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60w, 5dThe Writer's Group
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21w, 4dCompleted Story Compendium
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“I am bushed,” Applejack said as soon as she came through the door of her home in Sweet Apple Acres. Like always, she had spent most of the day working on the farm, from apple bucking to weed pulling and various other jobs in between. After such a long day of work, it was always nice to come back to the house for a hot meal.
“I sure hope Granny Smith has got dinner goin’ already. I’m starvin’.” Applejack was about to make her way onto the kitchen to filch a little taste test of dinner when she noticed Apple Bloom sitting in the living room, staring at a piece of paper in front of her on the table.
“Hey Apple Bloom. Whatcha doin’ there?”
“Lookin’ at my homework.”
“Okay… Shouldn’t you be, I dunno, workin’ on your homework?”
Apple Bloom slowly looked at her sister disheartedly. “I don’t even know where to start.”
“Well if you’re that lost, I guess I can help ya till dinner.” Applejack pranced into the living room and sat down next to her sister as she removed her hat. “What kind of homework is it?”
“Math.”
Applejack paused for a moment. “Really?” She cleared her throat. “So what kind of math is this? Times tables or somethin’? I’m sure I could help ya with that.” Applejack grinned and read the first problem on the sheet. “A pegasus flyin’ from town A to town D must first pass through town B and then through town C. It is 10 miles farther from A to B than from B to C and 10 miles farther from B to C than from C to D. If it is 390 miles from A to D, how far is it from A to B?”
Silence.
Apple Bloom raised an eyebrow. “Hey Applejack, whatcha doin’?”
Applejack frowned. “Starin’ at your homework.”
“Shouldn’t you be, I dunno, workin’ on it?”
“Don’t you sass me. It ain’t my homework,” Applejack retorted sternly.
“But I still don’t get it.”
“I know and I promised to help ya, so that’s just what I’ma goin’ to do. I just uh…,” Applejack looked around until she spied Big Macintosh passing by the room. “I just need a little backup. Big Macintosh, help your sisters out here. We… I mean Apple Bloom needs a little math educatin’.”
Macintosh paused, shrugged, and sat down across from them. “Whatcha got?” Apple Bloom read the problem again as Big Macintosh listened thoughtfully. As she finished, Macintosh blinked a few times. “Really? Kids are doin’ that kinda math already?” He took a few minutes to think it over. “You got some scratch paper?”
Applejack paled. “You know what, why don’t we just move on to the next question. Let’s see…,” Applejack glance at the paper and looked at problem number two. “A hardware store owner purchased 144 identically priced hammers from a wholesaler. When the hardware store owner wanted to set his sellin’ price, he checked the shop’s record for the wholesale price. His accountant had written a total of 1,#25.4# bits where the #'s represent illegible digits because the receipt was smudged. Determine the wholesale price of a single hammer.” Applejack stared. “You gotta be kiddin’ me. I didn’t even understand that. Ain’t somethin’ missin’?”
“See what I mean? I can’t figure out any of these,” Apple Bloom whined. “What am I gonna do? I have to get this done by tomorrow.”
Feeling for her sister’s predicament, Applejack put a hoof around her. “Don’t you fret none little sister. Mac and I ain’t gonna let you fail this. Let’s just go about this logical-like. We’ll start with the easiest question and work our way up to the harder ones. Right, Big Macintosh?”
Macintosh didn’t answer. He was busy trying to figure out the hardware problem on a piece of scratch paper.
“All right. We’ll just leave the hard ones to you. Let’s see…,” Applejack scanned the homework sheet again. “Ah, here’s a short one,” She said excitedly. “This one aught to be easy.” She smiled as she read the question. “Evaluate the integral of cos(x)/(1+x^2).” And that was it. Applejack blinked and read it a second time. “What? What does that mean? Is this even math?”
“I have no idea…,” Apple Bloom said softly.
“This is ridiculous. How many problems are even on this thing?”
Apple Bloom smiled apologetically. “Thirty.”
Silence.
“You’re jokin’ with me. You are jokin’ with me, right?”
Apple Bloom’s ears drooped. “I wish I was.”
Applejack gaped for a moment, but the look on her sister’s face filled her with determination. “We can’t give up, Apple Bloom. We’re gonna finish this homework of yours or my names not Applejack.”
Rarity smiled as she put the finishing garnish on the dinner plates. “There we go. Perfection,” she said happily. “It could not have been done better if I had done it myself. Oh, but I did do it,” she squealed, metaphorically patting herself on the back. “Sweetie Belle, dinnertime!” Rarity listened for a moment, but she didn’t hear her younger sister’s voice. She didn’t hear her getting into any kind of mischief. She didn’t hear anything. Suspicious.
Making sure to place the dinner plates on the table just so, Rarity left the kitchen in search of her sister. She didn’t have to wander far. She found Sweetie Belle feverishly writing with a pencil, almost looking as if she were about to explode if the slightest thing disturbed her. Rarity was astonished. She had never seen her sister working so hard on anything like this before. Before she could wonder if an alien had traded places with Sweetie Belle, her sister let out a huge groan and laid her head on the table.
“I’m never gonna finish this,” she moaned.
“Sweetie Belle, it’s time for dinner. Is everything all right?”
Sweetie looked at Rarity quite disgruntled. “I’ll be there in a second, sis. I’m just trying to figure out this homework problem first.”
“Homework?” Rarity said with a slight flair of anger. “Sweetie, how many times have mother and father told you that you should start your homework as soon as you come home?”
