My IQ has been increasing year by year.

Chen Zhuo lived a harmonious life in the laboratory.

I'm curled up in the lab enjoying the warm air.

He flipped through the red book that Lao Zhou had given him.

Occasionally, he would help Lao Zhou by explaining problems to Li Hao and Zhang Wei, and giving them extra lessons.

Some time ago, Lao Zhou appointed Chen Zhuo as their team leader, even though their team only had three people.

Li Hao and Zhang Wei naturally agreed wholeheartedly.

Ever since Chen Zhuo explained the problems to them a few times, they called him "captain" with complete sincerity and without any reservations.

What seemed like an insurmountable problem to them, a problem that was impossible for a human to solve, seemed to Chen Zhuo to be able to solve in no time at all.

The key is that they can easily understand the methods Chen Zhuo teaches.

That's amazing.

As for Lao Zhao's side, there are five people in the math group, three men and two women, plus Chen Zhuo, making a total of six.

On the evening of the day when enough people had gathered, Lao Zhao went over and threw a problem onto the blackboard.

Not surprisingly.

Chen Zhuo became the captain of the math group without any trouble.

I just don't know why.

It seems he's getting more and more snacks.

......

Wednesday evening, 7:30 p.m.

The dedicated classroom for math competitions on the top floor of the administration building of the No. 1 Middle School.

It's very dry here, and the air is filled with a calming, sour smell, unique to old paper.

The heavy, deep red velvet curtains were drawn tightly shut, completely isolating the night outside and the school's evening study bell.

The room contained only a huge mahogany table, with a high-wattage incandescent bulb shining on it.

Five people sat around the lamplight.

Three men and two women.

These five people form an all-star lineup for the mathematics competition group of the junior high school of the city's No. 1 Middle School.

Wang Yang, a ninth-grade student and the top math student in his grade, was wearing glasses thicker than the bottom of a bottle and was frantically biting his pen.

Zhao Chen, a ninth grader, is also a math fanatic. At this moment, he is grabbing his hair, turning his already messy hair into a bird's nest.

There's also Liu Kai, a chubby boy in the second year of junior high, and two girls, Nan Xiaoyun and Lin Xiao.

They were very quiet.

Apart from the scratching of the pen on the paper and the occasional sigh, there was almost no other sound.

He sat at the very end of the long table.

He was holding a copy of "Intermediate Mathematics" that he had pulled from the shelf, the cover of which was already half torn off, and he was reading it with great interest.

The five people were stumped by a question.

A classic combinatorial geometry problem.

The question is drawn on the draft paper:

Can a 6x6 square chessboard be covered without overlap using 1x4 rectangles (dominoes)? If not, please explain why.

The question is very simple.

It's so simple that even elementary school students can understand it.

But it's very troublesome to solve.

"Is it possible?"

Wang Yang drew grids on the paper with a pen.

"Look, the area is 6 x 6 = 36, and the area of ​​the dominoes is 4. 36 is a multiple of 4, so there's enough area!"

"Having enough area doesn't mean you can cover the whole place!" Zhao Chen retorted. "I tried for ages, and every time there was an extra piece sticking out from the corner."

"Should we divide the 6x6 into several smaller rectangles?" Nan Xiaoyun was also trying. "For example, cutting it into 2x4 blocks? Oh no, 6 divided by 4 isn't a whole number..."

"Forced connections won't work; there needs to be a pattern," Liu Kai said, biting his pen. "Should we use proof by contradiction?"

The argument grew louder and louder.

Too noisy.

That kind of haphazard trial and error is like stumbling around in the dark.

Chen Zhuo closed the book "Intermediate Mathematics" and sighed softly.

He grabbed his book, jumped off the chair, and slowly walked to the other end of the long table.

He stood between Wang Yang and Zhao Chen.

"Is it stuck?"

Chen Zhuo's voice was flat, revealing no emotion, as if he were asking if he had eaten.

The argument stopped abruptly.

All five people were looking at the nine-year-old group leader.

"Yeah, it's stuck."

Wang Yang pushed the messy draft paper over and scratched his head a little embarrassedly.

"I feel like this problem can be filled completely, but I just can't seem to draw it. The area is clearly a perfect match."

Chen Zhuo glanced at the question.

"Area matching is a necessary condition, but not a sufficient condition."

Chen Zhuo reached out and pulled a red pen from the pen holder.

He didn't draw those complicated rectangular dominoes.

He took the 6x6 grid.

"Don't draw."

Chen Zhuo said calmly.

"dyeing."

"Dyeing?" Nan Xiaoyun was taken aback. "Like coloring black and white checkers in chess?"

"Black and white checkered patterns won't work."

Chen Zhuo shook his head.

"That's for solving 1x2 dominoes. This problem is 1x4."

"We need to use four colors."

Chen Zhuo wrote the numbers 1, 2, 3, 4 in the grid with a red pen in his hand.

He didn't fill it in randomly, but rather in a very regular, cyclical order:

First row: 1, 2, 3, 4, 1, 2

Second row: 1, 2, 3, 4, 1, 2

……

Continue until the entire 6×6 chessboard is filled.

"Look."

Chen Zhuo pointed to the number matrix.

"No matter how you place them, any 1x4 domino, whether placed horizontally or vertically, will always cover four squares with the numbers 1, 2, 3, and 4."

"In other words, each domino consumes one set of 1, 2, 3, and 4."

"If the board can be completely covered, then the number of 1s, 2s, 3s, and 4s on the board must be equal."

Chen Zhuo put down his pen, looked up, and looked at the senior students through his glasses.

"Now, count them."

How many 2s are there on this chessboard?

Wang Yang was stunned for a moment, then quickly went to count the matrix drawn by Chen Zhuo.

"There are two 2s in each row... there are six rows in total... that's 12 2s."

"How many 4s are there?" Chen Zhuo asked.

Wang Yang continued counting, when suddenly his expression changed.

"The first line... there's no 4? No, there is a 4."

"Each row is 1, 2, 3, 4, 1, 2. There's only one 4!"

"There are six lines in total, and only six 4s!"

The classroom fell silent instantly.

The logic is complete.

To fill the entire area, you must consume an equal number of 2s and 4s.

But on the chessboard, there are 12 2s and only 6 4s.

It's completely unequal.

"Therefore, it's impossible."

Chen Zhuo put down his pen.

"This is proof by contradiction; you don't need to make up the numbers, just count them."

Zhao Chen stared at the paper, his mouth agape.

"Is this...is that all the proof?"

"Um."

Chen Zhuo dusted off his hands and turned to walk back.

"Coloring is the foundation of combinatorics. When you encounter this kind of covering problem in the future, don't rush to draw a diagram. First, think about how to use coloring to create contradictions."

He sat back down in his seat and opened his book.

"Alright, stop daydreaming, next question."

Behind them, five senior students looked at each other in bewilderment.

Wang Yang, in particular, felt as if his intelligence had been thoroughly insulted when he looked at that simple numerical matrix.

It's not because the questions are difficult.

Rather, it's because this solution is too elegant, too cunning, and too...

"Awesome."

Wang Yang struggled for a long time, but only managed to utter these two words.

There are no complicated calculations or tedious classification discussions.

It's just about drawing a few numbers, counting them, and ending the battle.

"That brain of his..."

Wang Yang muttered something under his breath.

"How did it grow?"