004
It was nothing special.
It was a typical Monty Hall problem—yet again.
What Ougi-chan explained to me the other day, when I infiltrated Nanahyakuichi Middle School.
To think that would be applicable to triplet maids… In any case, the “you have two chances” doesn’t simply mean “you can miss once,” that’s the nature of the problem.
If I designate one of them as the eldest, regardless of whether that is correct or incorrect, I can remove one of the remaining two from the options—and after having moved from a three-way choice to a twoway choice, I have the right to change my selection.
I can change, or I can not change.
In other words, this was a question based on intuition.
Changing or not changing might appear to have the same probability, but in reality changing is the correct choice. With that, the chance to guess the correct one goes up from one third to two thirds.
The detailed explanation is already published somewhere (also, people would point out I make my special volumes too thick) so I’ll keep it short here. Anyhow, using the right to change my answer is correct—in normal times.
This wasn’t normal hours.
The triplet maids were killing their emotions and waiting for my answer whilst acting as motionless mannequins, but I couldn’t possibly follow the textbook method here. After all, I want to fail this test.
I desperately wanted to fail it.
I absolutely must not use my second right to choose, and more importantly, I can’t use my first one without thinking of anything. I must raise, even if by a little, my chance of misfiring my guess at who the eldest was.
I mean, one of the reasons the Monty Hall problem is hard to understand is that even if you choose randomly, don’t make the correct choice, and follow your gut, you will win one out of three times. If my odds of winning are as high as in rock-paper-scissors, I have to think about it.
I can’t make a gamble with a one-third probability of losing Hanekawa.
I want some additional ingredients to help my decision-making process at least.
I started turning in place and observing the three surrounding me in turns… I wouldn’t ever have imagined I would someday be able to observe maids at such a close distance in my life.
Even if this was an exterior teahouse, I wouldn’t have been allowed to stare so much.
But, no matter how much I worked up my eyes, I couldn’t distinguish any differences between those three. Are triplets always this similar? I thought that Teruko might have had some traces from the glasses she was wearing until just earlier, however nothing came up from inspecting all three of their noses.
“Is it OK if I touch?”
“It isn’t.”
Akari-san or Hikari-san or Teruko-san refused on the spot. Yeah, I guess it’s normal.
“Please make your decision by relying on observations.”
“Can I ask questions?”
“We don’t mind, but you’re not assured we will answer truthfully.
Especially Teruko, because she’s a liar.” Then that approach isn’t valuable.
Trying out something else, I asked “Then, please show me your fingerprints.”
No matter how much they look the same, be it twins or triplets, their fingerprints should differ. If their DNA is the same, how about their luster? Well, it’s not like I collected their fingerprints beforehand so it’s not like checking that will change anything… But in any case, my ideas would stay entangled if I didn’t find any difference.
I needed a linchpin for my thoughts.
That said, the fingerprints and palm prints they showed me all looked the same to me. At the very least, those three would get the absolute same results from a palm-reading divination.
Umm. There’s too few clues to start anything.
This relentlessly abnormal situation of being surrounded on three sides by maids didn’t allow me to think logically. How much worth does logic hold in front of the miraculous existences that are triplet maids?
First, I heard that in case of twins their order of birth gets reversed… The convention is that the twin born after becomes the eldest… But what’s up with that flimsy convention?
Just, if that were the case, what about triplets? Would the order of birth become youngest, middle, eldest? However, even then, since they first introduced themselves as “Triplet maid, eldest daughter Akarisan,” “Triplet maid, middle daughter Hikari-san,” and “Triplet maid, youngest daughter Teruko-san,” the one I should guess (to miss) was
“Triplet maid, eldest daughter Akari-san.”
If possible I would have preferred to decide based on their personality, but they started shuffling before I could grasp their individual character… Apart from the glasses-wearing, taciturn, inexpressive Teruko-san, Hikari-san and Akari-san were still mixed up in my head when the test started.
