16Touhou Project by Shanghai Team Alice

Knights and knaves accredited to Raymond Smullyan

The red moon beamed down on the Scarlet Devil Mansion as Remilia Scarlet, the Eternally Young Scarlet Moon, perched atop the spire that was the highest point for tens of kilometers about her. The red mist she had spread throughout the land would enable her to walk out in sunlight. However, the lack of said sunlight seemed to trouble humans, which is why two of their number were now at the mansion, on the flat roof facing her.

There was the local miko, a young thing of fourteen tender years and dressed in white and red livery, one Reimu Hakurei, the Wonderful Shrine Maiden of Paradise. There was a mischievous human magician with her, dressed in a black-white witch costume with a black wide-brimmed pointed cap and riding a broom, one Marisa Kirisame, the Ordinary Magician.

Surveying these strange intruders, Remilia purred, "Looks like it's going to be a fun fight. And it looks like it's going to be a long night."

Just as the mistress of the mansion was about to begin the danmaku battle that would decide the fate of the sun over Gensokyo — whether it would emerge once more, or remain forever hidden behind the veil — Reimu held up a hand. "Wait! Before we begin, there's something I wanted to know."

Remilia paused to consider, but then nodded in agreement. "Very well. Ask."

"What is the origin of the pink color of your dress?" asked Reimu out of sheer curiosity.

Remilia was about to announce that the pink color was the faded stains of the blood of her many victims, being a vampire and all. But instead of this shocking revelation, a much more mundane and truthful one emerged.

"It's just a pink color, because I'm a little girl!"

Remilia's hands went to clamp over her mouth as her eyes grew wide. The secret was out — the coloring was nothing but ordinary dye, suitable for a little girl like her (even if she was 500 years old). Any bloodstained clothes she owned have long since been replaced, and Sakuya kept all her clothes scrupulously clean.

The two humans were trying desperately to hold in their laughter. Their cheeks puffed and their eyes were wide and tearing up at the pain of withstanding their spasms. Suddenly, neither could stand it any longer, and burst into peals of hilarity.

"Marisa! Marisa! Did you hear that! She's a pink clad little girl!" gasped Reimu through gut busting laughter.

The magician overbalanced at that point, depositing Marisa onto the ground. She pounded the concrete with her fist, burying her face in the crook of her other arm. "I'm dying! I'm dying of laughter!" she gasped, sounding like a suffocating hyena.

"S-Stop it! Stop laughing!" shouted the vampire kid, desperately trying to regain her charisma. Her eyes burned, and tears spilled from them. "Take me seriously, damn it!" she screeched. However, the two only intensified their laughter, which Remilia didn't even think was possible.

It all proved too much, and Remilia squatted down gripping her mob cap and let out a pitiful keening wail, "U~~! U~~!"

~THUD~

Remilia blinked her eyes open. She was in her usual jammies, partially sprawled across the floor right next to her bed.

"We gotta get this thing resolved!" she mumbled, as the Scarlet Devil resigned to the fact she wasn't going to be able to sleep through the day.

In the sealed, secret world of Gensokyo, a shocking change has overtaken the land and its people. Through the application of a forbidden template, all of the inhabitants have now found themselves either unable to lie, or unable to tell the truth.

All of this was the result of one Yukari Yakumo, the Youkai Sage, reading a certain book of logical exploits by one Raymond Smullyan.

Now, an inhabitant who finds him- or herself unable to lie is called a knight, and an inhabitant who finds him- or herself unable to tell the truth a knave.

Remilia Scarlet, the Scarlet Devil, has awoken this night to find herself unable to lie, and therefore a knight. She has also discovered that her faithful servant Sakuya Izayoi, the Dangerous Illusionist, is a knave, who always lie.

It seems that it is up to Remilia to solve this incident, to return lies and truth to equal distribution amongst Gensokyo's inhabitants.

This day, Remilia has woken prematurely from her nightmares (knightmares?) of people in Gensokyo learning the horrible secret of the Scarlet Devil, and consequently be called the 'Frilly Pink Vampire.'

Knights and Knaves:

A Logical Adventure of Gensokyo

by Wyrm

Chapter 3:

In Which Remilia Scarlet Scales Youkai Mountain

"Morning, m'lady," one Sakuya Izayoi, the Perfect, Elegant and Knavish Servant, said in greeting, setting Remilia's breakfast in front of her mistress. It was an ordinary breakfast, consisting of a light meal with more grains than meat, perfect for a stomach only just gearing up for the day.

Of course, Sakuya, being a knave, would maybe call it midmorning tea.

Or dinner.

Or boiled ox-hoof.

"This is your tartan electric massage unit with sunlamp attached."

Or that.

"Taking a nosedive right into the ridiculous, Sakuya?" came Remilia's rhetorical question.

"No, I'm not. This is a perfectly reasonable description of your breakfast," Sakuya replied with a wide grin on her face, "It's not amusing at all, either."

"You are having way too much fun with this," Remilia observed.

"Better to have way too much fun than not enough!"

Remilia looked up to find one Flandre Scarlet, Sister of the Devil (that is, of Remilia herself), sitting at the other end of the table with a cute little lobster bib tucked into her collar. Flandre had driven herself mad in the basement of the Scarlet Devil Mansion, confined there due to her awesome destructive powers. But currently, she seemed as sane as anyone, her cute girlish face beaming as she held fork in one hand, spoon in the other. It was like she was about to childishly bang the table, demanding her food under threat of holding her breath.

"Flandre..." Remilia began carefully, "...why are you outside the basement?"

"Sakuya told me that you'd be super-glad if I joined you for breakfast!" came her chirping reply.