“But I did. I’ve been working on it ever since I came back.”
“Pardon?” Rarity looked at the clock. “That was five hours ago. What have you been doing all this time?”
“Homework.” Rarity raised an eyebrow at her. “I swear, sis. I really have been working on it the whole time.”
“Sweetie…,” Rarity said sternly.
Before Sweetie Belle could explain though, the two sisters heard a knock at the door.
“Hold on, Sweetie. We’ll discuss this in a moment.”
“But Rarity…,”
Rarity ignored her sister however, and headed for the door. After all, who could possibly be calling right at dinnertime? “Coming!” she called just before she opened the door. She was only a little surprised to see a young filly with pegasus wings standing outside. “Scootaloo? What are you doing here so late?”
“Hi Rarity. Is Sweetie Belle here?” If Rarity didn’t know any better, she could almost swear that Scootaloo looked nervous about something.
“Yes, but its dinnertime, let alone rather late to come out and play. Shouldn’t you be home as well?”
“I just need to ask her something real quick,” she said, smiling as large as she could.
As if sensing that her friend was there, Sweetie Belle came to the door just then. “Hey, Scoot. What are you doing here?”
“Sweetie Belle. Heeeelllllp!” Scootaloo suddenly wailed.
“Let me guess, you only just now looked at the homework.” Scootaloo nodded her head rapidly and whimpered in reply. “I don’t know if I can help you. I only answered three problems and I don’t even think they’re right.”
“What?” Rarity interjected. “You’ve been doing homework for five hours and you have only answered three questions?” Rarity stormed back inside and over to the table where Sweetie Belle had been working. “This is completely unacceptable, Sweetie Belle. I am not going to permit you to fail because you don’t understand some silly homework.”
“But sis, it’s really, really hard.”
“No buts about it, Sweetie. Now you and Scootaloo set your bottoms down over here and I’ll show you how to do this homework.”
Twilight looked up from her studying when she heard a knock at the door. Glancing at the clock, she noted that it was already 10PM. “Now who could that be this late?” She got up and went to the door, but paused as she was about to open it. “It couldn’t be Cheerilee. Even she wouldn’t drop by now.” Or would she? Twilight still wasn’t finished researching career planning methods and found herself unprepared to deal with Cheerilee at the movement. “Who is it? If this is a certain pony looking for a student then this is just a recording.”
“Twilight, I can see your shadow underneath the door. If you want to come up with poor excuses, at least make them plausible. Now please open up. I need to ask you something.”
That voice! It certainly wasn’t Cheerilee. Twilight opened the door to find a white unicorn and two fillies standing there. “Hi Rarity. Is something going on?”
“Oh no. Nothing that important really.” Rarity smiled coyly. “I know it’s late and all, but I know you often work late into the night so… um… I was just wondering… could you perhaps help my sister and Scootaloo with their homework?” she asked, pointing to the two fillies, both of whom waved a hello.
“Homework?” Twilight brightened. “I guess I could use a break. I’d be happy to.”
“Thank you so much, Twilight. I mean, I would love to help my dear sweet sister, but I am just swamped, and I mean completely busy with a very important order for a very important client of mine right now, otherwise, I would have helped her right away, but seeing as I’m sooooooooooo incredibly busy…,”
“Okay. I get it,” Twilight said quickly. “I’ll help them. Don’t worry about it.”
“Thank you so much, Twilight. Now if you’ll excuse me-”
“Wait just one second. Why are you coming over now? It’s ten o’clock already. Shouldn’t they have finished it earlier?”
Rarity’s smile wavered slightly. “If it comes to it, would it be all right if they spent the night? Scootaloo has already asked her mother.”
“I guess but-”
“Thank you so much, Twilight. Well… tootaloo.” And Rarity disappeared before Twilight had a chance to say another word.
“Wow. That must be some client.”
“Don’t believe her, Twilight,” Sweetie Belle said with an annoyed expression. “She’s just saying that because she couldn’t figure out any of my homework.”
“Ah, Sweetie Belle, don’t say that. You know Rarity often has important orders to fill.”
“You haven’t seen the homework yet,” Scootaloo said knowingly.
“Now, now, my little ponies. Homework is just a tool to help young minds grow and learn all kinds of wonderful things. In fact, homework is fun. Here, I’ll show you.”
“You’ll be sorry,” Scootaloo told her.
“Nonsense. I’ll have you understanding your homework in no time.
Apple Bloom, Applejack, Big Macintosh, and even Granny Smith sat around the living room table. Between them, a series of papers with various numbers, marks, and half erased answers, were strewn about.
Applejack rubbed her temples and groaned. “Okay, read it just one more time.”
Apple Bloom sighed and read from the paper in front of her. “Every month, a filly gets allowance. Assume last year she had no money, and kept it up to now. Then she spends 1/2 of her money on clothes, then 1/3 of the remaining money on games, and then 1/4 of the remaining money on toys. After she bought all of that, she had 7777 bits left. Assumin’ she only gets money by allowance, how much money does she earn every month?”
Applejack stared into open space for a moment before throwing her hooves up. “I give up! What the hay kind a homework is this!? I ain’t never seen mathematics like this before!” Applejack’s stomach chose that moment to growl, reminding her that she hadn’t eaten dinner yet. “And I’m still hungry. Do you have the answer, Big Macintosh?”
Big Macintosh scribbled a few numbers on the paper in front of him, examined it and then answered, “Nnope.”