If I had to say, Akari-san was the proper one and Hikari-san the more familiar and kind…? But, being maids, they erased their presence perfectly so I couldn’t read much into that.
Well, I guess it’s useless to think any more.
If I stay at a deadlock for too long they’ll eventually figure out I’m a fake Hanekawa, so let’s make the situation progress anyway.
There are two guesses so I only need to reach the touchstone of the first guess.
I need to observe the triplet maids’ reaction to that.
“Then, I designate you first.”
It was completely random but I pointed at one of the maids. I didn’t have any grounds, but she was the one to answer my “Can I ask questions?” earlier. Setting aside the “You’re not assured we will answer truthfully,” I leaned heavily on the words that came after that: “Especially Teruko, because she’s a liar.” She only said that because she wasn’t Teruko-san, you can reason that out.
So I decided, if she were feigning that.
You were trying to lure out the fact you weren’t Teruko-san, but in fact you, who spoke, aren’t you the taciturn Teruko-san? That’s the sharp deduction of the Boy Detective Araragi Koyomi.
Well, whatever the circumstances might have been, it was more instinct than a proper and logical deduction, but… However, well, that should be quite the feat for my first answer.
The choice fundamentally had no definitive answer, so in the end the real Monty Hall problem started now—sure enough, the one I designated, Akari-san or Hikari-san or Teruko-san, smiled lightly and by saying “I see, well then,” she prompted the other two, Akari-san or Hikari-san or Teruko-san.
Among the prompted Akari-san or Hikari-san or Teruko-san, one Akari-san or Hikari-san or Teruko-san mirrored the movement of the other Akari-san or Hikari-san or Teruko-san whom I pointed at, and smiled in the same way. Yet, the remaining Akari-san or Hikari-san or Teruko-san shrugged her shoulders, still expressionless, took out a pair of glasses from the pocket of her apron, and put them on.
She then took one step back.
So she was Teruko-san? Is that what it meant?
So the Teruko-san I aimed at (trying to miss) wasn’t in fact Teruko-san but Akari-san or Hikari-san?
Regardless, after my first answer the three-way choice changed into a two-way choice—among the remaining two, one of them was the eldest daughter Akari-san and the middle daughter Hikari-san… No, not necessarily.
It is not certain that, just because she put glasses on, the remaining maid is actually Teruko-san—during the shuffle motion they might have passed the glasses to each other somewhere I wasn’t looking, they looked like they had enough leeway to pull off such a trick. The refined step technique of maids isn’t to be taken lightly.
The lack of sound when walking is comparable to ninjas.
Well, whether the two remaining choices were Akari-san and Hikari-san or Akari-san and Teruko-san, it shouldn’t make a big difference for the person answering… no, hold on?
There’s no way it wouldn’t.
Teruko-san (or Hikari-san) appealed that she was the wrong choice by putting on glasses, but… wasn’t there something unnatural in this exchange? I only thought from the perspective of the person taking the test, but what about the maids’ perspective?
… I can’t visualize it at all, but if I were one of those triplet maids, a living example of the Monty Hall problem—then, after the person taking the test answers, there should be a meeting to decide what to do, right?
I mean, they didn’t know until that very moment who would get designated—I chose one of the maids randomly, welding myself on a single statement, but I could have taken that statement another way and chosen another maid.
If I had no criteria, then they didn’t either.
So there was no way for them to be sure of who would be chosen the first time, therefore… they shouldn’t have been able to decide who will be removed from the options after.
So in this case they would need a signal—in the case both of them were wrong.
However, the maid prompted by the Akari-san or Hikari-san or Teruko-san I chose, Akari-san or Hikari-san or Teruko-san smiled without even an eye contact, and the other one put glasses on.
I’m not allowing for telepathy among triplets.
I shouldn’t be saying that, being a resident from a world messing with oddities, but I’ll ban any abilities that surpass human understanding. Being totally identical triplets was enough of a cheat.
