(Author's note: I had intended to post everything we had in one chapter, but I decided the dinner math needed its own chapter. There'll be one more short chapter after this, followed by an epilogue. We were kind of relieved that this chapter was as low on angst as it was, and that they were able to resolve some of the concerns that had been lurking.

I imagine it's no secret by now that I am a hopeless romantic, and all I really want is for these guys to be happy. It just needs to happen in the right way. We hope you will agree this is a good start. -amy)


Dave noticed Puck was picking up the book about Cantor less and less. He eyed it lying unopened on the nightstand several evenings in a row before he tucked it under his arm and brought it downstairs, placing it on the coffee table, where Puck couldn't miss it. Puck didn't.

"Hey," he said, nudging the book with his foot. He glanced at Dave, looking mildly uncomfortable.

"I thought we'd read a chapter or two tonight," Dave said. He settled into the couch, his hands on his knees, and waited for Pascal to make the leap from the bookshelf to the space next to him. "Unless you're sick of it."

"Not sick of it," Puck assured him, and paused only a moment before picking up the book. "I, uh, love it when you read to me."

"Okay," said Dave, nodding. "So what is it?"

Puck sat there staring at the book, his shoulders hunched. "It's just that... everybody in here, all these European guys, they made something of themselves. Did stuff with their math, wrote all these long papers and... stuff." He gestured in irritation. "I don't know what I'm saying."

Dave nodded again. He placed a hand on his back, waiting, while Puck sat with his thoughts.

"You could do that," said Dave, eventually.

Puck laughed unhappily. "Uh, no, I couldn't. I'd suck at it. You saw me at the Chicago conference. I was a fucking mess, thinking about writing all that shit down." He shuddered. "I can't imagine having to do that all the time. You - what you're doing, Dave, at the university, writing grants, publishing - it would drive me fucking bugnuts."

Dave felt something inside him ease, even as he soothed Puck, rubbing small circles on his back. "I think you're right," he agreed. "I don't think that would make you happy."

"Yeah, so... why am I even bothering?"

"Bothering what? Taking my class? Reading about math, working through things on your own? Can't it just be for you?"

Puck shrugged. "I guess. Seems kind of pointless." He rested the book on the table, letting his head hang. "Fuck. I can't even do this right."

Dave sighed. "Okay. You know what? Come here." He put an arm around Puck's waist and pulled him back onto the couch, so he rested between Dave's legs against his chest. Puck went willingly, his tense posture relaxing as he sighed against him. "You're freaking out, and I'm not sure about what, but I don't think it's math."

"Maybe," Puck mumbled.

Dave reached out and managed to snag the book with one hand without dislodging Puck, and leafed through until he found the turned-down corner of the page where they'd stopped. He started reading. After a few minutes, Pascal climbed on top of Puck's back and kneaded himself a nest between his shoulder blades, settling into a tiny ball while Dave read aloud about Karl Weierstrass.

Weierstrass was some kind of genius, but he was athletic and outgoing, more interested in fencing and drinking with his friends than the accounting he was meant to study. He left college after four years without a degree, a disappointment to the family. Dave read about how Weierstrass gave up on academics and decided to train as a teacher instead. He spent years working by himself in his small village, solving problems in mathematics that no one else had managed, without any input from the academic community. He didn't even stop to publish any of his work until it was complete.

"Weierstrass," Dave said, setting the book down for a minute, resting his hand. Puck turned his head to look at Dave. "His professor wanted to stop him from teaching, because he thought it would be a waste of that brain."

"Yeah." Puck shifted, and Pascal climbed down to fill the warm spot where he'd been lying on Dave's chest. "When they gave him an honorary doctorate after he published his work, and he moved to Berlin... that kind of pisses me off. I mean, maybe he just wanted to stay in his little town and do what he was doing."

Dave considered Puck. "Have you ever thought about teaching math?" he asked. "I mean, high school or something?"

"Me?" Puck looked startled. Dave nodded.

"When you were giving your presentation at the Chicago conference, you were really good. You held the audience's interest; you didn't seem nervous or anything."

"No," Puck agreed. "I like that part. Talking in front of a group, that doesn't bother me."

"It's more than that, though. Your kids at the dojo, they listen to you. You teach them more than just karate. Can't you imagine that teaching math could be like that, too?"

Dave wasn't sure if he should mention all the ways that Weierstrass's story reminded him of Puck's - coming from a working class background, his diverse interests, the way he figured things out all by himself - but Puck was nodding slowly, thinking it through.

"You have some general coursework done, right?" Dave went on. "You could apply that toward a teaching degree. I'm sure Elliott would walk you through the steps if you wanted to know what specific classes you'd need, and find you an advisor in the education department." He watched Puck carefully, not wanting to push too hard. "Babe, just so we're clear... I'm not saying you should do this for me, okay?"

