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

by Coyotek4

Puzzle 16 solution

….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

Applejack takes the sheet of summary results back and peruses it. “Seriously? You gone figured out the whole thing based on this? Even with the missing row and mistake row?”

“Uh huh,” Silverstream replies.

The other students turn to each other and exchange odd looks. Finally, Gallus speaks: “I don’t mind sitting this one out; anyway, I came to play buckball, not go on about scores.”

“And I still need a break after last night,” Smolder adds. “Anyone else mind if Silverstream solos this one?”

The remaining students shrug, and Silverstream beams at the chance of demonstrating her knowledge.

Applejack sighs. “Guess I shouldn’t be surprised anymore. Still, where do you even begin with this one?”

“With row ‘A’,” the hippogriff replies. “That one has to be the ‘prank’ one.”

“Why’s that?”

“Because it’s not possible for ‘A’ to have the same number of goals for as goals against if they have at least one win and no losses; they would have to have more goals for. So all those numbers are off by one, and that means ‘A’ played two games, with no wins, one loss, and one tie.”

“Well Ah’ll be …”

“And more! Since ‘A’ has a loss and no win, they have to have more goals against than goals for … so they must have three goals for and five goals against.”

“Huh … hold on while Ah jot this down.” Applejack picks up a pencil from the ground and fills in the correct information:

….GP...W L T...GF GA
------------------------------
A....2.....0 1 1.....3 5
B....2.....0 1 1.....2 4
C....2.....1 1 0.....2 1
D

“So Ah take it that means ‘D’ played two games as well?”

“It has to be an even number, and it can’t be zero or four, so yes: ‘D’ played two games. And since the other teams combined for one win and three losses, ‘D’ has to win both its games.”

“This is really helpful,” Applejack admits as she jots down the further information. “But that still don’t give us the final scores.”

“Well for that, look at ‘A’s goal totals. They had one tie and one loss, so their loss had to be by two goals. Their two games had to have scores of either 0-0 and 3-5, 1-1 and 2-4, 2-2 and 1-3, or 3-3 and 0-2 … but the first two of those can be ruled out since no team scored more than three goals, and the last case is out since a team that got to three goals won immediately. So ‘A’s games had to be scores of 2-2 and 1-3. And since only ‘B’ tied as well, ‘A’ must have played ‘B’ to a 2-2 tie.”

Applejack scribbles notes as fast as Silverstream recites her solution.

“Now ‘C’ didn’t score three goals in total, so they didn’t beat ‘A’; ‘D’ must have, so ‘A’ lost to ‘D’ by a 1-3 score and ‘A’ didn’t play ‘C’ at all. That means ‘B’ didn’t play ‘D’, and their other game must have been a loss to ‘C’ by a 0-2 score. That leaves ‘C’ with one goal against them, so ‘C’ lost to ‘D’ by a 0-1 score, and that’s all the games played.”

“Was anyone timing that?” Gallus asks.

Sandbar looks up at a clock hanging on the gymnasium wall. “That was, what, 3 minutes?”

“Sounds like a record,” Ocellus points out. “Good job!”

“Ah’ll say … that was remarkable.”

Silverstream beams.

“Seriously, if there’s anything Ah can do to repay you …”

“Maybe professor give Silverstream one-on-one lesson on plumbing,” Yona suggests.

The students laugh, while Applejack ponders the request.

“Sounds strange … but Ah do know mah way around a toolbox. Shoot, Ah helped out the spa ponies not too long ago. Ah’ll talk to Twilight about settin’ somethin’ up.”

“Really? That’d be super-awesome!!!” Silverstream does aerial somersaults in celebration.

“Hey now, save some of that energy for buckball. Alright, everycreature, split up an’ lets get yer bodies a workout for a change …”

Comments

[son_of_heaven176]

That was an easily followable solution, and a promised, this puzzle was indeed a breather after the last one. Nice.