"Flandre..." Remilia began even more carefully, "...have you fully realized that Sakuya is a knave?"

Flandre's face fell just a fraction. "...You're not super-happy that I joined you for breakfast?"

"Not super-happy. More apprehensive," Remilia corrected, trying to navigate around her knight nature, to take the edge off a normally sharp truth. "You have tremendous power to destroy things. Your past antics are proof enough of that. If they were more under control, I would be more amenable to letting you out of the basement."

Flandre looked downcast while Remilia broke down the problem and a few moments after, but then she perked up again. "How about I work on my control!" she shouted triumphantly.

Remilia paused in eating her breakfast. "That sounds like a good idea, but I have no idea how one goes about taming the power of destruction," Remilia admitted.

"I'll just go ask Patchy!" Flandre announced. Then, she asked with concern, "Is Patchy a knight or a knave?"

"Knight. But Koa's a knave, so be careful." She was not about to let Flandre play any more logic games (where she could get frustrated) until she learned more control.

Few words were spoken as they finished their meal. It was hard to catch up on four hundred years of being locked away in one sitting, but baby steps would carry them for now.

Remilia quietly nursed her tea after finishing breakfast, enjoying the quiet moment after a meal before starting the day's activities. Remilia was almost startled out of her skin as a pair of deceptively frail arms hugged her neck.

"I love you, sis. And because I'm a knight, that's the truth!" giggled Flandre, "And because you're a knight, I know you love me!"

Remilia let out a sigh of exasperation. "Hey. Don't be spreading it around, okay?" replied Remilia.

"'Kay!" the younger vampire chirped as she pulled away, then pranced away, off to the library.

She'll probably scare what little blood Patchy has out of her. Maybe this knight/knave thing isn't so bad after all, thought the mistress of the mansion, as she took a further sip of tea.

The sudden image of Marisa and Reimu laughing their guts out caused her to spew that tea all over the table. I take that back!

"Oh my! Spewing tea befits a lady of your level of elegance, m'lady!" came the maid's slightly teasing voice as she set about wiping up the mess.

Remilia knew Sakuya's words were a lie. She knew that they weren't her faithful maid's true thoughts, and that she was chastising her for such unladylike behavior. But she'd be damned if she for one minute though that Sakuya wasn't milking her knavehood for all the amusement it was worth.

—/—

"Patchy! Where are you, you recluse?" shouted Remilia as she entered the great library again.

"Here!" came a call from the opposite end.

Remilia quickly located Patchouli. The bookworm was surrounded with small jotted notes. "That was a dirty trick, mistress," came a flat voice that wasn't even a growl, "The younger sister gave me a fright."

"It is the mistress's prerogative to play tricks on her household," reminded Remilia. "Were you able to help her?"

"I have some ideas for Flandre's training," admitted the purple-haired bean sprout, "I don't know if any method will help. We can only try." Patchouli sat up, a more animated look on her face. "For now, I have something intriguing to show you."

"What is it?"

"Observe, mistress." Remilia watched as Patchouli pulled out a small card and began writing on it with her left hand, somewhat awkwardly curling it around so that she did not smudge the writing. "Read this, please," Patchouli requested, handing Remilia the card. Remilia did so.

Remilia Scarlet is human.

Remilia blinked, then her eyes grew wide. "Patchy! This sentence is false!"

The magician nodded. "Indeed."

"But you're a knight! You must utter the truth!" Remilia protested, feeling as if the one thing she could be sure of shift beneath her feet.

"But the written word is not an utterance!" Patchouli said in correction of Remilia's obviously wrong assumption. "That's one of the facts I have discovered about how writing works in Gensokyo in this incident. So far, everyone whom I've tested (and who are literate), have one hand that can only write truths, and another that can only write lies. That applies to knights and knaves alike.

"Unfortunately, which hand writes the truth and which hand writes only lies is random for each person. For me, the truth-writer happens to be my right hand. For Sakuya and Koakuma, they are their left hands."

"Sakuya was right handed before yesterday," Remilia interjected.

"As was Koakuma, but the former dominant hand now has nothing to do with which hand will now write lies and which writes the truth. I've tested all our literate staff, and there is an even split between those whose right hand is knighted and whose right hand is knaved, and they bear no clear relation to the former dominant hand.

"Everyone is now ambidextrous in terms of how well they write. What's more, it seems to be complete ambidexterity! I can't tell the difference between sentences written by my left hand and with my right, other than by content. Same for anyone literate in this household — except maybe you, since I don't even know your present handedness. I've taken to calling a literate who is a completely ambidextrous a 'symmetric literate,' just to avoid the clunkiness of 'completely ambidextrous literate being.'"

Remilia frowned, suddenly sour as a realization came to her. "There's going to be a puzzle based on this, isn't there?"

"I wouldn't bet against it, mistress," Patchouli advised. A moment later, she asked, "Have you gotten another message relating to our next challenge?"

"No."

Patchouli quirked an eyebrow in curiosity. "Presumably Yukari, or whoever is orchestrating this incident, is keeping tabs on your progress. If you had completed your task, we probably should have gotten another message by now."

"I think I did complete my task. I found out the types of myself, you, Koakuma, Sakuya, and Flandre. All the rest are fairy rabble."

"You realize someone's missing from that list."

Remilia was silent for several seconds. "Ah. China."

—/—

The Chinese Gatekeeper

11. The Safe Key

"Do we even have a room in the mansion for her?" asked Remilia in a sort of general sense. They were outside the Scarlet Devil Mansion building, walking along the path toward the main gate in the outer wall. The sun was high in the sky, such that it would have been the teensiest bit deadly to Remilia to be standing in it without shade. Fortunately, shade she did have in the form of a parasol.