"No, I get that," Puck said. He sighed. Dave felt the motion of his body on top of him, and held him closer. "I think you'd have to convince me I could actually handle the classes. That's a lot of reading."

"You could get through it," Dave said. "I'd help you."

The silence that followed was heavy with questions that neither of them had brought up. Dave thought, not for the first time, of the conversation he'd overheard with Puck and Connor at their band rehearsal. Why would you want to close your school? he wanted to ask. What are we going to do after this semester is over? What's going to happen with us?

Neither of them brought up any of those questions now, either, but Dave guessed Puck knew some of what was going through Dave's head, because he sighed again. Then he kissed Dave before stretching and standing up. His mouth wasn't smiling, but his eyes were, even though they were also little bit sad. "I'll think about it. And thanks for reading to me. Really."


Dave had been taught, somewhere in the morass of awkward parenting he'd received, that you never show up at someone's house empty-handed. Puck didn't seem to understand this at all.

"Dude, I've been going to Finn's house since I was eight," he said, wrinkling his brow, "and the best thing I ever brought with me was a pizza."

"Well, I was never a good enough friend to get invited to Finn's house when we were kids, even when we were speaking to each other without yelling," said Dave, sliding the bottle of wine into a paper bag. "I'm not going to treat this like a fast food delivery."

"It's just Finn." Puck looked downright uncomfortable. Dave wished he could make light of it, but it didn't feel like a small thing, coming to Finn's house with everyone there.

And it really was everyone. After all the complaining Puck did to Shelby about Beth being gone for Thanksgiving yet again, she decided to stay in town. Once he found out about it, Uncle Finn was quick to call and invite them, too, bringing the total to eleven.

"It would have been twelve," Finn explained, taking their coats, "but I broke up with Jenny."

"I'm sorry," Dave replied. He was a little relieved she wouldn't be there; at least now he didn't have to pretend to remember her name. Finn shrugged.

"No big. She wasn't interested in sticking around Lima anyway. I don't think a mechanic at Hudson-Hummel Tires and Lube was enough to get her to stay."

"She didn't laugh at your jokes, either." Dave turned to see Kurt smiling at them from the doorway, and he smiled back as he accepted Kurt's hug. "And Puck tells me she had absolutely no taste in music."

"She didn't!" Puck assured him. He leaned against the hall closet door, crossing his arms in indignation. "She thought our band was playing, like, Whitesnake or some shit. She couldn't even keep a beat."

"Well, then." Dave grinned down at Kurt. "No sense in even bothering, then. Where's Vincent?"

"Helping Carole mash the potatoes." Kurt's eyes went dreamy and far away. Puck barely suppressed his snicker. "He's a much better cook than he lets on."

Shelby and Beth were already there, too. Beth had Finn cutting a hole in a giant cardboard box with a utility knife while she waited anxiously, hopping from foot to foot and shouting commands: "Make it pointed at the top, Uncle Finn! No, like a rocket ship, not a triangle. Hi, Dave. And give it rays, like a sun. Lots of them."

Mr. Hummel looked like he might be staying out of the way, seated on the couch in the corner of the family room, focused on the television. Dave attempted to escape his notice as long as he could, but he knew it was pointless, since they'd eventually be seated at the dining room table together. He tried to smile as Mr. Hummel approached him.

"David," he said.

"Happy Thanksgiving, Mr. Hummel," Dave replied, shaking his hand. "Thank you for having us over."

"Yeah, well, apparently Finn has decided to invite everybody and their boyfriend to my house this year," he said, frowning. "Something about me having the biggest oven."

"No, it's because you have three bathrooms and Finn only has one," Kurt corrected, kissing his dad's cheek. Mr. Hummel turned his glare on Kurt. Dave had the weird feeling that this glare was a kind of affectionate expression. He let his shoulders relax a little.

Mr. Hummel jerked his thumb at the kitchen. "And now Kurt's boyfriend is in there, charming the pants off my wife and taking over the only thing I'm qualified to do in the kitchen at Thanksgiving, which is mash the potatoes." He shrugged. "So, hey. I'm watching the game. Want to join me, David?"

"Sure," said Dave.

It was only a little strange to sit on the couch next to Mr. Hummel and share his olive and pickle tray while trading comments about the Lions and the Texans. Kurt's smile made it so worth it. He disdained to watch the game, but he sat nearby, reading a manuscript, making occasional furious scribbles with his red pen.

Eventually Vincent came out of the kitchen to beam at Kurt, leaning down over the back of the chair to kiss him. Mr. Hummel pointedly ignored this.

"Carole said the turkey will be ready to carve in about twenty minutes," he said. "We should set the - Dave! How long have you been here?"

"Since you started mashing the potatoes," Kurt said, nudging Vincent with the heel of his hand. "Seriously, you have remarkably singular focus."

Vincent came over and hugged Dave with his usual enthusiasm. "I brought something," he whispered conspiratorially. "A math activity for the whole group. You're going to love it."

