A Question of Rankings: a Logic Puzzle Fic

by Coyotek4

Rating: everyone
Tags: Applejack, My Little Pony: Friendship is Magic, Sandbar, Gallus, Twilight Sparkle
Length: 3120

Sandbar is curious to know how his classmates did on a recent series of tests, but not all his friends are honest with him. Can he figure out how they all did ... and can you?

An illness kept Sandbar away from the School of Friendship just as quizzes were being given out. His friends all know how they did, but their hints are cryptic and not all of them are true. Twilight is able to sort out truth from falsity ... but can the reader?

Published 2018-04-11 09:30:07 UTC
Last updated 2018-04-13 01:18:40 UTC

Honesty, Loyalty, and Kindness

During the early days of the School of Friendship, much of the curriculum was designed by the EEA, and Twilight Sparkle made sure to follow that curriculum to the letter … much to the chagrin of the students. A portion of that curriculum was the requirement of regular quizzes in the Elements of Harmony, with students being ranked within their classes. So it was almost with great relief that a bout of pony pox kept Sandbar away from the school on a day when three such quizzes were given to his non-pony friends. Shortly thereafter, the group of six ditched a class, and the sequence of events which followed led to massive upheaval in the system.

Though much has now changed for the betterment of all involved, some aspects of education do not change …

“An honesty project? Due tomorrow???”

Gallus’s incredulous outburst does little to phase Applejack. “Yessir. And Ah’ll give y’all free reign in how you want to illustrate the benefits of bein’ truthful to one’s self and to others. Ah’ll even let y’all work together on this.”

Ignoring the muted groans from the others, Applejack walks towards the door. “Ah’ll be right back; Twilight wanted to observe some of the class proceedings. Feel free to discuss what you’d like to do. Let yer creativity shine! ”She gives the class one final glance before disappearing into the hallways.

“At least she told us we could work together on this,” Ocellus points out. “Many appendages make light work, right?”

“Yaks always work ONLY with other yaks,” Yona pointedly counters … “but maybe Yona make exception. Yona have no idea where to begin.”

Smolder continues: “I mean, if it was a generosity project, then we could just hold a fundraiser or something. Or work at an animal shelter if it was a kindness project. ”The thought gives her a brief shiver. “Then again, maybe an honesty project would be better.”

“Oh, what if we got a laughter project? Wouldn’t that just be really fun? I think that would be really fun! I hope Professor Pinkie gives us a laughter project!”

The others turn to Silverstream, then laugh in unison at the outburst. Soon though, they go quiet again.

Gallus turns to their pony pal. “So, you got any ideas, Sandbar?”

“Nothin’,” he replies. “Honestly, all I’ve picked up from Professor Applejack’s classes is a greater appreciation for farmwork.”

“So maybe that’s what we do,” Smolder suggests; “be honest in telling our ‘honesty’ professor that we’re not learning anything about honesty in her class.”

“Yeah, that’ll work out real well,” Gallus adds. “Point out the flaws in the pony who’ll be grading our efforts.”

“Yaks GREAT at pointing out flaws in other creatures!”

“I figured that out pretty quickly, Yona.”

“And griffins aren’t?”Smolder’s retort to Gallus causes them to briefly lock eyes.

“Whoa, whoa, whoa, calm down everyone.” Sandbar’s quiet but earnest demeanor quickly eases the tension in the air.

Smolder shakes her head. “Sorry … it’s my competitive nature. It’s kinda ingrained in all dragons.”

“Yona competitive. All yaks strive to be greatest.”

“I think that’s something a lot of us can agree on,” Gallus adds. Sandbar and Ocellus roll their eyes slightly, while Silverstream looks at all of them in slight bemusement.

“Hippogriffs can be competitive. Like when we all had to take those quizzes right before we ran away? Those were fun, right? Wait, not fun … weird.Is that the right word? Or boring? Maybe boring. But I still wanted to be best at … whatever it was we were supposed to be doing on those, right?”

Gallus, Smolder, and Yona all sigh in agreement, while Sandbar and Ocellus look at them in confusion.

“What quizzes?” Sandbar asks. “I don’t remember taking any quizzes.”

Ocellus answers: “Oh that’s right, you were out sick that day. We had quizzes in honesty, loyalty, and kindness. All paper-and-pencil stuff. They wanted to see how much we knew about the Elements of Friendship, so they could tailor our education to our weaknesses. ”She turns to the others. “Honestly, I didn’t see why those were so horrible.”

