Touhou Project by Shanghai Team Alice

Knights and knaves accredited to Raymond Smullyan


"I'll take this one."

Rinnosuke Morichika, the Unmoving Used Goods Seller and proprietor of Kourindou, looked up at one Yukari Yakumo, Youkai Sage of Boundaries, her voice cutting through the normal stillness of Kourindou. She held up a small, orange, ragged paperback book that loudly proclaimed its own title in one of those western scripts as What is the Name of This Book? with a subtitle 'The Riddle of Dracula and Other Logical Puzzles'.

It was a strange title, and the book's author Raymond Smullyan was unfamiliar to Rinnosuke Morichika, but Rinnosuke had determined that the odd book was exactly what it said on the tin, for the most part. It was a book of logical puzzles, with a small treatise on the subject of the nature of proof.

Rinnosuke had not known Yukari to be at all interested in logic in the time he'd known her. He supposed this would be an improvement, since exercising her logic may calm her down.

She even paid full price for it.

—/—

As Yukari Yakumo gapped into Mayohiga, clutching the strangely-titled book and wearing a huge fox-like smile on her face. Ran saw that smile and immediately knew that her master was up to no good.

"Yukari-sama, you're getting one of your ideas again, aren't you?" Ran said, more like a statement than the question it was dressed up as.

"Oh, yes. Amusing ideas. Tantalizing ideas. Ideas that will twist the heads of our friends into little knots and drive them to frustration," she said with a chuckle.

"Master, you are already known more as the 'Troll of Gensokyo' than the 'Youkai Sage of the Boundary.' May I suggest... you know... behaving a bit more sage-like?"

Yukari's smile did not slip as she turned toward her shikigami. "Tell me, dear Ran, why is someone called a sage?"

"Because they have demonstrated deep experience, sound judgement, and impeccable wisdom," Ran replied, as if from a dictionary. "None of which you've displayed of late. Playing pranks on people demonstrates none of those. Fairies play pranks, and they're dumb as rocks."

"Oh, ye of little faith. This will be cool, I promise."

"Your words do not inspire much confidence."


Knights and Knaves:

A Logical Adventure of Gensokyo

by Wyrm

Chapter 1:

In Which Remilia Scarlet Awakens as a Knight


Months Later

Evening fell upon the Scarlet Devil Mansion, situated on an island in the middle of the Misty Lake. It was time for one Remilia Scarlet to rouse herself into wakefulness.

To all appearances, today was as any other. Remilia waking in the night in her pajamas. Shuffling out of bed, yawning and rubbing her eyes of the sleep-boogers they'd collected. "Mmm... Woke early today. Perhaps Sakuya doesn't even know it."

A knock at the door.

"M'lady, the midnight meal," came Sakuya's voice.

"'Midnight'?" gasped Remilia in surprise. "Did I really sleep that late?"

"Indeed you did, m'lady. Do you wish to have your meal in bed?"

Even though she had just gotten out of bed, she did indeed wish to take her meal in bed. "Yes," she immediately and truthfully answered, then stopped, puzzled. It wouldn't do for the lady to be seen having breakfast, or the midnight meal, in bed where crumbs would get into the sheets. "But I must decline," she added, "for there are too many problems for breakfast in bed, especially for cleaning it up."

"Indeed, there is a problem. M'lady does need concern herself about how she takes her meals. It's an embarrassment."

A deadly chill of a silence descended upon the immediate area. "Care to say that again, Sakuya?"

"I-I said, 'There is no problem, and the lady of the house need not be embarrassed taking her meal anywhere she wants,'" came Sakuya's stuttering response.

"That's not what I heard, but I accept your correction," Remilia replied, and went to her bed, a bit steamed. She thought about her words. Why hadn't she said, 'That's what I thought!' in a sarcastic, reproachful tone? It was on her mind, but instead Remilia delivered a completely candid response.

Sakuya Izayoi opened the door with a sickly look on her face and a forced smile. The perfect maid had made her first slip-up, and it was a doozy. "M'lady, this is your midnight meal," she said as she set the tray down with no small nervousness in front of Remilia.

