Chapter 85: How Is It You Again

"How is it possible that I got none of them right? You must be saying this on purpose to win the bet, it must be!" Yang Wei glared fiercely at Zu An. He had expected to get at least ten questions correct, so getting none was simply unbelievable.

"Yeah, how could Teacher Yang not get a single one right?""He's a math teacher, Zu An is going too far.""Lying deliberately to win a bet is truly despicable."

Hearing the students' whispers, Zu An didn't get angry. Instead, he took out the exam paper he had marked and said, "Alright, let me show you why you lost. Look at the first question: the correct answer for these two numbers is 2 and 2, but you wrote 10 and 15. It looks like you just guessed, didn't you?"

Yang Wei's old face flushed. He had indeed guessed the answer to that question because the more he thought about it, the more confused he became, so he just picked some numbers at random. However, he refused to admit defeat verbally. "This question is clearly designed to be difficult," he retorted. "How could anyone deduce that answer from such jumbled conditions?"

"Is that so?" Zu An sneered. "If you don't understand, then let me explain..."

"Person A knows the sum of the two numbers but doesn't know what the individual numbers are. If the sum were 3, wouldn't you know the numbers are 1 and 2? If it were 40, wouldn't you know 20 and 20, or 4 and 10? What about 19 and 20 for a sum of 39? Therefore, there's a potential range here: the sum must be between 4 and 38.

Let's start by reasoning from the case where the sum is 4. The possible pairs are (1,3) and (2,2). So, Person A cannot determine the specific pair.

Now let's consider Person B. If Person B has a product of two numbers like 2, 3, 5, 7, 11, 13, 17, 19, or other prime numbers, they would immediately deduce that the numbers are 1 and the product itself, as there's only one way to factor them. But Person B said they didn't know, which proves that the number they hold is not one of these primes.

Returning to Person A: suppose they have the sum 4. Since Person B didn't know, we can rule out the pair (1,3). That leaves only (2,2), which fits the conditions.

For any other sum, there would still be multiple possibilities, preventing Person A from quickly identifying the numbers, and subsequently preventing Person B from identifying them either."

Zu An couldn't help but sigh. "You see, if you use the right method, you find the answer with just the first number. Isn't it simple? That's why I put it as the first question. Who would have thought you couldn't even do such a simple problem, sigh."

The surrounding people immediately began to whisper:"Huh, when he explains it like that, it actually seems quite simple.""Pfft, then why couldn't you figure it out earlier?""I just didn't think of it, you see, even Teacher Yang didn't."

Hearing Zu An's tone, implying Yang Wei was unteachable, Yang Wei's face turned beet red. "Even if I made a careless mistake on that question, what about the next one? The probability of choosing any door is the same, so how could I be wrong?"

This was the first question he had answered, and the one he felt most confident about.

The people around him chimed in, "Yeah, isn't the probability the same for each door? Changing your choice shouldn't make a difference, right?"

Yang Wei's statement indeed reflected common understanding.

Zu An sighed. "It's one thing for students to make this mistake, but for you, a math teacher, to make the same error... truly... sigh."

Seeing Zu An's hesitant yet pointed remarks directed solely at him, Yang Wei felt his lungs might burst from anger. "Stop with your verbal tricks! Tell me where I went wrong!"

Anger value from Yang Wei: 472!

Only then did Zu An explain, "The door you initially chose, isn't the chance of finding the treasure behind it one-third? Then the combined probability of the remaining two doors having the treasure is naturally two-thirds. Now, if I eliminate one of those incorrect options for you, doesn't the probability of the remaining door become two-thirds? Of course you should switch doors; that way, your chances of winning are higher."

"Nonsense," Yang Wei retorted. "The winning probability for each door is independent; it should always be one-third. How could it suddenly become two-thirds?"

Zu An shook his head. "It seems your intelligence indeed makes it hard for you to grasp such complex concepts. Let me explain it another way. Imagine you have ten thousand doors in front of you, with treasure behind only one. If you pick any door at random, isn't your chance of winning only one in ten thousand? Isn't that such a small probability that it's practically impossible to win? Wouldn't 9,999 out of 10,000 chances of finding the treasure be among the remaining doors?"

"At this point, I open 9,998 of the remaining 9,999 doors, revealing them to be empty. If I then ask you the same question, would you still not switch?"

"Of course I'd switch," Yang Wei said subconsciously. But as soon as the words left his mouth, his expression changed. Could he really have been wrong?

"You truly are a math teacher, to grasp it so quickly. Teachable indeed," Zu An nodded, satisfied.

Yang Wei's head felt like it was steaming. This guy was praising him on the surface, but why did it sound so grating?

Anger value from Yang Wei: 333!

Zu An continued, "Next is the problem about pirates distributing Yuan Stones. Pirate A's optimal distribution plan is (97, 0, 1, 2, 0) or (97, 0, 1, 0, 2). Check if your answer is correct."

Yang Wei immediately jumped up. "Nonsense! Such a distribution plan is practically a monopolization! How could the other pirates agree to that?"

Zu An shook his head. "I already said these pirates are extremely intelligent individuals, capable of rationally analyzing gains and losses. It seems if you were in charge of the distribution, you'd most likely be dead."

This time, he didn't prolong the suspense and continued, "We'll use a reverse induction method. First, let's consider Pirate #5, as he is the safest and faces no risk of being thrown overboard. Therefore, his strategy is the simplest: ideally, everyone before him dies, allowing him to claim all 100 Yuan Stones for himself.