Applejack groaned again. “Granny?”
Granny rocked silently in her chair. Finally she answered, “Could you repeat the question?”
“Oh for the love of…,” Applejack groaned yet again. “I can’t believe this. What time is it? My gosh. What is Cheerilee thinkin’?”
“Cheerilee didn’t assign it. She got fired yesterday. Didn’t I tell you that?” Apple Bloom said.
Applejack stared at her. “What? Cheerilee? Cheerilee got fired? You’re kiddin’ me.”
“No. It’s the new teacher Ms. Plum, who assigned this.”
“Oh really.” Applejack picked her hat up off the floor and pulled it tightly over her head. “Well, I might just have to have a talk with this she-devil and the Principal tomorrow.”
“Eeyup,” Big Macintosh said, writing some more numbers with his pencil.
“I don’t know, Applejack. She’s kinda scary. And really mean too. She even thinks I’m the dumb kid in class.”
“Did she actually say that to you?”
“Uh… not exact-”
“No way! Nopony calls my little sister dumb. Where does this Plum pony live? I’m goin’ straight over there and drag her hide outta bed and get to the bottom of this right now.”
“Um… actually I have no idea where she lives.”
“Well somepony’s gotta know,” Applejack said angrily, aiming for the door.
“You’re really goin’ now?”
“Sure as shootin’ I am. I’ll teach this new teacher a thing or two.” That said, Applejack went out the door, almost slamming it behind her.
Apple Bloom wasn’t sure what to say. Silently, she was celebrating. If anypony could straighten out that scary teacher, it was Applejack.
“There we go,” Big Mac suddenly announced. “2592.33 bits a month.”
“Whoa! Really? That’s huge?” Apple Bloom stared at her brother. “I wish I got allowances like that. How’d you figure it out?”
“Like that.” Big Macintosh pointed at the paper.
Apple Bloom gazed at the paper for a few moments. “You’re writins awful, Big Mac.”
“Eeyup.”
Apple Bloom sighed. She had no idea what Macintosh had written down, but if Applejack really did get after Plum, then maybe she wouldn’t have to worry about it. Hopefully.
Spike yawned and scratched his stomach as he got out of his basket. It was six in the morning, but it was his turn to make breakfast, so he had to get up before Twilight. Except, Twilight wasn’t in bed. Wondering where she could be, Spike walked downstairs to the main sitting room on his way to the kitchen. Before he could get there though, he spotted something that wasn’t normal. Two fillies sleeping underneath a blanket near the fireplace. And at the table…
“Twilight? Are you still up?”
Twilight was busily scribbling away on a piece of paper. Oddly, she was using a pencil rather than her usual quill, and even more strange, using her mouth rather than magic. What she was using her magic for was to hold up five different books and an abacus that floated around her as if in orbit. Every now and then, she glanced up at one of the books that floated by, some of the beads on the abacus would move, and then she would write something down. A small stack of books with titles like ‘Mathematical Theorems’ and ‘Calculus for Advanced Studies,’ sat on the table in front of her.
Spike walked up behind her and looked over her shoulder. “Uh… Twilight?”
Abruptly, Twilight dropped the pencil, the books and abacus around her fell to the ground, and she threw up her hooves. “Yes! Done!” Raising his eyebrows at Twilight’s strange behavior, Spike examined the paper she had been writing on. It was filled with various equations, calculations, and even some numbers so strange, Spike hadn’t known they even existed.
“I did it, Spike,” Twilight said excitedly after she noticed him. “I finished every last problem of the homework.”
Homework? Is that what she had been doing all night? And why math homework? Twilight specialized in magic and science related topics. That’s when Spike noticed something. “Hey Twilight, I’m no math expert or anything, but didn’t you forget to carry the 2 here?”
“Huh?” Still smiling and holding her hooves up, Twilight looked over the equation Spike had pointed at. A few moments later, she face planted onto the table.
“Twilight! Are you okay?”
Twilight slowly turned her head to face Spike. Her eyes were bloodshot red. “Coffee. Need… coffee.”
“I think sleep might work better-”
“Just get the coffee!” she shouted in agitation, loud enough to startle the sleeping fillies awake.
“No! Not Rainbow Dash!” Scootaloo shouted, spinning around, not remembering immediately where she was.
“Are you okay Scootaloo?” Sweetie asked her.
Scootaloo slowly wiped sweat from her forehead. “I was having this horrible nightmare where Ms. Plum told me that she was Rainbow Dash’s sister. It was awful.”
Spike slipped into the kitchen to make coffee as Twilight furiously erased an answer with her pencil and scribbled in the right one after carrying the 2. She honestly didn’t look much better than Cheerilee had the day before.
“Oh, that’s right,” Twilight said painfully. “I forgot about Cheerilee. Stupid homework!”
“Whoa. You actually finished it?” Sweetie Belle stared at the scribbled on paper in great appreciation and respect. “You’re the smartest pony ever, Twilight. Can you show us how to do it now?”
Twilight felt a small blow to her heart as she imagined going through all thirty problems again. True, she understood them now, but she didn’t have the energy to go over them anywhere in the next twelve hours.
“Why don’t you two come by after school. I need to… see about a few things first.”
Though the two fillies seemed a little let down, they were glad to finally get the horrors of the homework out of the way. With Twilight around, maybe they wouldn’t fail Plum’s class.
Twilight took a deep breath and wandered into the kitchen when she smelled the inviting aroma of coffee. As soon as Spike poured her a cup, she downed it in one gulp.
