The Path Through the Forest
As Twilight ties down the balloon at the edge of a dense forest, Pinkie eyes the surrounding area. A dirt path leads into the undergrowth, but also continues in the other direction into the distance. “So where do you think this path ends, Twilight?”
“I couldn’t say; I’ve never been to this part of Equestria before. But as the Cutie Map led us to the towns inside the forest, that’s where I think we should head.” Satisfied that the balloon is secure, Twilight trots over to Pinkie. “Anyway, the walk might give us a chance to hone our logic skills.”
“ ‘Logic skills’? That’s your forté, right?”
“Anypony’s mind can be honed, Pinkie Pie, and we don’t know exactly what’s expected of us. The way I see it, we’re bound to pass various groups of ponies as we head down the path. I’ll ask those we meet about which town they’re from, and you can solve the ensuing puzzles.”
Pinkie looks quizzically at Twilight. Before Twilight can clarify, a pair of unicorns emerge from the forest. “Here, I’ll show you.”
Twilight walks over to the unicorn pair. “Excuse me,” Twilight asks one of them, “but could you tell me from which town the two of you come from?”
“We both come from Paradise,” the one unicorn replies. The twosome then continue their walk down the dirt path, as Pinkie just stares at Twilight in confusion.
“What was that all about,” Pinkie asks.
Twilight smiles as she responds, “This is your first puzzle, Pinkie. Can you tell me where each of those two unicorns comes from?”
“Well duh! They both come from Paradise. The one unicorn told us.”
“But remember, Pinkie: unicorns from Paradise always lie. If they both did come from Paradise, then the unicorn who replied to us would have told us the truth. That cannot be.”
Pinkie let out an ‘oooOOOOooohhh’ before replying, “… that really seems silly. So then I guess we can’t tell where they really come from.”
“Oh, but we can,” Twilight giddily responds, “and that’s where logic comes into play. “Consider this: the unicorn who replied lied to us, so that unicorn cannot come from Utopia; she must come from Paradise. Now if her friend also came from Paradise, then she would have been telling the truth, which also cannot be. That means that the other unicorn must actually come from Utopia.”
While trying to process all this information, Pinkie looks up to the sky, down to her hooves, over to the unicorn pair as they disappear from their view, and finally turns back to Twilight. “Why do you think I was asked to come along? I don’t think I’m going to be much help here.”
“The Cutie Map has never been wrong,” Twilight assures Pinkie. “You’re here for your unique skill set, just like me. And you can learn this reasoning, just like me; all it takes is some practice. Look, we’re bound to pass more groups of ponies on our way to the twin towns. I’ll ask each group where they’re from, and you can figure out where each pony resides. C’mon, it’ll be fun!”
Twilight’s bright smile does little to console her confused friend, but Pinkie puts on a determined face and agrees. She forces out an ‘okie-dokie’ and follows Twilight along the path.
By the time she and Twilight came to a fork in the path, Pinkie Pie was mentally exhausted. The two had come across no less than five groups of ponies; each time Twilight asked the group where they came from, and each time one or more from the group would respond. And each time, Twilight pulled out a quill and parchment and jotted down the responses.
The first group consisted of a pair of pegasi. When asked, one responded, “At least one of us comes from Utopia.”
The second group consisted of a unicorn and a pegasus. When asked, the unicorn responded, “We come from the same town.” The pegasus, in turn, replied, “No we don’t!”
The third group also consisted of a unicorn and a pegasus. The unicorn said that the pegasus came from Utopia; the pegasus then stated that the two came from different towns.
The fourth group consisted of three unicorns. One unicorn stated that at least two of them were from Paradise; a second unicorn then stated that she and the third unicorn came from different towns.
The fifth group consisted of two pegasi and a unicorn. The unicorn stated that the two pegasi were from the same town. One pegasus then stated that an odd number of the threesome was from Utopia, and the other pegasus stated that she and the unicorn were from the same town.
After each group had passed the twosome by, Pinkie attempted to contemplate how the responses could be used to determine where each pony came from. Over time, the rationalization process tired the pink earth pony out.
“My head is spinning,” Pinkie pleads at the fork. “Can we take a break from these puzzles?”