Remilia stared at it.

Buttered toast and jam.

Tea and juice.

Very light. Not much meat or dairy.

Was it brunch? No, Sakuya said it was the midnight meal. A full lunch. It should be heavier. Remilia was about to address this when she spied the time on her mechanical clock: just after sunset.

The mistress's anger deepened. "Sakuya, I thought you said this was the midnight meal! This is a usual breakfast, and the clock says that it should be around the time I should have breakfast anyway!"

"Th-The clock isn't correct!"

Remilia, her suspicions raised, turned to stare out the window. She noticed the dusk not quite ended, and the particular placement of the stars indicated that it was indeed early evening. "Sakuya..." she murmured dangerously, "...the stars and the last fading traces of twilight indicate that the clock is accurate. This is early evening. This is breakfast. Why did you lie and say this was the midnight meal?"

"I-It was a j-joke!" came her pitiful excuse from her pitiful face.

Remilia set firmly down the butter knife she'd been idly playing with. "A joke? It's not very funny, Sakuya."

"Yes, it is!" contradicted Sakuya, increasingly distraught.

"Don't you dare contradict me, Sakuya! If I say something is not funny, it isn't funny!"

Sakuya cringed in mortification, and feebly tried to disengage from that conversation. "I hope you don't enjoy your meal," she murmured. At realizing the words that escaped her mouth, as well as Remilia's furious look, Sakuya tried to recover, "I-I mean, I hope you choke and die on it! I mean—"

"ENOUGH!" barked Remilia. "It's woefully apparent that you resent your employment here!"

"Th-Th-That's true, m'lady" blurted Sakuya, flustered at her mouth seeming to spiral out of control. "I mean, I do resent being under you! I mean, I'd rather die than—"

"SHUT UP!"

Sakuya did as she was told with only a whimper. Tears were spilling from her eyes and took on a miserable face.

Remilia sighed. It was the end of an era. Even being the evil Queen of the Night, Sakuya was the one human she felt closest to, and wanted to see happy. It was obvious to her now that Sakuya was unhappy and rebellious. Perhaps she needed to let her go.

"You're fired, Sakuya."

Sakuya broke down, openly sobbing. "M'lady, I am grateful that you have fired me!" she wailed.

This drove Remilia absolutely livid. "Fine! If you're so happy about it, then I'm lucky I discovered this now rather than— ack! What?"

The 'ack' was yelp of surprise as a small, orange, ragged paperback book popped out of nowhere to whack her on the back of the head.

Remilia snatched it up and brandished it hotly. "What the hell is with this book?"

Sakuya said nothing. Her mouth wasn't serving her very well thus far, so it was probably a good choice.

Remilia finally deigned to look at it, and blinked at what she saw. "'What is the Name of This Book?' Strange name for a book. It's like the author couldn't commit to a title. Like the Dracula on the cover, though." She plucked contemplatively at the bright pink Post-It note in the book, serving as a persistent bookmark. "There's a bookmark, too. Someone wants is to read this, I think. Let's see what it has to say..."

And she read.

She read about a mystical island in the unknown parts of the world. It was a land divided into two kinds of inhabitants: scrupulous truth tellers and unrepenting liars, called knights and knaves, respectively. The book used that premise as the basis for various puzzles.

Then she thought of Sakuya's behavior. It almost seemed to Remilia that she was saying something other than what she wanted to say. As if she wanted to tell her something different, but the words tumbled free without her consent. Could Remilia have a similar affliction.

She tried to formulate a lie to tell. An untruth that would prove that the book was nonsense. But she could not. No matter how she tried, a sentence she knew to be untrue could not pass her lips: 'two plus two equals five,' 'I am a teapot,' and many others. No amount of force could get them past. If she were distracted by a stressful circumstance, like damage control caused by (say) unbridled truth telling, those words could easily get away from her and she would spout truth after dangerous truth.

