Chapter 85: You Again!

“How could I have possibly gotten all of the answers wrong? You must be saying that in order to win the bet! There’s no other reason for that!” Yang Wei glared at Zu An angrily. He was confident that he should have gotten at least ten questions correctly, so there was no way he could believe that he actually got everything wrong.

“Indeed! How could Teacher Yang possibly get everything wrong? He’s our academy’s arithmetic teacher!”

“Zu An is going too far here for lying to win the bet. It only shows how despicable he is as a person!”

… 

Zu An didn’t lose his temper despite all of the criticisms directed at him. Instead, he raised the paper Yang Wei had just completed up high and said, “Very well, I’ll enlighten you on your mistakes then. Look at the first question. The right answer is 2 and 2, and yet you wrote 10 and 15. You must have just made a random guess hoping that you’d somehow get it right.”

Yang Wei’s face heated up in embarrassment. It was true that he had guessed two random numbers. He simply got more and more confused thinking about it that he eventually gave up. However, there was no way he was going to admit to it. “Your question is simply illogical. Given these conditions, how can anyone possibly deduce the answer?”

“Oh, is that so?” Zu An shook his head disdainfully. 

“Since you don’t understand it, allow me to enlighten you then. A knows the addition of the numbers, but he doesn’t know what each number is. If the addition of the number is 2 or 3, naturally, he would immediately know that the two numbers are (1, 1) and (1, 2) respectively. Similarly, if the addition of the number is 40 or 39, he would know that the numbers are (20, 20) and (20, 19) respectively. With this underlying notion, the boundary of the addition of both numbers is automatically narrowed down to 4 to 38.

“Let’s take 4 as an example. If 4 is the addition of both numbers, the two numbers could possibly be (1, 3) or (2, 2), so A is unable to determine which is it.

“Now, let’s move over to look at B. If the number B got is a prime number, namely 2, 3, 5, 7, 11, 13, 17, 19, so on and so forth, he would be able to deduce right away that the number is 1 and the multiplied number itself. Those are the only two factors after all. Since he was unable to deduce what the number is right away, we can eliminate all prime numbers.

“Moving back to A, assuming that the addition of the numbers is 4, and the multiplication of the numbers isn’t 3—which B immediately know the answer right away since it’s a prime number—it only leaves the combination of (2, 2) that fulfills the criteria.

“As for the other numbers above 4, there are many more possibilities aside from that, such that A is unable to deduce what the two numbers are, and B is unable to follow up with a corresponding deduction too.”

At this point, Zu An shook his head and sighed deeply. “See, as long as you had the right direction in mind, you would have gotten the answer on your first try. Isn’t it simple? That’s why I chose to put this question at the very front. Yet, who could have thought that you can’t even solve such a simple question? Haaa~”

The surrounding students also began gossiping amongst themselves.

“Hmmm, the logic is pretty simple now that he has explained it out.”

“Tsk, why weren’t you able to solve it then?”

“I just wasn’t able to think of it on the spot! I mean, even Teacher Yang couldn’t get it right either!”

… 

Hearing those darned mutterings of the student, Yang Wei’s face reddened. “Fine, let’s take it that I answered this question wrongly out of carelessness. What about the next question then? Isn’t the probability the same no matter which door is chosen? There’s no way I could be wrong about that!”

That was the question that he was the most confident about.

The crowd also murmured in agreement with Yang Wei’s verdict too. “Indeed, the probability should be the same no matter which door is chosen. Whether he chooses to switch to another door or not shouldn’t make a difference.”

Yang Wei’s words were in line with common sense.

However, Zu An sighed deeply and remarked, “It’s one thing for the students to get this question wrong, but how could an arithmetic teacher like you make the same mistake too? This sure is… Hai…”

His irritating attitude of putting Yang Wei down made the latter feeling so angered that he was on the verge of exploding. “Why don’t you put away that mysterious act of yours and point out what’s wrong with my logic?”

You have successfully trolled Yang Wei for +472 Rage!

Zu An finally began deciphering the question, “No matter which door you select, the chances of selecting the treasure is one-third. In other words, the total probability of the treasure being in the two remaining doors is two-third. So, if I remove a wrong answer between the two remaining doors, wouldn’t the probability of the only remaining unchosen door be two-third now? Given so, you should definitely change the door since the chances of getting the treasure are higher!”

