Silverstream: A beat B, B beat C, E beat B, E beat D
Sandbar: A beat C, A beat E, B beat D
Yona: B beat D, C beat A, D beat C
Smolder: A beat E, D beat A, B beat D
Gallus examines the statements placed on the portable chalkboard. “I guess I shouldn’t be surprised that you have a chalkboard in your office,” he notes.
“I like being prepared,” Twilight replies somewhat defensively.
“For what, someone giving you a pop quiz?” Ocellus asks.
“One never knows,” Twilight states, envisioning the day Princess Celestia makes an impromptu visit.
OK, Gallus, you’re smart, you can figure this out. He stares at the predictions for a few minutes …
“So … three of you all said that B beat D,” he starts, talking the problem out aloud to himself as the others listen in. “But you couldn’t all be on teams B or D … so that means B didn’t beat D, and it had to be Silverstream and Ocellus who were on teams B and D, in some order.”
“Well started,” Twilight says.
“OK … so Sandbar, Yona, and Smolder were on teams A, C, and E, in some order. And both Sandbar and Smolder said that A beat E … and at least one of them had to be on either A or E … so that statement has to be true, and both Sandbar and Smolder are on teams A and E. And that means—”
“Yona on team C!!!”
The group turn to Yona, who sheepishly smiles. “Sorry … Yona excited.”
“Yeah,” Gallus says before continuing: “so anyway, knowing that Yona was on team C means that both of her other statements were true: C beat A and D beat C … and the first of those two contradicts Sandbar’s claim that A beat C, so Sandbar couldn’t have been on team A … he was on team E, and Smolder was on team A.”
“Nicely done, dude,” Sandbar says with encouragement.
His confidence growing, Gallus proceeds: “Now I know that Smolder was on team A, and that means that D beat A.” He pauses and ponders for several seconds. “Now what?”
“Would you like a hint?” Ocellus asks.
“No … I need to get there on my own,” Gallus insists. He ponders for several more seconds.
“Let me recap,” he says aloud to himself: “A beat E, C beat A, D beat C, D beat A … wait a minute … so A played E, C, and D … but no team played every other team … so A didn’t play B at all.”
“I think you’re going to do it!” Silverstream exclaims.
“So that means Silverstream was wrong by saying that A beat B … Silverstream couldn’t be on team B, so she was on team D and Ocellus was on team B. That’s all the teams!”
“Excellently done!” Twilight states. “Now can you finish the results?”
“Silverstream was on team D, so E did beat D. And now … yes … I got it now! D played A, C, and E, so D couldn’t have played B either! But since every team played at least two games, B must have played C and E. And since both of Silverstream’s remaining statements must be false, C must have beaten B and B must have beaten E. And that’s all the results: A beat E, B beat E, C beat A, C beat B, D beat A, D beat C, and E beat D.”
“You got them all!” Ocellus proclaims. “Way to go!!!”
The student all crowd around Gallus to embrace him. He winces slightly at the pressure put on his left wing, causing the others to back away slightly. “It’s OK, everyone,” he reassures the group, “I’ll be all right. Just, maybe not so much crowding right now.”
“Puzzle-solving may not be to everycreature’s taste,” Twilight concludes, “but still, you should be proud of your capabilities. Problem-solving skills in general are useful everywhere, to solve all sorts of problems, friendship-based and otherwise.”
“Thanks, Headmare Twilight … but if it’s all the same, I hope that next time I’ll be playing rounds of buckball instead of solving a puzzle about them.”