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

by Coyotek4

Puzzle 2: Who got the 96?

“Another ‘history of friendship’ quiz in the books,” Gallus exclaims with relief as he passes his paper up along with his classmates. “You’d think saving Equestria would be enough for graduation purposes.”

“From what I’ve seen in my days in Ponyville, we’re not even in the Top Ten around here.” Sandbar’s retort brings about a fresh round of laughter.

“It won’t take long to grade these,” Twilight asserts, “so you can just chat amongst yourselves as I get these marks in.” Her horn glows as a quill dips into in an inkwell and she peruses the first of the six papers.

The students adjust their desks in a circle and begin pondering how they fared:

“Yona think Yona did well. Yona think Yona earn score of 97.”

“Why 97?” Sandbar asks.

“97 prime, like yaks. Yaks renowned for ways in mathematics.”

“I’ll have to take your word on that,” Gallus says, “but I feel like I did better than you did.”

Yona’s eyes glare at the griffin.

“It’s not a knock on you, Yona. I’m not usually confident on quizzes like this, but I think I did well. Besides, professor Pinkie Pie’s been pushing me to make more predictions.”

“Well, I’m not as confident as some of you are,” Smolder states, “but I don’t think I got the lowest score of the six of us.”

“Then who do you think did?” Ocellus asks. Smolder replies with a shrug and a trite ‘meh’.

“So how did you do?” Sandbar asks Ocellus. The latter opens her mouth to reply, but Silverstream breaks in:

“Oh, Ocellus always does well on these. I bet her score is one of the top three among the six of us.” The comment draws a slight blush from the changeling.

“OK, that’s four predictions so far,” Sandbar recaps. “So, Yona thinks she got a 97, Gallus thinks he did better than Yona, Smolder thinks her score wasn’t the lowest, and Silverstream thinks Ocellus had one of the top three scores. So I guess that just leaves—”

“FINISHED!”

Twilight’s exclamation causes the students to suddenly turn to face their headmare. “That was quick,” Smolder asserts.

“It’s easy to grade papers when they’re all of such high quality,” Twilight replies with a broad smile. “All of you did incredibly well!”

“Really?” Gallus reflexively asks.

“Yep. In fact, all of you got scores ranging from 94 to 99. But none of you got the same score.”

“All right … A’s for everyone!” Sandbar exclaims.

“So tell us,” Ocellus prods, “who got each score?”

“Well it’s funny,” Twilight starts.

“She sure has a strange notion of funny,” Gallus quietly tells the others, as Twilight continues.

“I couldn’t help but overhear your predictions while I was grading. As it turns out, anyone who made a true prediction ended up with an even-numbered score, while anyone who made a false prediction ended up with an odd-numbered score.”

Silverstream laughs, causing the others to turn to her. “Oh, she said it was funny, so I thought …”

Ocellus turns to Twilight, anticipation in her voice. “So does that mean we can figure out who got what score?”

“Oh, not at all. At least not with only that information.” Twilight ponders the situation further. “Although … this is actually quite interesting. IF I told you which of you got the score of 96, then you WOULD have enough information to figure out everyone’s score.”

“Whoa … now Yona confused.”

“So who did get the 96?” Smolder asks.

“I don’t need to tell you that anymore,” Twilight replies. “But, I’ll forego homework assignments for a week if you can figure out who got what score.”

“DEAL!”

...

Everyone turns to Gallus, surprised by his renewed enthusiasm. “What’re you all staring at, let’s solve this!”

Author's Note:

Admittedly, this puzzle turned out FAR harder than originally intended. Nevertheless, there IS a unique solution, as will be explained in the next 'solution' chapter.

Comments

[Starlight Glimmer1]

I’m not sure if there’s enough information to solve this one. Especially since determining whether or not one of the predictions is true or not relies on what one of the other scores is which seems to require more information than you’ve given us. There’s also the fact that we don’t have any information that can be used to determine Sandbar, Ocellus, and Silverstream’s scores.