They all rose to help set the table as Puck emerged from the basement with Finn, Beth and Shelby. The others seemed to be bickering about a game of Apples to Apples, but Puck was strangely subdued. Dave pulled him aside.

"What's going on, babe?" he asked.

Puck shifted his gaze from the door to the table. "It's Ma," he said in a low voice. "She'll be here soon, coming off her shift. She'd originally said she couldn't make it, but Sarah talked her into it."

Dave nodded. "You wish she hadn't?"

"Fuck, yeah," he said testily. "Seriously, I think I wish we would have just stayed home."

Dave tried not to feel a little twinge at the word home, and was about to pull him into a hug when he thought better of it. Puck's family - his real family - was here, watching. Maybe Puck wouldn't want to do that in front of them. So Dave just stared at Puck, his hands twitching to hold him, and eventually Puck moved away.

Puck's Ma and Sarah arrived while Mrs. Hudson was bringing out the turkey. Dave saw the tired expression on Ruth's face, and the strain on Sarah's, and sat on his hands while Puck's tension level went up at least twenty percent.

"Sorry to be so late," Ruth said, as Finn took her coat. "It smells amazing."

Sarah ended up wedged next to Dave, and he passed her the bowl of stuffing, wondering what might be appropriate to say. Beth sat on the other side of Sarah. She apparently had no compunction about not talking, nattering on about the musical instrument she'd created for her school science fair project, and the kid on her hockey team who threw up right on the blue line at practice. Sarah let her fill the silence, giving her a watery smile, and filled her plate with food she didn't eat as the dishes of turkey and mashed potatoes circled the table.

There were plenty of other conversations going on, but it was hard for Dave to pay attention to any of them with all the voices competing for airspace. It made his head hurt to have so many people talking at once. Puck was having a quiet and very civil argument with Shelby about something, but Dave wasn't quite sure what the topic was until he heard the phrase parent-teacher conference.

"I can go," Puck was saying with an obstinate frown as he took another helping of sweet potatoes. "You don't have to reschedule your appointment."

"You're teaching," Shelby said, shaking her head. "Don't be an idiot. A whole class of martial arts students trumps one annoyed second-grade teacher who wants to make us do it on that day."

"No, I'll have said goodbye to nearly all the classes by then. Owen's taking the senior student class, and the others' last sessions are next week. I -" He clearly had more to say, but when Puck realized Dave was listening, he closed his mouth and stared at his plate.

"What?" Dave asked, but Puck gave him a little shake of his head.

This pissed Dave off. It wasn't like he could deal with it right in the middle of the Hudson-Hummel Thanksgiving dinner, and damn Puck for making him hear that conversation. He tried another bite of turkey. It was excellent, but he just couldn't sit there and pretend he belonged at that table any longer.

"Excuse me," Dave muttered, pushing out his chair. Puck didn't watch him leave.

Dave considered going out to sit on the front porch, but it was almost freezing outside, and it would have been a damp, uncomfortable place to be. He ended up taking a seat on the wooden stairs leading to the basement. It was just about as lonesome and stark a place as he needed at that moment. He had to roll his own eyes at himself, at how melodramatic that sounded.

Then a pair of large sneakers appeared on the step beside him, and he glanced up in surprise to see Finn.

"Hey," Finn said, sitting down beside him. There was barely enough room for both of them on the step, but Dave moved over a little, and they managed. "You're not going to miss pie, are you? 'Cause my mom makes awesome pie."

"I don't know. Maybe." Dave watched him warily.

Finn shook his head, looking sad. "Is it Puck's Ma? She's sober today, at least. I thought that was a good sign."

Dave hadn't even said one word to her since she'd arrived, other than pass the gravy. "No. She's fine. She's never been anything but nice to me, actually."

"Yeah, Puck's kind of sensitive about her moods, but she's always been nice to me, too." Finn paused, then added, "I guess there's stuff you never see, unless you're living with a person. Things they don't show anybody else."

Dave nodded slowly, taking this in. "I... yeah. That's true."

Finn squinted at the wall. "Hey, Vincent's great. Kurt's totally crazy about him, I can tell."

"Yeah, they're a good match. Kurt needs somebody like him: smart and romantic and a little goofy."

Finn laughed. "I thought, for a while, Kurt wasn't going to find anybody out there in California who understood him, who liked him the way he is. He was just going through the motions of being happy, but..." He shrugged. "A career can only take you so far, you know?"

"I know," Dave agreed.

"Yeah. So I'm really glad for him. I mean, even though my family's kind of big and loud and crazy, I love them a lot, and... I think Vincent fits in just fine, don't you?"

Dave grinned. Finn was getting better at being subtle. "You know he's originally from Ohio, too, right?"

"No kidding," Finn said, grinning back. "I don't think he's looking at moving back any time soon, though."

