Twilight's Logic Puzzle Adventureby Coyotek4ChaptersUtopia and ParadiseThe Path Through the ForestThe Alicorn SocietyThe Earth Ponies of ElysiumThe Pebble Paradox and the Rainbow SevenOne HugUtopia and ParadiseThe doors to the throne room burst open as Pinkie Pie barges in. “Sorry I’m late! I got here as fast as I could … well, maybe not the fastest fast, but everypony kept saying ‘Hi Pinkie’ and ‘Where you off to, Pinkie?’, and I couldn’t just ignore them, so I kept greeting them back with ‘Hi there Carrot Top’ and ‘I’m off to the Castle of Friendship, Lyra’, and before you know it …” Pinkie’s runaway chatter is interrupted by the sight of her alicorn friend staring at a section of the Cutie Map with their two cutie marks hovering above it. Her front hooves are propped on the table as she fixates on an area in southwestern Equestria. Pinkie walks over to Twilight and eyes the map. “Oooo, is that where we’re heading? Looks like a far cry from Griffonstone, and nowhere near Canterlot. Does the train run there? Do we need to take the balloon? Oh, it’s been like forever since I’ve been in the balloon!” Twilight remains silent as she continues to stare at a pair of dots surrounded by forest on the map, still lost in thought. “You know, conversations are funny this way, but usually they involve more than one pony, ‘cause otherwise one pony just dominates all the discussion and … uh … … Twilight?” Blinking, Twilight finally realizes that she’s not alone in the room. She takes her forehooves off the table and turns to Pinkie. “Sorry, Pinkie Pie. It’s just that … I feel like I recognize these towns. I know I’ve seen them before; I just can’t remember where.” Pinkie takes another look at the map. “What’s to recognize? They’re dots.” “I know, but there’s something about this location that’s haunting me. I’m sure I’ve seen this area before, but I’ve gone through all my maps, atlases, and geographic texts, and I can’t find anything resembling this. You’d think I’d recognize something as distinct as two cities surrounded by forest, but …” Twilight turns back to the map, hoping for a moment of inspiration. “You’re thinking too hard about this, Twilight. Let’s just go and see where this adventure takes us!” Pinkie starts bouncing in place, rife with anticipation. “Pinkie, you know how I like to be prepared for callings like this,” Twilight states without turning, still focusing on the map. “Yeah, I know; Fluttershy told me all about your trip to the Hooffields and McColts. How ‘bout this time, we just go and be surprised by what we find? It’ll be more fun that way.” Twilight turns to Pinkie, a slight undertone of frustration in her voice. “Look, I appreciate your care-free attitude towards life. It’s who you are, and I’ve learned not to seek explanation. But I’m just not like that. I need order and reason in my world. I live for the cold truth that logic brings and …” Twilight suddenly stops mid-sentence and ponders. “Wait a minute. It couldn’t be.” Before Pinkie can ask what it is that could not be, Twilight bolts from the room; she returns minutes later with a dusty text. Quickly scanning through the tome, Twilight soon comes to a page with a map of two towns surrounded by forest. Her eyes dilate with the realization: “I don’t believe it … the twin towns of Utopia and Paradise are real!” Pinkie looks over Twilights forehoof to inspect the pages. “Utopia and Paradise? I never heard of those towns. They sound nice, though.” Twilight suddenly turns to Pinkie with wide eyes and a broad grin. “Do you know what this means! A friendship problem that can be solved with logic puzzles!” She proceeds to bounce around the room, mimicking Pinkie’s usual method of pronking about Ponyville. “Well you seem more chipper now,” Pinkie observes. “What do you mean by using ‘logic puzzles’ to solve a friendship problem? What’s so special about these towns?” “We’ll take the balloon to get there; I’ll explain on the way. You grab the food, while I grab some quills and parchment. Oh, I can’t wait to get started on this!” Twilight rushes out of the throne room, as Pinkie looks on with curiosity and slight apprehension. From her vantage point high above the grassy plains, Twilight gazes towards their destination upon the horizon. “We’re making great timing. We should be there in another 30 minutes.” A munching sound causes Twilight to turn back; Pinkie’s mouth is filled with hay sandwich, which she hurriedly gulps down. “Pinkie, did you eat the last of our balloon provisions?” “Well, I was in a hurry to get out the door this morning, so I didn’t have time for more than two bowls of oatmeal, a couple blueberry muffins, six carrots, a daisy, and two-thirds of a cake. Say that reminds me, I need to cut down on my daisy intake.” Twilight rolls her eyes before turning back towards the horizon. “Well I’m too excited to eat anyway. I still can’t believe the twin towns of Utopia and Paradise really exist. I wonder if the tales from my logic book are true.” “So what’s so special about these towns, Twilight? Nopony I know has ever mentioned them, and I know a lot of ponies.” Twilight turns back to Pinkie and explains. “Among the courses I took while studying in Canterlot was a course in logical reasoning, taught by Professor Stallyan. It was one of my favorite classes; it was basically a series of puzzles that tested one’s ability to make sense of given information.” Pinkie could already hear Rainbow Dash’s voice in her head, screaming out “EGGHEAD!”, but simply bid her friend to continue. “One of the chapters focused on the twin towns of Utopia and Paradise. According to the textbook, Utopia and Paradise were settled shortly after the events of the first Hearthswarming, when tensions between unicorns, pegasi, and earth ponies were still high. A faction of unicorns and pegasi attempted to settle a single town deep within a forest, but infighting between the two races led to two towns being formed instead. The unicorns created the town of Utopia, and the Pegasi created the town of Paradise.” “Unicorn Utopia and Pegasus Paradise.” Pinkie recites the alliterative phrase to herself a couple times. “That’s easy enough to remember.” “Anyway,” Twilight continues, “tensions between the two eventually died down, and over time a number of unicorns from Utopia moved to Paradise, while a number of pegasi from Paradise moved to Utopia. In the book, each town has both unicorns and pegasi.” “So all this sounds …” Pinkie pauses before continuing, “I won’t lie to you Twilight, I don’t see where any of this is going.” “Well here’s where it gets weird. According to the story, the unicorns who moved to Paradise still harbored deep feelings for Utopia, and when asked, would state that they were from the town of unicorns even if they were from Paradise. And the same held true for pegasi who resided in Utopia; they would insist that they were from the town founded by pegasi. From there, it became natural for these particular ponies to lie about any statement made in reference to residence. Eventually, it came to pass that every statement from a unicorn from Paradise, or from a pegasus from Utopia, was a lie.” “Every statement? So wait Twilight; does that mean that a unicorn from Paradise would state that grass is red, and maple syrup falls from the sky?” Twilight shrugs. “I guess so.” “Well that should make for interesting conversations!” Pinkie smiles broadly at the notion. Author's Note I have long been a fan of the work of Raymond Smullyan, and this fic is my attempt to merge the myriad of puzzles he has created with the MLP:FIM universe. The reader is encouraged to try to solve the puzzles that appear before reading ahead to the answers that eventually follow. The Path Through the ForestAs 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. Author's Note Special thanks to 'son_of_heaven176', who caught a number of errors that I have since fixed! The Alicorn Society“What would you say, Zodiac?” “I would say she suffered a logic bomb. I would say we’ve all had one at some point, and I haven’t seen either her or her pink earth pony friend before.” “So what do you think she is? Unicorn or pegasus?” “I would say I don’t know; in either case, this is some incredible work. I would say even Cloudstitch wouldn’t be able to tell.” “Well what do I do with that earth pony friend of hers waiting outside?” “Show her around. Treat her to breakfast, if you like. I would say I need some time with this one; she could prove to be a valuable addition to our society.” “Understood, sire.” Twilight hears the clip-clop of hooves leaving her room as she rubs her eyes and sits up. She is in her bed in Utopia’s inn, with a charcoal-grey unicorn standing at the room’s entrance … and then she notices his wings … “You’re … an alicorn?” The grey pony promptly responds, “I would say I’m as much an alicorn as you are, miss …” “Twilight Sparkle, Princess of Friendship.” Her use of the word ‘princess’ causes the stranger to look her appearance over a second time. “So, you fancy yourself a true alicorn, eh? I don’t suppose you can prove this claim.” “Well …” Twilight flaps her wings and slowly rises into the air. Her horn emits a low brightness as a pillow levitates up to her. The combination of these mundane tasks catches the stranger off-guard as he stammers in his response. “Whoa, you really are … I mean, my apologies, Your Highness. I, I did not intend to impugn the word of … oh, this is most embarrassing.” “It’s quite all right,” Twilight soothingly replies as she floats back down to the bed and stands eye-to-eye with the stranger. “But, I’m surprised that you’re so surprised. I mean, you’re an alicorn, too … right.” The stranger looks over his forehoof, then walks over to the room’s entrance and closes the door. He turns back to Twilight before responding. “What I am about to show you, I must ask that you never reveal to anypony else. Can you promise me that?” “I can Pinkie-promise if you like,” Twilight happily replies. “I do not know what that means, but I believe I can trust you.” Taking one last look to the closed door, the stranger turns to face Twilight. A glow emanates from his horn, and the wings on his body come off and levitate into the air. Twilight can only gape as the wings hover for many seconds, before returning to their placement on the pony’s body. “So … those wings are fake? I don’t understand; why go around pretending to be an alicorn.” “There is much that I need to explain to you, Princess Twilight Sparkle.” “Just call me Twilight; I’m still not used to the whole ‘princess’ thing.” “Very well,” the grey unicorn responds. “My name is Zodiac, and I am a member of the Alicorn Society.” “The what?” “The Alicorn Society consists of a select group of unicorns and pegasi, from both Utopia and Paradise. Our goal is to maintain the harmony that exists between unicorns and pegasi in these towns, mostly by setting a higher standard of conduct.” Twilight eyes Zodiac quizzically. “I don’t understand. Why would there be a need for policing harmony?” “Based on recent events, I assume you are familiar with the history of the twin towns.” After Twilight nods, Zodiac continues: “Even after the mixing of the two pony types between our fair towns, there resided an air of contempt for pegasi residing in Utopia, and vice versa. There were many arguments, and grudges persisted between neighbors. Then Cloudstitch showed us a better way.” “Who is this ‘Cloudstitch’?” “One of the most logical thinkers in all of Equestria … and an incredible seamstress. She recruited a number of our brightest and most rational, myself included, and brought us to her home. There, she showed off a pair of prosthetic wings … the very wings that you see me wear today. She also displayed a vast array of carefully-designed horns. Both the wings and horns, when attached, were practically indistinguishable from the real thing.” “Her idea was simple: give select unicorns a custom-made pair of wings, and give select pegasi a custom-made horn. Then, have those chosen ponies mingle among the townsfolk in both towns, setting a standard of tolerance and friendliness. Aid those in need, settle disputes calmly and rationally … act like you would like others to act, basically.” “Mostly, though, the reason for the wings and horns was to promote tolerance towards the ‘alicorns’ themselves. Though thoroughly rational in thought, many chosen still harbored deep resent for ‘the wrong kind’ … but if one couldn’t tell unicorn from pegasus among his or her fellow alicorns, one couldn’t harbor any latent hatred.” Silence pervaded for many seconds. After taking in Zodiac’s story, Twilight finally responded. “I have to say, this is one of the most unusual ideas I’ve ever come across … and yet so incredible. But has it worked?” “It’s been many moons now since this all began, and the results speak for themselves. This is an idyllic community now, along with Paradise. No more arguments, no more dissention. And I must say, we’re very proud of what we’ve accomplished.” “So this ‘Cloudstitch’,” Twilight continues, “is there a chance I could meet her?” “As a matter of fact, I wish to introduce you to her … but first, you will have to pass a test.” Twilight starts bouncing in her bed, giddy with anticipation. “Ooo, ooo, when can we start? Can we do this now? This is gonna be awesome!” “I must say,” Zodiac notes, “I’ve never had that kind of reaction upon informing somepony of a test.” After watching Pinkie Pie devour a bowl of oatmeal in her usual, head-in-the-bowl fashion, her silver ‘alicorn’ companion cannot help but comment: “I would say that I’ve never met anyone quite with your, shall we say, dining etiquette.” Wiping drops of mush from her muzzle with her forehoof, Pinkie responds, “What can I say, I’m one-of-a-kind.” Shrugging off what sounds like a mutter of ‘Thank Equestria’, she then asks, “So what’s your name, anyway? I never got it.” “I would say my name is Spiral.” “OK,” Pinkie replies, “but is that really your name?” “I would say that, yes, Spiral is my name.” Pinkie looks at the ‘alicorn’ with a blank expression before asking, “What is with you using the phrase ‘I would say’ all the time? It seems weird, and boy do I know about weird!” “Well,” Spiral starts, “are you familiar with the history of our towns?” “Twilight told me all about how all you ponies are all either truthful or liars. That’s why I can’t tell whether you’re lying now or not, especially when you start each sentence with ‘I would say’.” “But I would say that’s the point. I would say all of the following: take any true sentence, like ‘Your name is Pinkie Pie.’ If I am truthful, then I would say such a statement; if, however, I am a liar, then I would not say such a statement … but then saying I would say that statement is itself a lie, which forces that statement to be true. You see?” “Oh I see fine,” Pinkie replies. “I hear very well too, and have a great sense of smell. But I don’t understand a single thing you just said!” “Perhaps we should start over,” Spiral states. “I would say my name is Spiral. Now then, what would you say if I were telling you the truth?” “If you’re telling the truth, then your name is Spiral. I get that.” “Excellent. Now, what if my statement was a lie? What would that tell you?” “That would tell me that your name isn’t Spiral,” Pinkie innocently replied. The ‘alicorn’ shook her head before explaining. “Again, I would say all of the following: if I am a liar, then the statement ‘I would say my name is Spiral’ would be a lie. That would mean I would not say my name is Spiral. But that, in turn, would mean that my name IS Spiral, since I would ‘not’ say any true statement. Thus, my name must be Spiral, whether or not I am truthful.” Pinkie let the explanation take hold in her head for some time. “So … any time you begin a statement with ‘I would say’, that makes the thing you say true?” “Inasmuch as I actually believe the sentence to be true, I would say yes.” “And that’s true for all the inhabitants of Utopia and Paradise?” “I would say yes, that is the case.” “Well go figure … I guess I can figure!” Pinkie beams with a sense of pride as she starts bouncing in place.” ‘One-of-a-kind’ indeed! Twilight eyes the solitary room Zodiac has led her to, thinking back to her study days back in Canterlot. In front of her is a single desk, with an ample supply of parchment and quills for scratchwork. Along the sides are bookshelves filled with dusty tomes. The lack of windows unnerves her slightly, but she trusts her guide not to have led her astray. “Let me explain this test, Twilight.” The ‘true’ alicorn nods. “Over many moons, some of our society brothers and sisters have formed close bonds. For this test, you will hear statements from 5 pairs of ponies. In each case, one is a unicorn and one is a pegasus. Either could come from Utopia or Paradise, and they could come from the same or different towns. As you know, unicorns from Utopia and pegasi from Paradise are truthful, while unicorns from Paradise and pegasi from Utopia lie. All you need to do is identify which pony is the unicorn and which is the pegasus. In some cases you will be able to identify place of residence for one or both; in other cases, you will not be able to do so.” Twilight thinks to herself that Rarity would be likely to ace this quiz by simply spotting the real wings and horns from the fakes, but she also trusts her own ability to solve the ensuing puzzles. “I understand. I’m ready to begin.” “Excellent,” Zodiac replies. “Write down your answers, and be prepared to explain your reasoning to me after everypony has given their statements. If you are as talented as I believe you to be, this should be no more than a formality.” Zodiac leaves the room, and one by one, a pair of alicorn-looking ponies walk in to deliver statements. Twilight is amazed by each pair’s appearance, never being able to discern real horns from fake or real wings from fake; nonetheless, she takes it upon herself to stay with the logical facilities within her to solve each puzzle. The first pair to enter are named White Rose and Blue Daffodil. White Rose states that she comes from Paradise, while Blue Daffodil states that she is a unicorn from Utopia. The second pair to enter are named Haystack and Corn Sheaf. Each claims to be a unicorn. Haystack then states that the two come from different towns. The third pair to enter are named Topaz and Amethyst. Topaz claims to be a pegasus, and Amethyst claims to be a unicorn. Topaz then states that the two come from the same town. The fourth pair to enter are named Lettuce Patch and Turnip Field. Lettuce Patch states that both ponies come from Paradise, and Turnip Field denies this statement. The fifth and final pair to enter are named Fianchetto and Knight Fork. Fianchetto states that she is not a pegasus from Utopia, while Knight Fork states that he is a pegasus from Paradise. Fianchetto then states that the two come from different towns. After each of the first four pairs made their statements and left, Twilight scribbled her solutions and thought processes. Minutes after the final pair makes their statements, Twilight asks Fianchetto to bring Zodiac to her. “It was nice of you showing me around Utopia, Spiral … if that is your real name,” Pinkie giggled. Her companion sighed. “I’d say that we’ve been over this before, and that you know that’s my name.” “Oh yeah, that whole ‘double-negative’ thingie; okie-dokey! Say, does that whole ‘I would say’ thing apply to everything you say?” “I would say not; only statements that could be true or false, but not questions or commands. I would also say that one gets used to it after awhile. And, I would say, we’re back to the inn; your alicorn friend should be back before too long.” “Well, thanks again. Your quirky town and its funny speech patterns will always have a special place in my head!” Spiral shakes her head one last time, turns, and walks away. Pinkie is alone to ponder her thoughts: I’d have Spike take a message for Princess Celestia, but he’s not here. I’d write it myself, but I don’t have digits on these hooves. Well, I’m sure I can retain all this information until Twilight returns, then she can help me write a letter. *hee-hee* … who would write ‘a’ letter, right? I mean, one has to write a whole lot of letters to convey any particular meaning, right? What would Princess Celestia say if I just sent her a piece of parchment with a big ‘Q’ on it? She’d probably wonder why I was so interested in ‘Q’. Pinkie’s thoughts are interrupted by the clip-clopping of hooves just outside her room. She turns to see a familiar blue-maned yellow unicorn. “Hey, I recognize you! You’re that unicorn we met last night. The one claiming to be from Paradise. So what’s up?” “I don’t have any particular reason for coming here. That said, would you be willing to come with me?” “Aww, I always look forward to making new friends … but I really should wait for my friend Twilight to return. She should be back any time now.” A pegasus and second unicorn come up and stand beside the yellow unicorn, who then removes the prosthetic horn from his head. Pinkie gapes as he speaks: “I will not insist that you come with us … but you’re coming with us.” “I am truly impressed, Princess Twilight Sparkle!” Zodiac could hardly hide his adoration for the alicorn’s intellect, upon reviewing Twilight’s solutions. Twilight blushed as