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

by Coyotek4


Puzzle 4: Squirrels and Chipmunks

“Yer just in time, sugarcube … uh, Ah mean, Headmare Twilight.”

Twilight chuckles at Applejack’s backpedaling. “There’s no need to be so formal with me.”

“Well, in front of the students is all … Ah thought a bit more formality would be in order.” Applejack turns from Twilight to the class, who all shrug in indifference.

“I’ve never been comfortable with anypony addressing me as ‘Princess’; as it is, I’m still adjusting to ‘Headmare’. Formality can be appropriate, but not among friends.”

“Uh … we can still call you ‘Headmare’, right?”

Twilight laughs at Ocellus’s question. “Whatever makes you most comfortable,” she replies before turning back towards Applejack. “So what do you have for today’s lesson plan?”

“So, for today Ah thought it’d be interesting for the students to see first-hoof how confusin’ it can be when competin’ groups try to be uncooperative towards one another. The point, of course, is to show that honesty is always the best policy.”

“I’m with you so far,” Twilight accedes. “So how does this work.”

“Ah’ve already assigned each of the students here to one of two groups; one group is called the Squirrels, and the other group is called the Chipmunks.”

Twilight ponders the names for a moment. “I think all those friendship quests you’ve been sent on with Fluttershy are starting to have an effect.”

The two share a laugh as the class quietly observes.

“Well, Ah didn’t want to just use ‘A’ and ‘B’ for this; she may have given me suggestions,” Applejack admits. “So anyway, Ah assigned three of ‘em to be Squirrels and three of ‘em to be Chipmunks. Then Ah laid down some simple rules for the students. They can each talk to only one other at a time, and Ah included a rule what causes confusion when ponies … well, any creature gets all underhoofed.”

“And what rule would that be?”

“Any statement made toward someone from the ‘other’ group has to be a lie, while any statement made towards someone from the same group has to be honest. So if, say, Gallus and Smolder are both Squirrels, they have to be honest when talking to each other … but if Gallus is a Squirrel and Smolder is a Chipmunk …”

The other four students burst out in giggles, as Gallus and Smolder sigh in unison.

“… uh, anyway, if Gallus and Smolder are in different groups, then any statement made by one to the other has to be a lie.”

“I think I got it,” Twilight states. “So I assume everyone knows their group.”

“Yes indeed.” Applejack turns from Twilight to the students. “How ‘bout a demonstration for the Headmare, y’all?”

“What are we supposed to say?” Ocellus asks.

“Ah dunno … maybe keep things simple, like makin’ comments to one another about yer affiliation.”

Gallus sighs a second time, swallows his pride, and turns to Ocellus: “I am a Chipmunk.” He pauses for a moment. “Grampa Gruff can never know I spoke those words in that order, okay?”

“Ooo, my turn!” Yona exclaims as she, too, addresses Ocellus: “Yona is Squirrel.

Smolder then beckons Yona to face her: “We are different types.

Sandbar goes next, getting Smolder to face him: “You are a Squirrel.” The comment draws rolled eyes from the young dragon.

“Oh, I want to go now!” Silverstream insists as she flutters towards Gallus: “You are a Chipmunk,” she states before moving on towards Sandbar: “Either Yona is a Squirrel or Smolder is a Chipmunk.

“Whoa now, love the enthusiasm there Silverstream, but Ocellus hasn’t even had a chance to speak.” Applejack double-checks her list and thinks about the comments made. “Ah think some of you may have forgotten the rule Ah put in place. Two of those statements wouldn’t’ve been made.”

“What do you mean?” Ocellus asks.

“What Ah mean is that one of those statements is true when it should be false, and one of those statements is false when it should be true … though the other four statements hold up. It’s alright, Ah know it’s a bit confusin’ at first … that’s why Ah always believe in honesty towards all.”

Applejack turns to Twilight, noticing the latter lost in thought. A notion quickly comes to her: “Oh shoot, Twilight … Ah never even told you which group each student was in.”

“You don’t need to,” Twilight replies with a smile.

“If this is going where I think this is going,” Gallus says, “can I just take my seat and observe this time? I’m still worn out from the last few puzzles.”