"Definitely not." Dave's smile slipped a little at the mention of moving. He hesitated, but really, if there was anybody who might understand, it was probably Puck's oldest friend. "I'm worried about Sarah, dealing with their mom, in that house all by herself."

"Because Puck's moving to Columbus." Finn didn't look at all surprised.

Dave shook his head. "How did you know I was going to ask him? I haven't even talked to him about it yet."

Now Finn did look surprised. "You? Puck told me it was something he hadn't talked to you about yet. Said he didn't want you to freak out."

"What? He didn't want me to..." Dave paused, his mind racing. "Are you talking about the stuff about him closing his dojo?"

Finn nodded. "He told me about what happened with Dayna and Hank last month, how they freaked out about him being, uh, with a guy. Said he'd rather hand off his students to someone else and go teach at Connor's dojo instead. He's always wanted to get out of Lima, anyway. His ideas are bigger than this little town."

Dave thought about Karl Weierstrass and had to smile. "Well, really, it's not like Columbus is all that much bigger than Lima. It's not like it's... Berlin, or anything."

"What?"

"Nothing. It'd be a step. Did you... did he say anything about where he might be planning to live? In Columbus?"

Finn raised his eyebrows. "Don't you think you should be talking to him about this?"

"I should, but... if he's already planning to move to Columbus, even without talking to me, that means he's already thought about leaving Sarah and his mom alone."

Finn gave a little half-shrug. "He might have said something to me about it."

On top of the adrenaline prompted by this new information, Dave suddenly felt ridiculously proud of Puck for dealing with all of this on his own. "And?"

"And I said Sarah could come hang out with Uncle Finn and Grandpa Burt at the garage any time she wanted. If they need money without Puck, we could probably manage to give her a job doing oil and filter changes."

Dave hadn't ever felt like hugging Finn more than he did at that moment, but he managed to keep it to a smile. "That's just... awesome of you, man."

"Yeah, well, Puck's basically my brother." Finn smiled back. "I'd do more than this to help him out, if he asked. He should be happy, and I don't think he's ever been this happy before."

Dave thought about how Sarah had said something similar to him. He supposed that when people cared about you, your happiness was important to them, even if it meant they had to go out of their way to make sure you got it. He cleared his throat. "You, uh... you know he makes me really happy, too."

"I figured," Finn agreed quietly.

They sat there for a few more seconds before Finn got to his feet and took a few steps up the staircase. He glanced back at Dave. "So, I'll save you some pie, huh?"

Dave nodded. "Yeah. I just need a minute."

"No problem, dude. You come find him whenever you're ready." Finn smiled. "Happy Thanksgiving, Dave."

"Happy Thanksgiving."

After that, the whole huge, loud family upstairs didn't seem any less intimidating, but Dave thought he might be able to handle it well enough to get through the rest of dinner when a small, blonde head appeared around the door frame at the top of the stairs.

"Hey, Dave!" Beth stared at him. "Why are you sitting in the basement?"

"I needed a quiet place to think. But I'm done, now. Did you have a good dinner?"

She climbed down to sit next to him, right where Finn had been sitting a few minutes ago. "I didn't like the green beans. Everything else was good, though."

He grinned. "Aren't you missing dessert?"

"Not yet. Vincent said he wants to do this thing, where we all have to stand up and go out of the room, and there are cards with our names on them. He needs you to come back, so I said I'd come get you." She cocked her head. "Are you and my dad having a fight?"

"What? No!" Dave sat back, assessing her solemn face. "No, we're not. We're... well, he's thinking about... uh..."

"It is because he's not gonna be my sensei anymore?"

"He... he's not?" Dave felt like he'd been half a step behind on every conversation tonight.

"No, Sensei Owen's going to teach us. It's okay, I like him, but he's not as good as my dad." Beth leaned her sharp little elbow on Dave's thigh. "Aunt Sarah told me you want my dad to move in with you. She told me not to say anything, so don't tell her I told you, okay?"

Dave weighed the value of giving Beth a lecture on integrity, but decided it was more important in this moment to just listen to what she had to say. "Okay. What do you think about that idea?"

She considered it. "Could we still ride bikes together?"

"Definitely," he nodded. "And you could come stay with us sometimes, if you wanted."

"At your house?"

Dave swallowed, feeling like he might be getting ahead of himself. "If it were your dad's house, it would be kind of like your house, too." His current house was definitely too small for three people, but they could always rent a bigger one. He let himself dwell on the terrifying idea of a little room for Beth for a few moments before smiling at her. "I'll have to talk to your dad, first. I don't even know if he wants to move in with me."

"Of course he does," she scoffed. "He loves you."

He felt himself melt in the face of that frank statement. So what if his smile was a little goofy? Nobody was going to see it, after all. "I love him, too."

"Yeah." She took his hand and tugged at it. "Come have pie now, okay?"

Dave took her hand, standing up. "Okay. Pie it is."