"She is probably dutifully standing at attention at the front gate," sighed Sakuya as she lied at Remilia's side. Remilia's translations were getting to be automatic: That means the layabout's probably asleep at her post.

The two stopped as the gate and its surroundings became clear. The tall form of the Chinese Girl stood erect in front of the main gate. As the wind wafted her blood-red hair behind her, she glared intensely at the two.

Remilia stared at the sight for a moment, then said, "Sakuya, I think Meiling has made a truth-teller out of you!"

"Buh? Wha? Bfft," sputtered the lying maid.

Remilia stepped forward to address the gate guard. "Meiling, make a statement to prove yourself a knave or a knight," she curtly ordered.

Meiling started shaking as she pressed her lips firmly together and said nothing.

Remilia frowned. She couldn't tell Meiling's type if she didn't speak. "Answer me, you easy-going gate guard!" she barked, noting the softened insult. She had meant to use 'useless' instead of 'easy-going.' It seemed that her insults were tempered a bit by her knighthood. She had a hunch that knaves weren't similarly affected (unless the target truly deserved the insult).

Nevertheless, the attentive and concerned easy-going gate guard remained silent, pressing her lips so hard together that they were turning white. She then pointed toward a sign that had been set up not far from two marble pedestals.

To Whom It May Concern,

I yet know of no logical way to completely prove the truth of this sign. You will just have to trust me that this sign is the complete truth.

Before you stands your gatekeeper, Hong Meiling, and two pedestals, each with a key laying on them: gold and silver. The gate to the Scarlet Devil Mansion is locked and a robust shield surrounding the property that prevents both entry and exit. One of these keys will open the gate (at the same time lowering that robust shield), while the other will result in locking your type forever. That is, if you are a knight, you will remain a knight even after the incident concludes; similarly if you are a knave.

Your gatekeeper has been instructed, under pain of infinite everlasting pain, not to reveal which key does which, or interfere with their use until the test is over. She is only allowed, again under pain of infinite everlasting pain, to answer one yes-no question about the keys and otherwise be silent until the test is over. She is, of course, a knight or a knave.

Good Luck.

—Ran Yakumo

"Oh, for..." Remilia spat. Not only did she have to determine the type of all the household, but she also had to use logic to leave her own estate?

"Allow me to be the test of the keys, m'lady! I would mind very much to remain a knave for eternity in your place," offered Sakuya.

Remilia held up a hand, stopping Sakuya from taking more than a step. "That will not be necessary. We don't need to know Meiling's type to solve this."

Solution: Remilia asked, "Were I to ask you, 'Is the gold key the one that opens the gates?' what would be your answer?"

Without loss of generality, suppose Meiling's answer to the straight question 'Is the gold key the one that opens the gates?' is 'yes.' If Meiling is a knight, this is the truth — the true answer is 'yes;' if she's a knave, it is a lie — the true answer is 'no.' But Remilia did not ask this question, she asked what Meiling's answer to the straight question would have been had she asked it. If Meiling is a knight, then the true answer to the straight question is 'yes,' so Meiling tells the truth and answers 'yes.' If Meiling is a knave, then the true answer to the straight question is 'no,' so the false answer —the one Meiling would have given if asked the straight question— is 'yes,' so she would lie and answer 'no' to Remilia's question. In both cases, Meiling's answer would be the true answer to the straight question. The same holds for if Meiling's answer to the straight question is 'no.'

—/—

Remilia took the silver key and confidently inserted it into the gate lock. Sakuya and Meiling held their breaths, even though Meiling knew the correct key. Remilia turned the key, and the lock made a satisfying click as the shield around the estate dropped immediately. The silver key was indeed the correct key.

While Sakuya elegantly released the breath she'd been holding, Meiling let out a loud roaring gasp of air being drawn into her volumous lungs. "Hyah! I'm still alive!" she bellowed.

"Ah. She's a knight," announced the vampire knight, noting the obviously true statement. She wondered if her supposition yesterday that Meiling would reveal herself with her first sentence counted, as she actually managed to keep her type secret for one answer to a question, albeit not of her own volition.

Sakuya got this wicked grin on her face. "No, Meiling. You're not alive anymore. This is hell, and I'll be your nightmare for the rest of eternity."

Oh, that's cruel! Bravo, Sakuya! "As I said before, way to much fun," Remilia announced, although her face bore an evil smile.

Meiling let out a frightened screech as Sakuya's lies hit home. "KYEEEE! SAKUYA-SAN! Or is it a demon from hell that just looks like you? I mean, like the head maid, Sakuya? Actually, I think I may prefer a demon to Sakuya-san!" she babbled.

"Meiling, shut up." Meiling's mouth closed with a sharp click. "Sakuya's just teasing you because she's a knave."

"'Knave'? What's a knave? What's this all about?" asked Meiling, disoriented by the strange words.

Remilia cocked her head to the side. "Meiling, did you read a beige pamphlet about knights and knaves?"

Meiling vigorously shook her head. It rattled.

"Were there any pamphlets?" Remilia pressed.

"Sure. All over the place. I spent most of the night gathering them up and burning them."

"All those pamphlets, and you didn't read a-one..." sighed the mistress. "I'll see to it that you get a copy. You will, however, read it, or I'll have to punish you personally." A fanged grin spread across her face. "I'm half hoping you'll disobey me, Hong Meiling; it's been a long time since I've properly punished one of my servants."

Meiling made an inarticulate strangling sound of terror.