“I can’t believe anypony would assign problems like that to kids,” she said as soon as she swallowed the coffee. “It took me all night to figure those out. Me! A student of Princess Celestia.” She turned to Scootaloo and Sweetie Belle when they came in hoping for pancakes. “Who is this new teacher of yours? I have a few choice words to discuss with her.”
The two fillies looked at each other a moment before unloading everything they had experienced with the horrible new teacher the day before. As the story went on, Twilight stared in growing shock. She didn’t even notice that Spike had become so engrossed in the tantalizing story that he had forgotten to stop pouring her more coffee. It spilled over the rim and onto the floor in a growing puddle of black water. Even after the two poor foals had finished, Twilight’s mind still hadn’t registered the spilt coffee.
“I don’t believe it. That’s not teaching. That’s… that’s just wrong. Cheerilee was replaced for that? What is the school thinking? Don’t they screen their teachers first?”
“The Principal said she came highly recommended,” Sweetie said sadly.
“By who? Tirek?” Scootaloo put in angrily.
A knock on the door interrupted them and Twilight went to answer it while Spike quietly mopped up the coffee stained floor. Rarity was at the door with a very apologetic expression on her face.
“Sorry to disturb you so early after coming by so late before, but I thought I would pick up my sister and Scootaloo and fix up some breakfast for them. I shan’t force you to feed them after… well after what I asked you to do last night.”
Yeah. Thanks for that, Twilight thought, though she was too good of a friend to say it out loud. Besides, she decided it would be better to focus on the new teacher who had assigned that ridiculousness.
“Actually, why don’t you come in and have breakfast here. I wanted to talk to you about this new teacher and her insane homework.” Some of those questions hadn’t even had identifiable answers. Whoever heard of putting trick questions on a child’s homework?
Rarity nodded. “After thinking it over last night, I concur. I want to get to the bottom of this absurd homework assignment. I was going to walk them to school and talk to the new teacher.”
“If that’s your plan then I think I’ll tag along too. Whatever reason they had for hiring this Ms. Plum has something fishy behind it. Besides, this might be the solution I promised Cheerilee yesterday.”
“Cheerilee? Have you talked to her since she was fired?”
Twilight paled. “You don’t want to know.”
Apple Bloom stood in front of the schoolhouse, staring up at the door. She had gotten this far, but found her hooves unwilling to go any further. She had hoped that Applejack had found Plum and talked some sense into her or straightened her out or threatened her or something the night before. Instead, she had spied Plum walking into the school ahead of her. She actually looked a little ruffled perhaps, but otherwise seemed to have an extra spring in her step. Apple Bloom hadn’t had a chance to talk to Applejack and in fact, hadn’t even seen her that morning. It seemed all her hopes for getting out of the homework had been dashed and she was going to be forced to turn it in, unfinished. Her life was over.
“Apple Bloom!” a voice behind her called. Scootaloo and Sweetie Belle ran up to her excitedly. “Morning, Apple Bloom. Ready for school?”
“Hey girls,” she replied halfheartedly. “What are you so happy about? Did you forget about Plum?”
“I’m not worried about her,” Scootaloo said with a smug expression. “We finished the homework.”
“No way!”
“Way!” the two fillies answered happily.
“How did you do on it?” Sweetie Belle asked her.
Apple Bloom drooped.
“Oh. Don’t feel bad though. It was impossibly hard.”
“I know. How’d you guys figure it out?”
Scoot and Sweetie looked at each other and pointed behind them. “Twilight did it for us.”
Twilight? Why hadn’t Apple Bloom thought of that? What was more, why were Twilight and Rarity walking behind them?
“What’s goin’ on?” Apple Bloom asked wearily as the two mares caught up to them. “What’s everypony doin’ here? Is this an intervention? I swear I’ll stop eatin’ them funny loookin’ flowers that make my head feel all dizzy.”
Twilight and Rarity both looked at her funny. “Yes… you probably shouldn’t do that… whatever it is…,” Rarity said slowly. “But anyway, we came to talk to your teacher. Is she here yet?”
Apple Bloom blushed. “Um… yeah. I just saw her walk in a little while ago.”
“Well, introduce us to her. We want to talk to her about his homework assignment of yours.”
Feeling a bit encouraged, Apple Bloom made her hooves walk into the building. The Cutie Mark Crusaders led the way to Ms. Plum’s classroom where they found the teacher writing something about Equestrian history on the chalkboard. The other students who had already assembled, which was everypony except Snips and Snails, were watching her nervously, almost as if mesmerized by the chalk.
“Ms. Plum?” Rarity asked.
Plum spit the chalk out of her mouth and turned with a rather arrogant air. “Yes? Can I help you?”
“We want to talk to you about the homework assignment you gave your students,” Twilight told her.
“What of it? It wasn’t anything too difficult,”
“Nothing too difficult? I was up all night trying to figure out that insanity you assigned. What was up with that?”
“Insanity?” Plum looked at the two mares as if just registering their presence. “I’m sorry, who are you two?”
“Rarity, Sweetie Belle’s older sister.”
“And I’m Twilight Sparkle.”
Abruptly, Plum went wide-eyed. “T-twilight?”
“Do you know me from somewhere?” Twilight asked her.
“Not really… Uh, students, why don’t you all prepare for class while I talk to these concerned ponies. I’ll be back to start class in a little while.” Plum smiled, actually smiled, at the Cutie Mark Crusaders before nodding to Twilight and Rarity. “Why don’t we step into the teachers lounge? We can discuss this over a nice cup of coffee.”