Puck intercepted them on their way back to the dining room. He nodded at Beth. "Hey, squirt. Thanks for getting him to come upstairs. I'll meet you back in there, okay? Tell Grandpa Burt to hold off on the dessert for a few minutes. We won't be long."

"Hurry up, or we'll eat it all without you," she said, grinning at Dave, and vanished through the doorway.

Puck gave him a long, hard look. "You're not freaking out on me, are you?"

"No. Well, maybe, but I think Finn got me out of it." Dave shook his head. "Puck... you've been planning to move to Columbus? Without talking to me about it?"

Puck looked momentarily uncertain, but he nodded. "I've been thinking about it for a while. But I wanted to take care of the details before I told you. I didn't want you to think I was doing it for you."

"Oh." Dave felt uneasy. "You didn't... it's not for me?"

Puck squirmed a little. "Fuck, Dave, of course it's for you. I just didn't want you to think it was."

Dave was startled into a laugh. After a pause, Puck laughed, too. He touched Puck's arm. "Okay, I get that, but... babe, I was going to ask you the same thing. I've been trying to figure out how to bring it up. I wasn't sure you'd even want to."

Puck's face lit up in a smile that dug its way into Dave's chest and made a home there. "Yeah? I figured, if I got my own place, you wouldn't have to worry about feeling too crowded. I've got a lead on some houses in your neighborhood." He eyed Dave. "But you were going to ask me to... what? Move in with you?"

"Either that, or get a bigger place." He thought of Beth, and then of Puck's dream with the kids' bikes on the wall of the garage. "You know... maybe so we could have an extra room. Whatever."

Puck nodded, still smiling. "You don't think that would be too awful? Me, moving in with you? It's save rent, that's sure as shit."

Dave glanced at the vacant door to the dining room, then decided, what the hell. He stepped into Puck's space, kissing him, and then held him tight. "You're practically living with me already. And if you haven't noticed, I haven't exactly been kicking you out the door."

"No." Puck sighed into his hug, and kissed the space behind Dave's ear. "You don't think we'd kill each other, huh?"

"I think my biggest problem would be keeping my hands off you," Dave murmured. "I overheard you and Connor, after band practice. Talking about closing the dojo."

"Oh," Puck said, startled. "That must have been a little while ago. Change in plans. Owen's taking over the business. I'll stay owner, but he'll manage the classes and the property, so that'll still make me a little money - a very little, assuming things go about the way they have been, but it's something. Connor says there's enough demand for teachers at his school that he can hire me as an instructor, and starting in January, I can begin my own classes."

Dave smiled at Puck's enthusiasm. "Sounds like you've got everything under control."

Puck smiled a little, looking pleased with himself. "I'm trying, you know, to make sure I didn't forget anything. There's a lot to think about, but, hey, I moved to Okinawa for a year. I can do this."

Dave couldn't help it, he had to kiss him again. "Babe, that's great," he said, still not letting Puck get very far away. "I mean. I don't want to push you. I know there's your family..." He looked towards the dining room again. "Sarah, but...I think Finn said something about keeping an eye on her?"

"Yeah." He grimaced. "I don't love the idea of leaving them alone with each other, but... it's going to have to happen sooner or later. Once Sarah graduates, I'm either going to have to give up on her, or make sure she's got a hell of a lot of people willing to help out. Finn, and Burt... they're top of my list."

"They're good people, I think." Dave held Puck a little tighter. "You're right, you know. It's going to have to happen eventually. And if you decide you're okay with that being now, or even if it's not..."

"No," he interrupted. "I... yeah, I want it now. Like, yesterday."

"Okay. Yeah." Dave didn't want to be selfish, but he had to admit, he agreed. "So. In that case...you could move in with me. I mean. I'm asking you. Because, I'd like that. If you want."

Puck's answer didn't involve any words, but Dave could tell it was an affirmative. It could have gone on like that for a while, too, if Kurt hadn't appeared in the door and cleared his throat.

"You're missing out on some classic family conversation. And pie. Didn't Beth come to find you?" He didn't really sound upset, though.

"She did. Sorry." Dave finally, reluctantly let go of Puck and started walking after Kurt, who took Dave's arm.

"Everything okay?" he asked, pleasantly enough, but his eyes looked concerned.

"More than okay," Dave replied. He felt echoes of the goofy smile he'd worn in front of Beth, but really, wearing it for Kurt, that wasn't a whole lot scarier. Right now, he felt practically invincible, like he could wear it in front of the whole math department and it wouldn't make a difference. "Puck said he'll move in with me. That he'll come to Columbus."

"Oh!" Kurt stopped, staring into his face, eyes wide. Then he hugged Dave hard. "Honey, that's wonderful. I'm so happy for the two of you."

"Yeah," said Dave, hugging him back. "Me, too."

Vincent was explaining something to the whole group, and they were already starting to look a little politely bewildered. Each person was standing behind the chair they'd been sitting in for dinner. He felt another touch on his arm.