"I can't lie!" Remilia said in revelation. "No matter how I try, I can't say statements I know aren't true!" She looked up at Sakuya. "And you have made clearly false statements, and given our long friendship I find it hard to believe the rest of it. Sakuya, we fit this book's description of 'knight' and 'knave.'"

Sakuya had by this time calmed herself. "What is a 'knight' and 'knave', m'lady?" she asked.

"So it seems earnest questions are unaffected..." Remilia observed to herself, then explained what she had learned from the book.

"That is certainly ordinary!" Sakuya said.

Remilia was about to shout that it damned hell was not ordinary before she remembered. "Right. You're a knave... I think."

Sakuya nodded gratefully, visibly relaxing. Then she blinked. "M'lady, there's no letter over there that mysteriously appeared," she said, pointing to the end-table.

Which, being a knave, meant that there was a letter over there that mysteriously appeared. And sure enough, there was.

Remilia opened the letter, as it seemed was addressed to her, but she couldn't be quite sure in this mixed-up world. She thus began reading.


Dear Remilia,

Two plus two equals four. That at least is true, and the same hand who wrote that sentence is the one that will write this entire message. Don't worry if you don't understand that right now; its significance will become clearer later should you get that far. For the moment, you will just have to trust that this message contains the truth of our situation.

I trust that you have read the marked place in Smullyan's book, and noted the similarity of your situation that the inhabitants of the Island of Knights and Knaves no doubt find themselves in. You may have already guessed this, but every inhabitant of Gensokyo is now sorted into one of these two groups, knight and knave, and are referred to in the same vocabulary.

Knights, of course, always utter what they know and believe is the truth and knaves can only utter contrary to their knowledge and convictions. This caveat will become important later, should you reach it, but for now we can crudely say that every statement that a knight says is the truth, while any statement a knave says is a lie. If the individual's knowledge does not allow them to know the truth or falsehood of their statement, then they cannot make that statement. If the individual's knowledge does not allow them to know the correct answer to a question, they cannot answer and risk answering contrary to their nature. It is now the nature of anyone who is either a knight or knave, and from now on any person you meet is either a knight or a knave, referred to as their type.

You cannot, under any circumstances, force a knight to state a lie, or a knave to utter the truth. Nor can you force a knight into action to make lie of his or her words, nor force a knave into action to make his or her words the truth. A knight or knave may ignore at his/her discretion any question you already know the correct answer to, but in general a denizen of Gensokyo will answer any other question. (That means, for instance, you cannot ask someone whether one plus one equals two and expect an answer, since you know the correct answer to that before you asked.) A knight or knave may volunteer such a piece of information —as I have done at the start of this message— but it must be volunteered.

In general, you are directed to determine the knighthood or knavehood of everyone you meet, when possible. You may ignore the knight- or knavehood of common rabble, such as your own fairy maids. You must, however, prove the knight- or knavehood of all your household (sans fairy maids) to proceed. You may already suspect some of them to be knights or knaves, but you must prove the case either way.

Good luck.

Ran Yakumo


"Pfft. An incident, probably caused by the Great Troll of Gensokyo," Remilia mumbled with irritation as she finished the letter. "We'll also probably encounter those other three along the way."

Remilia did find certain appeal in this new kind of incident — one that changed the inhabitants' nature rather than came from an external threat. It was at a change of pace from the usual 'lay the smack down on a random youkai' incident that had become the norm. She might have called herself intrigued had the incident, except for two facts: she was directly affected, and she found logic rather tedious. Like in the Fake Moon incident, the sooner it was solved, the better. She stood in her jammies, with clenched fist, "Come, Sakuya. The game is afoot. You're rehired by the way."

"M'lady, you are wearing your normal clothes."

Which meant Remilia wasn't wearing her normal clothes. Indeed, as she looked down, she saw and remembered she was in her jammies. "Let's start after I get dressed and have breakfast," she mumbled, cheeks glowing a bit in embarrassment.

"M'lady."

(To be continued, only if I'm not a knave.)