“I’ve had plenty of coffee today, thank you,” Twilight answered quickly. “I just want to talk about the homework assignment.”
“Yes, of course. Follow me right this way.” Plum actually sounded a little nervous. Then the two mares nodded and proceeded to follow her.
“See. My sister and Twilight will take care of her. You don’t have to worry about a thing,” Sweetie said confidently to Apple Bloom. The small yellow filly smiled. She had been saved.
Snips and Snails had finally shown up, or rather they had raced into class just as the bell rang. However, that had been ten minutes ago. Everyone was talking quietly, wondering what the two mares were saying to Ms. Plum. To think she hadn’t come back to start class yet. The two unicorns must have been chewing her out like nopony’s business…
The only one who wasn’t talking was Sweetie Belle, who had busied herself with a drawing she had started a few minutes before. Even though it was only in pencil, it didn’t look half bad. Maybe she and her friends could try for drawing cutie marks later.
As it happened, Sweetie Belle was sitting in the front row to the left of Silver Spoon, who had been forced to sit front and center the day before. Sweetie’s row was closest to the windows in the room and she just so happened to look out the window just then. Then she did a double take. Plum was walking away from the school followed closely by Twilight and Rarity. Where were they going? It didn’t appear that her sister or Twilight were chasing Plum. That sure was odd. Shrugging, Sweetie returned to her drawing.
About five minutes later, the students all hushed when the Principal walked into the room.
“All right, quite down, quite down everypony,” he said, despite the fact that they already had. “I have an announcement to make. It seems Ms. Plum, has gone home sick. Bless her heart that she had the courage to show up in such a state. It just shows how hard a worker she is and you should all learn from her example.”
Learning from her example was one thing none of them wanted, but that was hardly important. A muffled cheer rose in the room. It was the best news since a few weeks before when the lunchroom had started serving chocolate milk.
“I know you’re all disappointed and worried about her, but she is going to be just fine.” At least two spitballs, three erasers, and a paper airplane flew past the Principal’s head, but he didn’t seem to notice them. “You’ll have study period for the next twenty minutes and then I will return and be your teacher for the rest of the day.” Then he left.
Though the students were all disappointed that class hadn’t just been canceled for the day, not having Plum around was a wonderful alternative.
However, Sweetie Belle wasn’t so sure. She had finally connected the dots. Plum sure didn’t seem ill, though it might have explained why Rarity and Twilight had decided to walk with her. But it was still strange. If she wasn’t sick, then why had the two unicorns followed her away earlier? For that matter, where had they gone?
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Nice update to the storyline as it shows just how strong the bond of Sisterhod really is in this tale of yours. 
I do wonder what did Twilight and the others did to Plum to make her leave the classroom for the rest of the day ? 
Please do keep up the good work upon such a great storyline like this one as I cannot wait to see what happens next in this storyline of yours. 
Heh...I can do those problems 
Of course, there is no way a young kid can be expected to do integration like that when the most complex they've been before is times tables. YOU TELL THAT MARE, TWILIGHT! 
SLAP HER ONE, RARITY! 
I mean, err...talk to her reasonably about the consequences of her actions. Yeah...
>>68560 nope, you did it right. 
this chapter was freaking awesome, man. the apple family doing math?? i was expecting some sort of big macintosh muddling the issue with his fancy mathematics, but you still made it awesome and great and 
i hope the next chapter's this good. i normally dont write cheesy awaiting-next-chapter things like that, but this deserves it. 
Finally a fanfic where Twilight is recognized as Celestia student. It seems that in so many fic's people end up insulting her or her friends or hurting them in some way and the only logical conclusion to the story is Twilight has Celestia imprision them on the moon. Good job for so far avoiding that problem.
Man, I'm currently taking a high-school Trigonometry/Pre-Calculus class and none of those problems made a lick of sense to me. Granted, some of them, if not all of them, are probably above my level of study to begin with, but still...geez! 
I also should probably take this moment to say that I'm actually really impressed with how intelligently written this fic is, whether it's Cheerilee lecturing like a madpony or getting punched in the face by math problems that should never have existed on the face of this Earth. XD So, basically, I wanna see moar, please! I always jump when I see that this fic has been updated. :D
Holy mother of god Ms. Plum sucks. I'm thinking of the possibility of mind control of some sort to make the principal [and/or whatever sadist(s) recommended her] think she wasn't a horrible horrible teacher. Or she's a teacher of epic-level math and doesn't realize she's not teaching grad students anymore, and the principal is a moron. Or something completely different and sinister is going on.
Bwuh?
Oh my lordy... What the fuck was that? I haven't taken a math class since Freshman year and I promptly repressed all of it to make room for psychology, English, and History. Too many traumatic memories in my math classes. I don't even remember what a cosine is. Still, I know that I didn't even HEAR of it until my Junior year of high school. These are Elementary school students, right?
Seriously. WTF is up with this school?!
>>69115 Whooooooops! Unfortunately you are mistaken: my solution WAS COMPLETELY WRONG!!! Here is the valid solution:
A=0
D=390
B-A=C-B+10
C-B=D-C+10
The answer is obviously:
A <-- 140 --> B <-- 130 --> C <-- 120 --> D
So your answer (140) was perfect, while mine was wrong.
