//------------------------------//
// Puzzle 12 solution 
// Story: School of Logic: a Collection of Puzzles involving the Student Six 
// by Coyotek4 
//------------------------------//



Unicorn A said “None of the others have the same hometown as me.”
Unicorn B said “F and I have the same hometown.”
Earth pony E said “C is from Utopia.”
Earth pony F said “D and E have different hometowns.”



The students ponder the four statements, aware that the two pegasi, C and D, said nothing, and also aware that of each pair of like-type ponies, one was truthful and one lied.

“There doesn’t seem to be much to go on,” Silverstream states to the group.

“When I solve puzzles like this,” Ocellus states, “I usually start with statements one makes about one’s self.”

“Like what B said?” Yona asks.

“Exactly. B said that she had the same hometown as F. Let’s start there.”

The group ponder in silence for a minute, before Sandbar speaks up.

“If B was truthful, she’d be from Utopia … and so would F.”

Smolder continues: “And that would make her a liar. It would also force E to be a truth-teller, and that would mean E was from Elysium.”

“But if F was a liar,” Silverstream adds, “then D and E would have the same hometown … they would both be from Elysium.”

“And if E truthful,” Yona says, “C from Utopia.”

Gallus concludes the train of thought: “So C would be from Utopia and D would be from Elysium … neither one would be a truth-teller, and that’s contrary to what we were told from the outset, that one of the two pegasi is truthful.”

“OK then,” Ocellus states, “that means that B is a liar and A is truthful. So A is from Utopia … the only pony from Utopia, as it turns out.”

“But if no one else is from Utopia,” Sandbar says, “then E lied. That means F is truthful, so F is from Elysium.”

“But B lied,” Smolder adds, “so B isn’t from Utopia. And if F is from Elysium, B isn’t … B must be from Paradise.”

“And since E lied,” Silverstream states, “that means E isn’t from Elysium, right? But no one else is from Utopia, so E must be from Paradise, too.”

“F told the truth,” Gallus adds, “so D and E do have different hometowns. If E is from Paradise, D isn’t … and D isn’t from Utopia either, since A was truthful. That means D is from Elysium … and would have lied if she said anything.”

“Then C truthful,” Yona says, “so C from Paradise.”

“So that’s the answer, right?” Ocellus asks. “A is from Utopia, B is from Paradise, C is from Paradise, D is from Elysium, E is from Paradise, and F is from Elysium.”

Coccyx clops his hooves together in applause. “BRAVO, everyone! That was some incredible deductive reasoning you demonstrated. I am most impressed!”


“These towns really do sound weird,” Smolder states. “I can’t speak for other dragons, but I get the feeling most wouldn’t care about these ponies’ oddball behavior.”

“Still, it’s incredible that ponies would go to such lengths for any reason,” Sandbar adds.

Ocellus adds: “You haven’t even heard about their alicorns.”

“ALICORNS???”

The group turn to Ocellus, then to Coccyx. “These out-of-the-way villages in some remote corner of Equestria have princesses?” Gallus asks incredulously.

“Not princesses, alicorns,” Coccyx corrects. But not in the way that you think.”

“Could you tell us more about these ‘alicorns’?” Sandbar asks.

Coccyx chuckles and smiles. “This, my friends, leads to a whole new level of logic puzzles.”