"I covered your plate and set it on the counter in the kitchen," Mrs. Hudson said quietly. Dave felt a grateful flush pass over his face.

"Thanks," he said. "It was really good." He wanted her to know that he hadn't left because of the food, but she seemed not to need any further explanation. She just nodded, giving his arm a little squeeze.

"Wait until you try the pie," she said.

"So let me get this straight," Mr. Hummel was asking. "We have to... go out of the room, and then come back one at a time?" Vincent nodded earnestly. Mr. Hummel indicated the table, where cards sat, face down, in front of each spot. "And then we, what, turn over some cards?"

"Half of them. Well, excepting me, because it should be an even number. Kurt didn't make a card for me."

Mr. Hummel swung his gaze to Kurt, who was smirking. "This is all your fault, huh?"

"I'm just aiding and abetting," Kurt affirmed coolly, slipping a hand into Vincent's and patting it. "I don't even understand the math. And no, Vincent, you can't explain that until everybody is sitting down with pie in front of them."

Vincent didn't look upset; he just nodded again, still smiling. "The goal is for each person to find their own card. They're all mixed up among the spots at the table. If you haven't found yours after you've turned over half - that would be five of them," he added, looking at Beth, "the game is over and we've all lost."

"How the hell are you supposed to do that?" Sarah poked at the forks at her spot, looking longingly at the pecan pie. "The odds are totally against us. Can't we just eat?"

"No," Kurt said, crossing his arms. "Consider this exercise before the last course."

"Fine," Sarah muttered. "But Noah has to tell me how to win. Come on, dude, you're the math genius."

Puck was startled, and stammered out a weak answer. "Uh... well, it's not a winning thing, right, 'cause we're all trying to do it together...?"

"You start by looking at your own spot," said Ruth. The table fell silent, everyone looking at her. She had barely said two words the whole night, but even though she looked exhausted, her eyes were clear. She nodded at Vincent. "And then, if you don't find your own name, you look at the spot of the person whose name you found. Right?"

Vincent was beaming. "Yes! See, the way it works is -"

"After pie," Kurt insisted, tugging his arm. "Come on, everybody into the family room. Beth, honey, you want to go first?"

It took a surprisingly short amount of time for each of them to go in and try the strategy Ruth had suggested. The exclamations of surprise each time someone found their own name were encouraging, and even Burt was grinning when he came back into the family room, rubbing his head. "I'll be damned," he said.

Dave approached Puck's Ma and smiled at her curiously. "How did you know how it worked?"

She looked a little perplexed herself. "I'm not really sure, actually. I think I must have read it somewhere. Don't they usually do this problem with lockers?" She shrugged. "Anyway. I like logic puzzles."

Dave nodded. He wasn't so surprised. Puck's little piece of genius had to come from somewhere, after all.

It was kind of amazing that they were all able to find their own names, but everybody looked a lot happier once they were back in their own seats and Finn was slicing the pie.

"Okay, I'm totally not interested in all the details," Sarah demanded, pointing her fork at Vincent, her mouth full of apples, "but you have to tell me why that didn't fail miserably. Weren't the odds, like, way high against that happening?"

"Yes," Vincent said. "They were. If you picked at random, the chance would have been about one in a thousand. Using the strategy, it still wasn't better than about one in three. We were lucky that it worked the first time."

"Uh, no, sweetheart," Kurt murmured, patting his hand, "you're lucky."

Dave imagined how annoyed everybody would have been if they had to do this three or even five times, and nodded. Vincent was, of course, oblivious, and went on with his explanation.

"The thing is, when you do it that way, you sort of coordinate everybody's picks. So either it works, or it doesn't - that all depends on how the cards got shuffled in the first place - but if you get a good draw, it works for everybody." He looked at Puck. "Think of it as a permutation. You know how you can decompose them into cycles? If they're all short enough, it works, and the chance of that comes out to about 30%." He smiled. "The first time I saw this problem I had to sit down and count all the different possibilities before I would believe it."

"Of course you did," Kurt said, and kissed him on the cheek.

Mr. Hummel brought out a fresh pot of coffee and made a cup of hot chocolate for Beth while they ate. Shelby and Puck whispered about something, but this time it didn't sound so bad, and when they were done, she caught Dave's eye and gave him a friendly nod. He nodded back, guessing it might have something to do with moving in together. Whatever it was, he'd take a little good will from Shelby.

"Did I tell you about the cake puzzle?" Vincent grinned at Dave.

Kurt rolled his eyes a little bit, but he was smiling, too. "Everything's a math problem to him," he said, shaking his head. "I'm more excited about eating it."

"Can't we do both?" asked Dave. "This is really good."

"Yes." Vincent smiled again. "This is a cake problem, anyway. A square cake. Nothing at all to do with pie."

Puck and Dave looked at each other. Dave sighed, but he had to admit he'd almost giggled. "He's always like that, sorry," he told Puck. "I thought he might have grown out of it, but...constant puns, all the time."

