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

by Coyotek4

Puzzle 9: Ocellus is Stumped

“Now everycreature take a number,” Pinkie instructs the class, “and starting tomorrow, you’ll all take turns baking cupcakes for the class.”

“I’ve never baked anything before,” Sandbar reminds his professor. “I’m not sure my batch will turn out OK.”

“It’s not about the quality, silly!” Pinkie reassures. “It’s about the act of doing something for your friends. And if they don’t come out exceptionally well, then you have a fun story to share.”

“I’m with Sandbar on this,” Gallus states. “What if my ‘fun story’ gets told in a hospital ward?”

Smolder dismisses Gallus’s concern: “Meh … I can taste-test if everyone else wants. We dragons have strong stomachs; it takes a lot to make us sick.”

“Is that a challenge?” Gallus slyly asks. The group laughs at the veiled threat.

“See … even this discussion is fun,” Pinkie declares. “Now come on up, one number per student.”

Each student, in turn, randomly selects a number from Pinkie’s desk. Each peruses his or her own number, without seeing any other number selected.

“Okie-dokie, that’s all for today! See you bright and early tomorrow!” Having concluded classroom proceedings for the day, Pinkie pronks her way out the classroom door.

“At least she’s not going on about the walls again,” Silverstream states.

“So when everyone else go?” Yona asks. “Yona second,” she adds as she shows off the ‘2’ to the others.

Smolder leans over to look at Sandbar’s number. “My number is three less than Sandbar’s,” she states.

Silverstream opens her mouth to speak, but Gallus stops her and turns to Ocellus.

“OK, you’re the puzzle-lover here. I’m guessing you can figure out everyone’s number just based on those statements, right?”

Ocellus looks at her number and ponders the previous statements. “I … I …”

“Is everything OK?” Sandbar asks.

“I … I don’t know.”

“You don’t know if you’re OK?” Silverstream asks.

“No … I don’t know everyone else’s number. In fact, I don’t know anyone else’s number, besides my own and Yona’s. That’s not like me.”

“ ‘Huh’,” Gallus says, taking a second look at his own number. “If that’s the case, then I know everyone’s number.”

“YOU DO???” the other students ask in unison.

“I do … and if I add that my number is higher than Ocellus’s, everyone can now figure out who has what number.”

Author's Note:

So … what number does each student have? (All numbers are from 1 to 6.)

(Admittedly a bit on the easy side ... I'll try to make the next one more challenging.)

Comments

[Duckgame4life]

Ok so
yona is 2
Smolder is 3 less than sandbar
With just the above info ocellus cant solve this
Gallus can now solve this
Gallus is higher than ocellus
Now solve
there is 2 options smolder and sandbar can be, 1&4 or 3&6
Since ocellus cant narrow it down, she cant have any of those numbers,so ocellus is 5
Gallus says he's higher than ocellus so he's 6
That makes smolder 1, Silverstream 3 and sandbar 4

[Starlight Glimmer1]

Smolder: 1
Yona: 2
Silverstream: 3
Sandbar: 4
Ocellus: 5
Gallus: 6

[Eroraf86]

Took me a minute to figure out the logic, but I got it.

Since Yona is second, Smolder's statement means her number must be 1 or 3, and Sandbar's number must be 4 or 6. Since Ocellus cannot eliminate any of these possibilities, her number must be 5. Then Gallus's number must be 6, Sandbar's number is 4, and so on. The final order, from first to sixth, is: Smolder - Yona - Silverstream - Sandbar - Ocellus - Gallus.

[Inspector Brown]

Huh. I think I saw this story when you first posted it, and then forgot about it, which is why I'm so late to comment. Normally, I don't like meta-puzzles, but this one seemed a little more accessible, so here goes nothing.
Assuming Smolder is honest (because we have no reason to doubt her), her number has to be less than 4. It can't be 2, because Yona has that number, so it must be either 1 or 3. Sandbar's number is either 4 or 6, depending on which number Smolder has. If Ocellus had any of these four numbers, she would have been able to solve Smolder's and Sandbar's numbers by process of elimination. But she couldn't, so she didn't, and therefore, she's holding 5. Gallus's number is larger than Ocellus', so he's holding 6. That means Sandbar must have 4, Smolder has 1, and Silverstream 3.

[son_of_heaven176]

It's 12:09 AM as I start typing this, and given that I gave up on the last puzzle a few minutes ago and solved this one, this is DEFINITELY easy. Thanks for the palate-cleanser before I head to bed.

Ahem.

Yona's number is 2.
Smolder said that her number is three less than Sandbar's. With Yona's number known, that would mean that there are only two possibilities: Sandbar has 4 and Smolder has 1, or Sandbar has 6 and Smolder has 3.

Ocellus said that the foregoing was NOT enough for her to know everyone's number. That means that Ocellus does not have any of the four numbers I mentioned before. Ocellus's number must therefore be 5.

Gallus said that with those pieces of information, he knows everyone's number. That means that his number IS either 1, 3, 4, or 6.

Gallus then added that his number is higher than Ocellus's.

That solves the puzzle. As already established, Ocellus's number is 5. Gallus, therefore, must have 6. That leaves 4 for Sandbar and 1 for Smolder. Process of elimination leaves 3 for Silverstream (who said absolutely nothing this puzzle).

To summarize:
1=Smolder
2=Yona
3=Silverstream
4=Sandbar
5=Ocellus
6=Gallus