Remilia wheeled about and started back towards the mansion. "Come, Sakuya. I think the next message from the fox will be waiting for us now."

—/—

Ran's Second Message

Sure enough, lying on Remilia's end-table there was a sealed envelope addressed to her that no fairy maid could honestly recall being there just minutes before.

Dear Remilia,

I apologize for being unable to verify the truth of any of these documents, calling upon you to place faith in them that they are true. Yukari-sama left many of the details of this incident to me, and have not yet come up with a logical means of proving these messages' truth. As of now, you only have my solemn promise that I have written all of these messages with the same hand (my 'knighted hand') in accordance to the recent discovery by your staff magician, Patchouli Knowledge.

Now that you have identified all of your household (sans fairy maids) as knights or knaves, you may now turn your attentions outside the Scarlet Devil Mansion. This will require you or one of your staff to leave the mansion to carry out these missions. Furthermore, you personally are likely the only one who can reliably do so. For Sakuya and Koakuma will have difficulty answering challenges due to their knave nature, Patchouli and Flandre are as yet too unhealthy and too unstable respectively to be trusted with missions involving long journeys, and Hong Meiling will probably only barely grasp that —for the time being— she can only utter truth, much less solve puzzles.

And before you get ideas, Yukari confiscated the magics that allowed Patchouli to communicate with Marisa during the Subterranean Sun incident. I apologize for my master's crass theft.

You are to go to the Moriya Shrine at Youkai mountain. As always, you must determine the type of all the inhabitants of Youkai Mountain, sans rabble (consisting of fairies, kappa and tengu). In addition, you must settle the question of whether or not Sanae is a good girl, and whether or not Aya Shameimaru will write the truth in her next Bunbunmaru edition. In addition, the kappa are up to something, and it would behoove us all to find out what they're doing.

Yukari-sama has just reminded me none of your retinue have visited Youkai Mountain. You might want to ask the miko or the black-white about the people there.

Good Luck.

—Ran Yakumo

"MUKYUUU!" came a cry of rage from the library.

Remilia didn't like the sound of that, so she literally flew to the library, bursting through the door. "Patchy! What's wrong, Patchy?"

The library was in disarray in this section. Books on magic were strewn willy-nilly. Notes on magic were scattered almost everywhere else. Patchouli was almost burrowing through a particularly unruly pile, shouting as she threw book after book over her shoulder, "I haven't found it! Despite my searching, I haven't found the magics that allowed me to communicate with Marisa, and I'm running out of places to look!"

"The Yakumos have it. I just read the message. It isn't here."

Patchouli's face grew wild-eyed with anger. Remilia felt a drop of sweat roll down her forehead; she'd only seen a look that mad on Flandre — granted, it was one of her younger sister's saner moments, but even that was quite mad. "If I could make some suitably nasty revenge stick, I would," she growled darkly, just before going into a horrid-sounding coughing fit.

Remilia smiled faintly. For a knight, it was as good as a promise to send someone to Shikieiki's court.

Patchouli finally got whatever was in her throat out, and spoke in a hoarse whisper, "That means you're on your own for solving the puzzles that will no doubt encounter in this incident."

"Ran says much the same thing," Remilia confirmed Patchouli's suspicion. "Don't worry. I may not be as smart as you, but I'm no dummy."

"I hope you are up to the challenge," came the witch's reply. "If you are to go to Youkai Mountain, you best know something about the inhabitants. A visit to the Hakurei Shrine or to the black-white's house would be most appropriate."

"Do you seriously believe Reimu or Marisa will sit still while this incident is going on?" asked Remilia rhetorically.

The reclusive witch made a thoughtful noise before answering. "Point taken. I'll compile what my research turns up into a brief for you to read," Patchouli said. She pointed sharply to Remilia, ordering as firmly as her weak lungs allowed, "And get some rest. I know you didn't sleep well."

"I will..." Remilia murmured as she shuffled out the library.

—/—

A Snake, a Frog, and a Girl

A few hours' siesta and a lunch later (Sakuya called it a 'metaphysical treatise on rotary engines'), Remilia found that Sakuya had prepared for the day trip to the Moriya Shrine. Koakuma jogged up to the two, and handed them a portfolio she referred to 'Mistress Patchouli's yaoi doujin.' Remilia grew suspicious: why that particular lie?

Remilia put that out of her mind as she and her maid took to the air, the vampire careful to always keep her parasol such that she was in its shade, while the human carried the bulk of the supplies. Fortunately, high noon meant that at no point did she need to obstruct her vision too badly.

The flight to the Moriya shrine was uneventful, if further than the mansion to the Hakurei shrine. This surprised Remilia because Patchy's report indicated she should encounter several gods and the kappa along the way.

It seemed they were expected, as one Sanae Kochiya, Skin-deep and Shallow Human, looked up and waved them down. She said not a word as she lead them to the shrine building, where one Kanako Yasaka, the Avatar of Mountains and Lakes, and Suwako Moriya, the Epitome of Native Gods, sat on the veranda. Sanae gave them a sharp, warning look before taking a seat by Kanako, opposite Suwako.

Kanako rolled her eyes at Sanae's warning look and asked, "What brings you here in the middle of the day, vampire?"

Remilia felt the buzz of still-strong deities gently urging her her to leave, even though she had been invited. "I came to ask you a question, and get your types." The three exchanged puzzled, unsure glances. "Ugh. One plus two equals three," she said in resignation.

Remilia's knighthood proven, Kanako said, "Ask your question, then."

12. Is Sanae a Good Girl?

"Very well. Is Sanae Kochiya a good girl or not?" Remilia asked.

