"How could you not get a single one right? You must have said that on purpose to win the bet, that must be it!" Yang Wei stared fiercely at Zu An. You see, he thought he could at least get ten right, but he didn't get a single one right. How could that be?
"Yes, how could Teacher Yang not get any of them right?"
"He's an arithmetic teacher, that guy Zaun went too far."
"To lie in order to win a bet is truly despicable."
...
Hearing the whispers of the students around him, Zu An didn't get angry. Instead, he took out the test paper Zu An had completed and said, "Fine, I'll let you lose clearly. Look at the first question. The correct answer is 2 and 2, but you wrote 10 and 15. It seems like you just guessed, right?"
Yang Wei's face flushed. He had indeed guessed randomly on this question because the more he thought about it, the more confused he became, so he just guessed a number. However, he refused to admit defeat and said, "This question of yours is deliberately difficult. How could you possibly deduce this answer with these messy conditions?"
"Is that so?" Zuan sneered. "If you don't understand, then I'll explain it to you..."
"A knows the sum of the two numbers, but doesn't know what the two numbers are. If you are given 3, wouldn't you know that 1+2=3? If you are given 40, wouldn't you know that 20+20=40? Would you not know that 19+20=39? So there is a potential range here, and the 'sum' should be between 4 and 38."
Let's start reasoning from the case where the sum is 4. 4 = 1 + 3 = 2 + 2, so A cannot determine which case it is.
Let's look at person B. If person B had two numbers whose product is a special number like 2, 3, 5, 7, 11, 13, 17, 19, etc., we could immediately deduce that the two numbers are 1 and the product itself, because there's only one way to split it. But if person B says they don't know, it proves that the numbers they have are not among these.
Let's go back to A. Suppose he has 4 in his hand. Since B doesn't know, we can eliminate the possibility of 1+3. That leaves only 2 and 2, which meet the conditions.
For any other number, there are still several other possibilities. Person A cannot determine the value of the two numbers so quickly, nor can Person B immediately follow suit.
Zuan couldn't help but sigh: "Look, as long as the method is right, you figured it out after just one try. Isn't it simple? That's why I put it as the first question. Who knew you couldn't even do such a simple question? Sigh~"
The people around immediately began to whisper among themselves:
"Hmm, now that he puts it that way, it seems pretty simple."
"Tch, then why couldn't you do it just now?"
"I just didn't expect it. Even Teacher Yang didn't expect it."
...
Hearing Zhou Jian's tone that implied he was hopeless, Yang Wei's face turned bright red: "Even if I made a mistake on this question due to carelessness, what about the next question? The probability of choosing either door is the same, so how could I possibly make a mistake!"
This was the first problem he solved, and also the one he was most confident in.
People around him chimed in, "Yeah, the probability of changing the door is the same for every door, so it shouldn't make a difference, right?"
Yang Wei's words do represent the common sense and understanding of the average person.
Zuan sighed, "It's one thing for the students to make mistakes, but for a math teacher like you to make the same mistake is really... sigh..."
Seeing his hesitant yet pointed remarks, Yang Wei was furious: "Stop trying to win with your words! Tell me what you did wrong?"
Yang Wei's anger level increased by 472!
Zuan then said, "The door you chose has a one-third chance of getting the treasure, right? So the overall probability of winning with the remaining two doors is naturally two-thirds. Now that I've eliminated one of the wrong options for you, isn't the probability of winning with the remaining door also two-thirds? Of course you should change doors; that way, your chances of winning are higher."
“Nonsense,” Yang Wei said. “The odds of winning for each door are independent and should all be one-third. How could it suddenly become two-thirds?”
Zuan shook his head: "It seems that with your intelligence, it's indeed difficult for you to understand such a complex concept. Let me explain it in another way. If there are ten thousand doors in front of you, and only one door leads to a treasure, and you randomly choose a door, isn't the probability of winning only one in ten thousand? Such a small probability is equivalent to having no chance of winning at all, right? So, the treasure is in the remaining nine thousand nine hundred and ninety-nine doors, isn't it?"
"Now, if I open 9998 of the remaining 9999 doors, and they're empty, and then ask you the same question again, won't you change them?"
"Of course we should change it," Yang Wei said subconsciously, but his expression changed as soon as the words left his mouth. Had he really made a mistake?
"You truly deserve to be called an arithmetic teacher. You grasped it so quickly. You are a promising student." Zu An nodded in satisfaction.
Yang Wei was practically fuming. This guy was praising me on the surface, but why did it sound so grating?
Yang Wei's anger level increased by 333!
Zuan continued, "Next is the problem of the pirate elemental stones. The best allocation for Pirate A is (97, 0, 1, 2, 0) or (97, 0, 1, 0, 2). See if your answer is correct?"
Yang Wei immediately jumped up: "Nonsense! Such a distribution plan is practically monopolizing everything. How could the other pirates possibly agree to it?"
Zuan shook his head: "I already said that these pirates are extremely intelligent people who can rationally analyze the pros and cons. It seems that if I let you make the distribution, you're probably doomed."
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