For a brief moment, Ocellus braces herself for a round of insulting laughter at her expense … but the friendly chuckles that ensue merely serve to reinforce the sentiment that she is around true friends.
“Always the bookworm,” Gallus dryly states.
“More like, book- … changeling,” Silverstream adds, before blushing and sheepishly going quiet. Another round of chuckles follows.
“Seriously, though,” Smolder says, “how could anyone figure out which of us got which professor based on those predictions. They were all over the place, and we don’t even know which ones are true.”
“It’s all about using logical deduction and reasoning,” Twilight states. “Focus on one or two statements whose veracity can be figured out, and use that information to determine that of the other statements.”
“Just like you did on that one trip we took, right?” Pinkie gleefully asks. Twilight nods.
“Yona confused. Where Yona start?”
“Yona starts with Yona’s prediction,” Twilight answers. Her response leads to further quizzical looks from the young yak. Twilight smiles and addresses Yona directly, as the others listen in.
“You predicted that you would not get me as your mentor. That prediction is either true or false. Now suppose it was false; that would mean you did get me as your mentor. Understand so far?”
Yona nods.
“But, I gave you the additional information that the student who got me made a correct prediction. And THAT is our contradiction.”
Yona ponders Twilight’s reasoning. “So … that means Yona’s prediction must be true. So Yona not get Headmare Twilight.”
Twilight nods in agreement, which in turn causes Yona to smile. “Yona getting less confused!”
“But there’s more,” Twilight continues. “Since your prediction was true, then you must have either myself or Pinkie Pie. And since you correctly predicted that you would not get me …”
Twilight pauses, waiting for Yona to reach the logical conclusion:
“… then Yona must have Professor Pinkie Pie! YONA GET IT!!!”
“WHEEEE … I get to mentor Yona!” Pinkie bounds over to Yona and gives her a big hug, causing Smolder to wince slightly.
“Sorry … still not used to all the touchy-feely and such.”
“What about when we were in the basement and …” Ocellus stops mid-sentence, upon seeing the dragon stare daggers at her. “Uh … never mind.”
Sandbar speaks up: “So, we know that Yona will be mentored by Professor Pinkie Pie. But what about everyone else? Where do we go from here?”
“We go to Gallus’s prediction,” Twilight states. Gallus and Smolder both react with surprised looks.
“ME??? I didn’t say anything useful at all!”
“Yeah, all he said was that I’d be wrong!”
“But that makes all the difference,” Twilight states. “Remember, only two predictions were true, and we already know that one of those was Yona’s prediction. So there’s exactly one other true prediction among the remaining five. Now think about Gallus’s prediction for a bit.”
The students go quiet as they ponder Twilight’s suggestion. Soon after, Ocellus speaks:
“If Gallus’s prediction was true, then Smolder’s prediction would have to be false. And if Gallus’s prediction was false, then Smolder’s prediction would have to be NOT false … it would be true.”
“Ooo, ooo,” Silverstream suddenly interjects. “But that means one of them HAD to have the other true prediction!”
Sandbar follows: “And that means the rest of us all made false predictions.”
Twilight clops her hooves together. “Excellent work, all of you! Yes … that means we know that all the predictions made by Sandbar, Ocellus, and Silverstream are false. Now think about what Ocellus predicted.”
Ocellus recollects her prediction. “I said that Silverstream would not get Rarity … and that means Silverstream DID get Rarity.”
“And that makes two pairs figured out,” Twilight states. “Can you go further?”
Smolder continues the train of thought: “Silverstream’s prediction was false, so Sandbar didn’t get either Rainbow Dash or Fluttershy. And he didn’t get either Pinkie Pie or Rarity, since those two were already assigned. So that leaves either Twilight or Applejack.”
“Wait,” Yona interrupts, “but seapony made false prediction, so Sandbar not get Headmare Twilight … Sandbar get Applejack!” she excitedly concludes.
“Wow … it’s like unraveling a dress by pulling on a thread!” Silverstream states before quickly backtracking: “Oh … maybe I shouldn’t use that when talking to Professor Rarity.”
“Three pairs down, three to go,” Twilight states. “Now back to Sandbar’s prediction.”
Sandbar thinks for a minute. “Uh … I said that Ocellus would get Rainbow Dash. That means she didn’t … and since her prediction was false, she didn’t get Twilight either. So Ocellus got Fluttershy as her mentor.”
“Very well done,” Twilight again states. “So that just leaves Smolder and Gallus, and myself and Rainbow Dash as mentors.” She turns to Gallus. “Can you figure out which pony you got?”
“Uh … no?”
Twilight laughs. “Come now, you’re an especially bright griffin. I know you can figure this out.”
“I can’t,” he starts with an air of exhaustion. “I mean, I know that either my prediction was true or false. And I know that Smolder’s prediction was either true or false. But how can I know which is which?”
“Think back to what Smolder’s prediction was.” Twilight suggests.
“Well … she predicted that she would get either you or Rainbow Dash.” Moments later, a revelation comes to him. “But those are the only professors left … so she must have made a true prediction! And that means she got either Twilight or Pinkie Pie … and THAT means Smolder got paired with you!”
“And that only leaves Rainbow Dash left to mentor you,” Smolder adds.
“And that is the final piece of the solution,” Twilight concludes. “To sum up: I will mentor Smolder, Pinkie Pie will mentor Yona, Rainbow Dash will mentor Gallus, Applejack will mentor Sandbar, Rarity will mentor Silverstream, and Fluttershy will mentor Ocellus.”
Brief silence gives way to a chorus of ‘ooo’s and ‘aaah’s from the class.
Smolder sighs. “So all this logic and stuff just comes naturally to you?”
“It’s something I’ve always been interested in, ever since I was a foal,” Twilight admits. “But we can discuss that in more detail during our one-on-one. And speaking of which,” she states as she beckons the class to rise from their seats, “it’s time for some counseling. Follow me, everycreature.”