Do you know where can I find the application forms for a magic kindergarten? :)
ps. do you have the answer to the 'little filly's allowance problem'? For me >3000 bits/month seems a tiny bit excessive, although the underlying math seems simple enough - just a sum of a finite geometric series.
I love math espacially algebra, but it's been years since i resolved problems dealing with graphs. I tried but I only resolved the first one, the others well I don't have the time to sit down and finish, got other thing to do. Aldo I love the Tirek part, But how does Scootallo know who Tirek is/was?
Good question. It was more just a reference to G1 which I watched as a kid and recently rewatched through Youtube just for kicks. It's amazing how poorly some of the episodes were put together put it was still nostalgic nonetheless. I even went ahead and watched G1.5. I also saw those when I was a kid and may have actually seen them when they first aired. I'm one of those bronies who still likes G1 and G1.5.
The answer to the integral is (and this is going to look a little sloppy here):
(cos(x)
1 + x^2) dx =
-i (1 + e^2) Ci (i - x) + i (1 + e^2) Ci (x + i) + ((e^2) - 1) (Si(i - x) - Si (x + 1))
4e
Where:
i = imaginary number
e = approximatly equal to 2.71828182845904523536028747135266249775724709369995...
Ci = the cosine integral
Si = the sine integral
I'm sure that makes perfect sense now.
You work that one backwards-- if she spent 1/4 of her money on toys and had 7777 left, then that 7777 is 3/4 of the money she had before buying toys. Then her pre-toy money is 2/3 of what she had before buying games, and that money is 1/2 of what she had before buying clothes. Multiply that out (7777 * 4/3 * 3/2 * 2), and she started out with 31108 bits. Over 12 months, that's 2592 1/3 bits per month, but to get 2222 like Big Mac did, you have to divide by 14 months.
Yes... I goofed... Or how about we just say that Big Macintosh goofed.
The real answer:
12x = year's worth of allowance
(1/2)12x spent on clothes = (1/2)12x = 6x
(1/3)6x spent on games = (2/3)6x = 4x
(1/4)4x spent on toys = (3/4)4x = 3x
Then
3x = 7777
x = $2,592.33
I wonder if I should go back and change that?
>>69459 Thank you for writing it out - it may help somepony else. I asked as I was sure she spent the money every month, not after the whole year of saving... So basically I solved a bit more difficult problem :).
Now we have only 2 problems left: the 'hammers' and the hell. The 'hammers' are trivial-to-solve using a computer but that would be cheating. They don't have the machines in Ponyville! The only hint I may give is: by Celestia, remember about carry! No, I do not have anything even close to a sensible solution :).
When it comes to hell, the only thing that comes to mind after looking at the solution is [safe for work] Euler's formula (look for Relationship to trigonometry).
I have to openly admit I put the hammer one and the crazy integral one in there without knowing the answers beforehand becuase I wanted something that just looked insane. I know what the answer to the integral one is and what all the symbols mean and even how to solve at least part of it, but I currently don't have the math skill to solve the Cosine integral and Sine integral part which I have never done before myself. What I should say is that I've never done the integral thing. I can solve stuff with Sin, Cos, ect. but integral? Not sure if that is a different process.
As far as the hammer one goes... I was killing myself over that one too. I swear there is not enough data to really find a definite answer but nemryn claims the answer is $8.51. Help me out here and tell us how you came to that conclusion becuase I'm feeling as lost as Applejack right now. 
Totally busted on those two questions. 
All the links in here are [safe for work]
The integral shown in the story (probably) does not have a solution in terms of elementary functions. That's why we had to define more functions to more easily exchange ideas. The Si() and Ci() are such 'shortcuts'.
> which I have never done before myself.
Me either! :). It's been ages since I did any integration...
> What I should say is that I've never done the integral thing. I can solve stuff with Sin, Cos, ect. but integral? Not sure if that is a different process.
Ehm... integrals are, from my experience, the toughest problems you can get to solve that look innocent (please, math Gods, don't hit me!). Some examples are in SOS Mathematics. Derivatives of functions are almost always easy but integrals are usually very hard to calculate.
nemryn is right - the answer to the hammers problem is 8.51, which is super-easy to prove by inspection: 144*8.51=1225.44.
> I swear there is not enough data to really find a definite answer
You're right - most probably there will be a few cases to check but the point is to reduce the number from 800 multiplications (every possible amount from $6.00 to $14.00 (any solution must be in this range, otherwise we won't get $1 # # #. # #.) - this is simple to check by hand) to a reasonable number (e.g. 10 or 20 multiplications).
A trick I used for the hammer question is, if a number is a multiple of 9, the digits will add up to a multiple of 9, and vice-versa. 144 is 16 * 9, so the total cost is also a multiple of 9. The digits we have add up to 12, so the two missing ones have to add up to 6 to get to 18. Also, 144 is even, so the total cost is even, which means the last digit has to be even. Given those two facts, the missing digits have to be 0 and 6, 2 and 4, 4 and 2, or 6 and 0. Now there's only four possibilities, which is few enough that you can just try each of them and see which one works. $1,225.44 / 144 = $8.51, and the other three possibilities give you fractional cents, so that's the answer.
I tried a couple different things on the integral before giving up and plugging it into Wolfram Alpha; I don't think it is solvable by hoof.