Sanae immediately proclaimed, "I am a good girl!" She the turned to glare at the two goddesses.

Kanako and Suwako glanced at each other. Then Kanako said to Remilia, "Among us three, at least one of us is a knight, and at least one of us is a knave."

"That is true!" Suwako agreed, nodding her head.

Remilia grinned toothily. She might not know everything about the Moriya shrine, but she had her principle answer.

Solution: Kanako and Suwako agree, so they are either both knights or both knaves. If Kanako is a knight, then her statement is true and therefore there is at least one knave among them. But Suwako is also a knight and therefore Sanae must be the knave. If Kanako is a knave, then her statement is false. However, it is true that at least one of them is a knave since Kanako is, so therefore it must not be true that at least one of them is a knight, and therefore Sanae is still a knave.

Being a knave, Sanae is lying when she says she is a good girl, thus Sanae is not a good girl!

13. But What are the Goddesses?

Sanae's face flushed with anger as her knave-ity was uncovered. "That's soooo fair!" she ranted (and lied), "A shrine maiden should be a knave! I wanted to be discovered! Why does a vampire get to be a knight while a shrine maiden has to be a knave?"

Remilia's grin threatened to split her face. "My, my! What would your ancestors say, seeing their decedent in such a state, throwing a tantrum like a child? Isn't a miko supposed to accept her lot in life?"

"Shut your mouth, Vampire!" Sanae wheeled on the two goddesses, pointing at them. "Remember what I instructed, you two!" Since they were commands, they were not affected by Sanae's knaveness.

For the moment, the two goddesses said nothing, but smiled at her tauntingly. Knights or knaves, they were certainly trolls.

"Nitori is a knight," Kanako began.

"But she's not a married knight," Suwako added.

Remilia did not know the types of Kanako, Suwako or Nitori before, and didn't know if the kappa was married before, but she knew now.

Solution: From the previous problem, we know that Kanako and Suwako are either both knights or both knaves. If Nitori is a knave, then she is certainly not a married knight, so Suwako is telling the truth and therefore a knight. But this means Kanako is a knight (since they are both the same type), and claims Nitori is a knight, so Nitori must be a knight. Therefore, if Nitori is a knave, she is a knight. Assuming Nitori is a knave leads to a contradiction, so Nitori must be a knight.

If Nitori is a knight, then Kanako is telling the truth and also a knight. Since Suwako is the same type as Kanako, she is also a knight and therefore telling the truth. Nitori is therefore a knight, but not a married knight, so she must be an unmarried knight.

14. Lowered Readership

"Fuck the both of you!" snapped the not-good girl who lies, then stormed into the shrine.

"What a rude girl!" huffed Remilia.

"Ah, Sanae is all bent out of shape that someone's discovered she's the only knave amongst us," Kanako laughed. "We got a message from Ran saying that you were going to be coming here to, among other things, find out our types, and it sent Sanae into a tizzy."

"Speaking of types, would you happen to know the types of the other residents of Youkai Mountain?"

Kanako scratched her chin. "Only that at least one of the three tengu —Aya, Momiji, or Hatate— is a knave. I heard one of them say that yesterday's Bunbunmaru extra was not ready yet, then I got beaned on the head with the selfsame extra edition immediately after."

"If Aya is a knave, I will not read the next edition," remarked Remilia.

"M'lady continues to read the Bunbunmaru," the Perfect and Elegant Maid piped up.

Kanako thought about Sakuya's words for a moment, then hiked a thumb at her. "Knave?"

"Yes."

Kanako laughed out loud. "Oh, you're a cruel one! You will never read that edition!"

Solution: Being a knight, Remilia is telling the truth that she will not read the next Bunbunmaru News if Aya turns out to be a knave. But Sakuya's lie means that Remilia has already stopped reading the Bunbunmaru News (if she ever started). This makes the consequent (the 'then' part) of the conditional true, and so the entire conditional is true regardless of the antecedent (the 'if' part), and therefore Remilia will not read the next edition regardless of Aya's type.

—/—

Tengu Girls are Publishing

"I have something a little more substantiative," Suwako piped up. "The territory of the tengu is divided up into two regions, the North and the South. In addition there are two schools of thought about how they should publish articles: Right-Justified and Left-Justified. The strange thing is that a tengu's type distributes according to whether they make their residences in the north or south of their territory, and whether they are of the Left-Justified or Right-Justified school. If a tengu is a northerner and is Left-Justified, or is a southerner and is Right-Justified, then he or she is a knight. Otherwise, he or she is a knave."

"How did you find this out?" Kanako huffed, slightly peeved that the little shrimp of a goddess knew more about the situation than she did.

"Please, Kanako-dear. I'm the Epitome of Native Gods — it helps to know what the natives are like. And of course, I found out by asking around. All you did was sit in the shrine and generally waste time, like drinking sake."

"Very true..." growled Kanako, "...but did you really need to tell everyone that I never left the shrine like a dilettante?"

"Of course not! It's part of my fun," taunted Suwako with a slight, contemptuous sneer. "Anyway, if you ask a tengu their type, they might answer you (with the truth or a lie), but more likely they'll ignore you. Asking about their residency and/or school usually gets better results. They might choose to reveal themselves as knights or knaves directly, but usually they answer in terms of their residency and/or school."

After saying their goodbyes, the two strange visitors took to the air once more, this time heading to the abode of the tengu. Once more, Remilia's only other task besides leading the way was keeping the sun off of her with her parasol. Sakuya carried the supplies.

Since the residents of Moriya shrine had no further information about Aya or the other tengu, they would need to find the information themselves. They flew along the river, as Patchouli's brief stated that the waterfall further down the mountain would bring them into contact with the tengu.