“They weren’t ‘horrible’, they were just pointless,” Gallus states. “Glad they got rid of those when we came back.”

Smolder agrees. “Yeah, and whatever order they settled on with our rankings … they may as well have just put our names in a hat and pulled them out in a random order.”

“Yaks ALWAYS first when pulled from hats.” Yona’s assertion draws laughs from the group, before Smolder continues.

“So,” Sandbar asks, “do you guys remember how you ranked? Like, on the three quizzes you took when I was out?” As he asks and his friends all turn to face him, Applejack re-enters the classroom with Twilight strolling in behind her; seeing that her class hadn’t noticed their entrance, the two quietly observe the responses to Sandbar’s question.

Ocellus answers first: “No one had the same ranking for any pair of quizzes. I ranked first for Kindness.”

Smolder follows up: “Everyone ranked first or second on at least one quiz. I ranked higher for Loyalty than for Honesty.”

Yona states: “Yona fourth for Honesty. Yona ranked higher for Loyalty than for Kindness.”

Silverstream then speaks: “So, neither Smolder nor Ocellus ranked fourth for Honesty. And Gallus didn’t rank second for Loyalty.”

Gallus responds last: “I didn’t rank fifth for any test. Silverstream ranked fifth for Loyalty.”

Sandbar mulls over the myriad of comments from his friends. “So … you’re trying to tell me that those quizzes really were meaningless!”

“EXACTLY!” Gallus triumphantly declares. The group shares another laugh, before an *a-hem* causes them to turn back towards their professor and their principal.

“Professor Applejack,” Smolder stammers, “sorry, we didn’t know you were—”

“No need for frettin’,” Applejack assures as she holds her front hoof out. “But Ah don’t know why yer messin’ with Sandbar like that. Ah know fer a fact that some of y’all been lyin’ with them comments. Actually …”

Applejack pauses for a moment before continuing: “Yeah, maybe there was somethin’ ‘bout them quizzes. The three of you who finished first, second, an’ third on the Honesty quiz were honest with yer comments, but the two of you who finished fourth an’ fifth, sure proved that you got somethin’ to learn; those comments were nothin’ but lies!”

“Wait,” Sandbar says, “you know how all of them finished in all the quizzes?”

“Well yeah, Ah chat with Rainbow Dash an’ Fluttershy all the time. Now it ain’t mah place to share how yer friends did, but if they wanna be more upfront an’ honest with you, then—”

“They don’t need to,” Twilight interrupts. “Sandbar’s heard enough to know everyone’s rank on all three quizzes.”

Author's Note

Can you figure out everyone's rank on all three quizzes?

I ask that anyone who wishes to post a solution to this story uses hidden text. Or just PM me with your solution, if you wish to know before I post the next chapter.

The following chapter will reveal the solution.

Anyone who enjoys this Fic might also enjoy other 'Logic Puzzle' Fics I've created:

Twilight's Logic Puzzle Adventure
Apple Bloom the Alchemist
The Chalice of Rhinyorgrun (which is an actual story in its own right, puzzles or not)

Quick nod to E. R. Emmet, who created a number of puzzles of this form.

Twilight's Reasoning

Silence pervades for several seconds. As Twilight scans the seven sets of eyes upon her, a sense of confusion comes over her. “What?”

“Uh, Principal Twilight,” Sandbar starts, “could you repeat what you just said?”

“Certainly: you’ve heard enough from everyone in the room to know how your friends did on those quizzes.”

“THAT’S IMPOSSIBLE!” Gallus immediately realizes who he’s outbursting to. “Sorry, I didn’t mean anything by …”

“You’re fine, Gallus,” Twilight assures. “But I stand by what I said: based on everything I just heard, I could deduce all your rankings.”

“But you probably know all our scores,” Smolder insists.

“Indeed I do,” Twilight replies, “but that doesn’t falsify my statement.”

“Yona confused.”

“Gallus confused too, Yona.”

“Silverstream confused … wait, shouldn’t that be ‘Silverstream is confused’? Actually, why is Silverstream referring to herself in the third-creature … I mean, why am I talking like that?”

“You guys,” Ocellus says to her friends before turning to Twilight. “So you’re saying that, just from a bunch of snippets, you can actually determine all that information? How? Honestly, I’d like to know.”

“Ah’d like to know mahself, Twi,” Applejack adds.

Flattered by the interest, Twilight levitates a piece of chalk to the chalkboard and writes out the statements made by the fivesome, as well as space underneath for the final rankings in each quiz:

Ocellus: “No one had the same ranking for any pair of quizzes. I ranked first for Kindness.”

