The group take another look at the three pages containing Quibble’s door puzzles. “We can probably solve these,” Gallus states, “but what does solving puzzles have to do with loyalty?”
“Oh, well … it has everything to do with loyalty,” Rainbow explains. “You see … one key aspect of loyalty is being there for your friends when they need you the most. And, uh … I need you, right now.”
“So … you’re not just our professor, you’re our friend?” Smolder asks.
“We’re all friends,” Rainbow earnestly asserts.
“So … all we do now is puzzles?” Yona asks.
“Sure looks like it,” Sandbar replies. “May as well get to it.”
The group focuses on the first puzzle:
Door 1: “This room contains a bear.”
Door 2: “This room contains a wolf.”
Door 3: “This room leads to freedom.”
“This one’s pretty easy,” Ocellus states. “The exit must be Door 2.”
“Why is that?” Rainbow asks.
“If Room 2 had a bear, the statement would be true, meaning the room had a wolf, which is doesn’t. And if Room 2 had a wolf, the statement would be false, meaning the room didn’t have a wolf, but it does.”
Rainbow’s head begins to spin. “Could you go over that one more time?”
“If statement true, room have wolf, but wolf room lies, so statement false, which mean no bear either, so room lead to freedom,” Yona sums up.
“Oh … I think I get it. But what about the other rooms?”
Silverstream takes a shot: “Well, Door 3 must be false now, so that’s where the wolf is. And that leaves Door 1 to lead to the bear. Easy-peasy.”
“Huh … not bad,” Rainbow admits. “What about the next puzzle?”
The students shift their focus to the second puzzle:
Door 1: “Rooms 2 and 3 both have bears.”
Door 2: “Rooms 4 and 5 both have wolves.”
Door 3: “Rooms 2 and 4 contain animals of different types.”
Door 4: “Rooms 2 and 5 contain animals of the same type.”
Door 5: “This room has the exit.”
“So now what?” Rainbow asks.
“To start,” Smolder says, “Room 5 can’t have a bear. If it did, the statement would be true and it would lead to the exit, not contain a bear.”
“Meanwhile,” Ocellus continues, “Room 1 can’t have a bear, either. If it did, then Doors 2 and 3 would both lead to bears as well, and there’d be at least three bears … but we know there’s only two bears to go with two wolves and one door to freedom.”
“So that means Door 1 is false,” Gallus says, “and either Room 2 or Room 3 doesn’t have a bear. And that means Room 4 has a bear.”
“Uh, Gallus?” Ocellus says. Gallus pays no heed and continues:
“And since Room 4 has a bear, Rooms 2 and 5 have animals of different types … but Room 5 doesn’t have a bear, so it has a wolf and Room 2 has a bear.”
“Gallus?”
“And since Room 2 has a bear, Rooms 4 and 5 both have wolves. So Room 3 has the other bear, and Door 1 leads to freedom. Nothing to it,” he concludes.
“GALLUS!”
The griffon turns to Ocellus. “What?”
“Door 1 CAN’T be false! You said Room 4 had a bear, but then you said Room 4 had a wolf. It can’t be both!”
Gallus blinks … and goes over his reasoning a second time. “Hmmm … if Door 1 was false, then Door 4 would have a bear, so Rooms 2 and 5 would different animals, but Room 5 doesn’t have a bear, so Room 2 has a bear, and then Rooms 4 and 5 have … so Room 4 would have a wolf … so there’s no solution!”
“No,” Ocellus insists. “There IS a solution.”
“How? Now I know Door 1 can’t be false so it has to be true, but there can’t be a bear in Room 1.”
“Right … so therefore …”
The realization dawns on the griffon. “Ohhh, Door 1 leads to the exit!” He continues to ponder the possibility: “Lesse … Door 1 is true means Rooms 2 and 3 have bears, leaving Rooms 4 and 5 to have wolves. Do all the statements work? … Huh, I guess they do.”
“Whoa … harder than it looked,” Smolder observes. “What about the last puzzle?”
