that.

Hermione hoped Dumbledore had him dusting every jar in the larder by hand.


Involving two variables, as opposed to many (multivariate), or one (univariate).

Sirius fidgeted beside her, tugging at the maroon tie that he had insisted on wearing despite the fact it didn't really match the style of his shirt. Still, he looked good, if more nervous than she had ever seen him. He gave her a small smile when he finally looked up, and she nodded back. Hermione rang the door bell before he had a chance to start the anxious ritual again.

The door opened almost immediately, making her think that Remus was standing just inside. He smiled politely, but didn't say anything.

"Hello, Remus," she greeted in his stead. She fought the urge to turn and make sure Sirius hadn't bolted.

He nodded and stepped aside so they could enter. It looked like a fairly normal Muggle home on the inside, except there was that sense of wrongness about the geometry that told her it had been expanded magically. The coat rack stirred sluggishly as they walked past, but Remus gave it a sharp whap with his wand and it settled back down.

They walked through the short entryway into a sitting room. A worn Persian rug covered most of the floor. Polished oak planks peeked out on the edges. A typical arrangement abutted the fireplace; a sagging couch and two wingback chairs surrounding a low coffee table. She deliberately chose one of the chairs, hoping Remus and Sirius would sit next to each other. Sirius chose the couch, but Remus sat in the other chair. Stubborn, stubborn men.

"Tea?" Remus asked.

They both nodded, and Remus left them again. She could hear him banging around in the kitchen, sounding more clumsy than she remembered him being. Sirius was entranced by the edges of his cuffs, worrying at them until she was sure they'd fray apart in a wild explosion of string.

It was one of the most unpleasant events she'd experienced since Voldemort's last stand.

Remus finally returned with a tray bearing a teapot and three cups, milk pitcher and sugar bowl. He poured the cups and turned to fixing one with several sugars and a splash of milk, which he handed to Sirius. He seemed to suddenly notice what he was doing, almost dropping the saucer before Sirius got it in his grip.

"Forgot the biscuits," Remus blurted, and then he was off to the kitchen once again.

Hermione sighed. The meeting could definitely be going better, but she wasn't sure how to ease the way. She stirred her tea to dissolve the sugar, then took a soothing sip. It was stronger than she usually took it, so she surreptitiously slipped some more milk into the cup.

Remus returned, balancing a plate with various biscuits and a basket of scones, enough to feed both Harry and Ron as well. He slid them onto the table, Sirius rescuing one of the stacks of books so that there was enough room. She chose a scone, pleased to discover they were cinnamon, her favorite. Neither Remus or Sirius took anything.

"So," she said, after it had become obvious the men in the room had left their Gryffindor courage cowering under the sofa, "how are you doing, Remus?"

He looked startled at the question, then cleared his throat. "Very well, thank you. And you?"

"I've been fine. The assistantship keeps me busy, but I enjoy it."

"Ah yes," he replied. "What are you studying again?"

She smiled. Even feigned interest was better than what she got from most of the people she knew. "Graph and number theory, with an interest in its application to Arithmancy. I've always been interested in how Muggle advances could intersect with Wizarding theory."

"Of course," Remus agreed, though she was sure he had no idea what she was talking about. "You are uniquely suited to make such a correlation. And you teach, as well?"

She nodded over her cup. "Two courses, introductory algebra. I don't understand how you did it, honestly. They drive me daft on a regular basis."

Remus smiled tightly. Perhaps it was a topic she should have let be, but she still thought Remus was the best teacher they had ever had, even better than Professor McGonagall. She glanced to her right; Sirius was studying Remus intently, oblivious to everything else around him.

"Yes. Well." Remus looked at Sirius, and they seemed to get caught in each other's eyes. Hermione held her breath, not sure what she was waiting for, but then Remus looked back at her.

"Every now and then a truly exceptional student makes it worth the hassle of dealing with the dullards and mischief makers."

Hermione beamed at the unspoken compliment. She was searching for a way to repay it when a snort of laughter startled her. She and Remus both looked at Sirius, who was chuckling quietly to himself.

"Sorry," he said when he noticed their questioning stares. "I just remembered something."

They waited expectantly, and finally he picked up the hint. "James and Lily's honeymoon suite. Do you remember, Moony?"

Remus smiled, the expression slowly spreading to his eyes. The lines of age at the corners slowly lifted, making him look younger and more relaxed.

"I remember."

"We charmed the tap of their fancy tub to spit out goldfish. Lily must have been right pissed."

"James said we spoiled a highly romantic moment," Remus agreed.

Hermione felt herself fade from notice, and she had never been so glad to be a third wheel in her whole life. She held still, trying not to break the moment.

"I don't remember that," Sirius said after a moment, ducking his head.

Remus sighed, then sets his full cup of tea on the coffee table. He crossed to sit next to Sirius on the sofa.

"I'm sorry, Pads. I'm so very sorry for everything."

Sirius shrugged. "Not your fault, is it now?"