she responds. “It really was nothing special, at least not to me. But I certainly appreciate your enthusiasm for my work. So I take it I got every problem correct.” “And so quickly. Pray, tell me how you solved these so effortlessly.” Full of pride from a job well done, Twilight proceeds to explain her reasoning to Zodiac. “Well, if you insist …” “One thing that really helped me solve these puzzles was the realization that any pony who claimed to be from Utopia must be a unicorn. In fact, anypony who was truthfully claiming to be from Utopia must be a unicorn, since pegasi from Utopia would lie; on the other hand, a pony who was lying about being from Utopia would be from Paradise, and only unicorns from Paradise lie. And by the same reasoning, any pony claiming to be from Paradise must be a pegasus. This really made the first puzzle trivial; I knew White Rose was a pegasus the instant she stated that she came from Paradise. Since you told me from the onset that each pair had one unicorn and one pegasus, this forced Blue Daffodil to be a unicorn. In this case, I couldn’t say which town either came from.” “What I find really interesting is that the reverse is true: any pony claiming to be a unicorn must come from Utopia, since a truthful claim from a unicorn could only be made by one from Utopia, and a false claim from a pegasus could also only be made by one from Utopia. Also, any pony claiming to be a pegasus must come from Paradise. This helped me figure out the identities of the second and third pairs.” “With the second pair, I knew that both Haystack and Corn Sheaf came from Utopia. Therefore, Haystack lied when stating that the two came from different towns, and only the pegasi from Utopia lie. Thus, Haystack was the pegasus and Corn Sheaf was the unicorn.” “Similarly for the third pair: I knew that Topaz was from Paradise and Amethyst was from Utopia. That meant that Topaz lied when stating that the two came from the same town. That forced Topaz to be the unicorn and Amethyst to be the pegasus.” Zodiac hangs on every word in awe as Twilight continues. “Another important fact that helped me was that, if the two ponies disagreed with each other, they must come from the same town. Either both come from Utopia, in which case the unicorn would be truthful and the pegasus a liar, or both come from Paradise, in which case the pegasus would be truthful and the unicorn a liar. With the fourth pair, Turnip Field disagreed with Lettuce Patch; therefore, they had to come from the same town. If Paradise, then Lettuce Patch told the truth and must be a pegasus; if Utopia, then Lettuce Patch lied and must still be a pegasus. I cannot say which was truthful, but I knew that Lettuce Patch was a pegasus and Turnip Field a unicorn.” “That fifth pair did take me longer than the others, since there was little to go on with their first comments. All I knew at first was that Fianchetto was not a unicorn from Paradise, as she would have lied and said she was a pegasus from Utopia … but if truthful, she could be either a unicorn from Utopia or a pegasus from Paradise. And further, she could be lying and be a pegasus from Utopia after all! As for Knight Fork, he could be telling the truth and be a pegasus from Paradise … or he could be lying, in which case he could be a unicorn from Paradise or a pegasus from Utopia. Anypony but a unicorn from Utopia. So to solve this, I had to ponder Fianchetto’s other comment.” “Let’s assume for the moment that Fianchetto lied when she same that the two came from different towns. I already knew she wasn’t a unicorn from Paradise, so she would have to be a pegasus from Utopia. This would mean Knight Fork was a unicorn, but also from Utopia since they would then have to be from the same town. But I already knew that Knight Fork couldn’t be a unicorn from Utopia … so the assumption that Fianchetto lied leads to a contradiction. She must have been telling the truth, so the two did come from different towns.” “Now, Fianchetto must be either a pegasus from Paradise or a unicorn from Utopia. If the former, that would force Knight Fork to be the unicorn, and again from Utopia … and once again, this is a contradiction to the fact that Knight Fork cannot be a unicorn from Utopia. The only possibility left is that Fianchetto is a uncorn from Utopia, and Knight Fork is a pegasus from Paradise.” “BRAVO!!!” The shout from outside the examination room causes both Twilight and Zodiac to turn to the doorway. A dark blue alicorn eyes Twilight’s figure carefully. “Cloudstitch! I mean … Your Excellency, I did not expect you to …” “That’s quite all right, Zodiac. And you need not worry about formalities around me; I would think that you knew this already, though.” Cloudstitch smiles as she speaks; her words are regal yet soothing; Twilight cannot help but make comparisons to Princess Celestia. Cloudstitch then addresses Twilight directly. “When I heard reports among the Society members that a true alicorn princess had come to our fair forest towns, I had to see for myself.” “So miss … I mean, princess? I must apologize; I don’t know how to address you.” “I might say the same about you, Princess Twilight Sparkle … but from what I have heard, I suspect that I may simply call you Twilight, as you may call me Cloudstitch. I have never been one for formality.” Twilight nods in acceptance, she herself still uncomfortable with the pedestal that so many have put her on. “So Cloudstitch, how long were you listening in?” “Long enough to hear your explanation of those final puzzles … especially the one with Fianchetto and Knight Fork. You would fit right in the Alicorn Society, perhaps moreso than the others since you’re an actual alicorn.” “It is good to see you, as always,” Zodiac starts, but Cloudstitch holds a forehoof up to stop him. “I wish I were only here for adulations, but I have troubling news for Twilight.” The smiles and pleasant feelings quickly drain from Twilight and Zodiac. “What news?” “I’ve been informed by Spiral that your friend Pinkie Pie has been accosted. She’s been taken by a rogue pony faction.” Twilight’s irises dilate at the information. “Rogue faction? Who took her? Where?” “There’s only one group that could have done this,” Zodiac declares. Twilight turns to the unicorn. “Pinkie’s been taken to Elysium … the town of the earth ponies.” The Earth Ponies of ElysiumTwilight felt conflicted at the start or her journey to Elysium. She was concerned for the well-being of Pinkie Pie, to be certain, but the assurances of both Cloudstitch and Zodiac that she would not be harmed were most comforting. She had grown to trust this twosome, even in a land where as many ponies lied as were truthful. And so it was, not long after starting back down the dirt path through the forest, with Zodiac by her side, that the apprehension and fear of what has become of her Ponyville friend had soon dissipated. But that did not mean that she didn’t have serious questions related to recent events: “I don’t understand. Pinkie and I never saw any earth ponies during our walk to Utopia. We never saw any earth ponies in Utopia. Where did they come from?” “They hide in plain sight, as it were,” Zodiac responds coldly. “The most logical explanation is that somepony in Elysium has mastered the same art of crafting prosthetic horns and wings that Cloudstitch had.” “Wait, so you mean that some of the unicorns and pegasi that we’ve come across are earth ponies?” “If everything else you’ve learned about our towns is to be believed … and I hope you do believe, as I have no reason to deceive you … then there is no other rational explanation. Tell me Twilight: do you remember what caused you to black out last night?” Twilight pauses as her eyes roll to the sky. “It was a statement by some yellow unicorn. It seemed to conflict with what I knew of these towns.” “Did this unicorn have a blue mane?” “Yes, he did. Do you know who I’m referring to?” “Sunbolt. He’s the leader of the earth pony rebellion. He and his group have wreaked a lot of havoc in our twin towns for some time now.” The ideas of rebellion and havoc coinciding with the idyllic nature of Utopia catches Twilight off-guard. “I’m not following you. I saw no strife among the ponies in Utopia. I’ll admit that I haven’t seen much of the town, but everything I did see seemed perfectly normal.” “Their mere existence causes strife,” Zodiac replies, an undertone of anger in his voice. These towns are founded on logic and reasoning; you have seen this firsthoof, and I’m sure you can appreciate that.” Twilight stumbles with a response. “Well, yeah, I do like logic and rational thought, but—“ “And look what happened to you. Let me guess: Sunbolt claimed that he was from Paradise, right?” Again, Twilight is surprised by Zodiac. “He did. But how did you—“ “And you couldn’t rationalize the statement, could you. As you already know, no unicorn would claim to be from Paradise. Those from Utopia would always truthfully claim that they came from Utopia, and those from Paradise would always lie and state otherwise. And Sunbolt’s very comment threw all that reasoning into utter chaos; your brain couldn’t process this, and you blacked out.” Twilight says nothing, and just nods in acceptance of the facts. “We’ve come to refer to these instances as ‘logic bombs’. And ever since the earth ponies started infiltrating our ranks, we’ve had to deal with these. Those in the Alicorn Society have come to accept that there are earth ponies in our ranks, pretending to be unicorns and pegasi. We have caught many, and tried to banish them from our towns … but it isn’t easy to keep them away for long. Worse, we’ve had instances where we knew that one from a group of ponies was an earth pony, but could not deduce which.” “Could you give an example of that?” Twilight innocently asks. “Well consider a pair of unicorns, let’s just call them ‘A’ and ‘B’ for the sake of simplicity. A states that B comes from Utopia, and B states that A comes from Paradise. What would you deduce from that?” Twilight talks out her thought process: “If A is truthful, then B really does come from Utopia; hence B is truthful, so A comes from Paradise … but no unicorn from Paradise is truthful. That means that A lied, so B would actually come from Paradise, meaning that B lied, so A actually comes from Utopia … but unicorns from Utopia are truthful.” She turns to Zodiac. “I can only conclude that such a scenario could never occur.” “And yet it did, not so long ago,” Zodiac retorts. “A pegasus who overhead the pair blacked out, just like you did. We in the Society gathered up the pair, knowing that at least one was an earth pony … and perhaps both. And it’s not just unicorn pairs: any group of unicorns and pegasi could have earth ponies in it, and it’s up to us to keep them separated.” Twilight considers Zodiac’s statement to be rather unfriendly in nature, but keeps the thought to herself as her companion urges her onward: “We’ve dilly-dallied long enough; we need to press on.” “… and as I was telling myself before you showed up, why would anypony write just a single letter. I mean, you need lots of letters to make words, but then you need lots of words to write a single letter. That’s just mind-blowing, isn’t it?” The ‘unicorn’ … that Pinkie learned was not really a unicorn … held his tongue for much of the journey, but at long last felt the need to interrupt the stream of consciousness emanating from the pink pony’s mouth. “Do you ever tire of talking?” “Not really. Well, I do get tired of course, and when I do I just go to sleep, but when I’m awake I just love taking everything in and enjoying life. You know, you really need to enjoy life while you can, ‘cause it’d be such a boring existence if you didn’t enjoy life, you know what I mean?” “ENOUGH!!!” The command paused Pinkie’s comments, if but for a moment. “Say, what do I call you anyway? We’ve been walking for a long time now, and left the forest area just a few minutes ago … ooo, and I saw the balloon I came in with Twilight! … but I still don’t know your name.” “Just call me Sunbolt.” “ ‘Sunbolt’? As in, bolts from the sun? I would think ‘Sunray’ or ‘Sunbeam’, or do I already know ponies with that name? Actually, even if I do, that’s no reason why some other pony can’t have that name. There are so many ponies in Equestria, it just makes sense that two have the same name, right? I wonder if there’s another Pinkie Pie out there. Maybe she’s a pegasus … what would it be like to have wings and fly? Sometimes I think I was supposed to have wings, but then I think about what flavor of cake I need to bake for the party.” “What party??? What are you even …” Sunbolt sighs, resigning himself to not figuring out his target. “You are so serious. Why is that?” Pinkie’s innocent question causes Sunbolt to stop dead in his tracks; Pinkie and the others in the group halt as well. Sunbolt then turns to address Pinkie. “I know you’re new around these parts, but did you notice anything unusual about that town Utopia you were in?” “Well hello! The town was in a forest! I mean, who puts a city in a forest?” “Not that,” Sunbolt argues. “Did you notice anything missing?” “… I didn’t see a spa in town. Maybe I’m just spoiled to have a spa in Ponyville. Oh, you would love our spa. Honestly, you do look tense, and—“ “Earth ponies!!!” “… what about earth ponies?” “You didn’t see any earth ponies in Utopia, did you? You felt like a stranger while walking around, didn’t you. All around you are unicorns and pegasi, living in harmony … but earth ponies? No, we’re cast aside by that ridiculous ‘Alicorn Society’. Banished from their precious twin-towns, because we upset their delicate balance of rationality.” Pinkie looks at Sunbolt in stunned silence; the latter appreciates the pause, recognizing that Pinkie takes his words seriously. “You’ve been banished from Utopia?” Pinkie asks. “And Paradise too? Well that doesn’t sound very nice.” Sunbolt smiles. “No … it’s not, is it. So we’ve taken to disguise to infiltrate the towns. We have an incredible designer in Elysium, who can produce horns and wings that are indistinguishable from the real thing … so long as you don’t ask me to actually perform magic, anyway.” “That horn really does look good on you. Say, you think I can get a pair of wings?” “I’m sure we can make arrangements for you. Now let us continue …” After a sufficient period of awkward silence, Twilight decides to initiate a new avenue for the recent topic of discussion. “So you said you felt it … ‘necessary’ … to separate out earth ponies from the unicorns and pegasi. But the examples you gave earlier didn’t seem to provide a way to determine which was which. You didn’t … physically …” Zodiac halts abruptly, perturbed at Twilight’s insinuation. “I can assure you, that nopony, either from the Alicorn Society or anywhere else in our fair towns, would ever touch another pony. That’s not just a matter of what is right, or what is honorable, but ours are towns of logical reasoning and not barbarism. No, instead we had trials where the accused would make statements; then, we would deduce which were earth ponies and which weren’t.” “So you’re saying that earth ponies who took the time to play dress-up would openly admit to being earth ponies, just to get banished from your towns?” “Not deliberately, to be sure, but it’s easy for a pony to let her focus slip when pressed. If you like, I can give you some examples … but I cannot divulge any names. What say you?” Twilight still felt uncomfortable with the notion of any sort of exclusionary policies, but her curiosity and yearning for more chances to exercise her thought processes, particularly on an otherwise isolated journey towards Elysium, won out. “I would like to hear these cases, Zodiac. I could always use the practice when it comes to puzzle-solving.” “Not from what I’ve seen of you,” Zodiac replies. “Very well: for each of the following cases, I can tell you that exactly one pony, described as either a unicorn or pegasus, is actually an earth pony from Elysium … and that all such ponies lie. All other ponies in these cases follow the same rules as you are accustomed to: the unicorns from Utopia and the pegasi from Paradise are truthful, while the unicorns from Paradise and the pegasi from Utopia lie. And as anonymity is the rule when it comes to all ponies that have been through a case, I will refer to all ponies by letter only. Now then:” “The first case featured two ‘unicorns’, though of course only one actually is a unicorn, while the other is an Elysian earth pony. Let me refer to them as A and B. A stated that both came from the same town, while B denied the assertion.” “The second case featured unicorn C and pegasus D. C stated that at least one of them came from Utopia; D agreed with the assertion.” “The third case featured three ponies: unicorn E, unicorn F, and pegasus G. E stated that at least two of the threesome were liars. F stated that either E came from Utopia or G came from Paradise. G said nothing.” “The fourth case featured three unicorns: H, J, and K. H stated that none of the three came from Utopia. J then shocked everypony by stating that he himself was the earth pony. This rendered K speechless; she said nothing.” “The fifth and final case I will share with you featured pegasus M, unicorn N, and pegasus P. M stated that N was really the earth pony, while N stated that M was not the earth pony. P then stated that no two of them came from the same town.” “Now,” Zodiac continues, “if you’re able to determine the five earth ponies from what I’ve related to you, I will be beyond impressed.” He cannot suppress a smile across his face as Twilight mulls over all the information. Minutes later, their journey takes them out of the forest. “I’d say we got another half-hour before we reach Elysium. Let us see if you’re able to figure all this out by then.” Five minutes later, Twilight recites five letters to Zodiac. She hides her feelings of superiority, satisfied by the stunned look on her companion’s face, as the two trudge on in silent contemplation. “… and that’s why I don’t like pauses in conversation, I mean who has time for quiet contemplation when there are parties to be planned and cakes to be baked and so many new friends to make. Any time spent alone or sad is just really lost time, don’t you think? I certainly think so, which is why I don’t like pauses in conversation, but wait, I just said that, didn’t I? Well that just proves my point; isn’t this much more enjoyable an experience?” I had to ask if she ever kept quiet. I just had to ask. “You’ve been real quiet, Sunbolt.” The faux-unicorn lets out a sigh and plods along. Pinkie, still curious as to the darker aspects of the history of the twin-towns, changes her conversational course. “I don’t understand. Why would Utopia and Paradise not want earth ponies around?” Pinkie’s question has the desired effect, as Sunbolt responds quickly. “I’m sure Twilight heard the story from that ‘society’, about how unicorns and pegasi came to this area to found a town shared by the two ponykinds … but that group fails to mention that there were three kinds. And as much animosity that existed between the two, the one thing they agreed upon early is that they wanted nothing to do with the earth ponies, who possessed no outer-worldly abilities. No horns or natural magic. No wings for flight. And they both dismissed the notion that earth ponies were special caretakers of the land. So even before the factions made it to the forest, the unicorns and pegasi forced our kind to start anew on our own, away from both of them.” Pinkie listens on in silence. Sunbolt, appreciating the gravity that Pinkie takes to his words, continues. “Of course, those two factions soon found that they couldn’t agree on much more than that, so two smaller towns were created instead. Over time, though, feelings towards each other’s kinds softened. That led to the strange nature of veritas that pervades there. Those who’ve come across the twin towns have been inspired by what they’ve experienced; I have even heard from some that whole stories have been created. Perhaps your alicorn friend learned about these towns from such a text.” “Yeah, she did read about Utopia and Paradise … but she didn’t mention anything about an earth pony town.” “Truth be told,” Sunbolt continues, “it was the earth ponies who first attempted to mend fences between the kinds. But perhaps it was too soon; the mere sight of a hornless, wingless pony set off cries of ‘Begone!’ from the townsfolk. That was when one earth pony came up with the idea of bluffing our way in, with prosthetic horns and wings.” “Pro … what?” “Fakes. Horns carved from wood, wings from stray feathers, both accented with whatever materials could be found. But this pony, I tell you, was incredible with her craftwork. One could hardly tell the difference between real and fake … so long as one wasn’t forced to actually demonstrate the use of magic or ability of flight.” “Wow, that’s funny,” Pinkie commented. “Not ‘ha-ha’ funny, but weird funny: Utopia also has a craftspony who makes fake horns and wings, too.” “It’s no coincidence; those ‘alicorns’ stole the idea, and used it to bring the unicorns and pegasi together … but still keep earth ponies away. Cruel irony, wouldn’t you say?” “But if the prosetuh … ‘fake’ horns and wings were so convincing, how did the ponies in Utopia and Paradise figure out the truth?” “Those from Elysium were not as well-versed with the traditions of the forest towns, and would occasionally make statements that didn’t fit; this led to unicorns and pegasi alike having logical breakdowns. This led to many of our kind being caught … and upon discovery of the prosthetics, the idea spread to their own kind.” Pinkie pauses for a moment. “So how do I know all of this is the truth? The way you spoke in Utopia sounded weird, like you were trying to lie.” “I was,” Sunbolt admits, “but the truth is that we earth ponies have no predilection for lying. We just don’t care. Normally, we would be as honest as possible; however, when trying to fit in, we attempted to mimic the customs of the forest towns … but not always successfully.” Before the conversation can continue, Sunbolt and his group eye the top of a skyline of a town down the dirt path. “Good, we’re almost there.” Sunbolt turns to Pinkie. “We have special plans for you, my dear.” “A-D-E-H-P.” Zodiac keeps repeating the five-letter string to himself over and over, shaking his head all the while. Eventually, Twilight asks her companion how he’s feeling. “I’m sorry, I just didn’t expect … and all while walking along this path, not in a study or anything. Truly, you have a dazzling intellect. You may be the Princess of Friendship, but you could just as easily be the Queen of Logic.” “You embarrass me with your comments, but I appreciate the sentiment all the same.” “I must know how you were able to deduce all those cases. Especially the last three; I thought those to be most perplexing.” Twilight, taking pride in her ability, is more than happy to share. “Well, let’s start with the first case. By your own stipulation, it isn’t possible for both ponies to come from the same town; one must come from Elysium, and the other from either Utopia or Paradise. That means that A lied and B told the truth; since one must be the earth pony, it could only be A. Also, B must come from Utopia.” “With the second case, either both ponies lied or both told the truth … but again, your given conditions imply that at least one of them lied. Therefore, they both lied and neither came from Utopia. Now if D actually was a pegasus, she would have to come from Paradise, but that would make her a truth-teller. The only remaining possibility is that D is the earth pony, while C comes from Paradise.” “The cases do get more interesting with three ponies. In the third case, let’s consider what E said. If E was truthful, then F and G are liars; if E lied, then F and G must in fact be truth-tellers. But this means that either E or G was truthful, and so either unicorn E comes from Utopia or pegasus G comes from Paradise … but that’s exactly what F stated. Therefore F is truthful, and so is G. Since E is the only liar, she must be the earth pony. Also, F comes from Utopia and G comes from Paradise.” “Moving to the fourth case: if H was truthful, then none of them came from Utopia; in particular, H doesn’t come from Utopia … but this would force H to be a liar, regardless of whether she was from Paradise or Elysium. Therefore H lied, and at least one of the others does come from Utopia and is truthful. Could it be J? No, because he stated that he was the earth pony; by your conditions, earth ponies only come from Elysium. That must mean that K comes from Utopia. Meanwhile, J cannot be the earth pony; none would admit to such, as that would be truthful. Hence, H must be the earth pony, and J must come from Paradise.” “The fifth case is the most intriguing of all. Consider P’s statement. If true, then P comes from Paradise and the others must come from Utopia and Elysium in some order. If M came from Utopia and N came from Elysium, then N would be lying when stating that M was not the earth pony … but this would mean that both M and N were earth ponies, contradicting your given conditions. If, instead, M came from Elysium and N came from Utopia, then N would be a unicorn from Utopia, hence would tell the truth … but he stated that M was not the earth pony, so she would be lying; this cannot be either. That means that P could not have been truthful; P is a liar and comes from either Utopia or Elysium, and two ponies must come from the same town. That town cannot be Elysium, since it’s given that there is only one earth pony, so either two come from Utopia or two come from Paradise.” “Suppose two come from Paradise. P cannot be one of them, so P would have to be the earth pony, while M and N come from Paradise. But that would mean M is a pegasus from Paradise, hence truthful, and M stated that N was the earth pony. This cannot be.” “Therefore, two ponies come from Utopia, and one comes from Elysium. Whichever town M comes from, she must be a liar; thus, N is not the earth pony. This forces N to come from Utopia, and since N really is a unicorn, she must be truthful; thus, M is not an earth pony either. That only leaves P as the earth pony, with the others coming from Utopia.” “Remarkable,” Zodiac admits. “You even figured out the home towns of all other ponies involved. You really are somepony special!” Twilight smiles … but quickly shakes off her feelings of pride and elation, remembering both Zodiac’s previous comments about the treatment of the earth ponies and the reason they continue to walk towards Elysium. “I appreciate logic puzzles as much as the next pony, but that still doesn’t excuse the actions you’ve described to me. Excluding anypony is wrong, and I would think you already know that.” “Our towns were collapsing into mental chaos. What would you have had us do, Princess of Friendship?” Zodiac’s sarcastic emphasis on Twilight’s title did little to ease the renewed tension. “Exactly! It’s all about friendship! Whatever issues the earth ponies were causing you could have been resolved in a fairer and more equitable way.” Zodiac sighs. “I couldn’t expect you to truly understand our plight. You weren’t here during the darker days. You’d have a different perspective if you did. But please: we’ll have more success retrieving your friend if we’re on the same side. And look; we’re almost there!” Twilight notices the upcoming landscape, with yet another village on the horizon. “So what do you think this town has planned for Pinkie Pie?” “I honestly cannot say. I doubt anything untoward; she is a fellow earth pony, after all. Perhaps they want to hold her as leverage for some sort of deal.” “Well whatever the reason, I hope Pinkie is OK … sweet Celestia!” Upon entering the village, Zodiac and Twilight are struck by the sight of numerous ponies … mostly earth ponies, but many unicorns and pegasi can be seen among the group … all kneeling and bowing their heads in reverence. In the center of the town, a lone alicorn stands majestically while grinning from ear to ear. A yellow unicorn … Sunbolt … walks up to the twosome. “Knew you’d come, and just in time for our coronation.” “What coronation?” Zodiac asks. “The coronation of Alicorn Pinkie Pie, Princess of Irrationality!” The Pebble Paradox and the Rainbow Seven“Alicorn Pinkie Pie??? Princess of Irrationality? Pinkie, what’s going on here?” Pinkie bounds over to Twilight, as the masses remain bowed with their eyes closed. “Isn’t this super? I love these wings, they look soooo great on me. Yeah, I know I can’t actually fly with them, but I just love the idea of flying, it really feeds the imagination, doesn’t it. And the horn! If I could use magic, the things I could do! Imagine me being able to teleport at will! So much to go on about with all this, but …” Twilight pays little mind to her friend’s ramblings as she inspects the artisanship of Pinkie’s newfound accessories. Had she not known Pinkie Pie for so long, she would swear she was looking at a hyperactive alicorn. “Remarkable …” “… but then I said ‘I’m off oatmeal for a while’, and … Twilight?” Twilight shakes her head and refocuses on the present. “Sorry Pinkie. And you’re right; those wings and that horn are incredibly realistic. But why?” “Maybe they got a touring theater group that needs attention to detail to their costumes,” Pinkie suggests. “Not that, Pinkie. Why is this town bestowing these wings and this horn on you?” “All in the name of unity, my dear princess,” replies Sunbolt. Twilight turns to the faux-unicorn, and then realizes that they’ve met. “I remember you now! You’re that unicorn we met when we first got to Utopia.” “Unicorn nothing: that’s Sunbolt, leader of the Elysium movement, and an earth pony through and through!” “Ah, Zodiac. A pleasure to run into you again, no doubt.” “To what end are you using this earth pony?” Zodiac angrily asks. Sunbolt answers in kind. “Utopia and Paradise saw fit to steal our idea of prosthetics, so it’s only logical that Elysium would do the same for the concept of alicorns. Your towns have spurned our advances for far too long, Zodiac. Rejected our kind. Forced us to fend for ourselves from the beginning. Well good luck figuring out which alicorns are earth ponies … oh that’s right, you don’t believe in luck. Just ‘reasoning’ and ‘rational thought’, right?” “The Alicorn Society has done what’s needed to be done. We wish no ill will on anypony.” “Exclusionary practices are ill will, Zodiac!” “The mental breakdowns the earth ponies have caused in our towns are serious, Sunbolt.” Twilight’s neck strains from the back-and-forth between the two ponies, as each volleys accusations at the other. “STOP THIS!!!”, she finally interrupts; Zodiac and Sunbolt briefly turn to the true alicorn in response. Twilight then addresses Zodiac. “I can understand your concern, having experienced a breakdown first-hoof, but this idea of excluding earth ponies from your towns has got to end. Everypony should be allowed to reside wherever they wish, and your towns will be richer for their presence.” As Zodiac processes Twilight’s plea, she turns to Sunbolt. “And while I agree that Utopia and Paradise should be open to earth ponies, I understand why this process needs to be gradual, so the townsfolk can adapt to the new ways.” Twilight’s next words are aimed at both: “As much as I’ve enjoyed the puzzles I’ve had to solve since coming here, such puzzles belong in texts and not reality. Now I urge you both, not as the Princess of Friendship but as a simple friend, to find common ground and begin the process of integrating all ponies to all towns.” A brief pause ensues, before Sunbolt responds: “If you’re insinuating that Elysium has held the same exclusionary practices as the forest towns, look around.” Twilight scans the town, and notices that a number of ponies that had been bowing have horns, while others have wings. “I can’t tell if they’re really unicorns and pegasi or not. I would have thought otherwise before coming here, but now?” “Exactly,” Zodiac retorts. “All the confusion that’s resulted from the appearance of these earth ponies in wing-and-horn clothing has made a mess of things for a long time now.” “Well, just wait until Pinkie and a horde of alicorns come to your twin-towns and mingle with the residents.” “Ooo, are we going back to Utopia?” Pinkie excitedly asks. “Or maybe Paradise! I haven’t been to Paradise yet! Sounds like fun!” “Pinkie Pie,” Zodiac begs, “do not enter the twin-towns as an alicorn. The resulting logic bombs would be cataclysmic.” “Gee, I don’t want to hurt anypony. Well, I can’t wait to show these off in Ponyville. What do you think Rarity will think of these? I think she’ll be utterly amazed!” “I’m afraid you misunderstand, Pinkie Pie,” Sunbolt corrects. “Your place is here now, in Elysium to raise the spirits of the earth ponies here. You can’t return home.” Sunbolt’s declaration enrages Twilight. “You can’t keep my friend here against her will! I won’t allow it!” “Yeah, I mean I love the wings, and the horn, and this is really a cool place to visit, but I don’t wanna leave my life and all my friends behind.” “I thought you would both feel this way,” Sunbolt cooly replies to Pinkie, “so how about a little wager. Win, and I will let you go, wings, horn, and all. Lose, and you promise to stay here. Would you be willing to swear by the results of this wager?” “We’re not going to play some game for my friend’s freedom!” Twilight flatly states. Zodiac brushes Twilight aside and confronts Sunbolt himself. “It’s not rational for one to risk something so dear on a mere gamble.” “Oh, but that’s just it. It’s not really a gamble. Think of it more as a test, where you have a two-in-three chance of succeeding.” Twilight eyes Zodiac suspiciously as he continues the conversation. “I suppose it won’t hurt to at least see what you have in mind.” “Not at all,” Sunbolt replies. “Follow me.” Sunbolt leads Zodiac, Twilight, and Pinkie to a large structure at the far end of the town. Twilight notes the combination of municipal and residential amenities while walking inside; she reasons that this must be where Sunbolt both lives and conducts his strategic planning. After traversing numerous hallways, the group is led to a spacious, empty room that contains only three boxes of similar size and shape resting on a table. The boxes have the numbers ‘1’, ‘2’, and ‘3’ inscribed on them. Sunbolt explains: “One of these boxes contains but a simple pebble, to represent the simplicity of earth ponies; the other two boxes are empty. Pick one box: if it is empty, Pinkie is free to go. But if you should pick the box with the pebble, she remains with us.” Zodiac inspects the table and notices stone tablets in front of each box. Messages are etched into the tablet; he studies these messages while Twilight again protests about the notion of keeping Pinkie in this town against her will. Suddenly … “We accept your offer.” Twilight suddenly turns to Zodiac, her face now the color of Pinkie’s mane. “Zodiac!!! You have no right to accept this proposition!” “You have to trust me on this,” Zodiac icily replies. He then turns to Pinkie. “Promise Sunbolt that you will abide by the results of this ‘wager’.” “Okie-dokie!” Pinkie cheerfully replies. “I Pinkie-promise!” “What??? Pinkie, no!” “Why not? Zodiac seems sure of something, so why not give him a chance?” “But Pinkie, if he’s wrong then you’re trapped here!” Sunbolt interrupts Twilight’s back-and-forth with Pinkie: “It does not matter now; Pinkie has accepted Zodiac’s offer. Now choose.” Resigning herself to Zodiac’s decision, Twilight inspects the messages etched into the tablets. In front of box 1 is the message “This box is empty.” In front of box 2 is the message “Box 3 contains the pebble.” In front of box 3 is the message “The messages in front of at least two of these boxes are false.” “I apologize for making you so angry, Twilight,” Zodiac states, “but you have nothing to fear. It is obvious which box I should pick.” “Oh please, explain your reasoning,” Sunbolt urges the faux-alicorn. “It’s all so simple. The message in front of box 3 is either true or false. If it’s true, then the messages in front of boxes 1 and 2 are false. In particular, box 1 is not empty. So there’s a chance the pebble is in that box.” “Go on …” “Meanwhile, if the message in front of box 3 is false, then it is not the case that at least two messages are false. That forces the messages in front of boxes 1 and 2 to be true. In particular, box 3 would have to contain the pebble.” Zodiac fails to see the slight, mischievous grin on Sunbolt’s face as he concludes: “That means that either box 1 or box 3 contains the pebble; it cannot possibly be in box 2. Thus, Sunbolt, I choose the middle box!” Triumphant in his demeanor, Zodiac magically opens the middle box and looks inside. The smile on his face quickly turns to a gasp as his pupils shrink to pinpricks. “No … that can’t be …” Moments later, he collapses to the ground. Twilight and Pinkie peer into the middle box, which contains a small stone lying atop a pillow. Sunbolt then opens the other two boxes, revealing each to be empty. “A deal’s a deal,” she declares, “Alicorn Pinkie is here to stay. And now I must prepare for the upcoming visit to the twin-towns. If you’ll excuse me …” Sunbolt then departs the room, leaving the two Ponyville residents alone. “Pinkie, let’s just get out of this town and reconvene back at the balloon. I can teleport us out of here if necessary; they won’t be able to stop us.” “But we still haven’t solved their friendship problem,” Pinkie notes. “I’m not saying we abandon our quest; I just think we need time to process everything that’s happened.” “I can’t leave here,” Pinkie states, tears emanating from her eyes. “I made a Pinkie-promise, Twilight! You of all ponies know I can’t break a Pinkie-promise!” “But Pinkie—“ “I’m staying,” Pinkie declares while fighting back further tears. “It’s my own doing, and I need to accept the consequences. Sometimes … sometimes I get caught up in the moment. Zodiac just seemed so certain of himself, and I really like these wings. I guess I got a little greedy. I should have just declined Sunbolt’s offer. I’m sorry, Twilight.” Pinkie turns away from Twilight. “Have Spike take care of Gummy for me. They’re both reptiles; they’re practically cousins. And give my regards to the others … maybe they can visit from time to time.” “No! I will not accept this!” Twilight is adamant in her declaration. “I’ll talk to Sunbolt; you wait here until Zodiac comes to; maybe you can figure out why he blacked out. But when all is completed here, we’re returning to Ponyville together! That’s a Twilight-promise!” Twilight gallops away from the room, leaving Pinkie to inspect the tablets and wait for Zodiac.” “Absolutely out of the question!” “Please!” Twilight begs of Sunbolt. “You cannot force my friend to leave behind her whole life just to satisfy your ponial desires. It’s not right, and deep down inside, I know you know that.” Sunbolt looks Twilight in the eyes. “This isn’t about me, Princess Twilight. This is about every earth pony whose ever been turned away by a unicorn or pegasus simply because she lacks special features. But I wouldn’t expect a true alicorn to understand that.” “There must be another solution,” Twilight continues to plead. “What if … what if you made another wager. How about ‘double-or-nothing’?” Sunbolt pauses. “Exactly what are you wagering?” “My own freedom. If I lose, I promise to remain in Elysium and follow your leadership. But if I win, you annul the Pinkie-promise and allow us to return home.” “Interesting,” Sunbolt mulls to himself. “An opportunity to have a true alicorn join our fight … all right, Princess Twilight: you have yourself a deal. And I know the perfect wager for you. Head back to the room with the three boxes, and I will meet you shortly.” “ ‘Annul’? What does that mean?” “It means the Pinkie-promise would never have technically taken place. It would be as if it never happened.” “So it would be like we went back in time?” “Well, not exactly … but I think you get the idea.” Pinkie, her eyes still moist from before, hugs Twilight as more tears flow. “Oh, thankyouthankyouthankyou!!! I knew you’d figure out a way to save me.” “Don’t thank me yet, Pinkie. I still don’t know what Sunbolt has planned for—“ The two hear hoofsteps from the hallway. Soon after, Sunbolt appears … followed by a group of ponies that cause both Twilight and Pinkie to gape in astonishment. Seven ponies enter the room, each of which is monochrome from mane to body to tail. Lined up, they appear to make up a rainbow. And, each appears to be an alicorn. “I meant for Zodiac or another one of those ‘Alicorn Society’ ponies to take this challenge, but I cannot ignore the possibility of gaining the services of a true alicorn princess.” “Where did you ever find monochrome ponies?” Twilight asks in astonishment. “I’ve never seen anything like this.” “I would have thought that after experiencing alicorns here, you wouldn’t be so surprised,” Sunbolt retorts. “If you must know, this is simply the result of body paint and mane dye.” “Remarkable,” Twilight admits. “You should totally start a theater company, Sunbolt,” Pinkie adds. “In any case,” Sunbolt brusquely states, “let me explain how this challenge will work:” “For purposes of this challenge, the names of these alicorns are Red, Orange, Yellow, Green, Blue, Indigo, and Violet. Now as I’m sure you have figured out by now, these are not alicorns. In fact, six of these fine ponies hail from either Utopia or Paradise … and in fact, two of those six are really earth ponies. Yes, there are earth ponies who come from those towns; they simply hide their true nature well enough to blend in.” “More specifically, three of these ponies come from Utopia: one unicorn, one pegasus, and one earth pony. Three more come from Paradise: again, one unicorn, one pegasus, and one earth pony. The seventh pony is also an earth pony, who comes from Elysium. Each of these ponies will make up to two statements; the only true statements will come from ponies whose type and town of residence start with the same letter. Thus: only the Utopian unicorn, Paradisian pegasus, and Elysian earth pony will be truthful; the other four will make only false statements. And your task, Twilight, is simply to classify all seven ponies. Do that successfully, and you will earn your friend’s freedom. But make any mistake, and you will serve in the ranks of the Elysians.” “I dunno Twilight,” Pinkie remarks. “That seems like a lot of