“Rubbish!” said Yang Wei. “The probability of each door having the treasure behind it is independent. It should all be one-third. How could one of them suddenly become two-third?”

In response to that, Zu An shook his head and answered, “I reckon that someone of your IQ won’t be able to answer such a complicated logic. Well, let me phrase it in a much easier way for you. Assuming that there are 10,000 doors before you, and only one of them has a treasure behind it. If you choose any of the 10,000 doors, your chances of getting the treasure is only 1-in-10,000, right? With such probability, it’s almost impossible for you to get it right. It’s almost certain that the treasure is in the remaining 9,999 doors.

“So, if I open 9,998 of the remaining 9,999 doors and show them they are all empty, given the same question, will you be willing to switch to the other remaining door?”

“Of course I would switch!” replied Yang Wei subconsciously. However, right after he responded, his complexion suddenly darkened. Could I really be wrong about that?

“As expected of an arithmetic teacher, you sure got it fast enough. It looks like you aren’t beyond salvage yet.” Zu An nodded in satisfaction.

Yang Wei looked as if steam was rising from the tip of his head. This fellow looks like he’s praising me on the surface, but why do his words sound so jarring?

You have successfully trolled Yang Wei for +333 Rage!

Zu An proceeded on to decipher the next question. “Moving on to the next question about the pirates, the optimal distribution of ki stones for Pirate A is (97, 0, 1, 2, 0) or (97, 0, 1, 0, 2). Look are your own answer. Is it right?”

Yang Wei immediately refuted Zu An’s answer in agitation. “Nonsense! Pirate A would practically be taking all of it for his own. How could the other pirates possibly agree to it?!”

“I told you that these pirates are smart people who are able to rationally weigh their gains and losses and make the best decision. If we were to put you in their place, I reckon that you would be dead by now!” replied Zu An with a shake of his head.

Without bothering to keep the suspense, he quickly proceeded to the answer, “Let’s work on this question backward, starting from Pirate E. He’s the safest one of them all since he’s in no threat of being thrown into the sea. Thus, his strategy is the simplest. As long as everyone ahead of him dies, he’d be able to monopolize all 100 ki stones.

“Moving on, regarding Pirate D, whether he survives or not depends on whether there are any survivors in front of him. If it ever comes down to a situation when only he and Pirate E is left, Pirate E is bound to oppose his distribution no matter what and feed him to the sharks so as to monopolize all of the ki stones. Thus, Pirate D is inclined to support Pirate C for his own survival.

“As for Pirate C, based on the logic of Pirate D, he would surely propose (100, 0, 0) since he knew that Pirate D would surely support him unconditionally in order to avoid getting killed by Pirate E. With his and Pirate D’s vote, he would be able to get the majority for his distribution proposal and monopolize all 100 ki stones safely.

“However, Pirate B, as a perfectly logical thinker, is aware of Pirate C’s distribution plan, so what he would do is to propose a distribution of (98, 0, 1, 1). Pirate D and Pirate E would be inclined to support him since they would be able to receive 1 ki stone, which is more beneficial to them as compared to Pirate C’s distribution plan. With that, he would be able to get the majority and monopolize 98 ki stones to himself.

“Unfortunately, Pirate A is also no pushover. After analyzing everyone’s strategy, he is aware of the scheme Pirate B is cooking up. So, he chooses to give up on Pirate B, who is likely to vote against him regardless of what he offers, and proposes a distribution of (97, 0, 1, 2, 0) or (97, 0, 1, 0, 2). With this proposal, Pirate C and Pirate D or Pirate E would be able to receive more than what they would earn in Pirate B’s distribution. Since that’s the case, they would support Pirate A, thus allowing Pirate A to secure three votes and claim a majority. With this, he easily secures 97 ki stones for himself.”

Everyone gasped in astonishment. “Aren’t those pirates way too smart?”

“How frightening it would be if the pirates in real life are that smart too!”

“Don’t worry, it’s just a hypothetical situation. If anyone is that smart, he doesn’t even have to resort to piracy anymore!”