Vincent snorted. "Okay, sorry. Anyway, you haven't heard it? So there's a grandmother, and she's baked a square cake, right? Chocolate. Not that that really matters, I think. Could be carrot cake. I like that better. And pumpkin pie." Kurt noticed him looking at the one on the table and pushed it in his direction. Vincent smiled and transferred a slice of it to his plate before he continued. "Anyway, she's got a square cake, nine by nine inches, and nine grandchildren, and she wants to divide it fairly between them. So how does she do that?" He drew a square in the air.

Puck stared at him. "Is this a trick question?"

"No," Vincent answered. "Hang on, it gets harder."

Dave didn't think Beth had been paying attention to their conversation, but he noticed her following Vincent with her eyes. "Do you have any ideas?" he asked her. "I could use some help here, and your dad doesn't seem to be taking this very seriously."

Beth looked a bit shy, but finally she upended the sugar bowl on the table. With her finger, she drew lines across it to make a grid, like a tic tac toe board. "Like that," she said, looking up at Dave for confirmation. He nodded.

"That's a good one. I was going to say nine one-inch strips, but I don't think they'd fit on a plate very well, so yours is better." He turned to Vincent. "We have our answer. Three inch squares. Is that acceptable?"

"Perfect." Vincent grinned again, and Dave thought the anticipation he was directing at Beth was a little worrisome. "You can't recruit her for research yet," he told him. "She's only in second grade."

"That's fine. I'm sure you and Puck will train her well, and I'll just try again in...ten years or so." He glanced speculatively at Sarah. "How about you? Any ideas about what what you might want to do in college?"

Dave and Sarah both laughed, but Puck looked suddenly serious. Dave put a hand on his thigh under the table. He didn't want Puck to get stuck in thinking about big things right now. "So, we solved that one, but I think you said you had a harder question?"

Vincent blinked and nodded. "Oh. Right, so she's divided the cake in nine equal pieces, but the kids aren't quite happy, because they all love chocolate frosting. And this way, some of them get a lot more than the others, because the cake is covered on top, and the sides, but not the bottom. Like a normal cake." He paused. "So how do you split it in nine so that everybody gets the same amount of cake and frosting?"

Dave and Puck both went very quiet. "What if..." Puck started, but then he stopped. They both thought about it while Vincent grinned smugly at them.

To Dave's surprise, Sarah was the first to offer a suggestion. "Can't they just scrape it all off and split it that way, if it needs to be so perfectly fair?" she asked.

"Oh, I see. Well, that would work, but we're looking for the more elegant solution, so, no."

Sarah scowled. "It would work."

Vincent shook his head. "Maybe you should think about engineering, or something. Or even physics. Puck, you have any ideas?"

"Yeah, but they're all really complicated and none of them work so far." Puck took another bite of his pie. "I don't think anything that requires calculus should be the answer to cutting up cake."

"I'll give you a hint," Vincent said. "No calculus, and only straight lines."

"Can you use a ruler?" asked Dave. "Or a measuring tape or something?"

"Sure. Ruler and knife." The hint didn't seem to help, though, and they all ate more pie and listened to the conversations around them, which seemed to involve a lot less math. Dave thought maybe Vincent's permutation group party game had scared a few of them off for good, but nobody seemed too grumpy.

Puck finished his slice of mince pie, which Dave personally thought was disgusting, but he wasn't going to judge anybody's choice of desserts, and it was traditional at Thanksgiving. He put down his spoon with a loud click. "I give up," he told Vincent. "I'm sorry, I'm not going to get this and it's going to drive me crazy, so can you please just tell us?"

"All right. Everybody else okay with that?"

"Yes," Dave sighed. "Please."

"Okay. So, you find the center of the cake, and then you measure out equal lengths along the edge...in this case, that would be four inches. And then you cut slices from the middle like you would with a circular one."

"Wait...yeah, okay. Of course. Triangles." Puck groaned. "Why didn't I think of that?"

"It's the first question, I think. It makes you think about squares, and then you get stuck there, you know?"

"Yeah, I know." Dave was familiar with how that worked. "Okay, I admit it, that was a pretty good one."

"Thank you," Vincent said, grinning. "I'll try to quit while I'm ahead, then. No more math problems today."

Kurt mumbled something that Dave didn't quite catch involving what else he might not get today, but the look he gave his boyfriend was definitely more loving than annoyed. And he apparently managed to hang on to his good mood through clearing the table, because he approached Puck and Dave later with another hug, this time for both of them.

"I think the romantic comedy script I'm reading has turned my brain," Kurt said, "because I'm feeling particularly emotional right now, but... I'm so happy for you two."

"News travels fast in the Hudmel house," Puck said, but he was smiling. "How about you and Vincent? Everything seems to be moving along there, too."