Yeah, I got $7.121 for the per hammer price, total of $1025.424. Brute forced it, that is I got a reasonable approximation to the answer and then covered a paper with multiplication. It's a possible answer, if you throw out the "no fractional cents" assumption. Did the Pegasus problem in my head, got the (12 month) solution to the filly's homework problem, and looked up bits of the integral in my Handbook of Chemistry and Physics (55th edition) before deciding that I really couldn't solve that one.
Image: http://media.tumblr.com/tumblr_lkkec92lH31qafrh6.png
>>69635 BIG KUDOS to you for showing us the light! Excellent thinking!!! I tried a more 'brute force' approach (analysing each digit separately) but the thing yields a monstrous set of equations with about twice the number of unknowns compared to the number of equations. I am amazed by the simplicity of your solution, nemryn!
>>69705 OK. You got me - Twilight probably has access to a mainframe. I doubt Apple family has one, though!
I posted an explanation on EqD of how to solve the Super Homework problems (except the integral problem) if anyone is having trouble.
By the way, something I noticed about the allowance problem: if the remaining bits at the end of the problem was 6666 instead of 7777, then the answer would have been exactly 2222, same as Big Macintosh's answer.
Loving the fanfic so far, looking forward to the next chapter!
>Plum gives problems no grade schooler could possibly solve and therefore is evil
Image: http://img.ponibooru.org/_images/cac0c1ea37fb2f5b47893ed22522a947/23161%20-%20answer%20cheerilee%20clean%20school%20you_should_be_able_to_solve_this.jpgO RLY
I love this picture. It rocks. Saved!
Well at least the pegasus one was easy. I would have trusted at least Big Mac would've gotten that after a minute or so with scratch paper, at least until he came up with the 2222 allowance.
The answer to the hammers was indeed $8.51, and it looks like something you might see on the Algebra II level AIME. With 144 hammers, the final digit must be even. To bound it between $1025.40 and $1925.48, we're looking at $7.12 < H < $13.38.
Lacking nemryn's brilliant insight at that point (seriously, man, props) I just said "buck it", opened up Visual Studio, and wrote a quick C program to just dump a table of all H values within those bounds and their corresponding totals into a text file. Maybe 20 lines of code, the majority of which was overhead -- the relevant code was shorter than this paragraph, and it took me longer to figure out where the hell the output file ended up in my hard drive than to write, build, and run the whole thing. I probably could have filtered it by parsing the total and actually checking the digits a bit, but it was quicker to just open the whole text file in notepad and ctrl-f search for "25.4" to match the middle digits. The only match dropped me right on the H = 8.51 line.
I gave the integral a shot before reading the comments, but the only approaches I can think of landed me in territory involving integrating trig-of-trig or trig-times-inverse-trig, which is usually a pretty clear signal that it's unsolvable by hoof and your teacher should be given an appointment with Krastos for even asking it. Then I tried to Taylor out the cosine and integrate the infinite sum by parts, expecting each term to itself be a sub-sum of arctangents. Which didn't work at all but was sure a blast trying! So yeah, seeing an unholy mess of vaguely Euler-ish/hyperbolic eldritch terror pop out of Wolfram doesn't really surprise me one bit.
Ultimately though, that whole debacle reminds me very much of something my mother had to go through back in the late 60's. It was called [url=en.wikipedia.org/wiki/New_Math]New Math[/url], an experimental attempt during the Cold War to fast-track elementary school kids into advanced abstract algebra without any of the necessary background, presumably so we could beat the Russians at...something. Probably space. It was exactly as cheese-brained as it sounds. I thought she was yanking my chain for a good chunk of my life until I stumbled across it by accident a couple years ago, thought "WTF am I reading" 
and called her to apologize.
More on topic, Rarity would probably never say "yeah". But wonderfully fun chapter!
Let a := dist(A, A); b := dist(A, B); c = dist(A, C); d = dist(A, D)
c - b + 10 = b -> c = 2b - 10
d - c + 10 = c - b -> d = 2c - b - 10
d = 390
390 = 4b -20 - b -10
420 = 3b
a = 0
b = 140
c = 270
d = 390
Answer = 140
----------------------------
The second problem should be in bits.
Hm, it must be something above 7 and below 14 judging from first digit. Not very helpful. Last digit is not so important, so lets assume 0 for simplicity. That would leave us with price of single hammer x.1 Now just multiply 144 by 7.1 through 14.1 and look for matches.
7.1: 14.4 + 700 + 280 + 28 = 1022.40
8.1: + 144 = 1166.4
9.1: + 144 = 1310.4
OK, this won't work, because 5 is odd. Let's try x.6
0.6 x 144 = 72 + 14.4 = 96.4
Won't do. Lets try x.01
8.01: 1.44 + 800 + 320 + 32 = 1153.44
9.01: + 144 = 1297.44
10.01: +144 = 1441.44
11.01: +144 = 1585.44
12.01: +144 = 1629.44
13.01: +144 = 1773.44
14.01: +144 = 1917.44
Dang it! Ok, what .zy * 144 give odd.4#?
z : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
*14.4: 0.00, 14.4, 28.8, 43.2, 57.6, 72.0, 86.4, 100.8, 115.2, 129.6
y : 1, 0or7, 6, 5, 2, 1, 0or7, 6, 5, 2
*1.44: 1.44, 0, 8.64, 7.2, 2.88, 1.44, 0, 8.64, 7.2, 2.88
What about y in {3, 4, 7, 8, 9} ?
y : 3, 4, 8, 9
*1.44: 4.32, 5.76, 11.52, 12.96
z : -, -, -, -
help for x: 10: 1440, 11: 1584, 12: 1628, 13: 1772, 14: 1916
Therefore:
x.01, x.10, x.17, x.26, x.35, x.42, x.51, x.60, x.67, x.76, x.85, x.92
1.44, 14.4, 24.48 37.44 50.40, 60.48, 73.44, 86.40, 96.48, 109.44, 122.4, 132.48
24, 11, 01, 88, 75, 65, 52, 39, 29, 14, 03, 93
-, -, -, 2, -, -, 8, -, -, -, -, -
The ONLY answer is 8.51 x 144 = 1225.44. Price of one hammer is 8.51
That said, I was halfway to giving up and writing a general program to solve this class of problems. The easy way is to figure out the bonds, write a loop in any programming language, even C, compile and 'a.out > grep 1.25.4.'