possibilities.” “Five thousand forty, to be exact,” Twilight answers. “But I have to trust my abilities.” “One other thing,” Sunbolt adds. “You have thirty minutes to complete this task.” “What???” “That’s the deal. Take it or leave it!” Twilight gulps, as beads of sweat start to form on her forehead. Shaking off her apprehension, Twilight answers Sunbolt: “I accept.” “Excellent. Now if you’ll be kind enough to levitate Zodiac here to the hallway, Pinkie and I will leave you alone with the Rainbow Seven. You time will begin when the last statement is uttered.” Using her magic, Twilight lifts the faux-unicorn and moves him to the hallway before gently placing him back on the ground. Sunbolt and Pinkie then exit the room, leaving Twilight with the seven monochrome faux-alicorns. Red makes one statement: “I’m a Utopian pegasus.” Orange makes two statements: “I’m a Paradisian pegasus. Blue and I come from the same town.” Yellow makes two statements: “I am not from Elysium. Indigo and Violet are the same pony type.” Green makes two statements: “I am from Elysium. Orange is not telling the truth.” Blue makes two statements: “I am a unicorn. I come from Utopia.” Indigo makes two statements: “I come from Paradise. Violet comes from Paradise, too.” Twilight waits for Violet to speak, but Violet just gazes at a wall and says nothing. After five minutes, Twilight leaves the room and addresses Sunbolt: “Is something wrong with Violet?” “Nothing is wrong with Violet … and you have twenty-five minutes left.” “WHAT???” “I never said that they would all make statements,” Sunbolt states, unable to hide a grin. “Twenty-four minutes left.” Angry at the ruse, Twilight runs back into the room and slams the door behind her. “That wasn’t very nice, Sunbolt!” “I would think you would appreciate that, Pinkie. But, I suppose I should not be surprised. After all: in just over twenty minutes, you and your alicorn princess friend will help me end the strife that my fellow earth ponies have suffered for far too long.” Pinkie looks to the motionless Zodiac, then back to the door to the room. Brain, don’t fail Twilight now … Author's Note The solution to the 'Rainbow Seven' puzzle will be revealed in the next, and final, chapter ... but if anyone wishes to know the solution before then, feel free to PM me. I kindly ask that no one posts the solution in the comments, though. One HugZodiac slowly comes to, groggy as he gets his bearings. He looks down the hallway he finds himself in, then notices Pinkie Pie, still wearing her custom-made wings and horn, staring back at him. “Rise and shine, sleepy-head! Feeling better?” Zodiac feels at his forehead. “Wha … what happened? Where’s Sunbolt?” “You collapsed after opening a box containing a pebble, and Sunbolt left about ten minutes ago to prepare for my leading a group of alicorn-looking earth ponies to Paradise and Utopia.” “What???” The news snaps Zodiac back to reality. “So I failed the test? But that’s impossible!” “It was unfortunate,” Pinkie corrects, “but wouldn’t ‘impossible’ mean ‘not possible’?” “But my reasoning … my reasoning was flawless. For the pebble to be in that middle box, that just makes no sense.” “It’s just a pebble. Physically, it could have been in any box. Why were you so sure?” “Because of the tablets, Pinkie! I remember quite clearly what the messages on those tablets said: Box 1’s tablet read ‘This box is empty,’ Box 2’s tablet read ‘Box 3 contains the pebble,’ and Box 3’s tablet read ‘The messages in front of at least two of these boxes are false.’ It should not have been possible for the pebble to be in Box 2.” “Why not?” Pinkie innocently asks. “With the pebble in Box 2,” Zodiac explains, “Box 1’s tablet is true since that box was empty. At the same time, Box 2’s tablet is false since Box 3 didn’t contain the pebble. But then Box 3’s tablet made no sense!” “Why not?” Pinkie innocently repeats. “Because that message has to be true or false. If true, then at least two messages are false … but only one is false: the one for Box 2. If false, then at most one message is false … but now two messages are false: the ones for Box 2 and 3. So again, the message makes no sense!” Pinkie ponders Zodiac’s argument for a minute. “Did Sunbolt state that the messages had anything to do with the location of the pebble?” “Well … uh …” Zodiac eventually stumbles to a ‘no’ response. “And why did you assume that that last message was either true or false? Couldn’t it be neither? I mean, I know that the statement ‘I hate baked goods’ is false, and I know that the statement ‘I love Gummy’ is true, but what about the statement ‘This statement is false’?” “Well,” Zodiac starts, “if true, then it’s false. If false, then it’s true. So that statement makes no sense, either.” “And yet here I am, telling it to you. They’re just words, right. Words formed from letters, like the one I was going to write to Princess Celestia while I was in Utopia. But why do you assume that every statement ever made is either true or false?” “I …” Zodiac goes quiet for several minutes. He then suddenly erupts: “SUNBOLT TRICKED ME!” “More like you tricked you.” “Pinkie Pie, I … I am so sorry that I got you into this mess. If you can ever forgive me …” “Well of course I forgive you. Now how ‘bout a hug?” Before Zodiac can satisfy Pinkie’s request, Sunbolt appears from a passage and approaches the two. “It is time. Where is Twilight?” “She’s still inside,” Pinkie replies. “Then she has lost her wager,” Sunbolt cheerfully concludes. He opens the door to the room, and notices that Violet now stands in its center, alone. He also notices Yellow, Green, and Indigo standing in one group to the left, and Red, Orange, and Blue standing in another group to the right. Twilight sees Sunbolt, Pinkie, and Zodiac enter the room and addresses Sunbolt. “I got them grouped by place of residence. If you prefer, I could have Red and Yellow paired off as the unicorns, Orange and Green paired off as the pegasi, and the others grouped as the earth ponies. but either way, a deal is a deal.” “You know, Twilight, Filthy Rich could make a lot of bits by selling smelling salts to these towns. Are there any ponies here that don’t pass out?” “I suppose Sunbolt learned what I did while coming here,” Zodiac remarks. “Don’t underestimate Twilight’s incredible sense of logical reasoning.” “I must admit, I got caught up by Violet not saying anything. But once I settled down, I realized that I had all the information I needed.” “We seem to have some time while Sunbolt comes to. Please, Twilight, you must share your reasoning with me. The way you explained this task, I have to know how you figured everything out.” Twilight smiles as she speaks. “OK, but hopefully this is the last time I do this for a while!” “The key was starting with Yellow’s first statement: ‘I am not from Elysium.’ If that was false, then Yellow would be from Elysium … but the only pony from Elysium was a truth-telling earth pony. That meant that Yellow spoke the truth, so her other statement, ‘Indigo and Violet are the same pony type,’ must also be true. From there, I focused on Indigo’s two statements.” “Suppose Indigo was truthful. Then she would come from Paradise, and that would force her to be a pegasus. That, in turn, would force Violet to be a pegasus too, since they must be the same pony type. Also, Violet would be from Paradise, as Indigo stated as much. But that would mean there were two Paradisian pegasi, and that contradicts the stipulations of the wager. Therefore, Indigo was lying about both statements: neither she nor Violet was really from Paradise. And since they are the same pony type, they cannot also come from the same town; one must come from Utopia, and the other must come from Elysium … but only one pony really does come from Elysium, and that one is an earth pony who speaks the truth. Since Indigo lies, it must be Violet who is the Elysian earth pony. That, in turn, forces Indigo to be the Utopian earth pony.” “Now I can look at Green’s first statement, ‘I am from Elysium.’ As Violet has been shown to be the one Elysian, Green must be lying; that makes his other statement, ‘Orange is not telling the truth,’ a lie as well. That means that Orange is truthful … and since there are only three truthful ponies, namely, the Utopian unicorn, the Paradisian pegasus, and the Elysian earth pony, it follows that Orange, Yellow, and Violet are the only truth-tellers; the others are all liars.” “Since Orange is truthful, she really is as she claims: she is the Paradisian pegasus, which forces Yellow to be the Utopian unicorn. That just leaves Red, Green, and Blue to be, in some order, the Utopian pegasus, the Paradisian unicorn, and the Paradisian earth pony.” “Blue made two separate statements that must each be false, so Blue is not a unicorn and does not come from Utopia. The only possibility is that she is really the Paradisian earth pony. And since Green lied, she and Blue come from different towns; Green cannot be the Paradisian unicorn, so she can only be the Utopian pegasus. And that leaves Red to be the Paradisian unicorn.” Zodiac, mesmerized by the solution Twilight meticulously presented, smiles broadly. “I have run out of superlatives for you, Princess of Friendship. You really are one-of-a-kind. Well done!” He then turns to Pinkie. “You would do well to learn from one as wise as her. You might offer much in terms of exuberance and enthusiasm, but a little rational thought would serve you well.” Twilight, insulted at the comment, starts to speak … but Pinkie stops her. “You’re probably right, Zodiac. It’s just who I am, I guess. But hey, you still owe me a hug, right?” “I suppose I do,” Zodiac replies, and starts to wrap his forehoofs around his fellow faux-alicorn … but Pinkie stops him, much to Twilight’s surprise. “You’re all about ‘true’ and ‘false’, right? Well I got one more proposition to make to you.” “Proposition?” Zodiac looks at Pinkie quizzically. “What sort of proposition.” “Allow me to make one statement to you. If I make a true statement, then you give me a hug. If I make a false statement, then you don’t give me a hug. Deal?” “Pinkie,” Twilight asks, “what are you doing?” Pinkie turns to Twilight. “I like to have fun; it’s who I am. You know that, Twilight!” Twilight notices a glint in Pinkie’s eyes, then shrugs and turns back to Sunbolt, who begins to come around. Pinkie turns back to Zodiac. “So, we got a deal?” “I see no harm in that,” Zodiac replies. “So make your statement. Something like ‘I like hugs’, no doubt.” “Let’s leave the room for a minute, so Twilight can talk to Sunbolt.” Pinkie walks out of the room, with Zodiac following behind. Twilight shakes her head, then turns to Sunbolt. “Are you OK?” “I’m fine,” Sunbolt dejectedly replies. “I guess I should have known better than to challenge your intellect. I just wish I could bring my fellow earth ponies to the forest towns.” “You have my word, Sunbolt, that Pinkie and I will not rest until we have fixed this friendship problem.” “I thank you for all you and your friend are trying, but it seems hopeless. Nothing can get ponies like Zodiac to come around to our way of thinking … what’s going on with your cutie mark?” Twilight checks her flank, and is stunned to see the glowing icons which normally indicate that a friendship problem has been resolved. “WHAT??? I … I don’t understand. We’ve solved nothing yet. What’s going on with my cutie mark?” Pinkie Pie pronks back into the room, her smile stretched from ear to ear and her cutie mark emitting the same glowing pattern as Twilight’s. Zodiac follows her inside and approaches Sunbolt. “On behalf of the Alicorn Society, and on behalf of all the residents of the twin-towns, I cordially invite you and all your fellow earth ponies to come to our fair forest towns.” The statement nearly causes Sunbolt to pass out again, but he keeps his composure. “Wait … are you serious? Just like that? I don’t understand.” “We can discuss details on the way back to Utopia. You should speak to Cloudstitch.” The two leave the room, followed by the Rainbow Seven. “Pinkie Pie, what’s going on? What did you say to Zodiac?” “Not much. I just made him an offer he couldn’t refuse.” Twilight takes a final look towards the forest, then back down the road leading to Elysium, before turning back to face Cloudstitch and Sunbolt. “I thank you both again for seeing us off. It’s a shame that Zodiac was too busy to do the same.” “He, Spiral, and the rest of the Alicorn Society have much to prepare for, with the upcoming meshing of pony types throughout both the forest towns and Elysium,” Cloudstitch soothing replies. “But they are all eager to put the past behind and start fresh, with everypony involved in the healing process this time.” “What you and Pinkie Pie were able to accomplish, the earth ponies of this area cannot thank you enough for,” Sunbolt adds. “And thanks again for the wings!” Pinkie interjects. “Too bad I never got to meet the pony who actually created them.” “What makes you think you haven’t?” Sunbolt asks with a sly grin. Twilight and Pinkie gape at the news. “You created those wings, Sunbolt? The horn, too? Wow … leader of the earth pony movement AND a master seamstress.” “What can I say, Twilight. I learned from the best … didn’t I, mom?” “MOM!!!???” Twilight and Pinkie exclaim in unison. “Indeed,” Cloudstitch admits, “though it has been so many moons since I adorned myself as such, I don’t know if I could remove them by now. They really have become a part of me, no matter the lack of function.” “So you really are an earth pony,” Pinkie restates, still shocked from the revelation. “Yes. I and the other earth ponies were shunned by the unicorns and pegasi and forced to begin anew, far from the forest. I bore no ill will; the fact is, many earth ponies preferred it that way. But I knew in my heart that all pony types were meant to mingle with one another, to bring out the best in all.” “But I don’t get it,” Twilight states. “How did you ever get the ponies of Utopia and Paradise to accept you as one of their own?” “It wasn’t easy,” Cloudstitch replies. “I knew myself to be an excellent seamstress and craftspony, but in my first visit to the twin-towns, I was unprepared for the level of sophistication that their reasoning had evolved to.” “And that first trip,” Twilight asked, “you clothed yourself as a pegasus?” “Indeed … but I made the mistake of heading to Utopia first. Merely speaking the truth betrayed my true nature, and I was cast out. I had to start over, but not before building a better foundation for my logic abilities. I vowed to never be found out again.” “When I felt I was ready, I headed to Paradise … but this time, I created wings AND a horn. I spoke little this time, letting them ask me about my true nature. And I was able to convince the townsfolk that I was either a unicorn or pegasus, but that my true nature be kept hidden, for the good of a town that still had infighting. Once I felt that I was accepted, I founded the Alicorn Society; my hope was that if all ponies looked the same from the outside, all would be treated fairly on the inside.” Sunbolt’s expression darkens. “But that didn’t work out as you intended, did it?” “I think all the ponies initiated into the Society had the best of intentions … but there were some who thought that the mission was to help only unicorns and pegasi mend their differences, and not earth ponies. Zodiac was probably the greatest exponent of this belief; I tried to convince him in private to be more open-minded, but I dared not reveal my true nature to him or anypony else, for fear of being cast out yet again. No, I thought it best to bide my time, and hope that he and the others would come around.” “But patience was never one of my virtues,” Sunbolt interjects. “I remember the first time my mother was forced to return. I could see the disappointment in her eyes, in her walk, in the way she carried herself. And I remember when she left the second time, adorned as you see now … and I didn’t hear from her again. I had to know what had become of her, so I created my own set of wings.” “Wings? But you have a horn now.” “I have both, Twilight. I tended to use wings in Paradise and the horn in Utopia, mostly so I would not be so easily recognized by those who frequented both forest towns. And I brought fellow earth ponies with me on these trips, trying to piece together what happened to my mom. And to this day, I never knew that she had risen to such a position within their ranks.” Sunbolt turns to Cloudstitch, a fresh tear forming. “I missed you, mom.” Cloudstitch hugs her son tightly. “I’m sorry I’ve been away for so long. You know I had the best of intentions, for us and for all of pony kind.” She tilts her head to Twilight and Pinkie. “Once again, we cannot thank you enough for all you’ve done.” “Just glad that we could help,” Twilight replies. “And thanks again for the wings and horn, Sunbolt!” “You’ve earned them, Pinkie Pie,” Sunbolt replies. “I’d like to think I do good work. Almost as good as you, mom.” “Almost nothing,” Cloudstitch retorts. “Ever since I gave you your first bolt of cloth to work on, I knew you inherited your mother’s special talent.” “Well, we need to head back to Ponyville while the sun still shines. I hope to visit your towns again someday … and maybe have more on my mind than logic puzzles.” The four share one final laugh and group hug, before Twilight and Pinkie climb into the balloon and sail back home … “I see a sheep down below. It’s got black wool … or at least it does on the top. Hey Twilight, you think it’s possible for a sheep to have black wool on top and white wool underneath?” “Uh … that would be new to me, Pinkie. But I suppose anything’s possible.” “And all the trees … all I see from up here is green. Maybe one of those trees is green all over. Green trunk, green branches … or what about red? A red tree with green leaves? Wouldn’t that be perfect for Hearthswarming?” Twilight chuckles to herself at Pinkie’s usual silliness. A thought then occurs to her. “Pinkie, you never did tell me what you said to Zodiac after my last test. Whatever you said, it sure must have been persuasive.” “Not really. He just agreed to give me a hug if I told a true statement, and not to give me a hug if I told a false statement.” “Yes, I remember that … but what did you say?” “Simple,” Pinkie replied, “I said ‘If you give me a hug, then you must invite all earth ponies to come and inhabit the twin-towns.’ ” Twilight paused for a moment to ponder Pinkie’s statement. “That’s IT? Zodiac changed his entire belief structure because of that statement?” “Well I don’t know if I got him to change his ponial beliefs. I just know that he had to invite all the earth ponies to come and inhabit the twin-towns, at least according to his own set of rules.” “I still don’t understand,” Twilight admits. Pinkie proceeds to explain: “Well my statement to Zodiac was either true or false. Suppose it was false. Well the opposite of the conditional statement ‘if A then B’ is ‘A and not B’, so my statement being false would be equivalent to the statement ‘You will give me a hug, but you will not invite the earth ponies’ … but he agreed that he would not give me a hug if my statement was false. That meant that my statement couldn’t be false without Zodiac going back on his word, so my statement had to be true. Now since my statement must be true, he had to give me a hug … and yes, Twilight, he did give me a super-squeezy hug! Well, now he had to invite the earth ponies; if he didn’t, he would make my statement false, but he already gave me a hug, proving that my statement must be true. Next thing I know, our cutie marks flash to show a job well done.” Twilight’s head starts to spin as she attempts to process the explanation. “Pinkie …” “Basically, ‘A’ and ‘If A then B’ implies ‘B’ … and here, ‘A’ is that I get a hug, and ‘B’ is that the earth ponies are invited.” “Pinkie,” Twilight continues, “how did you know all that?” “Well, logic was part of my schooling as a filly back on the rock farm. When the time came for testing, I was told that I had a pony intelligence quotient of 217.” “You have a pony IQ of 217??? Pinkie Pie, that’s higher than mine! You really are a genius!” “Well, I don’t like to talk about that. It’s just a number, after all; it doesn’t define who I am. And all that logic and reasoning is just boring and a lot of work to me. Now, applying that knowledge … like knowing the perfect mixture of ingredients for a cake batter mix, or the precise temperature and timing for baking … that’s where I like to show off!” “Wow … I am speechless, Pinkie.” Twilight looks towards to horizon, and sees the skyline of Ponyville in the distance. “Hey, guess where we are!” “Well duh … we’re in a balloon! And I thought you were speechless. Oh, what do you think Rarity will say when she sees me? Or Rainbow Dash? Do you think they’ll think I’m an alicorn? Hey ‘corn’ is in ‘alicorn’ … but it’s also in ‘unicorn’ How come ‘alicorn’ doesn’t use any part of ‘pegasus’? Maybe the term should have been ‘pegacorn’. Or maybe ‘unisus’. But what would the plural of ‘unisus’ be? ‘Unisuses’? That’s a lot of esses at the end, isn’t it. I like the letter ess. It’s so fun, with its curvy nature, and it turns a friend into friends. I like friends better than friend; more to enjoy, and …” Author's Note NOTE: If this story ever gets to at least 20 positive thumbs, I shall post a sequel to this story.