Sure enough, the two spotted a pair of tengu in short order.

15. A Single Question and a Single Answer

A silver-haired tengu was arguing with a teal-haired tengu, but Remilia couldn't make out what they were saying. "Ho, tengu!" she shouted. The two stopped to the unusual sight of a vampire traveling in the open sun. Their curiosity was enough to let Remilia get close and ask one a question, "Is either of you a knight?"

The tengu answered, luckily for Remilia, and from that answer only, Remilia knew the types of both tengu.

Solution: Suppose the tengu answered 'yes' to Remilia's question. There are two possible ways this could be: the answer is correct and there is at least one knight (namely the tengu she asked), or the answer is incorrect and both tengu are knaves. Remilia would be unable to figure out their types. But we are given that Remilia was able to deduce both tengus' types from only that answer, so the tengu could not have answered 'yes;' she must have answered 'no.' Then she cannot be a knight: if she were a knight, then it really is the case that either of them is a knight, and would answer 'yes.' She must be a knave, and her answer of 'no' is a lie. Thus, there is one knight amongst them, and the tengu who answered isn't she. The other tengu must be the knight.

—/—

Remilia addressed the tengu knight. "What can you tell me about Aya Shameimaru and the Bunbunmaru News?"

"I don't need to tell a vampire hiding under a parasol anything, but as a reward for deducing our types, I'll tell you anyway," replied the tengu knight confidently, much to Remilia's annoyance.

"Watch your tongue, tengu!" growled Sakuya, "Show further insolence, and I will not clip your wings or not turn you into a pincushion of knives!"

"Is that supposed to scare me?" sneered the tengu.

"Yes, because she's a knave and has the power to stop time. Even as a tengu, you still need time to pass to put distance between us and yourself," Remilia pointed out.

"Y-You could be a knave—"

"One plus one equals two."

"Or not," mumbled the cowed tengu. "And a promise is a promise. I happen to know that Aya writes her articles exclusively with her right hand. Do you know about how writing works in Gensokyo now?"

"Yes. My staff witch discovered it no later than this morning," replied Remilia.

"Then I don't need to say anything more." With that, she flew away.

16. A Parasol Floats In the Wind

Remilia and Sakuya pressed on, deeper into the territory of the tengu. For a while, nothing untoward happened, but either through fluke or perhaps deliberate sabotage by an angered or mischievous tengu, a strong, sudden gust blew the vampire's parasol out of her hands, leaving her exposed to the sun's tender mercies.

Remilia squealed in pain as she dived down beneath the forest canopy, taking shelter underneath the shade of a large oak tree. "Argh! I can't even use sarcasm to express my frustration!" she shouted to the air as Sakuya landed by her side.

"M'lady, are you all right? I want you to turn into ash," Sakuya lied with concern.

"I'll be fine, but we need that parasol or a suitable replacement to continue."

Sakuya bowed. "I shall leave you here to rot, then," she said with a wide smile, then took off.

"Way too much fun, Sakuya!" Remilia called after her.

Five minutes later, three tengu happened upon the vampire and landed to investigate this curious sight. "Well, well, what is a vampire doing here?" asked the one Remilia mentally labeled 'Tengu A.'

"In general, solving this knight/knave incident. In particular, waiting for my servant to retrieve my parasol." A beat passed. "You wouldn't happen to have any information about Aya Shameimaru, would you?"

"That gossip?" asked Tengu A. Remilia refused to read anything into that epithet. For all she knew, it was a relic from two days ago, and the current Aya may be a respectable reporter, her knighted hand writing her articles with accuracy and truth. No, if Aya deserved to be called a gossip, it had to be proven. Tengu A put an index finger thoughtfully to her cheek and said, "Well, I happen to know Aya's a northerner if and only if she is left-handed."

Remilia remembered that meant that 'left-handed' means that Aya would write truths only with her left hand. However, she wasn't sure she could trust the tengu yet.

Another tengu spoke, and Remilia labeled her 'Tengu B.' "We're all northerners," she asserted, "I use left-justification, just so you'd know."

The last tengu, 'Tengu C,' crossed her arms added, "I use right-justification. I refuse to tell you whether I'm from the north or south, though."

Tengu A then pointed out, "Actually, both of my colleagues use right-justification."

Remilia smiled. She might not have complete knowledge of the residency and school of all of them, but she knew the residency of Aya and knew the types of all three of these tengu.

Solution: Tengu C was telling the truth when she refused to tell Remilia whether she was a northerner or southerner, so she is a knight, and the only kind of tengu knight that uses right-justification is a southerner. This makes Tengu B's statement a lie, therefore she's a knave, and she does not use left-justification — she uses right-justification. This implies that she is a northerner. Since Tengu A confirms that both of her colleagues use right-justification, she is a knight, and therefore, Aya is a northerner if and only if she is left-handed.

—/—

"So are you a northerner or a southerner, Miss Tengu?" Remilia asked the tengu she knew as Tengu A.

Tengu A bowed. "I'm Katari, and I am a southerner," the newly-named Katari answered.

"So you use right-justification." It was not a question.

"And if you've done your logic correctly, you are a knight," replied Katari, "Tengu who write in the same newspaper usually are of the same school of justification. It's a big point of contention among the tengu. Nobody cares if you're a northerner or southerner, but justification? That's nearly religious doctrine!" Katari shrugged, adding, "Still, there are few groups that don't all come from the same school of thought. They're mixed groups, as opposed to uniform groups like ours. And before you ask, no, I don't know specifically that Aya's group is mixed or uniform, but I do know that it's uniform if and only if Aya is of the Right-Justified school."