OK, how to do this: since it is between 1025 and 1925 divide those amounts by 144 to get bounds. Next figure out what combinations of z * 0.1 + y * 0.01 give ###.4# There aren't that many. Next using bounds on first two digits of solution (7 to 14) figure out what works.
--------------------------------
cos(x)/(1+x^2) Looks very tricky, and its been a while since I've done any integrals. And when I say tricky, I mean 'I would rather try to flirt with a girl than try to solve it.' It looks THAT difficult and painful. I give up.
--------------------------------
7777 is a LOT of bits, BTW. She is richer than Diamond Tiara.
OK, she has left 1/2 * 2/3 * 3/4 = 1/4 = 7777
So she had 7777 * 4 = 28 + 280 + 2800 + 28000 = 31108
By how many months am I supposed to divide that?
If 12 than 2592 and 4/12
Either I don't understand this assignment or something is wrong with it.
Hm, 31108 / 2222 is 14 months. But that is over 12 months, and last year she had no money.
If it was formulated "At start of year she had 0. At end of year she had 7777. Each month she was spending [proportional amounts]. How much did she get per month?" it would at least be clear.
It doesn't matter if she is spending it monthly or at the end of year as long as each month she spends the same amounts from that month's allowance, not her total money.
------------------------------------
First problem should be doable by a kid. Second is tedious, and needs a few ideas to reduce math to manageable levels. It could also use a second part to calculate the sales price from sales tax and profit margin as icing on a cake. Third is beyond understanding for a kid an apparently everyone in this thread. Fourth has some missing information, I think.
OK, GWFan, but You cheated and used Wolfram Alpha for that integral. Can we see it done the normal way with all intermediate steps? Maybe there is a simpler solution.
Please restrain yourself from insane integrals. Mensa / mathematical Olympics algebraic problems are fair game.
I only used a calculator to CHECK some of my results while nailing the issue with second problem. I found a few errors, but didn't bother correcting them. Answers are correct.
@ nemryn:
Hey, that's clever. I reduced the number of calculations, but Your solution is simpler and more elegant.
@ IntheCloset (guest)
You can't do that. Firstly, prices normally have a quantum of 0.01 <currency>. Secondly, You would get more than one answer, which means you couldn't figure out the correct price.
@ GWFan:
It would be even funnier, if Twilight was sitting in her basement using books and terminal (but not abacus), then printed the results.
@ Guest
> x - 7 = 19 + x
Ans = NaN
The hay is this?
Physics major here. Live and breathe calculus. Even I was at the integral problem and looked it up on Wolfram Integrator. Then I was . Called bullshit on the smudged receipt problem as missing data means you have to approximate then guess and check like crazy. Math problems should never require repeated guessing! 
Rest was easy though.
alright, distance is 140 miles
bits is 2592.33
and the integral of cos(x)/(x^2+1) can't be done with out using imaginary numbers (1/4e)(-i(1+e^2))Ci(i-x)+i(1-e^2)Ci(x+i)+(e^2-1)(Si(i-x)-Si(x+i)))
the derivative is -((x^2+1)(sinx+2xcosx))/(x^4+2x^2+1)
the smudged number is $1225.44 meaning $8.51/ hammer
stupid evil math beeotch
>>68312 OBJECTION The last one the Apple family had pondered and puzzled over was imossible!
“Every month, a filly gets allowance. Assume last year she had no money, and kept it up to now. Then she spends 1/2 of her money on clothes, then 1/3 of the remaining money on games, and then 1/4 of the remaining money on toys. After she bought all of that, she had 7777 bits left. Assumin’ she only gets money by allowance, how much money does she earn every month?”
A simple interest (I) is the principle(P) times the rate (r) times the time(t). the equation to figure it out looks like this
I=prt
To figure this out you will need to work backwards, and subtract and/or divide depending on the process you choose. we know that we must subtract the remaining sum with the starting sum, but first we must find a starting sum. So written as an equation, that would look like this(supposing a, b, and c are the three purchases:
I=[(P-(a+b+c)]/?....
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAUGH! I WON FIRST PLACE IN THE FRICKIN DISTRICT MATH TEAM, I SHOULD KNOW THIS!!!! But alas, i do not
The calculus problem does not have a closed-form solution. And believe me, I was loathe to give up and check it by running it past Mathematica. That's a much easier problem for a filly who can just say outright that she doesn't know calculus yet.
And by the way, it's "ought", not "aught". They're entirely separate words.
And now you lose math cred. The filly with the allowance has spent 3/4 of her money, or nine months' allowance, and so has three months' allowance left. 7777 is not divisible by 3, and I doubt her parents include a third of a penny in her allowance each month. Nor do I think she could spend that penny every three months.
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