“Once we’re at Utopia,” Twilight replies as she looks down each path, unsure of which way leads to the unicorn town.
“Does it really matter which town we end up in, Twilight? I mean, I’m an earth pony and you’re an alicorn.”
“Well yes,” Twilight replies, “but I was a unicorn, and I think there could be a stronger bond between myself and the inhabitants of that town. After all, I studied magic for a long time before coming to Ponyville.”
“Okay then …” Pinkie eyes a pegasus approaching from the right-hand path and asks, “Are you coming from Utopia?” The pegasus replies ‘Yes’, and Pinkie turns to walk down the right-hand path. Twilight grabs Pinkie’s tail with her mouth to stop her.
“Don’t forget: we don’t know if that pegasus is being truthful or lying. We need a question that will conclusively tell us which town is which.”
Twilight asks a different question of the pegasus, who indicates the right-hand path, then thanks the stranger for the information before nudging Pinkie towards the left-hand path.
For a half-mile, the two ponies stride along the dirt path, surrounded on both sides by evergreen trees. Though they continue to pass by ponies, both individuals and groups, Twilight maintains an uneasy silence while noting Pinkie’s mental fatigue.
Eventually, the path widens into a clearing with numerous buildings dotting the area. Rather than a unicorn-centric locale, Twilight notes the similarities between this town and a smaller-scale version of Ponyville. Unicorns and pegasi meander to and fro from various locales.
“We made it, Pinkie Pie!”
Pinkie ekes out a faint ‘Yeay’ before collapsing. Twilight levitates her and trots over to a nearby inn.
“Feeling better?”
Pinkie rises from a bed and looks around; she sees Twilight and breathes a sigh of relief. “Oh Twilight, I just had the craziest dream where you were giving me all these weird puzzles.” She resumes scanning the area, then turns back to her friend: “Hey, this isn’t Sugarcube Corner!”
“Pinkie,” Twilight calmly replies, “we’re in Utopia. You’ve been out for a couple hours. It’s getting dark now, but we can probably grab some dinner before turning in and starting fresh in the morning.”
“Food sounds good!” Pinkie bounds from the bed and starts bouncing in place in anticipation of a tasty meal.
“But first, let’s go over my puzzles for you.” Twilight’s words cause Pinkie to stop bouncing as she groans and walks backs to the bed to lie down.
Paying no heed to her friend, Twilight levitates out from her bag a number of parchment pieces, each indicating the responses from the various groups of ponies they passed by while strolling down the path in the forest. “We had five encounters before coming to that fork. Let’s take a look at each one in turn.” Pinkie nods in acceptance after each solution is revealed.
“First, we had a pegasus state that either she, her friend, or both came from Utopia. Now if she were lying, she would actually be from Paradise, but all pegasi from Paradise tell the truth. Therefore, the pegasus who spoke to us was being truthful, hence she was from Paradise. And since she told the truth, her friend must come from Utopia.”
“Second, we had a unicorn and pegasus with a difference of opinion. Now if a unicorn and pegasus agree on the validity of a statement, they must come from different towns: either they’re both truthful, meaning the unicorn comes from Utopia and the pegasus from Paradise, or they’re both lying, meaning the unicorn comes from Paradise and the pegasus from Utopia. Since these two disagreed with each other, they must come from the same town; if Utopia, then the unicorn is truthful, and if Paradise, then the pegasus is truthful. But this means the unicorn’s statement is true; therefore, they both come from Utopia.”
“Now consider the third group. If the unicorn came from Utopia, then she was truthful and the pegasus did come from Utopia; if the unicorn came from Paradise, then she lied and the pegasus must have come from Paradise. In either case, they must come from the same town; this means the pegasus lied. Thus, they both come from Utopia as well.”
“Let’s move on to the fourth group. If the first unicorn came from Utopia, then she was truthful and the other two must come from Paradise; if the first unicorn came from Paradise, then she lied and the other two must come from Utopia. Either way, the other two unicorns come from the same town; this makes the second unicorn’s statement a lie, so that unicorn must come from Paradise. That means that the first unicorn actually does come from Utopia, with the other two coming from Paradise.”
