Who Farted?

by Ragnar

First published

A short examination of the mechanics of a three-pony argument.

Three ponies sit together in a room. Two are innocent. Each of the two innocents have two possible suspects, including one another. The third must pretend to be in the same predicament. How can the two innocents recognize each other as such and catch the true culprit? Conversely, how may the guilty pony redirect suspicion from herself?

I am a child.

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Rarity, Twilight Sparkle and Applejack sat together at the bottom floor of the Ponyville library, each reading her own book in companionable silence.

AppleJack sniffed, frowned, and looked up from last year's edition of the Farmer's Almanac. "All right, who tooted?"

Rarity gasped and dropped her novel. "Oh, you're right! Let's move upstairs. Twilight, please at least say 'excuse me.'"

Twilight, oblivious, turned another page. Applejack and Rarity glared. Without looking up, Twilight muttered, "I smell something. Where's Spike?"

"Huh," said Applejack. "Rarity, maybe you want to say something."

"I beg your pardon?!"

"Thank you," said Applejack, and went back to her book.

"No!" shouted Rarity. "I beg your pardon because, excuse me, but you're wrong."

Twilight, quizzical, looked up. "What are we arguing about?"

"Rarity tooted," said Applejack. "Or you did. Twilight?"

"It was Rarity," said Twilight, and went back to reading.

Rarity opened her mouth to retort and then closed it. She turned slowly to Applejack. "You know, I think we're ignoring the other possibility. You've really been quite vehement that it was anyone other than you..."

"Now you're just tryin' to deflect!" shouted Applejack, standing.

Rarity stood up as well and faced her down. "Oh, stop. Being aggressive doesn't make you sound any less guilty."

Twilight sighed, placed a slip of paper in her book, and set it on her coffee table. "Girls, I think we're blowing this out of proportion. Let's all just agree you both passed gas simultaneously, and let it—"

Applejack pointed a furious hoof at Rarity. "She's callin' me a liar! We're getting to the bottom of this if it takes all day."

It needn't take all day if you'd just admit it," said Rarity evenly. "Applejack, honestly, this would be out of character for me. I have control over myself."

"And I don't lie."

Rarity threw her hooves in the air. "Clearly there's a first time for everything!"

"Yeah, well Twilight can judge. Twi, who did it?" Then Applejack's eyes narrowed. "Now hold on."

"Hold on indeed," said Rarity. She gave Twilight a sideways glance. "Applejack, please drop all pretenses, forget the fight, and be completely honest."

"Always," growled Applejack.

"Was it you?"

"NO! That's what I been tellin' you, if you'd listen."

"And it really wasn't me," Rarity said thoughtfully. "Applejack, have you ever played rock-paper-scissors with Twilight?"

Applejack raised an eyebrow.

"If you had, you'd know Twilight always seems to win. Don't you, hon?"

Twilight now lay on the floor, her head propped up on crossed hooves, scowling. "And now we're back to me. You know, this is an awful lot of argument over a natural bodily function."

Applejack hadn't taken her eyes off of Twilight. "What I remember is poker night. You were quite the bluffer, sugarcube. "

Twilight rolled her eyes. "I told you, I won so much because it's not really about bluffing. It's about counting and probability."

"Mm-hmm, spent the entire game talkin' about numbers and percentages, just like that. You talked and talked about math until we started ignoring you outta self-defense, and then you'd swoop in and take the best pots every time because nopony was keeping an eye on you."

"I think she's got your number," pronounced Rarity, "so to speak."

"What?" said Twilight.

"Your number, Twilight. Please pay attention when I'm denouncing you."

Twilight rolled on her back and shrugged. "Fine, I did it. It was me, sorry everypony, the argument is over and everyone is done yelling, and now I can go back to reading." She picked her book back up.

"Good," said Rarity, and sat back down.

"Fine," said Applejack.

The room descended into disgruntled silence. Rarity picked her book back up and glared at the pages.

"Unless..." said Applejack to the ceiling.

Twilight kicked the table. "Oh, come on!"

Rainbow Dash alighted on the window frame. "Hey. Are you guys yelling?"

Applejack looked back and forth between Rarity and Twilight. "Someone farted and won't admit it, and we're gonna work out who."

Rainbow sniffed the air. "It smells like books. Does that mean it was Twilight?"

"She'd like me to think that, wouldn't she?!" She paused. "What I mean is, she tried to end the investigation before I could really prove it. She's sowing doubt and reaping lies and I won't stand for it."

"One second. Rainbow, do you think I eat books?" Twilight asked.

"Well of course it sounds silly if you put it like that," said Rainbow.

Rarity closed her book. "This conversation is disgusting and I'm taking my book upstairs."

"You know what?" said Twilight. "Fine. Let's investigate. There are three possibilities: Rarity, Applejack, and Rainbow Dash."

"Nope!" said Rainbow. "I was way over there." She pointed at a distant cloud.

Twilight smiled. "Ah, but maybe you were, in fact, just outside the window."

"Or it was you," said Rainbow. "Hey, no judgment. It's your library."

"Hmph," said Rarity, now sitting on the bed upstairs.

"Hold on, I can prove I didn't do it," said Rainbow. She turned and yelled, "HEY, DOGWOOD! WHERE WAS I A MINUTE AGO?"

Two ponies poked their heads out from behind the distant cloud. One cupped his hooves around his snout and shouted, "Get back here and help!"

Rainbow nodded to herself. "See? Anyway, you left yourself off the list, so that's interesting."

"Obviously I akready know I didn't do it," said Twilight.

Rainbow flew up on a bookshelf and pointed dramatically. "Aha! That's the very thing a pony who secretly farted would say."

"For goodness' sake!" bawled Rarity from upstairs.

"It's also something an innocent pony would say," Twilight said. "Do I have to make a chart?"

Applejack stomped a hoof. "Now don't you threaten us. Wouldn't trust your charts right now anyway."

"Don't be absurd. Here, let me show you." Twilight wheeled her chalkboard out of the corner, revealing Pinkie, who waved at everypony and pronked away.

Twilight opened a new box of chalk. "Ahem. First, let's try turning this into a simple logic matrix. Let me just draw the grid."

"Oh no, I ain't fallin' for this. It's just a rhetorical cloud of ink to escape my cross-examinations. Rainbow, are you paying attention?"

Rainbow Dash watched Pinkie bounce happily out of the door and into the street, then disappear around a corner. "Uh..."

Twilight rapped a piece of chalk against her new chart. "Rainbow, if you're not going to listen then you can go back to work." Twilight wrote "Fart Matrix" above the grid. "So the Y axis represents each of us, and the X axis is whether or not she passed gas, and the Z matrix—just imagine one, I can't draw it—can represent her accusation. Now, if we consider our respective personalities and communication styles, we can consider probabilities—"

Rarity stomped out the door. As Twilight lectured, Applejack stared at the chart like it owed her money, already raising a hoof to object. Rainbow looked back and forth between them and made a decision. She flew away.