“I guess so…”

… 

Yang Wei’s eyes had already blanked out. He stood dazed on the spot, unable to hear anything at all.

Zu An was quite displeased with his reaction. Hey hey hey, can you not succumb so easily? You haven’t provided me with enough Rage points yet! 

To his dismay, even as he slammed Yang Wei’s answers down and explained the remaining questions, the latter only provided him with a few hundred Rage points. From the looks of it, he had already suffered a mental breakdown. 

“My gosh, he really didn’t get a single question right! Isn’t Teacher Yang a little too incompetent?”

“He always sticks up nose up high as if he’s a big deal. Yet, it turns out that he’s all talk!”

“Tsk, why does our academy have someone like him as a teacher? Won’t he mislead the students at this rate?”

… 

The criticisms of the surrounding students were like knives stabbing into Yang Wei’s heart. He finally caved in and roared frenziedly before rushing out of the classroom with his hands covering his ears. No matter how anyone shouted at him, he didn’t stop at all. He only wanted to get out of this darned place as soon as possible.

It was too humiliating! He thought that he could easily trample all over Zu An, but who could have thought that he would end up being the one trampled on instead? After this incident, there was no way he would dare to show his face in Brightmoon Academy anymore.

For a teacher to be unable to answer any of the questions posed by his students, he would definitely become a laughingstock not just in Brightmoon City but the surrounding municipalities too!

“Boss, you’re incredible!” Wei Suo rushed forward to massage Zu An’s shoulders.

The other students also stepped forward to offer him tea and snacks. With such arithmetic prowess, even if he was completely inept as a cultivator, he would still have a bright future ahead of him. Naturally, it would be good if they could fawn on him right now.

Chu Huanzhao was also going to rush forward to talk to her brother-in-law, but a huge crowd had already formed around Zu An before she knew it, squeezing her out. Frustrated, she stomped away with a cold harrumph, “Bootlickers!”

Ji Xiaoxi’s face was also reddened in excitement at the impressive feat she had just witnessed, but at the same time, she was worried for Zu An too. Won’t he be in trouble for offending a teacher of the academy like this?

Pei Mianman’s lips curled upward with a hint of seduction, leaving the men around her swooning for her. “I was still regretting my decision for making a deal with that fellow, but it looks like I might just be able to get something out of him.”

Not too far away, Zheng Dan caught sight of the reactions of those women, and it shocked her. She thought that Zu An’s relationships with them were just hearsay—how could Zu An possibly charm all of these outstanding women?

It was then that a loud bellow sounded. “What are all of you doing here instead of attending classes? Are you trying to rebel against the academy?”

The voice sent shudders down people’s spine. This was an instinctive effect arising from the traumas created by their past experiences with the owner of the voice.

A middle-aged man sporting a bald spot on his head and holding onto a ruler approached the crowd. Who else could it be other than discipline master Lu De?

The crowd automatically parted to open up a path for him to walk through. At the very center of the commotion, he saw Zu An seated grandly on a chair, served by his fellow students. This sight made him frown a little.

However, when he saw that Shang Liuyu was in the vicinity as well, his frown immediately smoothened out. “Ah, Teacher Shang is here too! What in the world happened here earlier? I saw Yang Wei rushing off with his head lowered. I called for him, but he wouldn’t respond.”

“He probably feels embarrassed,” replied Shang Liuyu with a faint smile. She quickly explained the events that had transpired earlier. Her smooth voice seemed to tingle one’s heart, making it pleasurable just to listen to her speak.

“It’s you again?” Lu De was still looking at Shang Liuyu with a gentle look on his a moment ago, but as soon as he turned his eyes toward Zu An, his expression turned severe.

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Footnotes not processed properly:

More details about the three doors and one treasure problem
This is called the Monty Hall Problem, named after the game show itself. It’s notoriously known to defy common sense. A statistician once wrote to a magazine column with the conclusion that it’s better to switch, but many people, including 1000 PhDs, refuted the point of view, saying that it’s ridiculous. It was only until someone ran a computer simulation that they were left with no choice but to accept the results. It’s one of the renowned paradoxes created by the magic of conditional probability.