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

by Coyotek4

Puzzle 8: Chaotic Reasoning

The last of their classes completed, the students head down the hallway leading to Starlight’s office.

“A non-eventful day for a change,” Ocellus points out. “Just a quick meeting with the counselor, and the rest of the day is ours.”

“It’s weird,” Silverstream says, “I got so used to dealing with solving puzzles in class, now it feels strange not to experience one in a class.”

“Just as well,” Smolder replies. “My brain could use a cooling down after the last couple days.”

“Yeah, it’s nice to just have a normal school day for a change,” Gallus adds as they reach Starlight’s office. He opens the door … as water pours from the office, quickly enveloping the hooves, claws, and talons of the students.

“Why do I tempt fate like that?” he asks as he and the other peek into Starlight’s office. They are surprised to see a downpour taking place within the confines of the office, as Starlight stands atop her desk while barking orders towards a familiar former administrator:

“FOR THE LAST TIME, DISCORD, STOP THE RAIN!!!”

Discord snaps his fingers; immediately, the clouds that had been enveloping the ceiling disappear as the precipitation ceases.

“I still don’t see why you’re so irate … you said you had to water the flowers, I thought I’d save you some time,” he replies. “And now that I’ve done you a favor, our friendship dictates that you reciprocate in kind.”

Starlight shakes off as much moisture from her coat and mane as possible. “There’s no position available at the present time, Discord.”

“Oh, be reasonable,” he insists, drawing a laugh from the unicorn. “And just what does that mean?”

“Discord, you are one of the most unreasonable creatures I’ve ever met! And I’m not saying that to be mean; it’s just your nature.”

“Why, I am aghast at your insinuation, Starlight. I can be plenty reasonable, much more than you, of course!”

Starlight rolls her eyes at the notion.

“Uh, Counselor Starlight,” Silverstream meekly asks, drawing the attention of the two in the office. “Is this a bad time, because we can come back later.”

An idea pops in Discord’s head. “Actually, my little nonponies, this is a perfect time to demonstrate my superior powers of reasoning.”

“Didn’t you say ‘reasonable’?” Sandbar asks.

“Six of one … speaking of six, how about each of you six think of a number, and I’ll try to figure out what numbers you’ve thought up.”

Smolder delivers a flat ‘No’ to Discord. “We’ve been doing all sorts of puzzles like that all week. We need a break!”

“Fine,” Discord responds in a huff. “I guess I’ll create my own puzzle, one that Starlight won’t be able to figure out. And to relieve you of the burden of thinking up numbers, I’ll assign numbers to you. I’ll even direct you as to what to say.”

“Nasty trickster can’t put words in Yona’s mouth,” the yak defiantly states.

Discord snorts, then snaps his fingers. Moments later, Yona feels a queasiness from her stomach, causing her to groan.

“What trickster do to … Yo … na … AAAUGH!” Before finishing her sentence, Yona spits out a scrolled-up parchment onto the floor. Similar groaning sounds cause her to turn to her fellow students, all of which have experienced the same sensation, and all of which now stand before similar parchments.

“Blecch,” Silverstream moans. “How does Spike do this on a regular basis.” Cautiously, she picks up her scroll from the ground and unfurls it; the others do likewise.

“What does this even mean?” Sandbar asks.

“Just read them, all of you,” Discord requests. “And you may want to take notes, Starlight.”

“And if we refuse?” Gallus asks.

Discord groans. “You want motivation? Fine, here’s my proposal: if your counselor can solve my puzzle, I’ll rescind my request for a more permanent position here.”

Starlight rolls her eyes. “Whatever … anything that will get you out of my office.” Her horn glows as a parchment and quill fly from a far, dry corner of the office.

“Excellent,” Discord says. “Now there are rules to follow, so pay attention: I won’t be repeating myself. I have assigned each of these six a number from 1 to 60. And because I like things on the odd side, all their numbers are odd, as well as different. All you have to do is figure out their numbers.”