I didn’t consider this development, but if they removed a maid without a single time lag, that means one of the two not-designated maids was Akari-san.
Originally, in the Monty Hall problem, the choices A, B and C are under the control of the game master. The choices don’t move of their own will… Even then, it contains the same problem. Thinking purely with probabilities, changing the choice on the second try gives you a two-thirds chance of winning. However, since humans are managing the game, the judges should require thinking time.
In the case the one-in-third correct option was selected— which one of the other two to remove? The conditions are totally identical so throwing in a bias wouldn’t let the game carry on.
The game master should choose randomly.
They must harden their heart and eliminate their own will.
You might think I’m insistent, but in short, you can establish that rule—if the correct option was among the non-selected ones, you have no choice. No need for a thinking time, the option chosen by the game master is set in stone. If the correct option wasn’t among the nonselected ones, you have a choice and a thinking time is necessary.
Therefore, the person taking the test can make such an hypothesis.
If the game master stopped to think, you shouldn’t change.
If the game master didn’t stop to think, you should change.
… Then it becomes more of a psychological battle than a logical one, but of course, the game master isn’t defenseless against that. Even when the correct option wasn’t selected and they don’t have any room to choose, they can pretend to have room.
Whether they are hesitating or not, they can systematically fix the thinking time to 10 seconds. Doing that, the person answering has no way to distinguish the two cases.
If you remove the reactions, there is no longer any material for judgment.
So if the triplet maids did that, I would be completely clueless. But, what they did was the contrary. The thinking time taken was nil.
As far as I could think, they should have been able to fake hesitation.
But they shouldn’t have been able to fake not hesitating.
There are lies you can’t tell.
For any liar.
In the case the two were both wrong, if they remove themselves from the choices at the same time (they would simultaneously say “Ah,” “Ah,” and they would awkwardly have to yield to the other), it would be like saying the other one is the correct choice. Then, since one of the prompted maids put on glasses instantly and the other one smiled, it’s settled that the remaining maid is the eldest daughter, Akari-san.
Bingo!
But, I’m not stupid enough to scream “Then I won’t change my decision!” Letting yourself be swayed over by the joy of deducing the correct choice and losing to the temptation of choosing the right answer would be the act of a real fool.
Here, I should pretend to not have noticed anything and follow the Monty Hall theory to the letter, going against your gut and changing your choice is correct—for me.
Perhaps the triplet maids didn’t make a mistake but gave me a hint. Maybe they’re saying that someone unable to notice this lack of thinking time doesn’t have the qualifications to have an audience with the mistress…
I don’t know how widely it is understood, but nowadays, being a time when the Monty Hall problem is completely solved, what is tested in order to enter the island might instead be skills like perception and concentration.
I can’t think Hanekawa wouldn’t notice the thinking time factors I noticed, so I’m deeply sorry for the maids having come from far away, but I’m going to logically commit an error.
As I was thinking that, and when I was about to proudly give out the Monty Hall answer (“Even if there were 100 options…”), the maid I chose in my first go… The one most likely to be Akari-san. “I’m sure it will be fun, Hanekawa-san.” That maid cheerfully said so.
Since Teruko-san was (seemingly) out of the equation, there was no need to keep the expressionless face, her smile was really kind, as if considering me.
“To compete with other geniuses of your level, it will be fun for Hanekawa-san.”
“…”
Those words—rendered me speechless.
Aaah… I see.
I was thinking about it in the wrong way.
I was thinking along the lines of “Don’t even joke about sending Hanekawa to an isolated island screaming ‘murder mystery’,” and “Why did that exiled mistress have to call Hanekawa over?” and “Hanekawa isn’t a spectacle, I’m the only one who should be able to look at Hanekawa.” But this invitation had a different meaning.
An isolated island gathering geniuses.
In other words, geniuses can exchange there.
