Regulus: Can somebody tell me …
Regulus: Why I constantly get locked up ever since I've known Vertin?
In a now neglected corner, the Rockin' Pirate is deep in thought.
Regulus: First locked up in a suitcase, then a Foundation cell, now this ...
Regulus: Ah!
Regulus: Oh! What else could it be if Vertin weren't the jinx?!
Regulus: Lads! I know what's going on! You got the wrong person! She is the most irrational number here!
The dungeon gate remains tightly locked. The wood made of it wouldn't understand her words.
Regulus: Aah, I'm narked! What does it say here?
Regulus: "Freedom will be granted once the proof is completed?"
Regulus: Hmm. That's to say, I have to prove myself not an irrational number to get out of here?
Regulus: Which is exactly what I've been trying to do, isn't it? Prat!
Her fist smashes against the wooden gate.
Regulus: Ugghh!
She drops to a crouch because of the pain.
APPLe: Captain, maybe you are in the wrong direction.
APPLe: This APPLe presumes that the followers on this island have a close connection with Pythagoreanism.
Regulus: Emm, Pythagoras, that ancient Greek mathematician? The guy who said something about the opposite side of a right triangle?
Regulus: Isn't he the guy who lives in some time BC?
APPLe: Maths is only a part of the Pythagoreans' achievement. But from a more universal perspective, they are a mysterious group of scholars.
APPLe: Believing things are made up of numbers, venerating integer numbers, abstaining from beans, and the religious collective lifestyle—these are all pointing to Pythagoreanism.
APPLe: The earliest Pythagorean school perished because of the discovery of irrational numbers, which explains their odium of it.
APPLe: At that time, a deviant student named Hippasus discovered root 2, and the theories based on the ratio of integers they hold dear were upended. Hippasus himself was drowned in the sea.
APPLe: This APPLe assumes they see the integers as the standard of virtue, and people can increase the number they rank through study and self-improvement.
APPLe: Besides, they are convinced that a numerical code is hidden in everything and everyone. Whoever can solve the code can obtain the truth of the world.
Regulus: Alright, now I know what's going on.
Regulus immediately gets off the ground.
Regulus: This Pirate has had enough of this moral standard, which is obviously prudish, backward, and lacks humanitarian spirit!
Regulus: I'm going to tackle the root cause of this misfortune!
Pirate, the believer in liberty, walks in circles in front of the gate and suddenly starts to pull the loosened strips on the door.
Regulus: I'm breaking out!!!
APPLe: Why am I not surprised? The captain quickly gives the sufficient and prerequisite condition to prove herself an irrational number.
APPLe: This APPLe may be able to offer some help.
As soon as APPLe puts his hands on the wall, he feels a violent shake come through it.
Regulus: What's happening? An earthquake?
The sound of birds and beasts echoes into the cell.
Chief Mate APPLe floats out from the gaps of the "guest room," making a thorough inspection.
APPLe: All Abraxases are flying in the same direction. Is this their habit? Or ...
Regulus: Errrhh! The roof is about to collapse!
Regulus: coughs So far, this place has made the London Juvenile Detention Center a heaven on earth.
Fortunately, the scattered rocks were not enough to fill the spacious guest room.
Regulus pulls herself together and resumes her prison-break once again.
Perhaps the collapse made the cell drafty. A cold, gloomy fog descends to the room.
The wooden gate, however, stands still.
Regulus: Hmm, is there a piece of paper?
Regulus: Did one of the Abraxases drop this? Strange …
Regulus: The Unsolvable Puzzle. Is this a maths problem?
Regulus: 0.4, 0.7, 1, 1.6, 2.8, 5.2, 10, and 19.6 ... Eight numbers in total are listed in this order.
APPLe: There are eight symbols below, respectively representing the sun, Mercury, Venus, Earth, Mars, Jupiter, Saturn, and Uranus.
APPLe: Maybe it is a hint that we should fill the symbols in the blank blocks after the numbers.
