eurekapd Chapter 140 Here's the pen, you be the teacher!
Chapter 140 Here's the pen, you be the teacher!
The question set by Lin Chen:
A snail is playing a game on a chessboard with 2024 rows and 2023 columns, where there are hidden monsters in 2022 cells.
Initially, the snail didn't know where the monsters were, but it knew that there was exactly one monster in each row except for the first and last rows, and at most one monster in each column.
The snail makes a series of attempts to reach the last row from the first row, each time choosing to start from any cell in the first row and then repeatedly moving to adjacent cells.
If the snail reaches a cell with a monster, its attempt ends and it is sent back to the first row to start a new attempt.
Determine the minimum value of N such that the snail has a strategy to guarantee reaching the last row on the Nth attempt or earlier, regardless of the monster's position.
Upon seeing the title, Chen Xiaoxiao's eyes lit up immediately.
Compared to the questions set by the teachers, Lin Chen's questions were indeed very much in the style of the International Mathematical Olympiad questions in recent years.
That is to combine the story and the title.
However, this also increases the difficulty of the questions exponentially.
Because compared to simple mathematical formulas, this type of problem requires an additional step: first, transforming the problem into a mathematical problem.
Just as Chen Xiaoxiao was frowning and pondering the problem.
Yang Zongyuan also looked worried, constantly looking at the questions.
He read it three times in a row and found that he still couldn't quite understand the question.
"Lin Chen, what are you doing?"
Finally, he couldn't resist putting aside his desire to solve the problem and asked a question.
"I'm giving Xiaoxiao some extra tutoring, why are you interested too?"
Yang Zongyuan was taken aback: "Special tutoring? You set these questions?"
"Yes."
Yang Zongyuan felt a chill run down his spine, realizing that the gap between him and Lin Chen had widened even further.
Everyone here is on the math Olympiad team, but Lin Chen is already so amazing that he can create math Olympiad level problems?
"Can I call the others too?"
"Whatever," Lin Chen said indifferently.
Yang Zongyuan immediately picked up his phone and sent text messages to the three people who had gone to lunch.
"Hurry to the classroom! Lin Chen is giving Chen Xiaoxiao extra tutoring!"
A moment later, the other three team members also arrived at the classroom.
At this moment, Yang Zongyuan was completely absorbed in the problem and did not even notice their arrival.
The other three were about to speak when their eyes also fell on the blackboard.
Then, just like a traveler in a myth whose soul has been bewitched by a monster, he too became entangled in the problem.
However, everyone scratched their heads and racked their brains for twenty minutes, just like monkeys.
With little time left before afternoon classes, Lin Chen put down his phone, stood up, and walked to the podium.
"Time is running out. If you can't solve it, I'll start answering the questions now."
However, no one paid attention to him. Even Chen Xiaoxiao kept her head down and was still struggling with the problem.
Lin Chen had no choice but to tap the blackboard.
This finally made everyone raise their heads.
"Gentlemen, time is running out. I'll give you the answer now, and you can go back and think about it yourselves."
Chen Xiaoxiao said, "No, Teacher Lin Chen, please give me some more time!"
Others chimed in, "Yes, Teacher Lin Chen, I'll have a lead soon!"
"I've already filled four pages of draft paper, give me a little more time!"
"Please, Teacher Lin Chen!"
Even though they called him "teacher" so affectionately, Lin Chen still didn't indulge them.
“But you’ve been doing this for twenty minutes already.”
"Only 20 minutes! In a real competition, we have 1.5 hours to solve a single problem!"
"But afternoon classes start soon. Maybe next time! Next time we'll give you more time."
After saying that, Lin Chen didn't delay any longer and immediately started writing the answer on the blackboard.
"This problem is actually a combinatorial optimization problem. We need to find the minimum number of attempts N required for the snail to reach the last row in the worst case..."
Just as Lin Chen was explaining the problem, Xiao Li, the leader of the math Olympiad team, was leading a special guest to the training room.
"Mr. Wu, I never expected you to be interested in the math Olympiad team?"
Beside Xiao Li was an elderly man with a full head of white hair, who was none other than Professor Wu Youguang, the vice dean of the School of Science!
Xiao Li dared not neglect the other party's identity, but what puzzled him was that Wu Youguang was clearly a physics teacher, so why was he interested in their math Olympiad team and insisted on visiting?
Seeing that they were almost there, Old Wu didn't hide anything and said, "I have no interest in the math Olympiad team."
But I'm very interested in one of your team members.
"Could it be Lin Chen?"
Old Wu nodded with a smile.
Although he already knew about Lin Chen, the two had never actually met.
So, since he had some free time today, he decided to come and see that kid at the math Olympiad team.
If possible, it would be even better if we could persuade him to apply to Tsinghua or Peking University.
Just then, they suddenly heard the sound of a lecture coming from the training classroom.
Old Wu chuckled, "Is your training camp that tough? You're starting classes so early?"
Xiao Li looked puzzled. He was the one who taught the afternoon training session, but he hadn't arrived yet. Who was teaching the math Olympiad team?
The two walked to the edge of the classroom and immediately saw Lin Chen standing on the podium.
"...Through the above analysis, we can obtain that the minimum value of N is 2023."
In other words, the snail has a strategy that guarantees reaching the last line within 2023 attempts.
After he finished speaking, the audience fell silent.
Xiao Li, who was outside, was wondering where Lin Chen had gotten the topic from when Yang Zongyuan asked:
"Lin Chen, did you really come up with this question yourself?"
"Yes, or have you seen it somewhere else?"
Yang Zongyuan was on the verge of tears. He had originally thought that as long as he worked hard, he could catch up with Lin Chen.
But I never expected that the questions Lin Chen would set would be so difficult that I would cry.
"Lin Chen, Teacher Xiao hasn't arrived yet. Could you also tell me about the last question on the morning's test?"
"alright."
Seeing that it was Chen Xiaoxiao who spoke, Lin Chen naturally agreed immediately.
Under Xiao Li's somewhat reluctant gaze, Lin Chen erased the questions on the blackboard and began to write and draw.
"The question this morning was actually a logic puzzle involving sequences, requiring in-depth analysis and rigorous proof of the patterns in the sequences. However, there's a simple approach to this type of question..."
As Xiao Li watched Lin Chen's explanation, her eyes gradually widened.
Because Lin Chen's problem-solving approach was completely different from the standard answer that their teaching team had prepared for this question.
Xiao Li listened outside the classroom for only a short while before realizing that Lin Chen's thinking was obviously more efficient and convenient, and even inspiring.
"This kid is truly better off seeing him than hearing about him!"
Suddenly, Xiao Li heard Old Wu sighing beside him.
"Old Wu, do you know Lin Chen well?"
"Although I haven't seen it with my own eyes, I knew long ago that this kid was very talented in science! Now it seems that he also has a great talent for teaching and nurturing students!"
Sigh! Why would someone with such talent give up a guaranteed admission to Tsinghua or Peking University?!
Old Wu looked unwilling.
I couldn't help but raise my voice a little.
This alarmed everyone in the classroom.
"Teacher Xiao?"
Upon seeing Xiao Li and an old man standing outside the door, Lin Chen grinned sheepishly and quickly stepped down from the podium.
"Teacher, please don't misunderstand, I was just talking to them casually."
Seeing that Lin Chen seemed to be about to end the lecture, Chen Xiaoxiao and the others immediately became anxious.
Before they could speak, Xiao Li walked in and directly picked up a piece of chalk and stuffed it into Lin Chen's hand.
"Lin Chen, here's the chalk. You'll be the teacher this afternoon and explain the morning's test to everyone!"