louisehourcade Chapter 51 Cooperation
Chapter 51 Cooperation
Su Hao lowered his eyes and focused his gaze on question 4.
Let P be a point inside the cube...
The moment the question stem comes into view, the decomposition and reconstruction of the question are completed simultaneously.
It was a geometric cut, an optimal stripping, a perfect fusion of symmetry and topology.
With Psyduck's incredible precision computing power, a magnificent and complex three-dimensional coordinate system was built in Su Hao's mind in less than a second.
The moment Su Hao's mathematical intuition captured the core idea, Psyduck seamlessly compiled that inspiration into an impeccable mathematical expression!
Swish!
Su Hao's pen struck the paper with almost afterimage speed.
Establish a coordinate system; set a central anchor point P(a, b, c); calculate its distances to each element of the cube...
Read, reflect, and write simultaneously.
There was no pause, no pause for thought.
The transmission delay from vision to the brain and then to the fingertips has been forcibly compressed to almost zero!
Psyduck systematically exhaustively enumerates and categorizes all possibilities in its mind;
Su Hao's intuition, on the other hand, was like a sharp knife, precisely extracting the most crucial entry point from this massive amount of data.
The two computing powers merged perfectly, and began to unleash a chilling chemical reaction!
However, the laws of physics are unforgiving.
Writing still takes time.
Su Hao glanced at the clock hand out of the corner of his eye, a resolute glint in his eyes.
The complete derivation steps in the conventional way are absolutely impossible to write out.
Without hesitation, he swung his pencil, cutting through the crux of the problem.
The original ten-step argumentation logic was forcibly compressed and folded into five steps!
The brush touches the paper, then the stroke ends.
Question 4, answer complete.
It took five minutes.
Without the slightest pause, the pen plunged headlong into the last question!
[Select r balls from n balls...]
This problem is a deep trap combining combinatorial mathematics and probability theory.
The moment Su Hao scanned the question, Psyduck had already laid out a huge grid array in his mind, making all the arrangements and combinations concrete.
Inclusion-exclusion principle, recurrence relation, generating function...
The mathematical tools that countless ordinary people spend their hair turning white trying to understand now roared through his mind like a meteor shower streaking across the night sky!
Su Hao's pen simultaneously left afterimages on the paper.
The essence of combinatorics lies in making choices.
In Psyduck's view, all n balls have been visualized as absolutely precise mathematical expectations.
Su Hao's terrifying intuition kicked in once again, keenly sensing the hidden chain reaction of conditional probability.
Psyduck instantly followed, and a massive probability distribution cloud exploded in his mind, transforming into a perfectly symmetrical infinite fractal tree!
[First selection: P1 = r/n]
[Second selection: P2 = (r-1)/(n-1)]
As he deduced the product of conditional probabilities, Su Hao's brain was working overtime, but his fingers holding the pen did not tremble even slightly.
The rigorous logical deduction and the afterimage of the pen tip achieved a strange synchronization!
With time running out, Su Hao made a snap decision, expressionlessly wielding his executioner's blade, cutting away all embellishments and preparations, leaving only the most formidable skeleton!
The mathematical logic that originally required fifteen lines of rigorous text to barely complete was condensed into a mere five lines by him in an extremely domineering manner.
However, there was no break, no logical leap.
Under Su Hao's cold and ruthless judgment, every character in these five steps of deduction exudes an irrefutable and absolute mathematical divinity!
With the final stroke, the pencil lead snapped with a "snap".
Question 5, the moment I finished answering it!
"Exam over! Everyone stop writing!"
The proctor's closing words echoed throughout the examination room.
Marcelo stood just two steps away, completely dumbfounded.
His eyes were wide open, his mouth was slightly agape, and his hands were trembling.
At the last moment, he witnessed a sprint that could only be described as a miracle!
The boy's focused concentration and his almost superhuman writing speed gave the seasoned mathematician an utterly absurd illusion:
He seemed to have glimpsed some kind of miracle that transcended the limits of human physiology!
After a period of euphoria, this veteran expert, who had spent most of his life working in the field of mathematics, felt an inexplicable unease and fear!
He moved forward a few steps almost uncontrollably:
"Child, are you... alright?"
The boy's eyes were unfocused, like a sleepwalker, and he didn't hear the old man's question at all.
His expression at this moment revealed a strange sense of disorientation, as if his soul had just fallen back into this body from some higher dimension.
He slowly stood up, looked around blankly, his brows furrowed, revealing an undisguised irritation and disdain, and muttered under his breath.
Why are the desks arranged like this?
This completely violates the principle of spatial symmetry.
Why are there 21 tables in the third column over there?
If the goal is to save space, wouldn't you know that using a hexagonal tiling structure would be the optimal solution?
This is not an act.
At this moment, Su Hao did indeed feel a kind of nausea-like physical rejection.
The examination hall layout, riddled with spatial flaws and array defects, appeared in his eyes, which had just lost their divinity...
It's like someone forcefully stuck a hangnail into his fingernail, making him extremely uncomfortable.
Marcelo noticed the boy's unusual behavior:
The pupil is in an abnormally dilated state, and the focal point of the gaze is constantly shifting at high frequency.
This is not how a normal human being should focus!
Marcelo gasped, his heart pounding!
As a top scholar who has been immersed in the field of mathematics for decades, he is all too familiar with this symptom.
This is not ordinary fatigue at all.
This boy is currently in a state of extreme "academic euphoria"!
But something still feels off.
That problem-solving posture, which seemed to be guided by divine will, absolutely cannot be explained by those mediocre "flow" theories in psychology.
Suddenly, a bolt of lightning struck Marcelo's mind, and a name long buried in the annals of academic history leaped to his attention:
Ramanujan!
The yellowed archives deep within the Cambridge University Library once recorded:
The Indian genius who once terrified the entire European academic community displayed the same demeanor as the young man before me when he was conducting theoretical derivations about black holes!
No need for cumbersome lemmas or mechanical deductions; it directly crosses the logical chasm and reaches the other side of truth!
That is an indescribable mathematical intuition originating from the deepest part of the human subconscious!
It is an academic insight that transcends all ordinary human logic and is almost surreal!
Su Hao's demeanor when destroying question 6 perfectly demonstrated this terrifying talent.
He doesn't seem to be solving a problem at all.
He seemed to have already reached the end of the truth, and with an almost merciful attitude, he was reconstructing a path of proof that ordinary people could barely understand!
Just as Marcelo felt his worldview crumbling, Su Hao lowered his eyes and said something in a very low voice.
"Stop it, Psyduck."
With those words, he forcibly severed his connection with that dimension and fell back to the mortal realm.
This was followed by slightly rapid breathing, indicating that the body's functions had not yet fully recovered.
To confirm the candidate's safety, Marcelo suppressed his inner turmoil and asked again in a trembling voice:
"Child...how are you feeling now?"
Su Hao finally raised his head and looked at the elder in front of him.
Just moments ago, their faces were filled with anxiety; now, they beamed with the brightest, most radiant smiles that belong to their age.
"It feels amazing! Because I just solved an incredibly ingenious problem!"
Upon hearing this, Marcelo's tense nerves finally relaxed completely, and he secretly breathed a sigh of relief.
As the core problem setter for this year's IMO competition, the boy's seemingly casual comment felt like a mountain to him!