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

by Coyotek4


Puzzle 16: More Buckball Games

Having missed the previous ‘buckball day’, Gallus was secretly thrilled to be able to participate in the next one. Not that anyone else had to see this enthusiasm.

“Looking forward to professor Dash’s class today?” Sandbar asks as the group make their way down the hallway.

Oh? What’s so special about today?”

“Oh please,” Smolder retorts. “Don’t act like you don’t know what today is; we flat-out mentioned it this morning!”

“Oh, right …” Gallus chuckles as they continue making their way. “Yeah, I want to make up for lost time. Show you all my mad skills as a defender.”

“Griffin get real mad after Yona score on him!” The group laughs at the young yak’s counter.

“Talk is cheap, Yona. You’ll have to prove it in competition.”

“Bring it on!”

Ocellus turns to Silverstream. “You think some creatures are getting the wrong lessons from professors Rainbow Dash and Applejack?”

“Eh … I’m still waiting on that plumbing lesson we’re owed. Who do you think would teach us that?”

Sandbar looks at Silverstream with a wry smile. “Maybe headmare Twilight needs to open a Friendship Vo-Tech school for you.”

The group reaches the gymnasium, but they’re surprised to see Applejack waiting for them instead of Rainbow Dash, her focus on a large piece of paper held in her forehooves. “Come on in, y’all,” she calls out to the group, her eyes still glued to the paper.

“Professor Applejack,” Ocellus calls out, “where’s Rainbow Dash? She usually runs the buckball games.”

“We’re still playing buckball today, right … RIGHT???

Applejack quickly alleviates Gallus’s concerns. “Yeh, ye’re all still playin’ buckball, just like the last group. Ah agreed to take over for Rainbow Dash for this period.”

“Did she take another trip to Las Pegasus?” Sandbar asks.

Applejack chuckles. “Not this time, Sandbar. She muttered somethin’ about another chapter by some friend of hers that she met at the Daring Do convention. Said she needed some time to figure out things …” She pauses for a moment. “Actually, Ah think she might be askin’ fer yer help about this.”

Gallus rolls his eyes, now aware of what’s to come later in the day. “Just to be clear,” he says, “we are playing buckball today, right?”

“Yes yes, of course …” Applejack dismisses as she turns to her attention back to the paper.

“Uh, professor?” Silverstream asks, “What’s that in your hoof?”

“Huh … OH, sorry, everycreature. Ah’m just tryin’ to make sense of these here results.”

“Results?” Ocellus asks.

“The previous group of students what come down here for some buckball. Rainbow Dash was here for that group, and Ah got here just before they all headed out. It was a big enough class that she split ‘em up into four teams and had ‘em play each other. RD told me every team played at least once and no two teams played each other twice. When they were all done, she had a member of each team summarize the results and asked me to record all the game results right before she took off. Unfortunately …”

“May I?” Silverstream asks as she reaches for the paper. Applejack obliges, and the students peruse the paper.

….GP...W L T...GF GA
------------------------------
A....3.....1 0 2.....4 4
B....2.....0 1 1.....2 4
C....2.....1 1 0.....2 1
D

“I take it ‘GP’ means ‘Games Played’,” Ocellus says, “with Wins, Losses, and Ties … but what do ‘GF’ and ‘GA’ stand for?”

“They stand for ‘Goals For’ and ‘Goals Against’,” Applejack replies. “She gave me summary totals, but she didn’t give me actual scores. Shoot, I don’t even know who played who?”

“Where are D’s results,” Sandbar asks.

“Ah guess all the members of that team left before Rainbow did. So I got nothin’ regardin’ their scores, and that ain’t even the worst of it.”

“Oh?” Yona asks. “What worst of it.”

“Last thing Rainbow said before leavin’: she said one team was havin’ a prank at her expense, and all the figures in that team’s row are all off by 1. Guess that prank is on me now. Dangit, Rainbow!”

“All right, so just so we’re all clear on all this,” Smolder states, “These results are missing anything regarding D’s games, one of the three rows is completely wrong with every number off by 1, and professor Rainbow Dash expects you to still recreate the results of every buckball game.”

“Eeyup,” Applejack replies, mimicking her brother’s verbal tick.

“Professor?” Silverstream asks, “Don’t buckball games usually go until some team scores 5 goals?”

“Usually, but due to time constraints, Rainbow only had teams play until someone got to 3 goals. Further, she had a time limit in place, so some games ended before any team got to 3.”

“Okay,” Silverstream says as she studies the paper a bit longer. “… aaand that’s it.”

Applejack blinks. “What’s ‘it’?”

“I figured out all your scores,” the hippogriff cheerfully replies.