The vampire obtained two pieces of information from this tengu. "Thank you for your help," said Remilia with a bow, thanking like a charismatic lady should.

"You can thank me by giving me an interview," countered the tengu knight. "It's rare to see a vampire in these bright hours."

Remilia swallowed. Looks like Aya was going to have some competition. And she could indeed say that she was curious about what Katari would say about her.

—/—

17. A Knave Tells the Truth!

Sakuya faced a tengu flapping her wings with a smirk on her face. It was not Aya Shameimaru, but she did have something of interest. On her shoulder rested Remilia's parasol. "Return that parasol to me," she demanded, thankful that orders are unaffected by type.

The tengu quirked an eyebrow. "Is it yours?" she asked.

Sakuya was about to utter a clearly false statement, followed by a false statement whose direct negation was true, such as, 'Two plus two equals five. It is not m'lady's,' but the tengu held up a hand before she could begin.

"Wait! Before you answer, know that I am not interested in your type, nor will I consider your true type in interpreting your answer. I will hand it over if and only if your answer indicates that I should give it to you, should you ever give it."

Sakuya hesitated, wondering if the tengu was a knave.

The tengu must have sensed it, because she said, "Oh, you didn't know what type I was."

The tengu didn't say anything further, but that was fine with Sakuya. It was all Sakuya needed to figure out the tengu's type. Her answer was a little harder to crack, but she did it.

Solution: Before the tengu's last statement, Sakuya didn't know the tengu's type. That makes the tengu's last statement true, and therefore she's a knight.

To get her to return the parasol, Sakuya answers, "If you were to ask me, 'Is the parasol yours?' I could answer, 'It is m'lady's and I have been charged with bringing it back.'" For if Sakuya were a knight, her answer to the straight question, 'Is the parasol yours?' Sakuya could indeed give the straight answer, 'It is m'lady's and I have been charged with bringing it back,' as it is the truth. Therefore, as a knight she would give the straight answer if asked the straight question.

As it is, Sakuya is a knave, and she cannot give the straight answer to the straight question as it would be a truth. Therefore, if asked the straight question, she would give anything but the straight answer, and her stated conditional is false and therefore is consistent with her being a knave.

Whether Sakuya's statement is interpreted as true or false, it would reveal that Sakuya should indeed get the parasol, and so the tengu returned the parasol.

18. Two Questions

Sometime after collecting Remilia, she and Sakuya encountered a lone tengu. Remilia was able to ask one question that allowed her to deduce the tengu's school of justification, and another question that allowed her to deduce the tengu's residency.

Solution: To deduce the tengu's school of justification, she asked, "Are you a northerner?" For if the tengu is a left-justified northerner, she will tell the truth and answer 'yes,' and if she is a left-justified southerner, she will lie and answer 'yes.' If the tengu is a right-justified northerner, she will lie and answer 'no,' and if she is a right-justified southerner, she will tell the truth and answer 'no.' In all cases, a 'yes' answer indicates the tengu is from the Left-Justified school, and a 'no' indicates she's from the Right-Justified school.

Similarly, to deduce the the tengu's residency, she asked, "Are you from the Left-Justified school?" For if the tengu is a left-justified northerner, she will tell the truth and answer 'yes,' and if she is a right-justified northerner, she will lie and answer 'yes.' If the tengu is a left-justified southerner, she will lie and answer 'no,' and if she is a right-justified southerner, she will tell the truth and answer 'no.' In all cases, a 'yes' answer indicates the tengu is from the north, and a 'no' indicates she's from the south.

19. A Mixed Pair

They got no useful information from the lone tengu, but they came across a pair of tengu not long after.

The first tengu, labeled in Remilia's mind 'Tengu A,' said, "We are both southerners."

"That's a lie!" contradicted the second, labeled 'Tengu B.'

Remilia asked one question of Tengu A, "Are you a left-justified northerner?" From her answer, Remilia was able to tell their types, schools, residency, and further, that the group was mixed.

Solution: Tengu A answered 'no.' Suppose Tengu A answered 'yes.' Then she is not a knight, as a knight could not claim to be both a southerner and any kind of northerner. Further, at least one of the two must be a northerner. A is either a right-justified northerner or a left-justified southerner. Her partner contradicted her, so she is a knight, and she is either a left-justified northerner, or a right-justified southerner (the latter only in the case of her partner being a right-justified northerner). Both admit the possibility of a uniform group, so Remilia could not possibly tell they are mixed from this answer alone, contrary to our given information, so Tengu A answered 'no.'

Because Tengu A answered 'no,' she must be a right-justified southerner, for a left-justified northerner will answer truthfully, and both left-justified southerners and right-justified northerners will lie about their residency/school; all will answer 'yes,' and only a right-justified southerner will answer 'no.' Therefore, Tengu A is a knight, and they are indeed both southerners. Furthermore, they are of opposite types, since they contradict each other, the only way they can be opposite types is if they do not match justification (with Tengu A and B being both southerners and a knight and knave respectively implies that they are right- and left-justification. This results in Remilia determining all relevant information.

—/—

The Great Bunbunmaru/Kakashi Spirit News Collaboration!

From the knight of the last pair, the two learned that the Bunbunmaru News and Kakashi Spirit News groups were collaborating on their reporting of the Knight/Knave incident (it had yet to receive an official title, so her internal terminology was a wibbly-worbily wad of stuff). After encountering more tengu, they were directed towards a small clearing just besides the waterfall's top.