The six ponder the final puzzle:
Door 1: “No two adjacent rooms contain animals of the same type.”
Door 2: “An even-numbered room has the exit.”
Door 3: “The room with the exit is adjacent to a room with a wolf.”
Door 4: “Either this room has a wolf or Room 5 has a bear.”
Door 5: “Room 2 has a wolf and Room 6 has a bear.”
Door 6: “Room 3 has a wolf.”
Door 7: “This room has the exit.”
“Anyone wanna start?” Gallus asks the group.
“Room 7 not contain bear,” Yona points out. “Just like last couple puzzles.”
“OK,” Gallus continues, “What else?”
…
A minute of silence passes.
…
“What about Room 4?” Sandbar finally says.
“What about it?” Smolder asks.
“It can’t have a wolf, right? Because if it did, the statement on the door would be true.”
“Good job!” Ocellus states. “I must be slipping.”
“Or we’re getting better,” Silverstream adds. The others, including Ocellus, chuckle at the comment.
“All right,” Smolder says, “so Room 4 can’t have a wolf. Can it be the exit?”
“Going right for the finish, huh?” Sandbar says. “But then the statement could be true or false.”
“So let’s start with ‘true’,” Ocellus suggests. “that would force Room 5 to have a bear, and that would mean Room 2 has a wolf and Room 6 has a bear.”
“But Door 2 true,” Yona states. “So Room 2 not have wolf.”
“That’s right,” Sandbar concurs. “So if Room 4 was the exit, the statement would have to be false.”
“Which means Room 5 doesn’t have a bear,” Ocellus adds. “And since it would have to have an animal, it would have a wolf.”
“Room 7 also have wolf,” Yona adds, “since it not exit.”
“And based on the statement on Door 6,” Gallus continues, “either that room or Room 3 has the final wolf.”
“Meaning Rooms 1 and 2 both have bears,” Smolder states, before pausing. “… but Rooms 1 and 2 are adjacent, so Door 1 would be false, and that can’t be.”
“And all of that goes to show that Door 4 doesn’t lead to the exit!” Ocellus concludes.
Rainbow eyes the students quizzically. “Wait … how long have you been doing these?”
Yona ponders her professor’s question. “Maybe one week?”
Rainbow blinks, then shakes her head. “That’s … that’s ...”
“So after all that,” Silverstream states, “what does that mean?”
“It means,” Gallus replies, “that Room 4 has a bear. Which means the statement on that door is true, and that means Room 5 has a bear as well.”
“And that mean Room 6 have bear and Room 2 have wolf,” Yona adds. “No more bears left.”
“But we have two wolves, too: Room 2 and 3,” Sandbar says. “All that’s left are Rooms 1 and 7.”
“What haven’t we used,” Smolder asks aloud. Several seconds pass.
“What about Door 3?” Silverstream finally asks. Ocellus responds:
“Door 3 has to be false … which means the room with the exit isn’t adjacent to a room with a wolf. So the exit can’t be Room 1, since Room 2 has a wolf. But it could be Room 7, since Room 6 has a bear.”
“And that means it has to be Room 7,” Gallus concludes.
“That’s funny,” Silverstream adds: “The room that says it’s the exit really is the exit this time!”
“Probably intentional, considering the previous puzzles,” Ocellus suggests. “ ‘Fool me once’, and all that?”
“So that’s that,” Smolder states. “Hope that helps, professor … uh, professor?”
The group all turn to face Rainbow, noting the spiral formation in her eyes.
“Is professor pony OK?” Yona asks.
“… why yes, I would love some eggs,” Rainbow replies in a half-daze.
Sandbar turns his attention to the clock on the wall. “Whoa, class is almost done for the day.”
“Looks like whatever that other puzzle she wanted us to look at is gonna have to wait,” Ocellus states.
“You guys wanna hang by the fountain for a bit?” Gallus suggests. The group collectively nod in approval, and quietly file out, leaving Rainbow Dash to stare blankly at the back wall.
“… no more eggs, I’m good …”