Utopia and ParadiseThe doors to the throne room burst open as Pinkie Pie barges in. “Sorry I’m late! I got here as fast as I could … well, maybe not the fastest fast, but everypony kept saying ‘Hi Pinkie’ and ‘Where you off to, Pinkie?’, and I couldn’t just ignore them, so I kept greeting them back with ‘Hi there Carrot Top’ and ‘I’m off to the Castle of Friendship, Lyra’, and before you know it …” Pinkie’s runaway chatter is interrupted by the sight of her alicorn friend staring at a section of the Cutie Map with their two cutie marks hovering above it. Her front hooves are propped on the table as she fixates on an area in southwestern Equestria. Pinkie walks over to Twilight and eyes the map. “Oooo, is that where we’re heading? Looks like a far cry from Griffonstone, and nowhere near Canterlot. Does the train run there? Do we need to take the balloon? Oh, it’s been like forever since I’ve been in the balloon!” Twilight remains silent as she continues to stare at a pair of dots surrounded by forest on the map, still lost in thought. “You know, conversations are funny this way, but usually they involve more than one pony, ‘cause otherwise one pony just dominates all the discussion and … uh … … Twilight?” Blinking, Twilight finally realizes that she’s not alone in the room. She takes her forehooves off the table and turns to Pinkie. “Sorry, Pinkie Pie. It’s just that … I feel like I recognize these towns. I know I’ve seen them before; I just can’t remember where.” Pinkie takes another look at the map. “What’s to recognize? They’re dots.” “I know, but there’s something about this location that’s haunting me. I’m sure I’ve seen this area before, but I’ve gone through all my maps, atlases, and geographic texts, and I can’t find anything resembling this. You’d think I’d recognize something as distinct as two cities surrounded by forest, but …” Twilight turns back to the map, hoping for a moment of inspiration. “You’re thinking too hard about this, Twilight. Let’s just go and see where this adventure takes us!” Pinkie starts bouncing in place, rife with anticipation. “Pinkie, you know how I like to be prepared for callings like this,” Twilight states without turning, still focusing on the map. “Yeah, I know; Fluttershy told me all about your trip to the Hooffields and McColts. How ‘bout this time, we just go and be surprised by what we find? It’ll be more fun that way.” Twilight turns to Pinkie, a slight undertone of frustration in her voice. “Look, I appreciate your care-free attitude towards life. It’s who you are, and I’ve learned not to seek explanation. But I’m just not like that. I need order and reason in my world. I live for the cold truth that logic brings and …” Twilight suddenly stops mid-sentence and ponders. “Wait a minute. It couldn’t be.” Before Pinkie can ask what it is that could not be, Twilight bolts from the room; she returns minutes later with a dusty text. Quickly scanning through the tome, Twilight soon comes to a page with a map of two towns surrounded by forest. Her eyes dilate with the realization: “I don’t believe it … the twin towns of Utopia and Paradise are real!” Pinkie looks over Twilights forehoof to inspect the pages. “Utopia and Paradise? I never heard of those towns. They sound nice, though.” Twilight suddenly turns to Pinkie with wide eyes and a broad grin. “Do you know what this means! A friendship problem that can be solved with logic puzzles!” She proceeds to bounce around the room, mimicking Pinkie’s usual method of pronking about Ponyville. “Well you seem more chipper now,” Pinkie observes. “What do you mean by using ‘logic puzzles’ to solve a friendship problem? What’s so special about these towns?” “We’ll take the balloon to get there; I’ll explain on the way. You grab the food, while I grab some quills and parchment. Oh, I can’t wait to get started on this!” Twilight rushes out of the throne room, as Pinkie looks on with curiosity and slight apprehension. From her vantage point high above the grassy plains, Twilight gazes towards their destination upon the horizon. “We’re making great timing. We should be there in another 30 minutes.” A munching sound causes Twilight to turn back; Pinkie’s mouth is filled with hay sandwich, which she hurriedly gulps down. “Pinkie, did you eat the last of our balloon provisions?” “Well, I was in a hurry to get out the door this morning, so I didn’t have time for more than two bowls of oatmeal, a couple blueberry muffins, six carrots, a daisy, and two-thirds of a cake. Say that reminds me, I need to cut down on my daisy intake.” Twilight rolls her eyes before turning back towards the horizon. “Well I’m too excited to eat anyway. I still can’t believe the twin towns of Utopia and Paradise really exist. I wonder if the tales from my logic book are true.” “So what’s so special about these towns, Twilight? Nopony I know has ever mentioned them, and I know a lot of ponies.” Twilight turns back to Pinkie and explains. “Among the courses I took while studying in Canterlot was a course in logical reasoning, taught by Professor Stallyan. It was one of my favorite classes; it was basically a series of puzzles that tested one’s ability to make sense of given information.” Pinkie could already hear Rainbow Dash’s voice in her head, screaming out “EGGHEAD!”, but simply bid her friend to continue. “One of the chapters focused on the twin towns of Utopia and Paradise. According to the textbook, Utopia and Paradise were settled shortly after the events of the first Hearthswarming, when tensions between unicorns, pegasi, and earth ponies were still high. A faction of unicorns and pegasi attempted to settle a single town deep within a forest, but infighting between the two races led to two towns being formed instead. The unicorns created the town of Utopia, and the Pegasi created the town of Paradise.” “Unicorn Utopia and Pegasus Paradise.” Pinkie recites the alliterative phrase to herself a couple times. “That’s easy enough to remember.” “Anyway,” Twilight continues, “tensions between the two eventually died down, and over time a number of unicorns from Utopia moved to Paradise, while a number of pegasi from Paradise moved to Utopia. In the book, each town has both unicorns and pegasi.” “So all this sounds …” Pinkie pauses before continuing, “I won’t lie to you Twilight, I don’t see where any of this is going.” “Well here’s where it gets weird. According to the story, the unicorns who moved to Paradise still harbored deep feelings for Utopia, and when asked, would state that they were from the town of unicorns even if they were from Paradise. And the same held true for pegasi who resided in Utopia; they would insist that they were from the town founded by pegasi. From there, it became natural for these particular ponies to lie about any statement made in reference to residence. Eventually, it came to pass that every statement from a unicorn from Paradise, or from a pegasus from Utopia, was a lie.” “Every statement? So wait Twilight; does that mean that a unicorn from Paradise would state that grass is red, and maple syrup falls from the sky?” Twilight shrugs. “I guess so.” “Well that should make for interesting conversations!” Pinkie smiles broadly at the notion. Author's Note I have long been a fan of the work of Raymond Smullyan, and this fic is my attempt to merge the myriad of puzzles he has created with the MLP:FIM universe. The reader is encouraged to try to solve the puzzles that appear before reading ahead to the answers that eventually follow.
The Path Through the ForestAs 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. Author's Note Special thanks to 'son_of_heaven176', who caught a number of errors that I have since fixed!
The Alicorn Society“What would you say, Zodiac?” “I would say she suffered a logic bomb. I would say we’ve all had one at some point, and I haven’t seen either her or her pink earth pony friend before.” “So what do you think she is? Unicorn or pegasus?” “I would say I don’t know; in either case, this is some incredible work. I would say even Cloudstitch wouldn’t be able to tell.” “Well what do I do with that earth pony friend of hers waiting outside?” “Show her around. Treat her to breakfast, if you like. I would say I need some time with this one; she could prove to be a valuable addition to our society.” “Understood, sire.” Twilight hears the clip-clop of hooves leaving her room as she rubs her eyes and sits up. She is in her bed in Utopia’s inn, with a charcoal-grey unicorn standing at the room’s entrance … and then she notices his wings … “You’re … an alicorn?” The grey pony promptly responds, “I would say I’m as much an alicorn as you are, miss …” “Twilight Sparkle, Princess of Friendship.” Her use of the word ‘princess’ causes the stranger to look her appearance over a second time. “So, you fancy yourself a true alicorn, eh? I don’t suppose you can prove this claim.” “Well …” Twilight flaps her wings and slowly rises into the air. Her horn emits a low brightness as a pillow levitates up to her. The combination of these mundane tasks catches the stranger off-guard as he stammers in his response. “Whoa, you really are … I mean, my apologies, Your Highness. I, I did not intend to impugn the word of … oh, this is most embarrassing.” “It’s quite all right,” Twilight soothingly replies as she floats back down to the bed and stands eye-to-eye with the stranger. “But, I’m surprised that you’re so surprised. I mean, you’re an alicorn, too … right.” The stranger looks over his forehoof, then walks over to the room’s entrance and closes the door. He turns back to Twilight before responding. “What I am about to show you, I must ask that you never reveal to anypony else. Can you promise me that?” “I can Pinkie-promise if you like,” Twilight happily replies. “I do not know what that means, but I believe I can trust you.” Taking one last look to the closed door, the stranger turns to face Twilight. A glow emanates from his horn, and the wings on his body come off and levitate into the air. Twilight can only gape as the wings hover for many seconds, before returning to their placement on the pony’s body. “So … those wings are fake? I don’t understand; why go around pretending to be an alicorn.” “There is much that I need to explain to you, Princess Twilight Sparkle.” “Just call me Twilight; I’m still not used to the whole ‘princess’ thing.” “Very well,” the grey unicorn responds. “My name is Zodiac, and I am a member of the Alicorn Society.” “The what?” “The Alicorn Society consists of a select group of unicorns and pegasi, from both Utopia and Paradise. Our goal is to maintain the harmony that exists between unicorns and pegasi in these towns, mostly by setting a higher standard of conduct.” Twilight eyes Zodiac quizzically. “I don’t understand. Why would there be a need for policing harmony?” “Based on recent events, I assume you are familiar with the history of the twin towns.” After Twilight nods, Zodiac continues: “Even after the mixing of the two pony types between our fair towns, there resided an air of contempt for pegasi residing in Utopia, and vice versa. There were many arguments, and grudges persisted between neighbors. Then Cloudstitch showed us a better way.” “Who is this ‘Cloudstitch’?” “One of the most logical thinkers in all of Equestria … and an incredible seamstress. She recruited a number of our brightest and most rational, myself included, and brought us to her home. There, she showed off a pair of prosthetic wings … the very wings that you see me wear today. She also displayed a vast array of carefully-designed horns. Both the wings and horns, when attached, were practically indistinguishable from the real thing.” “Her idea was simple: give select unicorns a custom-made pair of wings, and give select pegasi a custom-made horn. Then, have those chosen ponies mingle among the townsfolk in both towns, setting a standard of tolerance and friendliness. Aid those in need, settle disputes calmly and rationally … act like you would like others to act, basically.” “Mostly, though, the reason for the wings and horns was to promote tolerance towards the ‘alicorns’ themselves. Though thoroughly rational in thought, many chosen still harbored deep resent for ‘the wrong kind’ … but if one couldn’t tell unicorn from pegasus among his or her fellow alicorns, one couldn’t harbor any latent hatred.” Silence pervaded for many seconds. After taking in Zodiac’s story, Twilight finally responded. “I have to say, this is one of the most unusual ideas I’ve ever come across … and yet so incredible. But has it worked?” “It’s been many moons now since this all began, and the results speak for themselves. This is an idyllic community now, along with Paradise. No more arguments, no more dissention. And I must say, we’re very proud of what we’ve accomplished.” “So this ‘Cloudstitch’,” Twilight continues, “is there a chance I could meet her?” “As a matter of fact, I wish to introduce you to her … but first, you will have to pass a test.” Twilight starts bouncing in her bed, giddy with anticipation. “Ooo, ooo, when can we start? Can we do this now? This is gonna be awesome!” “I must say,” Zodiac notes, “I’ve never had that kind of reaction upon informing somepony of a test.” After watching Pinkie Pie devour a bowl of oatmeal in her usual, head-in-the-bowl fashion, her silver ‘alicorn’ companion cannot help but comment: “I would say that I’ve never met anyone quite with your, shall we say, dining etiquette.” Wiping drops of mush from her muzzle with her forehoof, Pinkie responds, “What can I say, I’m one-of-a-kind.” Shrugging off what sounds like a mutter of ‘Thank Equestria’, she then asks, “So what’s your name, anyway? I never got it.” “I would say my name is Spiral.” “OK,” Pinkie replies, “but is that really your name?” “I would say that, yes, Spiral is my name.” Pinkie looks at the ‘alicorn’ with a blank expression before asking, “What is with you using the phrase ‘I would say’ all the time? It seems weird, and boy do I know about weird!” “Well,” Spiral starts, “are you familiar with the history of our towns?” “Twilight told me all about how all you ponies are all either truthful or liars. That’s why I can’t tell whether you’re lying now or not, especially when you start each sentence with ‘I would say’.” “But I would say that’s the point. I would say all of the following: take any true sentence, like ‘Your name is Pinkie Pie.’ If I am truthful, then I would say such a statement; if, however, I am a liar, then I would not say such a statement … but then saying I would say that statement is itself a lie, which forces that statement to be true. You see?” “Oh I see fine,” Pinkie replies. “I hear very well too, and have a great sense of smell. But I don’t understand a single thing you just said!” “Perhaps we should start over,” Spiral states. “I would say my name is Spiral. Now then, what would you say if I were telling you the truth?” “If you’re telling the truth, then your name is Spiral. I get that.” “Excellent. Now, what if my statement was a lie? What would that tell you?” “That would tell me that your name isn’t Spiral,” Pinkie innocently replied. The ‘alicorn’ shook her head before explaining. “Again, I would say all of the following: if I am a liar, then the statement ‘I would say my name is Spiral’ would be a lie. That would mean I would not say my name is Spiral. But that, in turn, would mean that my name IS Spiral, since I would ‘not’ say any true statement. Thus, my name must be Spiral, whether or not I am truthful.” Pinkie let the explanation take hold in her head for some time. “So … any time you begin a statement with ‘I would say’, that makes the thing you say true?” “Inasmuch as I actually believe the sentence to be true, I would say yes.” “And that’s true for all the inhabitants of Utopia and Paradise?” “I would say yes, that is the case.” “Well go figure … I guess I can figure!” Pinkie beams with a sense of pride as she starts bouncing in place.” ‘One-of-a-kind’ indeed! Twilight eyes the solitary room Zodiac has led her to, thinking back to her study days back in Canterlot. In front of her is a single desk, with an ample supply of parchment and quills for scratchwork. Along the sides are bookshelves filled with dusty tomes. The lack of windows unnerves her slightly, but she trusts her guide not to have led her astray. “Let me explain this test, Twilight.” The ‘true’ alicorn nods. “Over many moons, some of our society brothers and sisters have formed close bonds. For this test, you will hear statements from 5 pairs of ponies. In each case, one is a unicorn and one is a pegasus. Either could come from Utopia or Paradise, and they could come from the same or different towns. As you know, unicorns from Utopia and pegasi from Paradise are truthful, while unicorns from Paradise and pegasi from Utopia lie. All you need to do is identify which pony is the unicorn and which is the pegasus. In some cases you will be able to identify place of residence for one or both; in other cases, you will not be able to do so.” Twilight thinks to herself that Rarity would be likely to ace this quiz by simply spotting the real wings and horns from the fakes, but she also trusts her own ability to solve the ensuing puzzles. “I understand. I’m ready to begin.” “Excellent,” Zodiac replies. “Write down your answers, and be prepared to explain your reasoning to me after everypony has given their statements. If you are as talented as I believe you to be, this should be no more than a formality.” Zodiac leaves the room, and one by one, a pair of alicorn-looking ponies walk in to deliver statements. Twilight is amazed by each pair’s appearance, never being able to discern real horns from fake or real wings from fake; nonetheless, she takes it upon herself to stay with the logical facilities within her to solve each puzzle. The first pair to enter are named White Rose and Blue Daffodil. White Rose states that she comes from Paradise, while Blue Daffodil states that she is a unicorn from Utopia. The second pair to enter are named Haystack and Corn Sheaf. Each claims to be a unicorn. Haystack then states that the two come from different towns. The third pair to enter are named Topaz and Amethyst. Topaz claims to be a pegasus, and Amethyst claims to be a unicorn. Topaz then states that the two come from the same town. The fourth pair to enter are named Lettuce Patch and Turnip Field. Lettuce Patch states that both ponies come from Paradise, and Turnip Field denies this statement. The fifth and final pair to enter are named Fianchetto and Knight Fork. Fianchetto states that she is not a pegasus from Utopia, while Knight Fork states that he is a pegasus from Paradise. Fianchetto then states that the two come from different towns. After each of the first four pairs made their statements and left, Twilight scribbled her solutions and thought processes. Minutes after the final pair makes their statements, Twilight asks Fianchetto to bring Zodiac to her. “It was nice of you showing me around Utopia, Spiral … if that is your real name,” Pinkie giggled. Her companion sighed. “I’d say that we’ve been over this before, and that you know that’s my name.” “Oh yeah, that whole ‘double-negative’ thingie; okie-dokey! Say, does that whole ‘I would say’ thing apply to everything you say?” “I would say not; only statements that could be true or false, but not questions or commands. I would also say that one gets used to it after awhile. And, I would say, we’re back to the inn; your alicorn friend should be back before too long.” “Well, thanks again. Your quirky town and its funny speech patterns will always have a special place in my head!” Spiral shakes her head one last time, turns, and walks away. Pinkie is alone to ponder her thoughts: I’d have Spike take a message for Princess Celestia, but he’s not here. I’d write it myself, but I don’t have digits on these hooves. Well, I’m sure I can retain all this information until Twilight returns, then she can help me write a letter. *hee-hee* … who would write ‘a’ letter, right? I mean, one has to write a whole lot of letters to convey any particular meaning, right? What would Princess Celestia say if I just sent her a piece of parchment with a big ‘Q’ on it? She’d probably wonder why I was so interested in ‘Q’. Pinkie’s thoughts are interrupted by the clip-clopping of hooves just outside her room. She turns to see a familiar blue-maned yellow unicorn. “Hey, I recognize you! You’re that unicorn we met last night. The one claiming to be from Paradise. So what’s up?” “I don’t have any particular reason for coming here. That said, would you be willing to come with me?” “Aww, I always look forward to making new friends … but I really should wait for my friend Twilight to return. She should be back any time now.” A pegasus and second unicorn come up and stand beside the yellow unicorn, who then removes the prosthetic horn from his head. Pinkie gapes as he speaks: “I will not insist that you come with us … but you’re coming with us.” “I am truly impressed, Princess Twilight Sparkle!” Zodiac could hardly hide his adoration for the alicorn’s intellect, upon reviewing Twilight’s solutions. Twilight blushed as she responds. “It really was nothing special, at least not to me. But I certainly appreciate your