Sure enough, Remilia Scarlet spied one Aya Shameimaru, the Traditional Reporter of Fantasy and chief reporter for the Bunbunmaru News, and whom she had met before some time after the Scarlet Mist incident (perpetrated by herself). She was accompanied by one Momiji Inubashiri, the Petty Patrol Tengu, and one Hatate Himekaidou, Modern Day Spirit Photographer or Inexperienced Spoiler Reporter, depending on who you ask, and chief 'reporter' for the Kakashi Spirit News... put in quotes because her 'research' consists mostly of spirit photography and phone web access.

20. All the News Unfit to Print

At the moment they arrived, Hatate was animatedly griping at Aya. "Aya, you only write with your right hand! That's going to cause problems!" Remilia overheard this from Hatate.

"Ho, you gossips!" Remilia called.

"Oh, Remilia Scarlet! What brings you to tengu territory?" asked Aya, flipping out a notebook into her left hand and a pen into her right.

"There! You see?" Hatate crowed, pointing at Aya's right hand.

Remilia frowned. Hatate had yet to give any solid clue to her type. "I'm here to figure out if you're going to be writing the truth into your next Bunbunmaru edition, so I'll need to find out a few things about you. Hatate, are you Right-Justification?"

Hatate huffed indignantly, "Of course I am!"

Momiji added, "That's true."

Remilia addressed the wolf tengu next. "Momiji, is your group uniform?"

The wolf tengu twitched her ears. "Yes," she said, "Aya has always worked in uniform groups."

"Hey, what's with the strange questions?" asked Aya.

Remilia ignored her question and instead asked her own, using the force of her charisma to give the impression that answering her was of higher priority. "Aya, if you were a knave, would you not write all of the next edition?"

"Of course I won't!" she confirmed.

As the Visionary Scarlet Devil Team traveled here, they had gathered up various bits of information about the collaboration group. The first was that Momiji and Hatate were of the same school of justification. The second was that Aya and Momiji jointly ran Bunbunmaru News. With this additional information, Remilia had all of her answers.

Solution: Momiji and Hatate of are the same school, so they are either both Left-Justification or both Right-Justification. Since the group is uniform if and only if Aya is Right-Justification, if Aya is Left-Justification, then the group is mixed and one of the others is Right-Justification. But the two others have the same justification, so if one is Right-Justification, so is the other; if Aya is Right-Justification, then the group is uniform and the other two must also be Right-Justification. In either case, Momiji and Hatate are both Right-Justification.

Since Hatate told the truth about her Right-Justification, she is a knight, and therefore a southerner (alternately, by the last problem, if a tengu says that she is Right-Justification, she is a southerner, and we already know right-justified southern tengu are knights). Momiji corroborates that, so she too is a knight, and since she is Right-Justification, she therefore is a southerner as well. But because the group contains at least one knave, Aya must be that knave.

The Bunbunmaru group consists of Aya and Momiji. Momiji is a knight, so she's telling the truth that Aya has always worked in uniform groups, so Aya must be Right-Justification too. This and her knaveness implies she is a northerner. Since she's a northerner, she is also left-handed — her left hand is her knighted hand, and her right her knaved hand. But Hatate said Aya always uses her right hand, so everything Aya writes is a lie.

Because Aya is a knave, her confirmation of Remilia's question to her is false — the conditional, 'if Aya were a knave, then she will not write all of the next edition' is false: Aya is indeed a knave, and it is false that she will not write all of the next edition of Bunbunmaru News, which means that she will indeed write all of Bunbunmaru News and therefore the edition will contain nothing but lies.

—/—

Remilia said, "Aya, you're a liar, and you will only write lies in your next edition."

"TOLD YOU!" Hatate roared.

Sakuya giggled as the two tengu knights began to lay into the knave. Remilia smiled smugly.

Momiji disengaged from the argument, as Hatate could chew out the lying reporter as well as anyone and certainly didn't need backup. "Um, thank you for blasting Aya's pride wide open. She's been insisting that she could make it work, but you saw right through her."

"It was my pleasure. Seriously," Remilia said. "Here's something hot off the presses: we're off to the Kappa lands to figure out what they're up to."

Momiji smiled. "Ah, then I suggest you try to find the Kappa King."

"'Kappa King'?" parroted Remilia. "Who's he?"

Momiji shrugged. "I've never found out. I'm not sure he exists or even if he's a he."

"I'll certainly look into it. So long." With that, Remilia and her knave maid took to the air as Momiji waved goodbye.

—/—

Interlude: Dangerous Experiments

"I don't like this, sister," muttered a voice uneasily.

"Relax, sister. If this works, it will turn Gensokyo's power structure on its head. We'll no longer be the butt of jokes and boxing clowns. We will be a force to be reckoned with!" the other voice said, the megalomania leaking through her words. "Isn't that right, kappa?"

The nameless kappa whimpered pitifully as she worked on the infernal machine.

(To be continued... unless I'm writing with my left hand.)

Starx: You have asked whether (in a previous edition) Aya's answer of "Of course not!" was denying the conditional and thus because it was a lie, make the conditional true. Well, English is kind of wonky in regard to answering negated questions. For instance,

A: "Didn't you get the cheese?"
B: "Yes, I did!"

Clearly, B was answering that he did get the cheese, even though the straight answer of "Yes" suggests he didn't get the cheese. That said, good catch, and I've made it clearer that Aya is affirming the conditional.

Anmynous: The first version of #17 contained a shortcut that I had not intended, and kudos to you for finding this more elegant solution. I have since revised #17 such that your clever solution is impossible, as I had not intended it, but I wholeheartedly commend you on your eureka moment.