APPLe: That sign says "to complete the proof." Does it mean to solve this puzzle?
Regulus: Hah! How "unsolvable" can it be? Clearly, each of these eight numbers should represent one planet. We can easily find the missing planet by trying them one by one!
Regulus: And our Mr. APPLe here is the King of The Times Crossword, yes?
APPLe: I think there is a difference between this and a crossword.
The mellow red fruit rubs his chin, contemplating the crossword.
APPLe: In this APPLe's humble opinion, the ratio of certain numbers should match this number sequence, such as the radius, volume, or rotation period.
Regulus: Wouldn't the sun be absurdly large if these numbers stand for their sizes?
A tiny squeak interrupts Regulus's thoughts.
Small, rustling figures have gathered at her feet without her noticing.
Regulus: Hey, the underground critters are back! Go away. Don't touch my note. It's not your food!
COMBAT
APPLe: Hold on, please, Captain. Seems like the critters are trying to tell us something.
APPLe: They are pointing at the sign of the sun.
Regulus: Is that so? Haha, even the critters on this island know maths!
Regulus: The sun, ooh, what if the sun is just here to serve as a reference point?!
Regulus: I read an IAU's report in The Times two years ago, you know, the International Astronomical Union.
Regulus: Earth's average distance to the Sun is approximately 93 million miles. As for Mercury, the average distance is 36 million, and Venus 67 million miles.
Regulus: Let's say if we take the distance between Earth and the Sun as 1 astronomical unit, then the distance between the Sun and Mercury would be approximately 0.4 units, and Venus 0.7 units …
Regulus: There you go. These numbers are the ratio of their average distance to the Sun to the Earth-Sun distance!
Touched by a flash of genius, she fills in the first three celestial bodies.
Once cloudy knowledge comes back with precise clarity.
Everything both logical and inevitable.
APPLe: The average distance from Mars to the Sun is about 142 million miles, Jupiter about 484 million miles, Saturn 886 million miles, and Uranus 1.786 billion miles.
APPLe: By rough calculation, and if we round the results to one decimal place ... Mars would be 1.6 units, Jupiter 5.2 units, Saturn 10 units, and Uranus 19.6 units.
APPLe: That's weird. All these numbers one can hardly remember have become so clear in my mind.
Regulus: But if these numbers stand for the ratio of distance, what's the planet for 2.8? There's no planet between Mars and Jupiter.
APPLe: If the Sun is the reference, we will have one planet missing here.
APPLe: Is it really a puzzle unsolvable?
Regulus: Hah, nothing is "unsolvable."
Regulus: You are looking at the solution! There must be one planet out there, unknown to us as of yet, located between Mars and Jupiter!
A massive vibration shakes beneath the ground.
Regulus: What, what now?!
A planet emerges from the darkness.
It rises in the air with little warning, shedding a cold gray light.
... In this damp and dark cave.
It's bright, gigantic, and noticeable.
Regulus: What is this?!
Regulus: A celestial body, which I have never seen before!
APPLe: Captain, this APPLe has an impression on this.
APPLe: There is indeed a star between Mars and Jupiter.
APPLe: It is called the Ceres, discovered by Piazzi Giuseppe, an Italian priest, in 1801.
Regulus: … Ceres?
Regulus: Did we, did we just validate its existence?
Regulus: Is the universe truly arranged according to ... this sequence?
Regulus: Could this be ... the ultimate key of everything?
???: Regulus!
???: Regulus!!!
Someone is eagerly shaking her arm.
Lilya: What are you doing? Got food poisoning after accidentally eating one of those critters?
Regulus: Hmm?!
Regulus: Odd. My head hurts. What was that?
All the stars have disappeared. Now there are only cold walls and damp air.
Oh, and Lilya, who is looking grave.
Lilya: I'll make it short.
Lilya: Sonetto is in detention. They are planning to sentence her to death by giving her the poisoned wine.
Regulus: They what?!