[Duckgame4life]

Well i dont have an answer but i found a few facts
yona must be false and thus 95 or 99
Smolder must be true thus 96 or 98
If Ocellus is top 3 Silverstream is even, if not Silverstream is odd
If Gallus beats yona, yona is 95 and gallus is 96 or 98, if yona beats gallus, yona is 99 and gallus is 95 or 97
Witch with the fact that the 96 will solve it means
smolder is known no matter who it is
if its gallus, yona is known
If its Ocellus, Silverstream must be odd
If its Silverstream, ocellus is top 3
It CANT be yona
If its sandbar we get nothing

So either i missed something or its impossible

[Lspaceship]

Known Assumptions (Unknown if true):
Yona: 97 (Predicted by Yona)
Gallus: better than Yona (Predicted by Gallus)
Smolder: NOT 94 (Predicted by Smolder)
Ocellus: 97 OR 98 OR 99 (Predicted by Silverstream)

RULES FOR THE PUZZLE:
Predictions may not be right.
Anyone who made a true prediction had an Even score
Anyone who made a false prediction had an Odd score

Conclusions drawn so far: Yona CANNOT be true, as she would have to be 97, then. Which is Odd. She, therefore, must be 99 OR 95.

Acting under the assumption that Gallus. Smolder, AND Silverstream are correct AND Oscellus is 99.
Yona is 95
Gallus must be an Even number above 95 (96 OR 98)
Smolder CANNOT be 94, but IS an Even number (96 OR 98)
Silverstream MUST be 94 for Smolder and Gallus to be correct.

Solution if this is the case:
Silverstream: 94
Yona: 95
Gallus: 96 OR 98
Sandbar: 97
Smolder: 98 OR 96
Oscellus: 99

Acting under the assumption that Gallus. Smolder, AND Silverstream are correct AND Oscellus is 98.
Yona is 95
Gallus must be an Even number above 95 (96 OR 98)
Smolder CANNOT be 94, but IS an Even number (96 OR 98)
Silverstream MUST be 94 for Smolder and Gallus to be correct.

CANNOT BE CORRECT

Acting under the assumption that Gallus. Smolder, AND Silverstream are correct AND Oscellus is 97.
Yona is 95
Gallus must be an Even number above 95 (96 OR 98)
Smolder CANNOT be 94, but IS an Even number (96 OR 98)
Silverstream MUST be 94 for Smolder and Gallus to be correct.

SOLUTION IF THIS IS THE CASE:
Silverstream: 94
Yona: 95
Gallus: 96 OR 98
Sandbar: 99
Smolder: 98 OR 96
Oscellus: 97

Let me know if I missed something!

[Duckgame4life]

9386766
While everything seems right i must add
if smolder is wrong, she gets 94,but wrong means odd so smolder is right (either 96 or 98)
AND
none of these solutions distinguish who of the 2 is the 96&98, and twilight said if we know the 96, we can solve it(no word on who it is) since we dont know we cant assume either one
This means smolder is definitely right and either Silverstream or gallus is wrong

[Lspaceship]

9386791
We know that Gallus or Smolder would be either of the two. So, if Twi told us which of them got 96, we know what everyone got. Once we knew everyone's score BUT the 96 or 98, we have solved it as much as possible.

[Duckgame4life]

9386795
Did you account for Silverstream being wrong?

[AstralMouse]

I think I got it? Had to guess and check a few times, but this answer seems to work, and if there is only one solution, then hopefully I got it.

Silverstream: 96
Smolder: 98
Gallus: 95
Yona: 99
Sandbar: 94
Ocellus: 97

[Coyotek4]

9386894
I hope to post the next chapter (containing the solution to this problem) tomorrow morning, and I need to double-check my work, but I believe this is the solution I have in mind.

[Eroraf86]

Okay, this one took some trial and error, but I think I found a unique solution.

This first part was the trial and error. Assume Silverstream got the 96.
Smolder can't be wrong because the lowest score is even, so Smolder got either 96 or 98. Therefore, Smolder got the 98.
Yona cannot be correct because 97 is odd, so she got either 95 or 99. If Gallus is correct, he got 96 or 98, so Gallus must have scored lower than Yona. The only way this is possible is if Yona got the 99.
If Silverstream got 96, her prediction is correct and Ocellus is in the top three. 98 and 99 are taken, so Ocellus got the 97.
Gallus is wrong, so he got 95 or 97. 97 is taken, so Gallus got the 95.
There is only one score left. Sandbar got the 94.

I tried several other possibilities for the 96, and they all had two indeterminate solutions. This was the only one I tried that yielded a unique solution, as per Twilight's statement. Let's see if I was right.