Remus reached out, awkwardly laying a hand across Sirius's shoulder. It was a frozen moment, like a frame from a silent movie. Then Sirius shifted a fraction, and the reel sprang to life as they clung to each other. She hurriedly stood, tiptoeing towards the kitchen. Breathy sobs followed her through the swinging door.

She stopped in her tracks when she saw a dark, imposing form in front of her.

"Hello, Hermione," Severus said.

She should have known he would be here, acting as second to Remus as she was for Sirius. He was leaning against the counter, and it took her a moment to realize why he looked different. He was in full robes. She'd got used to seeing him in casual Mugglewear.

"Hello, Severus," she said happily. She was amazingly glad to see him.

"I take it they have not hexed each other into oblivion. Unless you were looking for the disposal?" he asked with sneering curiosity.

She laughed, feeling the tension that had hovered about her all day break like a crusting of ice, leaving her shaking in its wake. Severus must have noticed; he steered her towards a kitchen chair with a light hand on her shoulder.

"Here, have a scone."

She nibbled at a corner–after all, she hadn't really eaten much of her first. A mostly empty take out box was on the table in front of her, from the same café they visited on a regular basis. She gave Severus a questioning look.

"Lupin was in a bit of a panic. He implored me to bring something you liked. Why he wasn't content with a bushel of biscuits, I'll never know."

Her stomach skipped strangely at the thought that Severus had remembered her preference. She took another bite of scone, hoping to settle her nerves.

"It was going well, I think," she told him.

Severus nodded. "I should hope so, after all the trouble we went through."

"You act like you don't care."

"Should I?" he shot back acidly.

"Honestly, Severus. You can drop the act with me. I for one hope that all the effort we put into this has a successful outcome."

Severus didn't reply, but he did walk to the kitchen door, peering through the slats in a manner that looked suspiciously like eavesdropping.

"Ugh," he said, disgust plain.

Hermione laughed. Things must have been going very well, indeed.


Undefined: An expression in mathematics which does not have meaning and so which is not assigned an interpretation.

As she approached the glass front of the café she saw Severus walking briskly from the other direction. Neither of them would be waiting today. She greeted him with a smile, and he held the door for her. There really wasn't a need for them to be meeting again; she'd seen enough of Remus recently to know his spirits were on the rise. Yet she was looking forward to their discussions, to getting Severus' perspective on things.

They seated themselves, Severus not going so far out of character to actually pull out her chair, and placed orders with the usual waiter. She chose a salad, struck with the sudden urge to get healthy. Severus raised an eyebrow but didn't comment.

"How are you today, Hermione?" he asked instead.

"I'm doing remarkably well. And you?"


They paused as the waiter returns with their drinks. She watched Severus go through his usual routine of unfolding his napkin and straightening the silver. Something looked different about him today; she thought he might have a new shirt. It flattered him, even though it was still the same unrelieved black.

"Do you have any news?"

She shook her head. "Nothing terribly important. Sirius seems much happier these days, certainly. The occasional sulk, but I think that's just part of his personality."

Severus snorted. "Indeed."

She smiled at his inability to resist a gentle jab at Sirius. "I don't think he'll be living with us much longer."

"Potter must be crushed."

"Well, he enjoys having Sirius close by, of course," she said. "But Harry prefers to see people happy."

Severus nodded, conceding her point. "It's my observation that Lupin is mentally competent once again. I suppose we no longer need to have these meetings."

The conversation ground to an awkward halt. Strangely, she found that prospect saddening. She picked at her napkin, wondering what to say. Severus studied his silverware. She looked towards the kitchen, wondering how long it could possibly take to put lettuce in a bowl.

"I don't suppose I'll be spending much time around Remus from here on out," he said softly. "I would appreciate any news of his well-being that you could pass on."

Her heart lifted at that overture. Still, she couldn't resist teasing him. "Severus! You're nothing but an old gossip!"

He looked completely startled, and she knew he was ready to come back with a scathing defense. She stopped him with a touch to his hand.

"Of course I'll pass on anything I hear. Though I wish you felt you could continue to spend time with Remus. Sirius really isn't the devil incarnate."

Severus shrugged, looking over her shoulder. "In time, perhaps."

It was a large admission, and she was oddly proud of him. She squeezed his hand before letting go.

"You know, someone owes me a fair amount of money. A matter of being left with the bill several times in a row. Quite a rude thing to do, honestly."

Severus' mouth quirked into a small smile before he controlled it. "Unconscionable. Why do you put up with such behavior?"

She struggled to keep her own face straight. "I don't really know. I ignored it initially in favour of the goal, but later I found I came to value the person's company enough that it didn't matter."

His eyes widened, and she knew she had surprised him.

"Well, then," he said after a moment. "As the wronged party, you would be within your rights to ask for recompense from this heinous individual."

She nodded vigorously. "I agree. Do you think dinner would be a fair request?"

Severus slowly smiled, the warmth actually entering his eyes and making them a melting brown. She couldn't help but smile back.

"I think that could be arranged," he said.

"I'll look forward to it," she said, and brushed his hand again.


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