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

by Coyotek4

Puzzle 11: Random Inference

“Just tell me, already!”

“Maybe Gallus tell Yona first!”

“You first!”

“No, you first!”

Unable to focus on her reading, Ocellus groans and turns her attention towards her two vitriolic classmates. “Why are either of you making a big deal about this?”

“It’s a matter of personal pride,” Gallus explains. “Look, I can accept that Yona scored higher than me on whatever you call that ‘random quiz’ thing Professor Pinkie Pie gave us, but I’d still like to know by how much.”

“Then just tell each other what you got,” Ocellus suggests with a tinge of exasperation.

“Private information is private,” Yona states, “and should be earned rather than given away.”

Ocellus shakes her head and returns to perusing her book, keeping an ear towards the conversation.

“How about this,” Gallus suggests: “we each ask a single question about the other’s score, then try to deduce what that score is. That sound fair to you? Up for the challenge?” he concludes with a grin.

“Fine,” Yona says. “And Yona ask first.”

“Go right ahead.”

Yona ponders for a moment before asking: “Is Gallus score multiple of six?”

Ocellus perceives a slight pause, assuming the griffon either nodded or shook his head.

“My turn,” Gallus counters: “Is your score a triangular number? Oh … do I need to explain what that is?”

“Yaks know what triangle numbers are!” Yona flatly states.

“OK then … well, is your number triangular?”

Ocellus perceives another pause.

A smile comes across both Gallus’s and Yona's faces. They announce simultaneously:

“I know your number.” / “Yona know Gallus number!”

“Well here,” Gallus says as he pushes a piece of scrap paper towards the yak. “You write down your guess, and I’ll write down my guess.”

“Yona not guess,” she replies in kind. She and Gallus write down their guesses and simultaneously show each other.

Moments later, Ocellus catches a pair of cries of “HEY!!!” She puts down her book and turns to the others. “What now?”

“YOU LIED TO ME!”

“GALLUS LIE TO YONA!”

“You two really deserve each other,” Ocellus states. Gallus and Yona look at each for several seconds, before bursting into laughter.

“This really did spiral out of control, didn’t it?” Gallus admits.

“Professor Applejack not approve,” Yona states.

“All right,” Gallus adds. “I’ll just tell you first, and then you tell me.”

“That quiz was out of 20 points, right?” Ocellus asks. Yona responds with a simple ‘uh huh’.

“Then it’s settled,” Ocellus says … before stating both their scores.

Gallus stumbles for a response: “How … how could you possibly know our scores???”

“Yeah, and how you know Yona score?”

“Well to be honest, I only knew for certain that one of those scores was correct … but apparently, your scores differ by more than one, and that’s all I need to know for certain.”

Author's Note:

So, what score did Gallus and Yona each receive? Also, what score did each think the other got?

Apologies for the delay; I was a bit under the weather, and was also in pure 'Netflix binge' mode. Also, I admit this puzzle is fairly simple … but I've struggled in the past with solving puzzles that require inference, and wanted to make my first such creation simple just to be sure I didn't err.

My next puzzle should have a bit more meat on it.

Comments

[GeneralOs]

Can I ask if Yona scored higher than Gallus?

“Look, I can accept that Yona scored higher than me on whatever you call that ‘random quiz’ thing Professor Pinkie Pie gave us, and I can even accept knowing that she outscored me by more than one, but I’d still like a more exact answer.”

I'm not sure if this is a throw-away line or part of the puzzle

[Duckgame4life]

Well, this is annoying
test out of 20
yona is more than 1 higher than gallus(i assume pinkie told them)
if yona is triangular, her number is 1,3,6,10 or 15
If gallus is a multiple of 6, he can be 6,12 or 18
Yona lies her answer and gallus thinks he knows
Yona then thinks she knows off that and gallus' lie
If yona says no, gallus thinks she has 20 cause he has 18
But yona cant determine gallus's number no matter what he said
If yona said yes, gallus think her number is 15 and he has 11
Gallus said he did have a multiple of 6 so yona thinks he has 12 when she has 20

[Eroraf86]

Okay, I'm stumped. If this is supposed to be simple, then I'm not seeing it.

[Coyotek4]

OK, This is why I should never hammer out a chapter in 30 minutes right before going to work!

I made a mistake: while it IS the case that Gallus's and Yona's scores differ by more than one, NEITHER OF THEM KNOWS THIS!!! All they 'do' know is that Yona's score is higher than Gallus's.

I have updated the story to reflect this. What both Gallus and Yona know is that Yona had a higher score than Gallus; neither knows by how much, though it will turn out that their scores differ by more than one … and that IS enough to solve.

My apologies to all who attempted to solve the initial, flawed version.

[Coyotek4]

9451840
It's NOT a 'throw-away' line: both know that Yona's score is higher than Gallus's, and that information IS needed to solve.

However, they do NOT know that their scores differ by more than one; that was a mistake on my part, and I have since fixed the chapter. (It turns out that their scores *do* differ by more than one; they just don't know that when making their guesses.)

[GeneralOs]

Still gives Yona TMI since Gallus announces before her that he knows her number allowing Yona to know that he has to have a number between 10 and 15 and since he answered yes to multiple of 6 question he must have the number 12.

[Coyotek4]

9453836
Tweaked the wording as you suggested.

Creating this type of puzzle is hard.