As the minutes ticked by, Ranger drew a portion of the 300×300 grid and began his deduction.

□□□□□□□

■■■■■■■

□□□□□□□

□□□□□□□

■■■■■■■

It is not difficult to deduce a result that will be the 2nd, 5th, and 8th in the grid table...... If all the squares in the 299 rows are dyed black, then any three of these black squares will not form a black L-shape in any way. But as soon as you dye any of the white squares, an L-shape consisting of three black squares will immediately appear:

■

■■

The number of black grids jumped on paper, 30,000 black grids.

Players with normal IQ can push the number 30,000 within 1 minute.

But Lan Jie knew that if he only wrote 30,000 on the paper, he was afraid that he would only get one point for the answer.

The 12-point process involves a proof question: Prove that the number of 30,000 black squares cannot be reduced.

In fact, we all know that this conclusion must be valid.

The hard part is how to prove it.

'Operate, must operate, operate it!'

Lan Jie forced himself to calm down and began his maneuver.

Assuming that the black b squares can meet the requirements, there are ω=90000-b white squares in the square table.

Write a 0 on each black box, and then do a subtle manipulation of the white box:

If a white grid is dyed black so that it becomes the center of a black L, then add 1 to each of the other two black squares of the L. If it is not the center of L, then add the number of L centers by 2.

In any case, only one of these operations is performed, so the sum of the numbers written in all Hagrid is 2 Ω.

After this wave of operations is completed, Ranger immediately implements the next wave of operations.

This series of operations follows a rigorous and rigorous logic, and if one link goes wrong, the subsequent operations cannot be continued.

If A does not have a black neighbor, then it will not be the center of the black L when it is blacked out on any of its white neighbors.

If A has no more than two white neighbors, then the number in A will not end up being greater than 4 because the operation on them all adds up to 2 in A.

Continue to dye C ......

......

'In short, the sum of all numbers is not greater than 4b, i.e. 2ω≤4b, ω≤2b!'

'In summary, b≥30000!'

Ranger thinks he's done with an invincible logic.

To solve this dyeing problem, Ranger didn't use any mathematical knowledge and skills beyond the scope of intermediate mathematics, it was purely a logic game.

Using advanced math knowledge and skills to solve high school math problems is actually a simple and easy thing, which is equivalent to a high-level player beating a low-level monster.

The CMO's teachers try to avoid the phenomenon of "high-level players beating low-level monsters", they are keen to play logic, at least the question of this staining problem is pure logic.

Playing logic is quite brain-burning, even if Lan Jie's logical thinking is a little bit unusual, he also feels a pain in his brain after completing this staining problem.

Ding Ding Ding!

Submit the papers!

It's Sunday, and Ranger is heading straight to the sheep after lunch.

The competition class only rests for a weekSunday morning, at one o'clock, Lan Jie came to the competition classroom, and he asked Wu Zihan, a tablemate in the competition class: "How did the CMO exam?"

"It's cracked. Wu Zihan said miserably, and then he took a long breath, as if he was completely relieved: "It's okay, I can concentrate on preparing for the follow-up schedule of CPhO." We don't like to do multiple-choice questions, we want everything, we count things double-open, even three-open, four-open, hehe, we think too much, all normal high school students can only open alone, our limited energy is really difficult to support double-open, multi-open. By the way, Brother Jie, how did you do in the CMO exam?"

"It's hard to say, wait for the results. ”

"I heard that Brother Jie is open?"

"Well, four open. If you count sports, it's five. ”

"Let's not talk about physical education for the time being, the four cultural courses of mathematics, physics and chemistry, Brother Jie, you can focus on one or two of them, one competition award and four competition awards, the number has changed, but there is no difference in essence. ”

"Who says there's no difference?"

"To be reasonable, even if Brother Jie you receive four offers, you can only go to one university!"

"Zihan, it's not a matter of offer. Love learning, is it just for an offer?"

"What's that for?"

"The offer must be taken, if there are four offers delivered to me, then I will choose the most competitive offer. In addition to the offer, there are many gains that learning has brought us, and the time is limited, so I will not elaborate on them one by one. The coach is here, let's take the class. ”

With the arrival of Tong Yuanhong, Lan Jie and Wu Zihan stopped talking.

"The preliminary round of CMO has just ended, and I wish the students who participated in the CMO good results. Some of your seniors have advanced to the semi-finals of two or even three subject competitions in the same year, and I believe that some of you here also have this kind of all-round strength. The new team will be formed next week, and if some of you are qualified and willing to switch to the team, I absolutely support it. Tong Yuanhong was very tolerant, she expressed her attitude, and then explained the knowledge points and problems of modern physics.

After class, Lan Jie reported to Tong Yuanhong alone: "Teacher Tong, I have a sports competition at the end of September, and I reported for the men's long jump event of the National Middle School Athletics Championships. I made an appointment with Mr. Wei Chaoqiang to practice the long jump in the afternoon, and if you approve it, I will go and practice the long jump. If you don't approve it, I won't go. ”

Tong Yuanhong was noncommittal, she asked: "Lan Jie, you have already taken all the courses of several coaches in the theory class, what do you think of what we are talking about?"

"Certainly excellent. ”

"To be specific, Lan Jie, tell me directly, do you need us to raise it a little more, or do you need to reduce the difficulty and intensity a little bit?"

"It's just for the CPhO rematch, and the coaching team's current teaching difficulty and intensity are OK. But I understand that Mr. Tong's goal is not just a rematch, if it corresponds to the national competition, the difficulty and intensity can be raised a little more. ”

"Okay, I see, Lanjie, you go and practice sports, I wish you good results in the sports arena. ”

Lan Jie swore and said: "Teacher Tong, I may ask for leave for the theory class of physical competition, but I will never ask for leave for the experimental class of physical competition." ”

Tong Yuanhong nodded and said, "Yes, go ahead." ”

"Well, I'll see you tomorrow, Teacher Tong. ”

Lan Jie left the school building and came to the large playground.

The old long jumpers have already gone to college, and the new long jumpers have not yet been added to the team, and Lan Jie is currently the only one left in the sheep long jump team.

Wei Chaoqiang said to the only team member: "Applejack, you still have to participate in the two competitions of chemistry and biology, will spending hours practicing sports at this time affect your performance in cultural classes?"

Lan Jie said: "The competition and the competition mainly rely on the spiritual play on the spot, and the spirituality is something that cannot be found, and I don't force it." Mr. Wei, let's start the long jump training. ”