“The fifth group was probably the most interesting of all. If the unicorn came from Utopia, then the two pegasi did come from the same town; thus, either all three came from Utopia, or only the unicorn came from there while the two pegasi came from Paradise. If the unicorn instead came from Paradise, then the two pegasi came from different towns, so exactly one of the threesome … specifically, one of the two pegasi … came from Utopia. No matter which of those scenarios is the actual one, this guarantees that an odd number of the threesome, either one or three, came from Utopia. This makes the first pegasus’s statement true, so that pegasus must come from Paradise. As for the others, note that if the second pegasus was truthful, she would come from Paradise and the unicorn would also come from Paradise, and if the second pegasus lied, she would come from Utopia and the unicorn would still come from Paradise; either way, this forces the unicorn to have come from Paradise. That means the unicorn lied, and so the two pegasi had to be from different towns, meaning the second pegasus came from Utopia. So to sum up: the unicorn and first pegasus came from Paradise, and the second pegasus came from Utopia.”
“And then, of course, was the little bonus puzzle I had for you when we came to the fork in the path. Pinkie, do you remember the question I asked that pegasus?” Twilight responds to Pinkie’s flat ‘no’ with “I asked, ‘Which path would a unicorn from your home town say leads to Utopia?’ A pegasus from Paradise would truthfully tell us that a unicorn from Paradise would lie about the true path, and a pegasus from Utopia would lie about the true path that a unicorn from Utopia would truthfully tell us; either way, we simply choose the other path.”
Twilight smiles broadly. “See? Isn’t this fun?” Pinkie shoots Twilight an expression that convinces her otherwise. “Well, I suppose logic puzzles aren’t for everypony.”
“Twilight,” Pinkie asks seriously, “do you know the names of any of those ponies that we passed?”
Twilight can only respond with a sheepish ‘no’.
“Exactly. How are all these puzzles supposed to solve whatever friendship problem that these towns have? You’re treating all the ponies in this town like your personal activity book, but you’re not actually helping anypony. And also … you’re wearing me out. Me!”
Pinkie’s assertions shame Twilight into silence for many minutes. “You’re right,” the alicorn finally admits. “I guess I got so caught up in the idea of a puzzle-adventure that I forgot who I was.” Her face brightens as she continues: “Well, no more! Let’s go find that friendship problem … but first, let’s eat!”
“Now you’re talking!” Pinkie once again bounds from the bed, enthusiastic for both a good meal and a fresh start.
The two trot out of their room, nearly running into a blue-maned yellow unicorn. Twilight quickly apologizes, but the unicorn cannot help but start at the horn-wings combination.
“I haven’t seen an alicorn ‘round these parts,” the unicorn states, causing Twilight to blush slightly.
“Oh … well, my name is Twilight Sparkle, and I’ve been brought here to solve a friendship problem.”
“Friendship problem, eh? Sorry, got no idea what yer talkin’ about.”
“That’s OK,” Twilight assures the unicorn, “right now we’re just looking for a place to eat. Can you recommend someplace in Utopia?”
The unicorn stares at the twosome for a few seconds before responding, “I come from Paradise. Sorry I can’t be more help to ya.” He then heads out the door of the inn.
Pinkie brushes off the comments. “Well, I’m sure we can find a place on our own, right Twilight. Uh … Twilight? You feeling OK?”
Twilight begins pacing around the area, muttering to herself. “… we’re in Utopia, so that statement is true, but that means we’re in Paradise, which makes the statement false, so we’re actually in Paradise, but that would make the unicorn a liar, which means we’re actually in Utopia, but that means, unless I’m wrong, so nothing we did made sense, and … oh dear …”
Twilight falls to the ground and passes out.
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I did not get a word of what Twilight said. Perfect story keep it up.
Uh, there's a MAJOR typo in Twilight's explanation of the second group. Since you established that the unicorn and pegasus both come from the same town, the unicorn is the truthful one, and thus they're both from Utopia, not Paradise.
8103937
Shoot, you're absolutely correct!
I fixed the typo. Thx again for catching that!
8104817 And thank you for getting to it so quickly--especially since there is another, bigger error in the story. Please check your PM.
8105345
You are absolutely correct ... again! This time I'm giving credit where credit is due.
Second pegasus.
(How did I miss that typo?)
9592158
The better question is, "How did I miss that typo?"
I fixed it. Thx for catching it!