Starlight turns to the students. “What do the scrolls say?” Each student, in turn, reads off his or her scroll:

Smolder goes first: “No one has a number that is a multiple of 9. I have the largest number.”

Gallus follows: “My number is a perfect cube. Yona’s number is a perfect square. Silverstream’s number contains a ‘3’.”

Ocellus goes next: “Yona’s number contains a ‘4’. Smolder's number contains a ‘9’. No two of us have numbers within 7 of each other.”

Sandbar continues: “My number contains a ‘1’. Silverstream’s number is 21. Gallus’s number is between 16 and 24.”

Silverstream follows: “My number is 10 less than Gallus’s number. Sandbar’s number is 27.”

Yona goes last: “Ocellus truthful. Sandbar lies. Both Gallus’s and Silverstream’s numbers prime.”

“Oh, and one other thing: any statement made by a creature with a number greater than 30 is true, unless the number is prime, in which case those statements are false. In addition: any statement made by a creature with a number less than 30 is false, unless the number is prime, in which case those statements are true. Got it? Good luck … I suspect you’ll need luck more than reasoning!”

Discord gives a final laugh before *POP*-ing out of the office.

Author's Note:

Probably my most contrived storyline, but I really like the puzzle I created. I hope you, the reader, enjoy solving the puzzle as much as I enjoyed creating it.

Comments

[Duckgame4life]

Well here's a tough one
for reference, here are the prime numbers below 60
3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59
Now for what everyone says
Smolder:nobody is a multiple of 9, im the largest
Gallus: im a perfect cube,yona is perfect square,Silverstream has a "3" in her number
Ocellus: yona has a "4"in her number,smolder has a "9"in her's, any 2 numbers are more than 7 apart
Sandbar: i have a "1" in my number, Silverstream is 21, gallus is between 16 & 24
Silverstream:my number is 10 less than gallus, sandbar is 27
Yona: Ocellus is true, sandbar is false, gallus and Silverstream are prime
Above 30 is true
Below 30 is false
Primes are opposite
now let's solve
smolder and Silverstream cant both be right,as if sandbar is 27 there is a multiple of 9
Gallus and yona cant both be right,if gallus is prime then he's not a perfect cube
Both sandbar and Silverstream state the other is false, so they are another pair of 1 right 1 wrong
If Gallus is true, he must be 27, but that is below 30 so its false
Sandbar and smolder are both right or both wrong
If gallus is 17,19,or 23 sandbar is right and yona is also right(gallus cant be 21 as that makes a paradox with sandbar's statement)
thats all i got so far

[Eclipse_Nova]

Here's my answer:

1. Gallus lies since no number fits his description
2. Assume Yona's statement is the truth (I tried assuming Yona's statement being a lie too. It ends with tons of possibilities)
3. Silverstream's statement is a lie since the only combination possible is Gallus=39 and Silverstream=29, with Sandbar's 27 contradicting Ocellus' statement
4. Using Gallus' and Ocellus' statements, we can conclude that Yona's number is 45
5. Point 4 proves Smolder's statement to be a lie
6. Also using Ocellus' statement, Smolder's number is 9
7. Taking into account of the remaining numbers, the only possible combination left is Ocellus=17, Sandbar=25, Gallus=37, and Silverstream=59
Conclusion: Smolder=9, Ocellus=17, Sandbar=25, Gallus=37, Yona=45, Silverstream=59

[Eroraf86]

Whew, that was a doozy! That, or I'm just tired. Possibly both. Anyway, I think I've got it.

