School of Logic: a Collection of Puzzles involving the Student Six

by Coyotek4

Puzzle 7 solution

(1) Gallus was higher than Sandbar
(2) Sandbar was higher than Ocellus
(3) Ocellus was higher than Yona
(4) Yona was 2 higher than Smolder
(5) Smolder was 3 higher than Sandbar
(6) Gallus was 4 higher than Yona
(7) Ocellus was 5 higher than Gallus

“Did I really blurt all these statements out?” Silverstream asks as she peruses Twilight’s notes.

“In about 5 seconds, yeah,” Smolder replies. “So, Ocellus, care to explain?”

Ocellus opens her mouth to answer, but Gallus puts a wing on her shoulder. “How ‘bout someone else take the lead for a change?” He turns to Smolder. “Why don’t you begin this one?”

Smolder groans. “What does it matter? For that matter, why don’t we just ignore this and hear our order from Fluttershy tomorrow?”

“If you haven’t noticed, we’ve been getting involved in a lot of these puzzles as of late, almost as if the universe wants us to keep our minds honed. I’m just saying we shouldn’t be overly reliant on a single creature to handle all the mental heavy lifting.”

The others give a quizzical look towards the griffin … before he and the others burst into collective laughter.

“Couldn’t keep a straight face with that one,” Gallus mirthfully admits. “OK, OK, Ocellus, care to start us off.”

“Actually, I do want to begin,” Smolder insists. “I mean, you never know, right?” she adds with a grin.

After a further round of chuckles dies down, Smolder inspects the list of sentences. “It was nice of Headmare Twilight to number the sentences for reference. So, they’re only true if both students mentioned are either above or below Silverstream at the same time, right?”

“That sounds right,” Ocellus says.

“OK then … where to begin …” Smolder inspects the statements for a few minutes before coming to a realization: “Wait … if sentence 7 was true and Ocellus was 5 higher than Gallus, then Silverstream would have to be between them. And that can’t be … so that statement is false.”

“Nice,” Sandbar states. “Can I give it a go?”

“Go ahead,” the young dragon replies as Sandbar peruses the statements.

“So … I see Smolder’s name in sentences 4 and 5, so if both were true, then Yona would be 5 higher than me … but that can’t be either, so at least one of those statements is false. But that’s all I got. What now? Anyone else want to jump in?”

“Yona give shot,” the yak replies. “… false statement mean students on opposite side of seapony. That mean Ocellus and Gallus on opposite sides, and Smolder opposite either Yona or Sandbar. So at least two above and two below seapony … Silverstream either third or fourth!”

“That’s brilliant!” Ocellus states. “Honestly, I was a little stuck there. OK, since Silverstream is either third or fourth, then statement 6 can’t be true, because that would force Gallus and Yona to be on the same side, which could only happen if Silverstream was either first or last. And that forces Gallus to be opposite Yona.”

“OK, let’s take another look at all those false statements,” Gallus suggests. “The last two statements are false; we know that now. That means that I’m on the other side of both Yona and Ocellus … so they have to be on the same side of Silverstream. And that means that statement 3 is true: Ocellus is higher than Yona.”

“And if statement 4 was true as well,” Ocellus adds, “then there would be four of us on the same side of Silverstream: myself, Yona, Smolder, and whoever was between Yona and Smolder … but then Silverstream couldn’t be third or fourth in that case. So statement 4 is false, and Yona is opposite Smolder.”

“But statement 5 can’t be true, either,” Sandbar states. “That would also force Silverstream to be somewhere other than third or fourth. And that means Smolder is opposite me.”

“Hey, can I work on this?” Silverstream asks. “They were my statements, right?”

The others laugh. “Our apologies,” Gallus states with a wry smile. “By all means.”

“OK, OK … so all the last four statements are false, so Ocellus is opposite Gallus who’s opposite Yona who’s opposite Smolder who’s opposite Sandbar. So … it’s like, every other student is on the same side, right? Because two wrongs make a right, or something like that?”

“Sounds about right to me,” Smolder admits.

“Cool! … so that means that Ocellus, Yona, and Sandbar are all on one side of me while Gallus and Smolder are on the other side. That means that Gallus and Sandbar are on opposite sides, so statement 1 is false; Sandbar must be higher than Gallus … and that means that Ocellus, Yona, and Sandbar are one, two, three in some order, I was fourth … aww, I was only fourth? … and Gallus and Smolder are five, six in some order.”

“We’ve all been doing well on all these quizzes,” Ocellus reassures. “I’m sure we all passed with flying colors.”

“I hope so,” Smolder adds with a tinge of derision.

“Calm down, everyone,” Sandbar says. “Let’s finish this, huh?”

“Yona finish,” the yak replies. “So, Sandbar, Ocellus, and Yona all above Silverstream … so statements 2 and 3 are true, so Sandbar first, Ocellus second, and Yona third.”

“That just leaves Smolder and myself,” Gallus states, “… but since Yona was third, Smolder couldn’t be fifth since statement 4 is false. That means I was fifth, and Smolder was sixth.” He turns to Smolder. “No offense meant.”

“Meh … none taken,” Smolder reassures. “I don’t think professor Fluttershy has ever given a student a bad grade.”

Ocellus muses for a moment. “About what I’d expect from the bearer of the element of Kindness.”

“So … that’s it, right?” Silverstream asks. “I mean, we did it, didn’t we.”

“Looks like it,” Gallus answers. “In order: Sandbar-Ocellus-Yona-Silverstream-me-Smolder. I hate to say it, but I’m starting to enjoy doing these.”

“Wow,” Yona says, “so which professor bearer of element of Miracles?”

The group shares one final laugh before eventually retiring for the night.

Comments

[Eroraf86]

“Wow,” Yona says, “so which professor bearer of element of Miracles?”

If by miracles you mean magic ...

[Windy0]

I'm looking forward to the next chapter.

[Ultimate Overlord]

9419088

Aaah, okay, I was figuring that was the answer. Should be able to figure this one out now.