enthusiasm for my work. So I take it I got every problem correct.” “And so quickly. Pray, tell me how you solved these so effortlessly.” Full of pride from a job well done, Twilight proceeds to explain her reasoning to Zodiac. “Well, if you insist …” “One thing that really helped me solve these puzzles was the realization that any pony who claimed to be from Utopia must be a unicorn. In fact, anypony who was truthfully claiming to be from Utopia must be a unicorn, since pegasi from Utopia would lie; on the other hand, a pony who was lying about being from Utopia would be from Paradise, and only unicorns from Paradise lie. And by the same reasoning, any pony claiming to be from Paradise must be a pegasus. This really made the first puzzle trivial; I knew White Rose was a pegasus the instant she stated that she came from Paradise. Since you told me from the onset that each pair had one unicorn and one pegasus, this forced Blue Daffodil to be a unicorn. In this case, I couldn’t say which town either came from.” “What I find really interesting is that the reverse is true: any pony claiming to be a unicorn must come from Utopia, since a truthful claim from a unicorn could only be made by one from Utopia, and a false claim from a pegasus could also only be made by one from Utopia. Also, any pony claiming to be a pegasus must come from Paradise. This helped me figure out the identities of the second and third pairs.” “With the second pair, I knew that both Haystack and Corn Sheaf came from Utopia. Therefore, Haystack lied when stating that the two came from different towns, and only the pegasi from Utopia lie. Thus, Haystack was the pegasus and Corn Sheaf was the unicorn.” “Similarly for the third pair: I knew that Topaz was from Paradise and Amethyst was from Utopia. That meant that Topaz lied when stating that the two came from the same town. That forced Topaz to be the unicorn and Amethyst to be the pegasus.” Zodiac hangs on every word in awe as Twilight continues. “Another important fact that helped me was that, if the two ponies disagreed with each other, they must come from the same town. Either both come from Utopia, in which case the unicorn would be truthful and the pegasus a liar, or both come from Paradise, in which case the pegasus would be truthful and the unicorn a liar. With the fourth pair, Turnip Field disagreed with Lettuce Patch; therefore, they had to come from the same town. If Paradise, then Lettuce Patch told the truth and must be a pegasus; if Utopia, then Lettuce Patch lied and must still be a pegasus. I cannot say which was truthful, but I knew that Lettuce Patch was a pegasus and Turnip Field a unicorn.” “That fifth pair did take me longer than the others, since there was little to go on with their first comments. All I knew at first was that Fianchetto was not a unicorn from Paradise, as she would have lied and said she was a pegasus from Utopia … but if truthful, she could be either a unicorn from Utopia or a pegasus from Paradise. And further, she could be lying and be a pegasus from Utopia after all! As for Knight Fork, he could be telling the truth and be a pegasus from Paradise … or he could be lying, in which case he could be a unicorn from Paradise or a pegasus from Utopia. Anypony but a unicorn from Utopia. So to solve this, I had to ponder Fianchetto’s other comment.” “Let’s assume for the moment that Fianchetto lied when she same that the two came from different towns. I already knew she wasn’t a unicorn from Paradise, so she would have to be a pegasus from Utopia. This would mean Knight Fork was a unicorn, but also from Utopia since they would then have to be from the same town. But I already knew that Knight Fork couldn’t be a unicorn from Utopia … so the assumption that Fianchetto lied leads to a contradiction. She must have been telling the truth, so the two did come from different towns.” “Now, Fianchetto must be either a pegasus from Paradise or a unicorn from Utopia. If the former, that would force Knight Fork to be the unicorn, and again from Utopia … and once again, this is a contradiction to the fact that Knight Fork cannot be a unicorn from Utopia. The only possibility left is that Fianchetto is a uncorn from Utopia, and Knight Fork is a pegasus from Paradise.” “BRAVO!!!” The shout from outside the examination room causes both Twilight and Zodiac to turn to the doorway. A dark blue alicorn eyes Twilight’s figure carefully. “Cloudstitch! I mean … Your Excellency, I did not expect you to …” “That’s quite all right, Zodiac. And you need not worry about formalities around me; I would think that you knew this already, though.” Cloudstitch smiles as she speaks; her words are regal yet soothing; Twilight cannot help but make comparisons to Princess Celestia. Cloudstitch then addresses Twilight directly. “When I heard reports among the Society members that a true alicorn princess had come to our fair forest towns, I had to see for myself.” “So miss … I mean, princess? I must apologize; I don’t know how to address you.” “I might say the same about you, Princess Twilight Sparkle … but from what I have heard, I suspect that I may simply call you Twilight, as you may call me Cloudstitch. I have never been one for formality.” Twilight nods in acceptance, she herself still uncomfortable with the pedestal that so many have put her on. “So Cloudstitch, how long were you listening in?” “Long enough to hear your explanation of those final puzzles … especially the one with Fianchetto and Knight Fork. You would fit right in the Alicorn Society, perhaps moreso than the others since you’re an actual alicorn.” “It is good to see you, as always,” Zodiac starts, but Cloudstitch holds a forehoof up to stop him. “I wish I were only here for adulations, but I have troubling news for Twilight.” The smiles and pleasant feelings quickly drain from Twilight and Zodiac. “What news?” “I’ve been informed by Spiral that your friend Pinkie Pie has been accosted. She’s been taken by a rogue pony faction.” Twilight’s irises dilate at the information. “Rogue faction? Who took her? Where?” “There’s only one group that could have done this,” Zodiac declares. Twilight turns to the unicorn. “Pinkie’s been taken to Elysium … the town of the earth ponies.”
The Earth Ponies of ElysiumTwilight felt conflicted at the start or her journey to Elysium. She was concerned for the well-being of Pinkie Pie, to be certain, but the assurances of both Cloudstitch and Zodiac that she would not be harmed were most comforting. She had grown to trust this twosome, even in a land where as many ponies lied as were truthful. And so it was, not long after starting back down the dirt path through the forest, with Zodiac by her side, that the apprehension and fear of what has become of her Ponyville friend had soon dissipated. But that did not mean that she didn’t have serious questions related to recent events: “I don’t understand. Pinkie and I never saw any earth ponies during our walk to Utopia. We never saw any earth ponies in Utopia. Where did they come from?” “They hide in plain sight, as it were,” Zodiac responds coldly. “The most logical explanation is that somepony in Elysium has mastered the same art of crafting prosthetic horns and wings that Cloudstitch had.” “Wait, so you mean that some of the unicorns and pegasi that we’ve come across are earth ponies?” “If everything else you’ve learned about our towns is to be believed … and I hope you do believe, as I have no reason to deceive you … then there is no other rational explanation. Tell me Twilight: do you remember what caused you to black out last night?” Twilight pauses as her eyes roll to the sky. “It was a statement by some yellow unicorn. It seemed to conflict with what I knew of these towns.” “Did this unicorn have a blue mane?” “Yes, he did. Do you know who I’m referring to?” “Sunbolt. He’s the leader of the earth pony rebellion. He and his group have wreaked a lot of havoc in our twin towns for some time now.” The ideas of rebellion and havoc coinciding with the idyllic nature of Utopia catches Twilight off-guard. “I’m not following you. I saw no strife among the ponies in Utopia. I’ll admit that I haven’t seen much of the town, but everything I did see seemed perfectly normal.” “Their mere existence causes strife,” Zodiac replies, an undertone of anger in his voice. These towns are founded on logic and reasoning; you have seen this firsthoof, and I’m sure you can appreciate that.” Twilight stumbles with a response. “Well, yeah, I do like logic and rational thought, but—“ “And look what happened to you. Let me guess: Sunbolt claimed that he was from Paradise, right?” Again, Twilight is surprised by Zodiac. “He did. But how did you—“ “And you couldn’t rationalize the statement, could you. As you already know, no unicorn would claim to be from Paradise. Those from Utopia would always truthfully claim that they came from Utopia, and those from Paradise would always lie and state otherwise. And Sunbolt’s very comment threw all that reasoning into utter chaos; your brain couldn’t process this, and you blacked out.” Twilight says nothing, and just nods in acceptance of the facts. “We’ve come to refer to these instances as ‘logic bombs’. And ever since the earth ponies started infiltrating our ranks, we’ve had to deal with these. Those in the Alicorn Society have come to accept that there are earth ponies in our ranks, pretending to be unicorns and pegasi. We have caught many, and tried to banish them from our towns … but it isn’t easy to keep them away for long. Worse, we’ve had instances where we knew that one from a group of ponies was an earth pony, but could not deduce which.” “Could you give an example of that?” Twilight innocently asks. “Well consider a pair of unicorns, let’s just call them ‘A’ and ‘B’ for the sake of simplicity. A states that B comes from Utopia, and B states that A comes from Paradise. What would you deduce from that?” Twilight talks out her thought process: “If A is truthful, then B really does come from Utopia; hence B is truthful, so A comes from Paradise … but no unicorn from Paradise is truthful. That means that A lied, so B would actually come from Paradise, meaning that B lied, so A actually comes from Utopia … but unicorns from Utopia are truthful.” She turns to Zodiac. “I can only conclude that such a scenario could never occur.” “And yet it did, not so long ago,” Zodiac retorts. “A pegasus who overhead the pair blacked out, just like you did. We in the Society gathered up the pair, knowing that at least one was an earth pony … and perhaps both. And it’s not just unicorn pairs: any group of unicorns and pegasi could have earth ponies in it, and it’s up to us to keep them separated.” Twilight considers Zodiac’s statement to be rather unfriendly in nature, but keeps the thought to herself as her companion urges her onward: “We’ve dilly-dallied long enough; we need to press on.” “… and as I was telling myself before you showed up, why would anypony write just a single letter. I mean, you need lots of letters to make words, but then you need lots of words to write a single letter. That’s just mind-blowing, isn’t it?” The ‘unicorn’ … that Pinkie learned was not really a unicorn … held his tongue for much of the journey, but at long last felt the need to interrupt the stream of consciousness emanating from the pink pony’s mouth. “Do you ever tire of talking?” “Not really. Well, I do get tired of course, and when I do I just go to sleep, but when I’m awake I just love taking everything in and enjoying life. You know, you really need to enjoy life while you can, ‘cause it’d be such a boring existence if you didn’t enjoy life, you know what I mean?” “ENOUGH!!!” The command paused Pinkie’s comments, if but for a moment. “Say, what do I call you anyway? We’ve been walking for a long time now, and left the forest area just a few minutes ago … ooo, and I saw the balloon I came in with Twilight! … but I still don’t know your name.” “Just call me Sunbolt.” “ ‘Sunbolt’? As in, bolts from the sun? I would think ‘Sunray’ or ‘Sunbeam’, or do I already know ponies with that name? Actually, even if I do, that’s no reason why some other pony can’t have that name. There are so many ponies in Equestria, it just makes sense that two have the same name, right? I wonder if there’s another Pinkie Pie out there. Maybe she’s a pegasus … what would it be like to have wings and fly? Sometimes I think I was supposed to have wings, but then I think about what flavor of cake I need to bake for the party.” “What party??? What are you even …” Sunbolt sighs, resigning himself to not figuring out his target. “You are so serious. Why is that?” Pinkie’s innocent question causes Sunbolt to stop dead in his tracks; Pinkie and the others in the group halt as well. Sunbolt then turns to address Pinkie. “I know you’re new around these parts, but did you notice anything unusual about that town Utopia you were in?” “Well hello! The town was in a forest! I mean, who puts a city in a forest?” “Not that,” Sunbolt argues. “Did you notice anything missing?” “… I didn’t see a spa in town. Maybe I’m just spoiled to have a spa in Ponyville. Oh, you would love our spa. Honestly, you do look tense, and—“ “Earth ponies!!!” “… what about earth ponies?” “You didn’t see any earth ponies in Utopia, did you? You felt like a stranger while walking around, didn’t you. All around you are unicorns and pegasi, living in harmony … but earth ponies? No, we’re cast aside by that ridiculous ‘Alicorn Society’. Banished from their precious twin-towns, because we upset their delicate balance of rationality.” Pinkie looks at Sunbolt in stunned silence; the latter appreciates the pause, recognizing that Pinkie takes his words seriously. “You’ve been banished from Utopia?” Pinkie asks. “And Paradise too? Well that doesn’t sound very nice.” Sunbolt smiles. “No … it’s not, is it. So we’ve taken to disguise to infiltrate the towns. We have an incredible designer in Elysium, who can produce horns and wings that are indistinguishable from the real thing … so long as you don’t ask me to actually perform magic, anyway.” “That horn really does look good on you. Say, you think I can get a pair of wings?” “I’m sure we can make arrangements for you. Now let us continue …” After a sufficient period of awkward silence, Twilight decides to initiate a new avenue for the recent topic of discussion. “So you said you felt it … ‘necessary’ … to separate out earth ponies from the unicorns and pegasi. But the examples you gave earlier didn’t seem to provide a way to determine which was which. You didn’t … physically …” Zodiac halts abruptly, perturbed at Twilight’s insinuation. “I can assure you, that nopony, either from the Alicorn Society or anywhere else in our fair towns, would ever touch another pony. That’s not just a matter of what is right, or what is honorable, but ours are towns of logical reasoning and not barbarism. No, instead we had trials where the accused would make statements; then, we would deduce which were earth ponies and which weren’t.” “So you’re saying that earth ponies who took the time to play dress-up would openly admit to being earth ponies, just to get banished from your towns?” “Not deliberately, to be sure, but it’s easy for a pony to let her focus slip when pressed. If you like, I can give you some examples … but I cannot divulge any names. What say you?” Twilight still felt uncomfortable with the notion of any sort of exclusionary policies, but her curiosity and yearning for more chances to exercise her thought processes, particularly on an otherwise isolated journey towards Elysium, won out. “I would like to hear these cases, Zodiac. I could always use the practice when it comes to puzzle-solving.” “Not from what I’ve seen of you,” Zodiac replies. “Very well: for each of the following cases, I can tell you that exactly one pony, described as either a unicorn or pegasus, is actually an earth pony from Elysium … and that all such ponies lie. All other ponies in these cases follow the same rules as you are accustomed to: the unicorns from Utopia and the pegasi from Paradise are truthful, while the unicorns from Paradise and the pegasi from Utopia lie. And as anonymity is the rule when it comes to all ponies that have been through a case, I will refer to all ponies by letter only. Now then:” “The first case featured two ‘unicorns’, though of course only one actually is a unicorn, while the other is an Elysian earth pony. Let me refer to them as A and B. A stated that both came from the same town, while B denied the assertion.” “The second case featured unicorn C and pegasus D. C stated that at least one of them came from Utopia; D agreed with the assertion.” “The third case featured three ponies: unicorn E, unicorn F, and pegasus G. E stated that at least two of the threesome were liars. F stated that either E came from Utopia or G came from Paradise. G said nothing.” “The fourth case featured three unicorns: H, J, and K. H stated that none of the three came from Utopia. J then shocked everypony by stating that he himself was the earth pony. This rendered K speechless; she said nothing.” “The fifth and final case I will share with you featured pegasus M, unicorn N, and pegasus P. M stated that N was really the earth pony, while N stated that M was not the earth pony. P then stated that no two of them came from the same town.” “Now,” Zodiac continues, “if you’re able to determine the five earth ponies from what I’ve related to you, I will be beyond impressed.” He cannot suppress a smile across his face as Twilight mulls over all the information. Minutes later, their journey takes them out of the forest. “I’d say we got another half-hour before we reach Elysium. Let us see if you’re able to figure all this out by then.” Five minutes later, Twilight recites five letters to Zodiac. She hides her feelings of superiority, satisfied by the stunned look on her companion’s face, as the two trudge on in silent contemplation. “… and that’s why I don’t like pauses in conversation, I mean who has time for quiet contemplation when there are parties to be planned and cakes to be baked and so many new friends to make. Any time spent alone or sad is just really lost time, don’t you think? I certainly think so, which is why I don’t like pauses in conversation, but wait, I just said that, didn’t I? Well that just proves my point; isn’t this much more enjoyable an experience?” I had to ask if she ever kept quiet. I just had to ask. “You’ve been real quiet, Sunbolt.” The faux-unicorn lets out a sigh and plods along. Pinkie, still curious as to the darker aspects of the history of the twin-towns, changes her conversational course. “I don’t understand. Why would Utopia and Paradise not want earth ponies around?” Pinkie’s question has the desired effect, as Sunbolt responds quickly. “I’m sure Twilight heard the story from that ‘society’, about how unicorns and pegasi came to this area to found a town shared by the two ponykinds … but that group fails to mention that there were three kinds. And as much animosity that existed between the two, the one thing they agreed upon early is that they wanted nothing to do with the earth ponies, who possessed no outer-worldly abilities. No horns or natural magic. No wings for flight. And they both dismissed the notion that earth ponies were special caretakers of the land. So even before the factions made it to the forest, the unicorns and pegasi forced our kind to start anew on our own, away from both of them.” Pinkie listens on in silence. Sunbolt, appreciating the gravity that Pinkie takes to his words, continues. “Of course, those two factions soon found that they couldn’t agree on much more than that, so two smaller towns were created instead. Over time, though, feelings towards each other’s kinds softened. That led to the strange nature of veritas that pervades there. Those who’ve come across the twin towns have been inspired by what they’ve experienced; I have even heard from some that whole stories have been created. Perhaps your alicorn friend learned about these towns from such a text.” “Yeah, she did read about Utopia and Paradise … but she didn’t mention anything about an earth pony town.” “Truth be told,” Sunbolt continues, “it was the earth ponies who first attempted to mend fences between the kinds. But perhaps it was too soon; the mere sight of a hornless, wingless pony set off cries of ‘Begone!’ from the townsfolk. That was when one earth pony came up with the idea of bluffing our way in, with prosthetic horns and wings.” “Pro … what?” “Fakes. Horns carved from wood, wings from stray feathers, both accented with whatever materials could be found. But this pony, I tell you, was incredible with her craftwork. One could hardly tell the difference between real and fake … so long as one wasn’t forced to actually demonstrate the use of magic or ability of flight.” “Wow, that’s funny,” Pinkie commented. “Not ‘ha-ha’ funny, but weird funny: Utopia also has a craftspony who makes fake horns and wings, too.” “It’s no coincidence; those ‘alicorns’ stole the idea, and used it to bring the unicorns and pegasi together … but still keep earth ponies away. Cruel irony, wouldn’t you say?” “But if the prosetuh … ‘fake’ horns and wings were so convincing, how did the ponies in Utopia and Paradise figure out the truth?” “Those from Elysium were not as well-versed with the traditions of the forest towns, and would occasionally make statements that didn’t fit; this led to unicorns and pegasi alike having logical breakdowns. This led to many of our kind being caught … and upon discovery of the prosthetics, the idea spread to their own kind.” Pinkie pauses for a moment. “So how do I know all of this is the truth? The way you spoke in Utopia sounded weird, like you were trying to lie.” “I was,” Sunbolt admits, “but the truth is that we earth ponies have no predilection for lying. We just don’t care. Normally, we would be as honest as possible; however, when trying to fit in, we attempted to mimic the customs of the forest towns … but not always successfully.” Before the conversation can continue, Sunbolt and his group eye the top of a skyline of a town down the dirt path. “Good, we’re almost there.” Sunbolt turns to Pinkie. “We have special plans for you, my dear.” “A-D-E-H-P.” Zodiac keeps repeating the five-letter string to himself over and over, shaking his head all the while. Eventually, Twilight asks her companion how he’s feeling. “I’m sorry, I just didn’t expect … and all while walking along this path, not in a study or anything. Truly, you have a dazzling intellect. You may be the Princess of Friendship, but you could just as easily be the Queen of Logic.” “You embarrass me with your comments, but I appreciate the sentiment all the same.” “I must know how you were able to deduce all those cases. Especially the last three; I thought those to be most perplexing.” Twilight, taking pride in her ability, is more than happy to share. “Well, let’s start with the first case. By your own stipulation, it isn’t possible for both ponies to come from the same town; one must come from Elysium, and the other from either Utopia or Paradise. That means that A lied and B told the truth; since one must be the earth pony, it could only be A. Also, B must come from Utopia.” “With the second case, either both ponies lied or both told the truth … but again, your given conditions imply that at least one of them lied. Therefore, they both lied and neither came from Utopia. Now if D actually was a pegasus, she would have to come from Paradise, but that would make her a truth-teller. The only remaining possibility is that D is the earth pony, while C comes from Paradise.” “The cases do get more interesting with three ponies. In the third case, let’s consider what E said. If E was truthful, then F and G are liars; if E lied, then F and G must in fact be truth-tellers. But this means that either E or G was truthful, and so either unicorn E comes from Utopia or pegasus G comes from Paradise … but that’s exactly what F stated. Therefore F is truthful, and so is G. Since E is the only liar, she must be the earth pony. Also, F comes from Utopia and G comes from Paradise.” “Moving to the fourth case: if H was truthful, then none of them came from Utopia; in particular, H doesn’t come from Utopia … but this would force H to be a liar, regardless of whether she was from Paradise or Elysium. Therefore H lied, and at least one of the others does come from Utopia and is truthful. Could it be J? No, because he stated that he was the earth pony; by your conditions, earth ponies only come from Elysium. That must mean that K comes from Utopia. Meanwhile, J cannot be the earth pony; none would admit to such, as that would be truthful. Hence, H must be the earth pony, and J must come from Paradise.” “The fifth case is the most intriguing of all. Consider P’s statement. If true, then P comes from Paradise and the others must come from Utopia and Elysium in some order. If M came from Utopia and N came from Elysium, then N would be lying when stating that M was not the earth pony … but this would mean that both M and N were earth ponies, contradicting your given conditions. If, instead, M came from Elysium and N came from Utopia, then N would be a unicorn from Utopia, hence would tell the truth … but he stated that M was not the earth pony, so she would be lying; this cannot be either. That means that P could not have been truthful; P is a liar and comes from either Utopia or Elysium, and two ponies must come from the same town. That town cannot be Elysium, since it’s given that there is only one earth pony, so either two come from Utopia or two come from Paradise.” “Suppose two come from Paradise. P cannot be one of them, so P would have to be the earth pony, while M and N come from Paradise. But that would mean M is a pegasus from Paradise, hence truthful, and M stated that N was the earth pony. This cannot be.” “Therefore, two ponies come from Utopia, and one comes from Elysium. Whichever town M comes from, she must be a liar; thus, N is not the earth pony. This forces N to come from Utopia, and since N really is a unicorn, she must be truthful; thus, M is not an earth pony either. That only leaves P as the earth pony, with the others coming from Utopia.” “Remarkable,” Zodiac admits. “You even figured out the home towns of all other ponies involved. You really are somepony special!” Twilight smiles … but quickly shakes off her feelings of pride and elation, remembering both Zodiac’s previous comments about the treatment of the earth ponies and the reason they continue to walk towards Elysium. “I appreciate logic puzzles as much as the next pony, but that still doesn’t excuse the actions you’ve described to me. Excluding anypony is wrong, and I would think you already know that.” “Our towns were collapsing into mental chaos. What would you have had us do, Princess of Friendship?” Zodiac’s sarcastic emphasis on Twilight’s title did little to ease the renewed tension. “Exactly! It’s all about friendship! Whatever issues the earth ponies were causing you could have been resolved in a fairer and more equitable way.” Zodiac sighs. “I couldn’t expect you to truly understand our plight. You weren’t here during the darker days. You’d have a different perspective if you did. But please: we’ll have more success retrieving your friend if we’re on the same side. And look; we’re almost there!” Twilight notices the upcoming landscape, with yet another village on the horizon. “So what do you think this town has planned for Pinkie Pie?” “I honestly cannot say. I doubt anything untoward; she is a fellow earth pony, after all. Perhaps they want to hold her as leverage for some sort of deal.” “Well whatever the reason, I hope Pinkie is OK … sweet Celestia!” Upon entering the village, Zodiac and Twilight are struck by the sight of numerous ponies … mostly earth ponies, but many unicorns and pegasi can be seen among the group … all kneeling and bowing their heads in reverence. In the center of the town, a lone alicorn stands majestically while grinning from ear to ear. A yellow unicorn … Sunbolt … walks up to the twosome. “Knew you’d come, and just in time for our coronation.” “What coronation?” Zodiac asks. “The coronation of Alicorn Pinkie Pie, Princess of Irrationality!”
The Pebble Paradox and the Rainbow Seven“Alicorn Pinkie Pie??? Princess of Irrationality? Pinkie, what’s going on here?” Pinkie bounds over to Twilight, as the masses remain bowed with their eyes closed. “Isn’t this super? I love these wings, they look soooo great on me. Yeah, I know I can’t actually fly with them, but I just love the idea of flying, it really feeds the imagination, doesn’t it. And the horn! If I could use magic, the things I could do! Imagine me being able to teleport at will! So much to go on about with all this, but …” Twilight pays little mind to her friend’s ramblings as she inspects the artisanship of Pinkie’s newfound accessories. Had she not known Pinkie Pie for so long, she would swear she was looking at a hyperactive alicorn. “Remarkable …” “… but then I said ‘I’m off oatmeal for a while’, and … Twilight?” Twilight shakes her head and refocuses on the present. “Sorry Pinkie. And you’re right; those wings and that horn are incredibly realistic. But why?” “Maybe they got a touring theater group that needs attention to detail to their costumes,” Pinkie suggests. “Not that, Pinkie. Why is this town bestowing these wings and this horn on you?” “All in the name of unity, my dear princess,” replies Sunbolt. Twilight turns to the faux-unicorn, and then realizes that they’ve met. “I remember you now! You’re that unicorn we met when we first got to Utopia.” “Unicorn nothing: that’s Sunbolt, leader of the Elysium movement, and an earth pony through and through!” “Ah, Zodiac. A pleasure to run into you again, no doubt.” “To what end are you using this earth pony?” Zodiac angrily asks. Sunbolt answers in kind. “Utopia and Paradise saw fit to steal our idea of prosthetics, so it’s only logical that Elysium would do the same for the concept of alicorns. Your towns have spurned our advances for far too long, Zodiac. Rejected our kind. Forced us to fend for ourselves from the beginning. Well good luck figuring out which alicorns are earth ponies … oh that’s right, you don’t believe in luck. Just ‘reasoning’ and ‘rational thought’, right?” “The Alicorn Society has done what’s needed to be done. We wish no ill will on anypony.” “Exclusionary practices are ill will, Zodiac!” “The mental breakdowns the earth ponies have caused in our towns are serious, Sunbolt.” Twilight’s neck strains from the back-and-forth between the two ponies, as each volleys accusations at the other. “STOP THIS!!!”, she finally interrupts; Zodiac and Sunbolt briefly turn to the true alicorn in response. Twilight then addresses Zodiac. “I can understand your concern, having experienced a breakdown first-hoof, but this idea of excluding earth ponies from your towns has got to end. Everypony should be allowed to reside wherever they wish, and your towns will be richer for their presence.” As Zodiac processes Twilight’s plea, she turns to Sunbolt. “And while I agree that Utopia and Paradise should be open to earth ponies, I understand why this process needs to be gradual, so the townsfolk can adapt to the new ways.” Twilight’s next words are aimed at both: “As much as I’ve enjoyed the puzzles I’ve had to solve since coming here, such puzzles belong in texts and not reality. Now I urge you both, not as the Princess of Friendship but as a simple friend, to find common ground and begin the process of integrating all ponies to all towns.” A brief pause ensues, before Sunbolt responds: “If you’re insinuating that Elysium has held the same exclusionary practices as the forest towns, look around.” Twilight scans the town, and notices that a number of ponies that had been bowing have horns, while others have wings. “I can’t tell if they’re really unicorns and pegasi or not. I would have thought otherwise before coming here, but now?” “Exactly,” Zodiac retorts. “All the confusion that’s resulted from the appearance of these earth ponies in wing-and-horn clothing has made a mess of things for a long time now.” “Well, just wait until Pinkie and a horde of alicorns come to your twin-towns and mingle with the residents.” “Ooo, are we going back to Utopia?” Pinkie excitedly asks. “Or maybe Paradise! I haven’t been to Paradise yet! Sounds like fun!” “Pinkie Pie,” Zodiac begs, “do not enter the twin-towns as an alicorn. The resulting logic bombs would be cataclysmic.” “Gee, I don’t want to hurt anypony. Well, I can’t wait to show these off in Ponyville. What do you think Rarity will think of these? I think she’ll be utterly amazed!” “I’m afraid you misunderstand, Pinkie Pie,” Sunbolt corrects. “Your place is here now, in Elysium to raise the spirits of the earth ponies here. You can’t return home.” Sunbolt’s declaration enrages Twilight. “You can’t keep my friend here against her will! I won’t allow it!” “Yeah, I mean I love the wings, and the horn, and this is really a cool place to visit, but I don’t wanna leave my life and all my friends behind.” “I thought you would both feel this way,” Sunbolt cooly replies to Pinkie, “so how about a little wager. Win, and I will let you go, wings, horn, and all. Lose, and you promise to stay here. Would you be willing to swear by the results of this wager?” “We’re not going to play some game for my friend’s freedom!” Twilight flatly states. Zodiac brushes Twilight aside and confronts Sunbolt himself. “It’s not rational for one to risk something so dear on a mere gamble.” “Oh, but that’s just it. It’s not really a gamble. Think of it more as a test, where you have a two-in-three chance of succeeding.” Twilight eyes Zodiac suspiciously as he continues the conversation. “I suppose it won’t hurt to at least see what you have in mind.” “Not at all,” Sunbolt replies. “Follow me.” Sunbolt leads Zodiac, Twilight, and Pinkie to a large structure at the far end of the town. Twilight notes the combination of municipal and residential amenities while walking inside; she reasons that this must be where Sunbolt both lives and conducts his strategic planning. After traversing numerous hallways, the group is led to a spacious, empty room that contains only three boxes of similar size and shape resting on a table. The boxes have the numbers ‘1’, ‘2’, and ‘3’ inscribed on them. Sunbolt explains: “One of these boxes contains but a simple pebble, to represent the simplicity of earth ponies; the other two boxes are empty. Pick one box: if it is empty, Pinkie is free to go. But if you should pick the box with the pebble, she remains with us.” Zodiac inspects the table and notices stone tablets in front of each box. Messages are etched into the tablet; he studies these messages while Twilight again protests about the notion of keeping Pinkie in this town against her will. Suddenly … “We accept your offer.” Twilight suddenly turns to Zodiac, her face now the color of Pinkie’s mane. “Zodiac!!! You have no right to accept this proposition!” “You have to trust me on this,” Zodiac icily replies. He then turns to Pinkie. “Promise Sunbolt that you will abide by the results of this ‘wager’.” “Okie-dokie!” Pinkie cheerfully replies. “I Pinkie-promise!” “What??? Pinkie, no!” “Why not? Zodiac seems sure of something, so why not give him a chance?” “But Pinkie, if he’s wrong then you’re trapped here!” Sunbolt interrupts Twilight’s back-and-forth with Pinkie: “It does not matter now; Pinkie has accepted Zodiac’s offer. Now choose.” Resigning herself to Zodiac’s decision, Twilight inspects the messages etched into the tablets. In front of box 1 is the message “This box is empty.” In front of box 2 is the message “Box 3 contains the pebble.” In front of box 3 is the message “The messages in front of at least two of these boxes are false.” “I apologize for making you so angry, Twilight,” Zodiac states, “but you have nothing to fear. It is obvious which box I should pick.” “Oh please, explain your reasoning,” Sunbolt urges the faux-alicorn. “It’s all so simple. The message in front of box 3 is either true or false. If it’s true, then the messages in front of boxes 1 and 2 are false. In particular, box 1 is not empty. So there’s a chance the pebble is in that box.” “Go on …” “Meanwhile, if the message in front of box 3 is false, then it is not the case that at least two messages are false. That forces the messages in front of boxes 1 and 2 to be true. In particular, box 3 would have to contain the pebble.” Zodiac fails to see the slight, mischievous grin on Sunbolt’s face as he concludes: “That means that either box 1 or box 3 contains the pebble; it cannot possibly be in box 2. Thus, Sunbolt, I choose the middle box!” Triumphant in his demeanor, Zodiac magically opens the middle box and looks inside. The smile on his face quickly turns to a gasp as his pupils shrink to pinpricks. “No … that can’t be …” Moments later, he collapses to the ground. Twilight and Pinkie peer into the middle box, which contains a small stone lying atop a pillow. Sunbolt then opens the other two boxes, revealing each to be empty. “A deal’s a deal,” she declares, “Alicorn Pinkie is here to stay. And now I must prepare for the upcoming visit to the twin-towns. If you’ll excuse me …” Sunbolt then departs the room, leaving the two Ponyville residents alone. “Pinkie, let’s just get out of this town and reconvene back at the balloon. I can teleport us out of here if necessary; they won’t be able to stop us.” “But we still haven’t solved their friendship problem,” Pinkie notes. “I’m not saying we abandon our quest; I just think we need time to process everything that’s happened.” “I can’t leave here,” Pinkie states, tears emanating from her eyes. “I made a Pinkie-promise, Twilight! You of all ponies know I can’t break a Pinkie-promise!” “But Pinkie—“ “I’m staying,” Pinkie declares while fighting back further tears. “It’s my own doing, and I need to accept the consequences. Sometimes … sometimes I get caught up in the moment. Zodiac just seemed so certain of himself, and I really like these wings. I guess I got a little greedy. I should have just declined Sunbolt’s offer. I’m sorry, Twilight.” Pinkie turns away from Twilight. “Have Spike take care of Gummy for me. They’re both reptiles; they’re practically cousins. And give my regards to the others … maybe they can visit from time to time.” “No! I will not accept this!” Twilight is adamant in her declaration. “I’ll talk to Sunbolt; you wait here until Zodiac comes to; maybe you can figure out why he blacked out. But when all is completed here, we’re returning to Ponyville together! That’s a Twilight-promise!” Twilight gallops away from the room, leaving Pinkie to inspect the tablets and wait for Zodiac.” “Absolutely out of the question!” “Please!” Twilight begs of Sunbolt. “You cannot force my friend to leave behind her whole life just to satisfy your ponial desires. It’s not right, and deep down inside, I know you know that.” Sunbolt looks Twilight in the eyes. “This isn’t about me, Princess Twilight. This is about every earth pony whose ever been turned away by a unicorn or pegasus simply because she lacks special features. But I wouldn’t expect a true alicorn to understand that.” “There must be another solution,” Twilight continues to plead. “What if … what if you made another wager. How about ‘double-or-nothing’?” Sunbolt pauses. “Exactly what are you wagering?” “My own freedom. If I lose, I promise to remain in Elysium and follow your leadership. But if I win, you annul the Pinkie-promise and allow us to return home.” “Interesting,” Sunbolt mulls to himself. “An opportunity to have a true alicorn join our fight … all right, Princess Twilight: you have yourself a deal. And I know the perfect wager for you. Head back to the room with the three boxes, and I will meet you shortly.” “ ‘Annul’? What does that mean?” “It means the Pinkie-promise would never have technically taken place. It would be as if it never happened.” “So it would be like we went back in time?” “Well, not exactly … but I think you get the idea.” Pinkie, her eyes still moist from before, hugs Twilight as more tears flow. “Oh, thankyouthankyouthankyou!!! I knew you’d figure out a way to save me.” “Don’t thank me yet, Pinkie. I still don’t know what Sunbolt has planned for—“ The two hear hoofsteps from the hallway. Soon after, Sunbolt appears … followed by a group of ponies that cause both Twilight and Pinkie to gape in astonishment. Seven ponies enter the room, each of which is monochrome from mane to body to tail. Lined up, they appear to make up a rainbow. And, each appears to be an alicorn. “I meant for Zodiac or another one of those ‘Alicorn Society’ ponies to take this challenge, but I cannot ignore the possibility of gaining the services of a true alicorn princess.” “Where did you ever find monochrome ponies?” Twilight asks in astonishment. “I’ve never seen anything like this.” “I would have thought that after experiencing alicorns here, you wouldn’t be so surprised,” Sunbolt retorts. “If you must know, this is simply the result of body paint and mane dye.” “Remarkable,” Twilight admits. “You should totally start a theater company, Sunbolt,” Pinkie adds. “In any case,” Sunbolt brusquely states, “let me explain how this challenge will work:” “For purposes of this challenge, the names of these alicorns are Red, Orange, Yellow, Green, Blue, Indigo, and Violet. Now as I’m sure you have figured out by now, these are not alicorns. In fact, six of these fine ponies hail from either Utopia or Paradise … and in fact, two of those six are really earth ponies. Yes, there are earth ponies who come from those towns; they simply hide their true nature well enough to blend in.” “More specifically, three of these ponies come from Utopia: one unicorn, one pegasus, and one earth pony. Three more come from Paradise: again, one unicorn, one pegasus, and one earth pony. The seventh pony is also an earth pony, who comes from Elysium. Each of these ponies will make up to two statements; the only true statements will come from ponies whose type and town of residence start with the same letter. Thus: only the Utopian unicorn, Paradisian pegasus, and Elysian earth pony will be truthful; the other four will make only false statements. And your task, Twilight, is simply to classify all seven ponies. Do that successfully, and you will earn your friend’s freedom. But make any mistake, and you will serve in the ranks of the Elysians.” “I dunno Twilight,” Pinkie remarks. “That seems like a lot of possibilities.” “Five thousand forty, to be exact,” Twilight answers. “But I have to trust my abilities.” “One other thing,” Sunbolt adds. “You have thirty minutes to complete this task.” “What???” “That’s the deal. Take it or leave it!” Twilight gulps, as beads of sweat start to form on her forehead. Shaking off her apprehension, Twilight answers Sunbolt: “I accept.” “Excellent. Now if you’ll be kind enough to levitate Zodiac here to the hallway, Pinkie and I will leave you alone with the Rainbow Seven. You time will begin when the last statement is uttered.” Using her magic, Twilight lifts the faux-unicorn and moves him to the hallway before gently placing him back on the ground. Sunbolt and Pinkie then exit the room, leaving Twilight with the seven monochrome faux-alicorns. Red makes one statement: “I’m a Utopian pegasus.” Orange makes two statements: “I’m a Paradisian pegasus. Blue and I come from the same town.” Yellow makes two statements: “I am not from Elysium. Indigo and Violet are the same pony type.” Green makes two statements: “I am from Elysium. Orange is not telling the truth.” Blue makes two statements: “I am a unicorn. I come from Utopia.” Indigo makes two statements: “I come from Paradise. Violet comes from Paradise, too.” Twilight waits for Violet to speak, but Violet just gazes at a wall and says nothing. After five minutes, Twilight leaves the room and addresses Sunbolt: “Is something wrong with Violet?” “Nothing is wrong with Violet … and you have twenty-five minutes left.” “WHAT???” “I never said that they would all make statements,” Sunbolt states, unable to hide a grin. “Twenty-four minutes left.” Angry at the ruse, Twilight runs back into the room and slams the door behind her. “That wasn’t very nice, Sunbolt!” “I would think you would appreciate that, Pinkie. But, I suppose I should not be surprised. After all: in just over twenty minutes, you and your alicorn princess friend will help me end the strife that my fellow earth ponies have suffered for far too long.” Pinkie looks to the motionless Zodiac, then back to the door to the room. Brain, don’t fail Twilight now … Author's Note The solution to the 'Rainbow Seven' puzzle will be revealed in the next, and final, chapter ... but if anyone wishes to know the solution before then, feel free to PM me. I kindly ask that no one posts the solution in the comments, though.