Smolder: “Everyone ranked first or second on at least one quiz. I ranked higher for Loyalty than for Honesty.”

Yona: “Yona fourth for Honesty. Yona ranked higher for Loyalty than for Kindness.”

Silverstream: “Neither Smolder nor Ocellus ranked fourth for Honesty. Gallus didn’t rank second for Loyalty.”

Gallus: “I didn’t rank fifth for any test. Silverstream ranked fifth for Loyalty.”

H: ___ , ___ , ___ , ___ , ___

L: ___ , ___ , ___ , ___ , ___

K: ___ , ___ , ___ , ___ , ___

“Now the first crucial clue,” Twilight starts, “came from Applejack.” The comment dumbfounds everyone else.

“Twilight, Ah didn’t make any comments about them rankings.”

“Actually, you did: you said those who placed first, second, or third on the Honesty quiz told the truth, and those who placed fourth and fifth lied.” Twilight then turns to the class. “And whether you know this or not, Applejack never lies.”

“Not anymore, anyways,” Applejack mutters to herself.

Twilight turns to Applejack. “What was that?”

“Nothin’, nothin’ … carry on, Sugarcube. Ah’m curious where you go from here.”

“Oohkay then.” Twilight turns back to the board. “Let’s look at Yona’s first comment. She claimed to finish fourth on the Honesty quiz, but if she did, then she would be lying. Therefore, Yona didn’t finish fourth on the Honesty quiz.”

Yona lowers her head. “Is true … Yona not very honest there.”

“However,” Twilight continues, “since Yona lied, she couldn’t have finished first, second, or third either. She must have ranked fifth for Honesty.” Twilight notes this on the chalkboard as she continues. “Now consider Silverstream’s first comment.”

“Ooo, my turn to be special!” the hippogriff cheerily announces.

“Yes … well, suppose Silverstream was lying.”

“But I didn’t lie!!!”

“I know,” Twilight says, “but reasoning sometimes involves starting with an assumption and showing it to lead to a contradiction.”

“A contra-what?”

“Contradiction, Gallus. Follow me here: let’s just suppose that Silverstream was lying. Well, that would mean that either Smolder or Ocellus did finish fourth. But if Silverstream was lying, then she herself would have to have finished fourth, since we already know that Yona was fifth and no one else lied. That is a contradiction: she couldn’t finish in the same place as someone else. And that means that the assumption that Silverstream was lying, was itself a lie. So now we know Silverstream was telling the truth.”

“That’s what I was trying to say!” Silverstream pleads, causing Twilight to chuckle.

“I know, Silverstream … but the funny thing is, both a truth-teller and a liar would claim to tell the truth. But now we’ve proven that you were truthful with your comments … and that means—”

“Smolder and I were also truthful!” Ocellus concludes.

“Wait,” Gallus says, “how you know that?”

Ocellus explains: “Because neither Smolder nor myself finished fourth for Honesty; Silverstream stated so, and now we *know* that’s true. And neither of us were fifth either, since Yona was fifth. That means we were in the top three for Honesty, along with Silverstream. And that proves that we were all truthful …”Her eyes narrow as she displays a grin.“… and there’s only one choice left for finishing fourth for Honesty.”

“Yeah, yeah, you got me,” Gallus admits, “I was fourth for Honesty, and I may have bent the truth with my comments.”

“Just like pretzel!” Yona states, getting a laugh from everyone.

“OK then,” Twilight continues after the laughter dies down, “Let’s recap what we now know: Silverstream, Ocellus, and Smolder were truthful, while Yona and Gallus lied. We also know that Gallus was fourth and Yona was fifth for Honesty.” She adds this knowledge to the board:

H: ___ , ___ , ___ , G , Y

L: ___ , ___ , ___ , ___ , ___

K: O , ___ , ___ , ___ , ___

“Why ‘O’ next to ‘K’?”

“Oh, sorry Yona, I got a bit ahead of myself. Ocellus stated she was first for Kindness, and since we now know her statements are true, I put that information up on the board.” Twilight’s explanation draws a nod from Yona.

“Now let’s consider Smolder’s first comments.”

“Finally …”Smolder quickly backtracks: “oh, sorry Principal—”

“That’s all right, Smolder. I know it took a while to get to your statements, but this one is very useful. Based on this comment, everyone finished first or second on at least one quiz. Let’s combine this statement with Yona’s second statement, which we now know to be false. This means Yona finished higher for Kindness than for Loyalty.”