Next, consider Pirate #4. His survival depends entirely on someone still being alive ahead of him. Because if pirates #1 through #3 are all fed to the sharks, leaving only #4 and #5, no matter what distribution plan #4 proposes, #5 will certainly vote against it to have #4 fed to the sharks and seize all the Yuan Stones. Even if #4 tries to appease #5 to save his life, offering a plan like (0, 100) where #5 gets all the Yuan Stones, #5 might still consider #4 a risk and vote against him to have him thrown to the sharks. Therefore, a rational #4 should not take such a risk, nor should he entrust his survival to #5's random choice. He can only guarantee his life by supporting #3.

Now, let's look at Pirate #3. After the logical deduction above, he will propose a distribution plan like (100, 0, 0). He knows that even if #4 gains nothing, #4 will still unconditionally support him with an affirmative vote. Adding his own vote, this would ensure he secures all 100 Yuan Stones.

However, Pirate #2, having also deduced #3's distribution plan, will then propose a plan of (98, 0, 1, 1). This plan is more favorable to pirates #4 and #5 than #3's plan, as they would each receive at least 1 Yuan Stone. Rational #4 and #5 will naturally find this plan more beneficial and will support #2, not wanting #2 to be eliminated and have #3 make the distribution. In this way, #2 can successfully take 98 Yuan Stones.

Unfortunately, Pirate #1 is no less cunning. After some reasoning, he too will see through #2's distribution plan. His strategy will be to abandon #2, give #3 one Yuan Stone, and give either #4 or #5 two Yuan Stones. This results in the distribution plans (97, 0, 1, 2, 0) or (97, 0, 1, 0, 2). Since Pirate #1's distribution plan offers more benefits to #3 and #4/#5 compared to #2's plan, they will vote to support #1. With #1's own vote, 97 Yuan Stones will easily fall into #1's pocket."

The surrounding people gasped in astonishment. "These pirates are far too clever, aren't they?""It would be terrifying if there were pirates this smart in reality.""Don't worry, this is just a hypothetical scenario. How could someone this brilliant ever become a pirate in real life?""That's true."

By now, Yang Wei's eyes were dull, and he stood there dumbfounded, unable to hear anything.

Zu An was a little displeased. He had broken so quickly! *No, wait, I still need his anger points!* So, he proceeded to explain the correct answers to the remaining questions. As expected, Yang Wei had gotten every single one wrong. Unfortunately, Yang Wei only contributed a few hundred anger points sporadically, clearly having completely broken down.

"Oh my god, not a single one correct! Teacher Yang is truly pathetic, isn't he?""Exactly! He usually acts like he's the best, with his nose in the air, but who knew his math skills were so terrible?""Hmph, and a person like that is a teacher at the academy. Isn't he ashamed?"

The students' gazes and sarcastic remarks pierced Yang Wei's heart like knives. He let out a yell, covered his ears, and fled the classroom in a panic. No matter how much people called out to him, he didn't stop for a moment. He just wanted to escape that place immediately. It was too humiliating. He had expected to easily put a common student in his place, only to be completely outdone by one. He knew that after this incident, he would no longer have the face to remain at the academy.

As a teacher, failing to answer even a single question posed by a student would not only make him a laughingstock in Brightmoon City but likely in all the surrounding counties as well.

"Boss, you're amazing!" Wei Suo, ever the sycophant, rushed over to massage Zu An's shoulders and back. Other classmates also hurried over, offering tea and water. With such mathematical prowess, even without any cultivation, Zu An's future was bound to be limitless. It would be foolish not to curry favor with him now.

Chu Huanzhao had originally wanted to go speak with her brother-in-law, but seeing the crowd surrounding him, she couldn't even get close. She couldn't help but huff resentfully, "A bunch of sycophants."

Ji Xiaoxi's small face was flushed with excitement, yet at the same time, she secretly worried for him, wondering if offending a teacher at the academy like this would lead to negative consequences.

Pei Mianman flashed a charming smile that made the men around her dizzy. "I was regretting making a deal with this guy earlier, but now it seems I might actually get a return from him."

From a distance, Zheng Dan took in the expressions of the various women, secretly astonished. She had thought the rumors were just that, rumors. But now it seemed Zu An had quite deep connections with these women. What kind of charm did this man possess, not only marrying the eldest Miss Chu but also attracting such outstanding women as them?

Just then, a furious shout rang out: "Why aren't you all in class? What are you doing gathered here? Are you trying to start a rebellion?"

Hearing that voice, many people flinched. Clearly, it had caused them much dread in the past. With his distinctive bald spot and a disciplinary ruler in hand, who else could it be but Director of Discipline Lu De?

Seeing his arrival, the surrounding people automatically made way. He walked in and noticed Zu An casually sitting in his spot, receiving shoulder rubs and back massages from his classmates, his brow furthering instinctively.

However, upon seeing the charming Shang Liuyu nearby, his furrowed brow immediately relaxed. "So Teacher Shang is here too. What exactly happened just now? I saw Yang Wei run out covering his face, and he wouldn't stop no matter how much I called him."

"Perhaps he felt a little embarrassed," Shang Liuyu said with a faint smile, briefly recounting what had happened. Her voice was soft and captivating; merely listening to her speak was an exquisite pleasure.

"Are you causing trouble again?" Lu De's expression was gentle when looking at Shang Liuyu, but it instantly turned severe when he looked at Zu An.