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

by Coyotek4

Puzzle 19 solution

The sole pony’s eyes now shut, Ocellus changes her appearance to mimic that of her hippogriff friends. Each takes a card, and the rounds begin:

[In each round, one Silverstream appears on Sandbar’s left (L) and one appears on his right (R).]

[Round 1]
L: “I am Silverstream. I have the 1.”
R: “I am Ocellus. I have the 2.”

Sandbar ponders the two sets of statements. “Oh wait,” he quickly says, pointing a hoof towards the one on his left. “You have to by lying; nocreature would claim to have the 1. So you’re Ocellus, and you can’t have the 1, so you have the 3.” He turns to the one on his right. “And that means you’re Silverstream, and you’re lying too so you have the 1.”

One flash of light later, the ‘Silverstream’ on his left reverts to her natural, changeling form. “Good job,” she remarks.

“But a pretty easy round, right?” Gallus states.

“They’ll get harder,” Ocellus promises. “Close your eyes again.”

Sandbar obliges, and the second round starts:

[Round 2]
L: “I am Silverstream. I do not have the 3.”
R: “I am Ocellus. I do not have the 4.”

Sandbar considers the two sets of statements, but quickly replies: “This is like the last one, but in reverse, right?” He turns to the one on his right. “Nocreature would lie and claim to not have the 4, just like nocreature would truthfully claim to have the 1. So you’re telling the truth, and you’re Ocellus with the 2.” He turns to the one on his left. “And that makes you Silverstream, and you’re truthful as well so you have the 4.”

Another flash of light reveals Ocellus as the ‘Silverstream’ on his right. “Right again,” she comments.

“Still pretty simple,” Gallus reiterates, drawing a glare from Sandbar. “Whaaat?”

“You could be a little more supportive, you know.” The dragon points out.

“Ready for Round 3?” Ocellus asks.

“Can I just check the note cards you gave me one more time?” Silverstream asks. “These later rounds get harder to remember.”

“Go ahead,” the changeling replies.

“Ooo, ooo, Yona want to play too!” She turns to Sandbar. “Unless you want to keep doing these yourself. Yona understand if you do.”

“I don’t mind,” Sandbar responds as he shuts his eyes. Smiling, Yona does likewise; moments later, the third round begins:

[Round 3]
L: “I am Silverstream. Both of us have even-numbered cards.”
R: “I am Silverstream. My card’s number is the smaller of the two.”

Sandbar turns to Yona. “What do you think?”

“Well, Silverstreams can’t both be Silverstreams, right? So one liar.”

“Sounds good to me … and that means the one on the left is lying when she says they both have even-numbered cards. So the one on the right is the real Silverstream.”

“But what numbers?” Yona asks. “Oh wait, right-hoof Silverstream truthful, so her card 2 or 4 and left-hoof Silverstream has 1 or 3.”

“But the one on the right has the smaller number,” Sandbar reasons. “So Ocellus is on the left with the 3 and Silverstream is on the right with the 2.”

Ocellus [on the left] reveals her true self once again. “Not so easy this time, was it?” she comments, her eyes focused on Gallus.

“I’ll admit that there was more to that one,” the griffon says. He turns to Smolder: “You wanna try to solve the next one?”

“Sure, why not?” the dragon replies. She and the others all shut their eyes as the fourth round commences:

[Round 4]
L: “Either I am Silverstream or I have the 1.”
R: “Ocellus has the 1. Neither of us has the 4.”

Yona looks at Gallus. “OK, smart guy. You know answer?”

“Uh …” he stammers, before admitting: “All right, this one has got some kernels on the cob.”

“What do you think,” Smolder asks of Sandbar. The young pony thinks about the statements made by the two Silverstreams.

“Well, suppose the Silverstream on the left was lying. That would mean she wasn’t Silverstream and she didn’t have the 1; she would have to be Ocellus, and she would need to have the 3. And that would like the other Silverstream’s first statement false, so they’d both be liars … but then her second statement would be true, and that can’t be!”

“I’m impressed,” Gallus says with conviction.

Yona picks up where Sandbar leaves off: “That mean Silverstream on left truthful, so she can’t have 1; it must be real Silverstream, and one on right Ocellus.”

“And since nocreature would claim to have the 1,” Smolder adds, “Ocellus is lying and must have the 3. And that means one of them does have the 4; it must be Silverstream.”

Ocellus [on the right] changes back to her usual form. “Well done!”

Silverstream turns to Ocellus. “We still have one more round, right.”

“We do … and it’s the hardest round. All of you ready?”

“I hope so,” Gallus says, hoping to redeem himself in the eyes of the others.

The group of four shut their eyes and the final round plays itself out:

[Round 5]
L: “Either Silverstream has the 1 or Ocellus has the 3. Neither of us has the 2.”
R: “Either Silverstream has the 3 or Ocellus has the 4. Neither of us has the 1.”

“Whoa,” Sandbar quietly says. “Where do we begin?”

“We gotta begin somewhere,” Gallus starts. “Let’s just say the one on the left is telling the truth. What would that lead to?”

Smolder continues: “Well if the Silverstream on the left is telling the truth, then that one has to have the 4 since neither would have the 2. And the Silverstream on the right would have to have either the 1 or 3, making that one a liar.”

“And since Silverstream on right liar, that one have 1 and not 3,” Yona follows.

Sandbar puts the information together: “So the one on the left is truthful with the 4 and the one on the right is lying with the 1.” He ponders for a minute … “That doesn’t work!”

The other three turn to Sandbar, awaiting an explanation.

“If Silverstream is on the left, then her first statement is false: she can’t have the 1 and Ocellus couldn’t have the 3 since she would have the 1. But on the other hoof, if Ocellus is on the left, then Silverstream’s first statement would be true since Ocellus would have the 4.”

“OK,” Gallus says, “that’s proof enough for me that you’re as adept at this as the rest of us.

“So what all that mean?” Yona asks. “We do all this for nothing?”

“Not for nothing,” Smolder corrects: “Now we know the one on the left is lying. And that means the one on the right has the 2.”

“And that means the one on the left has the 3, since neither can have the 1,” Gallus adds.

Sandbar concludes the process: “Silverstream can’t be on the right, ‘cause that would make her first statement false. Silverstream must be on the left with the 3, and Ocellus might be on the right with the 2.”

At long last, the ‘Silverstream’ on the right morphs back into Ocellus. “Great job! she exclaims. “I really didn’t think you were going to get that.”

“I had good help,” Sandbar replies somewhat bashfully.

“Sandbar stop selling self short,” Yona pleads. “Sandbar smart, like all Yona’s friends.”

“And Yona herself,” Gallus adds.

“That looked like fun for you guys,” Silverstream states. “Can I play along too?”

Ocellus ponders the hippogriff’s request. “I do have some more challenges, but I thought those might be a bit too much. Besides, if you’re playing, then who am I copying?”

Smolder raises a claw …

Comments

[katzoo12]

Yep, I had a feeling I got the first two right! I may need to sharpen up my logic skills, but at least I got those two!