“Wait a minute.” Ocellus asks, “Couldn’t Yona have finished the same place for both quizzes.”

“Funny you should mention that, Ocellus, as it’s your own second comment that prevents that from being a possibility.”

“Oh yeah …”Ocellus sheepishly smiles as Twilight continues.

“Now Yona had to finish either first or second on some quiz. Not Honesty, where she finished fifth. And if she finished first or second for Loyalty, she would have had to have been higher for Loyalty than for Kindness. So she must have finished first or second for Kindness … but Ocellus was first, so that forces Yona to be second for Kindness, and either third or fourth for Loyalty.”

“Now Gallus had to finish first or second on some quiz, but it can’t be Kindness anymore, and it wasn’t Honesty. He must have been first or second in Loyalty, but Silverstream’s second comment—”

“Back to me!!!”

“Yes, Silverstream, back to your comments … you stated that Gallus wasn’t second for Loyalty, so he must have been first. And since his first statement was false, Gallus had to be fifth in something; that means he was fifth for Kindness. Meanwhile, Smolder stated that she was higher for Loyalty than for Honesty. The only way that’s now possible is for her to be second for Loyalty and third for Honesty.”

Twilight adds these facts to the board:

H: ___ , ___ , Sm , G , Y

L: G , Sm , ___ , ___ , ___

K: O , Y , ___ , ___ , G

“It’s like putting together a jigsaw puzzle,” Ocellus admits. “It’s amazing how everything fits together. And all that from a bunch of random comments.”

“We’re not done yet,” Twilight giddily states.“Smolder and Silverstream were third and fourth for Kindness in some order, but Smolder was already third for Honesty; that forces her to be fourth for Kindness, and that means—”

“I was third for Kindness!!! Oh wait, I already knew that. But that you figured all that out … I mean, *wow*.”

“By the same reasoning, Ocellus couldn’t be first for Honesty since she was first for Kindness. That means Silverstream was first for Honesty, and Ocellus was second.” Twilight adds this information to the board:

H: Silv , O , Sm , G , Y

L: G , Sm , ___ , ___ , ___

K: O , Y , Silv , Sm , G

“Just a little bit left,” Twilight says. “Now Silverstream—”

“—couldn’t be fifth for Loyalty,” Sandbar says in a laid-back voice now filled with conviction, “because Gallus said she was and that was a lie. But she couldn’t be third either, since she was third for Kindness. That means she was fourth for Loyalty … and since Yona was already fifth for Honesty, she couldn’t be fifth for Loyalty. That means Yona was third, and Ocellus was fifth.”

“Well done, Sandbar!” Twilight’s declaration is followed by a myriad of ‘attaboys’ and ‘good jobs’ from his friends.

“So that’s it, then,” Twilight concludes as she writes on the board one last time. “The rankings must have been as follows:”

H: Silv , O , Sm , G , Y

L: G , Sm , Y , Silv , O

K: O , Y , Silv , Sm , G

“Well Ah’ll be,” Applejack admits with a sigh. “Ah never thought so much information could be taken from so little.”

“All part of what makes me the pony I am today,” Twilight meekly states. “But I must say, Sandbar, you and your friends put together a fascinating Honesty project.”

“WHAT???” The chorus from everyone else in the room … including Applejack … forces her to continue.

“Well of course.This was a wonderful demonstration of how much simpler life can be if everyone would be honest and forthcoming with information, instead of striving for deception and untruths. Wouldn’t you agree, Applejack?”

“Huh? … Oh, Ah mean, great job everyone! Guess you all get top marks on this one.”

The class erupts in sighs of relief, while Applejack mentally thanks Twilight for giving her less to grade, allowing for more time to catch up on farmyard chores.

“Well I must say, this observation was a lot of fun. Thank you again for having me in your class.” Twilight’s comment is met with a mix of hoof-stomping and applause, and in the name of appreciation.

“Um … Principal Twilight?”

“Yes, Ocellus?”

“You said this was ‘all part of what made you who you are’. You have any stories from your past like this?”

“I do have one interesting tale,” Twilight admits, “but that’s for another day … and who knows, you may have stories of your own to regale. At the least, you got this one.”

Author's Note

For now, I'm considering this story to be complete ... but if there's enough interest, it would not take much to add chapters (i.e., puzzles) to this story.

Thanks to all who read this and actually solved the puzzle before reading the solution.