Start with Gallus's first statement. The only odd cubes less than 60 are 1 and 27, which are both non-primes less than 30. Therefore, Gallus must be lying.
If Sandbar tells the truth, then Silverstream's number is 21. However, this also forces Gallus's number to be 21, the only non-prime between 16 and 24. Since Discord stated that all the numbers are different, Sandbar must be lying.
Since Sandbar is lying, this means both Yona and Ocellus are truthful. Therefore, Yona's number starts with a 4. Since Yona tells the truth, her number cannot be prime. Since Gallus is lying, Yona's number is not 49. Yona's number is 45.
Since Ocellus is truthful, Smolder's number ends with a 9, and no two numbers can be within 7 of each other. For Smolder to be truthful, her number would have to be 59. Since this is a prime greater than 30, Smolder must be lying. Since 39 is within 7 of Yona's number, Smolder's number must be less than 30. And since Smolder is lying, her number cannot be prime. Thus, Smolder's number is 9.
Since Gallus's number must be prime, it must also be greater than 30. The only available options are 31, 37, 53, and 59. None of these options allows Silverstream's number to be 10 less than his. Therefore, Silverstream is lying, and her prime number must also be greater than 30, while also not containing a 3. Thus, Silverstream's number is 59.
Since Sandbar is lying, his number cannot contain a 1. And since Gallus's number is either 31 or 37, and there are no options greater than 30, Sandbar's number must not be prime. The only possibilities are 25 and 27. Since Silverstream is lying, Sandbar's number cannot be 27. Therefore, Sandbar's number is 25.
Since 25 is within 7 of 31, Gallus's number is 37.
There is only one remaining prime number less than 30 which is not within 7 of the other numbers. Therefore, Ocellus's number is 17.

Ow, my brain. That took longer than I would have liked, with several false starts and unnecessary backtracks. Still, I'm glad I saw it through to the end.

[Ultimate Overlord]

Okay, I think I got it.

Gallus' statement is self contradictory; the only perfect cube between 1 and 60 is 27, which isn't prime but is less than 30, thus his statement would have to be false. This means his number isn't a perfect cube, Yona's isn't a perfect square, and Silverstream's number doesn't have a 3 in it.

Smolder and Silverstream can't both be correct, since 27 is a multiple of 9.

Sandbar and Silverstream can't both be correct, since two of them would have 27.

From here, let's assume Yona is true. This means Ocellus is true, Sandbar isn't, and Gallus and Silver both have prime numbers.

This means that Sandbar's number doesn't have a one in it, Silverstream doesn't have 27, and Gallus is outside of 26 and 24.

It also means Yona's has a 4, Smolder's has a 9, and no numbers are within 7 of each other.

Since we already know Gallus is false, this means his number must be greater than 30.

Silverstream is lying because if Sandbar had 27, her number and Gallus' number couldn't fit anywhere. This part's tricky to explain but looking at the list of primes, the only option for their numbers to be 10 apart with Gallus being more than 30 are 31-41, 37-47, and 43-53, all of which would make Silverstream false anyway. Thus, Silverstream must also be greater than 30.

If Ocellus is true, Yona's only valid number is 45. 41, 43, and 47 are all prime, which would make her lie, violating our assumption, and 49 is a perfect square, violating Gallus' description.

Also from Ocellus, Smolder's only numbers are 9 and 59. 19 and 29 are prime and less than 30, which would make her truthful when whe know she isn't, and 49 isn't prime which would also make her truthful. Since we know she doesn't have the biggest number, which 59 would have to be, she must have 9.

Silverstream's only possible numbers are 41, 47, and 59, since all the other prime numbers above 30 have a 3 in them, and since Gallus was false, she can't have a 3. However, from Ocellus, 41 and 47 are too close to Yona, so she must have the 59.

At this point, the only valid numbers must be between 17 and 37 inclusive. Gallus' only two possible numbers are therefore 31 and 37. However, that wouldn't leave enough room for Sandbar and Ocellus, since Sandbar's number can't have a 1 and can't be prime, making 25 his only option since he can't have 27, and 25 is too close to 31. Thus, Gallus has 37, Sandbar has 25, and Ocellus has 17.

Final score: Yona has 45, Smolder has 9, Silver has 59, Gallus has 37, Sandbar has 25, and Ocellus has 17.