"He's my kind of scum: fearless and inventive," Kurt agreed. "So what if he can't cook? He wrote me a palindromic sonnet for my birthday. What could top that?"

Dave thought it might be tempting fate to ask that question, but he just grinned. "I'm glad he didn't piss your dad off too much with that math puzzle."

Kurt waved him off. "My dad, pissed off, is equivalent to anyone else's dad beaming with pride. Speaking of, I suspect there might be more football on the television, if your brain isn't entirely saturated with pie and math. Come grab some couch space while the grabbing's good."

While Mrs. Hudson, Puck's Ma and Finn finished cleaning up the kitchen, Beth - who couldn't sit still for very long - lured Puck and Sarah into the front yard for some sparring. Dave alternated watching the Turkey Bowl and gazing out the window at his boyfriend helping his sister and his daughter with their roundhouse kicks. He heard Kurt sigh quietly in the love seat beside him, where he and Vincent sat together, holding hands.

Mr. Hummel didn't shift his own eyes from the television. "Things sure have changed since high school, huh, David?"

"Um, yes, sir," Dave agreed, startled. "They really have."

"I got my fill of titles in congress, son. Call me Burt." He nodded at the window. "You two weren't even friends back then, were you? You and Puck."

A memory of Puck in high school, coated with blue slushie, flashed through his mind just moments apart from an earlier memory of middle-school Puck, kneeling half-naked on top of him in Finn Hudson's guest bedroom. "No. Not friends. He... he was always important to me, though, long before I could admit to myself why that was."

"Huh." Burt did turn and smile at him now, and his eyes were exactly like Kurt's. "Is that right?"

"Yeah," Dave nodded.

"You just thought he was hot," said Kurt with a grin.

Dave felt warm and drowsy with turkey and pie and good company, so much that he didn't even resist Kurt's teasing. "I did," he agreed, "but that wasn't all it was. Puck kept a lot of things hidden, even back then, but I guess I could see the kind of guy he was, underneath."

Burt nodded, returning to the television. "Sounds a lot like what Kurt told me a couple years ago, when he explained how you two had become friends." He settled back against the couch. "You overcame a lot of hard stuff to become who you are now."

"Everybody has flaws, Dad," Kurt said. He leaned against Vincent, who Dave realized had fallen asleep. "They're not enough to keep us from deserving love. Maybe we even need them, to be who we are."

"Way too complicated for Turkey Day, Kurt," Burt growled. "You and your boyfriend both, I swear. Can't we just relax and enjoy what we've got?"

Out in the yard, Puck paused in mid-kick, explaining something to Sarah. When he caught Dave's eye through the window, his smile grew soft, and Dave found himself smiling back. "Sounds good to me," he said.


Dinner math notes, courtesy Penthea

Place cards (awesome table diagram deleted, due to annoying lack of graphics):

The game Vincent gets everybody to play is a variation of a problem that usually involves lockers, or boxes, and often prisoners. People with a math background can go read an article about it here: www. maths. tcd. ie /~onash/ pity_the_prisoners_files/ locker-problem. pdf, or look up permutations, orbits and cycles on Wikipedia.

For everybody else: If you keep looking in the spot of the person whose name you find, because there's a limited number of names, you will eventually come full circle and find yourself back where you started. So the question is really, how long will that take?

Most of the time, you're going to make it all the way around to your own name before you've turned over all the cards. The path you follow on the way forms what's called an orbit, or a cycle. When you use Vincent's strategy, all the players follow the orbits directed by the cards. They're all on the same paths, and if only the paths are short enough, they'll all make it around.

In this example, there are three cycles, and their lengths are 2, 4, and 4. Because everybody starts with their own spot, they know they're entering the right cycle, and in four moves they'll all make it around and find their name.

When you sort all the possible ways of placing 10 cards in 10 spots (10*9*8*7*6*5*4*3*1=3628800, so Vincent probably did his counting with a smaller number!) according to how long the longest cycle is, it turns out that about 30% of the time, there's no cycle longer than five, and this strategy wins the game.

That's a lot better than random guessing, which comes out to about 0.1% (multiplying the 50% chance that each person has, so for one person, it's ½, for both the first and the second, ½* ½ = ¼, three people ⅛, etc, until you get to 1/1024 for ten people).

Cake (likewise awesome cake diagram deleted)

This is what the solution to the cake cutting problem looks like. Because every slice has the same amount of edge, they get equal amounts of frosting from the sides.

What's a little harder to see is that they also have the same area, meaning equal amounts of cake and top-of-cake frosting. This is true because the area of a triangle only depends on the length of its base, and its height, it doesn't matter how skewed it looks.

That takes care of the triangular pieces, but what about the corners? Looking at the bottom right corner, the dotted line divides the piece into two nice, easy-to-calculate triangles. Since the heights are all the same, and the sum of the two corner triangles' bases is still four inches, same as one simple triangular piece, the total area will be the same for those, too.