One HugZodiac slowly comes to, groggy as he gets his bearings. He looks down the hallway he finds himself in, then notices Pinkie Pie, still wearing her custom-made wings and horn, staring back at him. “Rise and shine, sleepy-head! Feeling better?” Zodiac feels at his forehead. “Wha … what happened? Where’s Sunbolt?” “You collapsed after opening a box containing a pebble, and Sunbolt left about ten minutes ago to prepare for my leading a group of alicorn-looking earth ponies to Paradise and Utopia.” “What???” The news snaps Zodiac back to reality. “So I failed the test? But that’s impossible!” “It was unfortunate,” Pinkie corrects, “but wouldn’t ‘impossible’ mean ‘not possible’?” “But my reasoning … my reasoning was flawless. For the pebble to be in that middle box, that just makes no sense.” “It’s just a pebble. Physically, it could have been in any box. Why were you so sure?” “Because of the tablets, Pinkie! I remember quite clearly what the messages on those tablets said: Box 1’s tablet read ‘This box is empty,’ Box 2’s tablet read ‘Box 3 contains the pebble,’ and Box 3’s tablet read ‘The messages in front of at least two of these boxes are false.’ It should not have been possible for the pebble to be in Box 2.” “Why not?” Pinkie innocently asks. “With the pebble in Box 2,” Zodiac explains, “Box 1’s tablet is true since that box was empty. At the same time, Box 2’s tablet is false since Box 3 didn’t contain the pebble. But then Box 3’s tablet made no sense!” “Why not?” Pinkie innocently repeats. “Because that message has to be true or false. If true, then at least two messages are false … but only one is false: the one for Box 2. If false, then at most one message is false … but now two messages are false: the ones for Box 2 and 3. So again, the message makes no sense!” Pinkie ponders Zodiac’s argument for a minute. “Did Sunbolt state that the messages had anything to do with the location of the pebble?” “Well … uh …” Zodiac eventually stumbles to a ‘no’ response. “And why did you assume that that last message was either true or false? Couldn’t it be neither? I mean, I know that the statement ‘I hate baked goods’ is false, and I know that the statement ‘I love Gummy’ is true, but what about the statement ‘This statement is false’?” “Well,” Zodiac starts, “if true, then it’s false. If false, then it’s true. So that statement makes no sense, either.” “And yet here I am, telling it to you. They’re just words, right. Words formed from letters, like the one I was going to write to Princess Celestia while I was in Utopia. But why do you assume that every statement ever made is either true or false?” “I …” Zodiac goes quiet for several minutes. He then suddenly erupts: “SUNBOLT TRICKED ME!” “More like you tricked you.” “Pinkie Pie, I … I am so sorry that I got you into this mess. If you can ever forgive me …” “Well of course I forgive you. Now how ‘bout a hug?” Before Zodiac can satisfy Pinkie’s request, Sunbolt appears from a passage and approaches the two. “It is time. Where is Twilight?” “She’s still inside,” Pinkie replies. “Then she has lost her wager,” Sunbolt cheerfully concludes. He opens the door to the room, and notices that Violet now stands in its center, alone. He also notices Yellow, Green, and Indigo standing in one group to the left, and Red, Orange, and Blue standing in another group to the right. Twilight sees Sunbolt, Pinkie, and Zodiac enter the room and addresses Sunbolt. “I got them grouped by place of residence. If you prefer, I could have Red and Yellow paired off as the unicorns, Orange and Green paired off as the pegasi, and the others grouped as the earth ponies. but either way, a deal is a deal.” “You know, Twilight, Filthy Rich could make a lot of bits by selling smelling salts to these towns. Are there any ponies here that don’t pass out?” “I suppose Sunbolt learned what I did while coming here,” Zodiac remarks. “Don’t underestimate Twilight’s incredible sense of logical reasoning.” “I must admit, I got caught up by Violet not saying anything. But once I settled down, I realized that I had all the information I needed.” “We seem to have some time while Sunbolt comes to. Please, Twilight, you must share your reasoning with me. The way you explained this task, I have to know how you figured everything out.” Twilight smiles as she speaks. “OK, but hopefully this is the last time I do this for a while!” “The key was starting with Yellow’s first statement: ‘I am not from Elysium.’ If that was false, then Yellow would be from Elysium … but the only pony from Elysium was a truth-telling earth pony. That meant that Yellow spoke the truth, so her other statement, ‘Indigo and Violet are the same pony type,’ must also be true. From there, I focused on Indigo’s two statements.” “Suppose Indigo was truthful. Then she would come from Paradise, and that would force her to be a pegasus. That, in turn, would force Violet to be a pegasus too, since they must be the same pony type. Also, Violet would be from Paradise, as Indigo stated as much. But that would mean there were two Paradisian pegasi, and that contradicts the stipulations of the wager. Therefore, Indigo was lying about both statements: neither she nor Violet was really from Paradise. And since they are the same pony type, they cannot also come from the same town; one must come from Utopia, and the other must come from Elysium … but only one pony really does come from Elysium, and that one is an earth pony who speaks the truth. Since Indigo lies, it must be Violet who is the Elysian earth pony. That, in turn, forces Indigo to be the Utopian earth pony.” “Now I can look at Green’s first statement, ‘I am from Elysium.’ As Violet has been shown to be the one Elysian, Green must be lying; that makes his other statement, ‘Orange is not telling the truth,’ a lie as well. That means that Orange is truthful … and since there are only three truthful ponies, namely, the Utopian unicorn, the Paradisian pegasus, and the Elysian earth pony, it follows that Orange, Yellow, and Violet are the only truth-tellers; the others are all liars.” “Since Orange is truthful, she really is as she claims: she is the Paradisian pegasus, which forces Yellow to be the Utopian unicorn. That just leaves Red, Green, and Blue to be, in some order, the Utopian pegasus, the Paradisian unicorn, and the Paradisian earth pony.” “Blue made two separate statements that must each be false, so Blue is not a unicorn and does not come from Utopia. The only possibility is that she is really the Paradisian earth pony. And since Green lied, she and Blue come from different towns; Green cannot be the Paradisian unicorn, so she can only be the Utopian pegasus. And that leaves Red to be the Paradisian unicorn.” Zodiac, mesmerized by the solution Twilight meticulously presented, smiles broadly. “I have run out of superlatives for you, Princess of Friendship. You really are one-of-a-kind. Well done!” He then turns to Pinkie. “You would do well to learn from one as wise as her. You might offer much in terms of exuberance and enthusiasm, but a little rational thought would serve you well.” Twilight, insulted at the comment, starts to speak … but Pinkie stops her. “You’re probably right, Zodiac. It’s just who I am, I guess. But hey, you still owe me a hug, right?” “I suppose I do,” Zodiac replies, and starts to wrap his forehoofs around his fellow faux-alicorn … but Pinkie stops him, much to Twilight’s surprise. “You’re all about ‘true’ and ‘false’, right? Well I got one more proposition to make to you.” “Proposition?” Zodiac looks at Pinkie quizzically. “What sort of proposition.” “Allow me to make one statement to you. If I make a true statement, then you give me a hug. If I make a false statement, then you don’t give me a hug. Deal?” “Pinkie,” Twilight asks, “what are you doing?” Pinkie turns to Twilight. “I like to have fun; it’s who I am. You know that, Twilight!” Twilight notices a glint in Pinkie’s eyes, then shrugs and turns back to Sunbolt, who begins to come around. Pinkie turns back to Zodiac. “So, we got a deal?” “I see no harm in that,” Zodiac replies. “So make your statement. Something like ‘I like hugs’, no doubt.” “Let’s leave the room for a minute, so Twilight can talk to Sunbolt.” Pinkie walks out of the room, with Zodiac following behind. Twilight shakes her head, then turns to Sunbolt. “Are you OK?” “I’m fine,” Sunbolt dejectedly replies. “I guess I should have known better than to challenge your intellect. I just wish I could bring my fellow earth ponies to the forest towns.” “You have my word, Sunbolt, that Pinkie and I will not rest until we have fixed this friendship problem.” “I thank you for all you and your friend are trying, but it seems hopeless. Nothing can get ponies like Zodiac to come around to our way of thinking … what’s going on with your cutie mark?” Twilight checks her flank, and is stunned to see the glowing icons which normally indicate that a friendship problem has been resolved. “WHAT??? I … I don’t understand. We’ve solved nothing yet. What’s going on with my cutie mark?” Pinkie Pie pronks back into the room, her smile stretched from ear to ear and her cutie mark emitting the same glowing pattern as Twilight’s. Zodiac follows her inside and approaches Sunbolt. “On behalf of the Alicorn Society, and on behalf of all the residents of the twin-towns, I cordially invite you and all your fellow earth ponies to come to our fair forest towns.” The statement nearly causes Sunbolt to pass out again, but he keeps his composure. “Wait … are you serious? Just like that? I don’t understand.” “We can discuss details on the way back to Utopia. You should speak to Cloudstitch.” The two leave the room, followed by the Rainbow Seven. “Pinkie Pie, what’s going on? What did you say to Zodiac?” “Not much. I just made him an offer he couldn’t refuse.” Twilight takes a final look towards the forest, then back down the road leading to Elysium, before turning back to face Cloudstitch and Sunbolt. “I thank you both again for seeing us off. It’s a shame that Zodiac was too busy to do the same.” “He, Spiral, and the rest of the Alicorn Society have much to prepare for, with the upcoming meshing of pony types throughout both the forest towns and Elysium,” Cloudstitch soothing replies. “But they are all eager to put the past behind and start fresh, with everypony involved in the healing process this time.” “What you and Pinkie Pie were able to accomplish, the earth ponies of this area cannot thank you enough for,” Sunbolt adds. “And thanks again for the wings!” Pinkie interjects. “Too bad I never got to meet the pony who actually created them.” “What makes you think you haven’t?” Sunbolt asks with a sly grin. Twilight and Pinkie gape at the news. “You created those wings, Sunbolt? The horn, too? Wow … leader of the earth pony movement AND a master seamstress.” “What can I say, Twilight. I learned from the best … didn’t I, mom?” “MOM!!!???” Twilight and Pinkie exclaim in unison. “Indeed,” Cloudstitch admits, “though it has been so many moons since I adorned myself as such, I don’t know if I could remove them by now. They really have become a part of me, no matter the lack of function.” “So you really are an earth pony,” Pinkie restates, still shocked from the revelation. “Yes. I and the other earth ponies were shunned by the unicorns and pegasi and forced to begin anew, far from the forest. I bore no ill will; the fact is, many earth ponies preferred it that way. But I knew in my heart that all pony types were meant to mingle with one another, to bring out the best in all.” “But I don’t get it,” Twilight states. “How did you ever get the ponies of Utopia and Paradise to accept you as one of their own?” “It wasn’t easy,” Cloudstitch replies. “I knew myself to be an excellent seamstress and craftspony, but in my first visit to the twin-towns, I was unprepared for the level of sophistication that their reasoning had evolved to.” “And that first trip,” Twilight asked, “you clothed yourself as a pegasus?” “Indeed … but I made the mistake of heading to Utopia first. Merely speaking the truth betrayed my true nature, and I was cast out. I had to start over, but not before building a better foundation for my logic abilities. I vowed to never be found out again.” “When I felt I was ready, I headed to Paradise … but this time, I created wings AND a horn. I spoke little this time, letting them ask me about my true nature. And I was able to convince the townsfolk that I was either a unicorn or pegasus, but that my true nature be kept hidden, for the good of a town that still had infighting. Once I felt that I was accepted, I founded the Alicorn Society; my hope was that if all ponies looked the same from the outside, all would be treated fairly on the inside.” Sunbolt’s expression darkens. “But that didn’t work out as you intended, did it?” “I think all the ponies initiated into the Society had the best of intentions … but there were some who thought that the mission was to help only unicorns and pegasi mend their differences, and not earth ponies. Zodiac was probably the greatest exponent of this belief; I tried to convince him in private to be more open-minded, but I dared not reveal my true nature to him or anypony else, for fear of being cast out yet again. No, I thought it best to bide my time, and hope that he and the others would come around.” “But patience was never one of my virtues,” Sunbolt interjects. “I remember the first time my mother was forced to return. I could see the disappointment in her eyes, in her walk, in the way she carried herself. And I remember when she left the second time, adorned as you see now … and I didn’t hear from her again. I had to know what had become of her, so I created my own set of wings.” “Wings? But you have a horn now.” “I have both, Twilight. I tended to use wings in Paradise and the horn in Utopia, mostly so I would not be so easily recognized by those who frequented both forest towns. And I brought fellow earth ponies with me on these trips, trying to piece together what happened to my mom. And to this day, I never knew that she had risen to such a position within their ranks.” Sunbolt turns to Cloudstitch, a fresh tear forming. “I missed you, mom.” Cloudstitch hugs her son tightly. “I’m sorry I’ve been away for so long. You know I had the best of intentions, for us and for all of pony kind.” She tilts her head to Twilight and Pinkie. “Once again, we cannot thank you enough for all you’ve done.” “Just glad that we could help,” Twilight replies. “And thanks again for the wings and horn, Sunbolt!” “You’ve earned them, Pinkie Pie,” Sunbolt replies. “I’d like to think I do good work. Almost as good as you, mom.” “Almost nothing,” Cloudstitch retorts. “Ever since I gave you your first bolt of cloth to work on, I knew you inherited your mother’s special talent.” “Well, we need to head back to Ponyville while the sun still shines. I hope to visit your towns again someday … and maybe have more on my mind than logic puzzles.” The four share one final laugh and group hug, before Twilight and Pinkie climb into the balloon and sail back home … “I see a sheep down below. It’s got black wool … or at least it does on the top. Hey Twilight, you think it’s possible for a sheep to have black wool on top and white wool underneath?” “Uh … that would be new to me, Pinkie. But I suppose anything’s possible.” “And all the trees … all I see from up here is green. Maybe one of those trees is green all over. Green trunk, green branches … or what about red? A red tree with green leaves? Wouldn’t that be perfect for Hearthswarming?” Twilight chuckles to herself at Pinkie’s usual silliness. A thought then occurs to her. “Pinkie, you never did tell me what you said to Zodiac after my last test. Whatever you said, it sure must have been persuasive.” “Not really. He just agreed to give me a hug if I told a true statement, and not to give me a hug if I told a false statement.” “Yes, I remember that … but what did you say?” “Simple,” Pinkie replied, “I said ‘If you give me a hug, then you must invite all earth ponies to come and inhabit the twin-towns.’ ” Twilight paused for a moment to ponder Pinkie’s statement. “That’s IT? Zodiac changed his entire belief structure because of that statement?” “Well I don’t know if I got him to change his ponial beliefs. I just know that he had to invite all the earth ponies to come and inhabit the twin-towns, at least according to his own set of rules.” “I still don’t understand,” Twilight admits. Pinkie proceeds to explain: “Well my statement to Zodiac was either true or false. Suppose it was false. Well the opposite of the conditional statement ‘if A then B’ is ‘A and not B’, so my statement being false would be equivalent to the statement ‘You will give me a hug, but you will not invite the earth ponies’ … but he agreed that he would not give me a hug if my statement was false. That meant that my statement couldn’t be false without Zodiac going back on his word, so my statement had to be true. Now since my statement must be true, he had to give me a hug … and yes, Twilight, he did give me a super-squeezy hug! Well, now he had to invite the earth ponies; if he didn’t, he would make my statement false, but he already gave me a hug, proving that my statement must be true. Next thing I know, our cutie marks flash to show a job well done.” Twilight’s head starts to spin as she attempts to process the explanation. “Pinkie …” “Basically, ‘A’ and ‘If A then B’ implies ‘B’ … and here, ‘A’ is that I get a hug, and ‘B’ is that the earth ponies are invited.” “Pinkie,” Twilight continues, “how did you know all that?” “Well, logic was part of my schooling as a filly back on the rock farm. When the time came for testing, I was told that I had a pony intelligence quotient of 217.” “You have a pony IQ of 217??? Pinkie Pie, that’s higher than mine! You really are a genius!” “Well, I don’t like to talk about that. It’s just a number, after all; it doesn’t define who I am. And all that logic and reasoning is just boring and a lot of work to me. Now, applying that knowledge … like knowing the perfect mixture of ingredients for a cake batter mix, or the precise temperature and timing for baking … that’s where I like to show off!” “Wow … I am speechless, Pinkie.” Twilight looks towards to horizon, and sees the skyline of Ponyville in the distance. “Hey, guess where we are!” “Well duh … we’re in a balloon! And I thought you were speechless. Oh, what do you think Rarity will say when she sees me? Or Rainbow Dash? Do you think they’ll think I’m an alicorn? Hey ‘corn’ is in ‘alicorn’ … but it’s also in ‘unicorn’ How come ‘alicorn’ doesn’t use any part of ‘pegasus’? Maybe the term should have been ‘pegacorn’. Or maybe ‘unisus’. But what would the plural of ‘unisus’ be? ‘Unisuses’? That’s a lot of esses at the end, isn’t it. I like the letter ess. It’s so fun, with its curvy nature, and it turns a friend into friends. I like friends better than friend; more to enjoy, and …” Author's Note NOTE: If this story ever gets to at least 20 positive thumbs, I shall post a sequel to this story.