And without any bias, there might be scholar geniuses, artist geniuses, maybe even sports or cooking geniuses, board games geniuses or martial arts geniuses. Anyway, this was an occasion to come in contact with people of outstanding talent.
On that island, you’d be guaranteed a rare experience you never could have had in a proper university… I can endure missing such an outrageous environment, but what about Hanekawa?
There was no doubt she would dislike being called a chosen genius. Being called like that was what she hated the most.
However, if you asked whether Hanekawa hated those called chosen geniuses, that wasn’t really the case—rather, she would faithfully assess those exceptional talents without any jealousy or envy.
In the same way she properly paid respect to the wandering psychedelic middle-aged man—or when she, as a normal human, analyzed the iron-blooded, hot-blooded, cold-blooded vampire who had lived 500 years.
Wouldn’t Hanekawa wish for interactions with geniuses?
She was currently wandering abroad, but wasn’t she spreading her outlook in order to meet people like that in the future, after she graduates? Wasn’t she spreading her wings for that?
Then I wonder if it’s really fine for me, in this burnt field, to make not the amateur decision but the commoner’s decision of tearing this invitation of hers to this other world in pieces… Crap.
I thought of something unnecessary.
I got cornered into making a totally different choice.
“… Are those geniuses… monster-like?”
“Pardon?”
“No, the people on that island… The people invited on that island.
What kind of people are they? You said geniuses of the same level—” As Hanekawa Tsubasa.
As that invincible and perfect class president.
“—Are there even comparable geniuses?”
“I cannot affirm. Because I’m not a genius. I’m only a maid—we’re only three maids. Triplet maids.”
The person that was suspected of being Akari-san said so.
That answer felt like a letdown, “However,” the maid on my right, Hikari-san (or perhaps Teruko-san not wearing glasses) continued.
“As a maid I’ve seen various geniuses—a colorful assortment of geniuses. Geniuses stimulate each other, influence each other, enhance each other, and kill each other.”
“K—kill…?”
“Ah, no. Of course in the sense of killing one’s self.”
No, even if you try to fix it by making that smug face…
Killing one’s self, what kind of situation is that? What kind of “of course” is that?
“For me geniuses are people I can’t understand, but isn’t that why geniuses profit from each other? Isn’t that why they attract each other? For someone not understood by everyone, isn’t having someone that understands you far more important than being liked or being hated?”
Although I can’t understand how Hanekawa feels about that— Hikari-san (or Teruko-san) smoothly added so, but that didn’t need to be added.
Of course that was the case for Hanekawa.
Ever since spring break I’ve continued affirming I couldn’t understand her, so there was no doubt.
If a genius appeared who was able to say the words “I understand you” to Hanekawa, not merely kindly or severely, but with plenty of persuasiveness… Just how much would her talent be fulfilled?
I don’t know everything, I just know what I know.
I know how much she, who continuously said that line, wanted to know herself.
I know.
“…”
Then.
Maybe I should not change my decision and continue designating Akari-san… but even then.
I was just pretending to hesitate.
I was just creating thinking time.
I was just pretending to think for Hanekawa’s sake… In reality that choice was an instant decision.
There was no room for doubt.
It’s not for me to decide what Hanekawa should do… What I should decide are only my choices.
My decisions.
She doesn’t need my protection.
So I should only follow my ego.
“Then, would you please soon proceed to your second choice. Now, who is the eldest daughter? Please point at the maid you think is her.” Being told that by the suspected Akari-san, I— I changed my choice.
But not towards the smiling maid, I pointed at the maid wearing glasses—right, the one removed from the options and who looked to be Teruko-san at first glance. “Splendid!” And.
The maid who looked to be Teruko-san removed her glasses and smiled.
“I am Chiga Akari. The eldest daughter of the triplet maids.”
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4 Hanekawa’s first name, 翼 (tsubasa), literally means “wings”.
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