CHAPTER XVI

Gu Lu noticed that Zhou Haihong was really depressed in the past few days.

I didn't even have the heart to practice my favorite Baduanjin.

Gu Lu was also very interested in not touching Zhou Haihong's moldy head, and let him relieve himself for a while.

It's Wednesday of the week again.

Gu Lu was on duty for self-study as usual.

In the office of the mathematics group at night, only Gu Lu was left.

As soon as Gu Lu turned on the computer and was about to watch a movie to relax, he saw Bi Qi knocking on the door and probing his brain in.

"Bi Qi, is there something wrong?" Gu Lu looked at Bi Qi with a smile.

Bi Qi strode up to Gu Lu, handed a test paper to Gu Lu, and said, "Teacher, I have already made the question you gave me!"

Gu Lu picked up the test paper full of formulas and glanced at it briefly, "Well, it's not bad, the answer is correct." ”

Bi Qi looked overjoyed.

In order to solve this problem, he put a lot of effort into it.

"Well, teacher, I have one more thing to trouble you. Bi Qi rubbed his hands.

Gu Lu raised his eyelids, "Speak directly, I won't trouble you." ”：

Bi Qi took out a piece of paper and put it in front of Gu Lu, "I want to ask the teacher for the solution to this problem." ”

On a piece of paper, a question is written with a carbon pen.

Gu Lu looked at it:

[Problem: Dye each square in 33X33 graph paper one of three colors so that the number of squares of each color is equal, if the two adjacent squares are of different colors, their common edge is called the "dividing edge".] Try to find the minimum value of the number of separators?】

The topic is very short.

But the difficulty is unusually high.

Gu Lu glanced up at Bi Qi, "Where did you get this topic?"

"The competition tutor gave us homework. Bizzie replied honestly.

"Homework?" Gu Lu chuckled, "That tutor of yours really trusts you." In the math league, there are no problems of such difficulty. ”

"That'...... Even you, teacher, can't you solve it?" Bi Qi hesitated.

He has already consulted many people on this topic.

But the replies to him were all helpless.

There was no way, he would find Gu Lu here.

If even Teacher Gu can't solve it......

"No, no, no. Gu Lu smiled, "Bi Qi, I'm afraid you misunderstood what I meant." Although this question is considered difficult at the top of the pyramid in high school, in my case, I can only say that it is nothing more. ”

That's all?

Bi Qi was stunned for a moment, and saw Gu Lu take out a carbon pen from the pen holder on the desk.

Gu Lu casually found a piece of scratch paper on the table, and casually turned a pen flower, "I'll write and talk about it, you must pay attention to it." ”

Bi Qi nodded subconsciously, and then reacted, "Teacher, don't you need to do the calculations first?"

Gu Lu shook his head, "There's no need." ”

"Focus, I'm going to get started. ”

This problem is a typical graph theory problem in combinatorial permutations, which can be regarded as a branch of topology.

And geometric topology happens to be one of Gu Lu's several interested directions.

Therefore, this kind of topic does not need Gu Lu to think carefully at all.

Gu Lu slowly spoke, "Find the minimum value of the number of separating edges." The easiest scenario that comes to mind is that the three colored squares are clustered together in each of the three areas of the entire graph paper. In this way, the following two situations will occur. ”

Gu Lu drew two drawings on scratch paper.

Figure 1

Figure II

It is obvious that the three-color vertical partition arrangement in Figure 1 has 66 dividers, while the three-color T-shaped arrangement in Figure 2 has 56 lines. ”

Bi Qi spoke, "Teacher, I have also calculated the number 56, but the point is, I don't know how to prove it, this is the 'minimum number of dividers'. ”

Indeed, the number 56 is only a conjecture and there is no rigorous proof process.

Gu Lu waved his hand, "Don't worry, listen to me slowly." ”

He wrote down a line of formulas on scratch paper and slowly said, "Let the number of separating lines be L, and below is proof L≥56." Write the rows of graph paper as A1, A2, A3 from top to bottom...... , columns from left to right are marked as B1, B2, B3...... The number of colors in the square of the row Ai is denoted as n(Ai), and the number of colors in the square of column Bi is denoted as n(Bi). The three colors are denoted as c1, c2, c3, and ...... respectively."

“…… Define δ(Bi,cj), so ∑(n(Ai)+n(Bi))=∑∑(δ(Ai,cj)+δ(Bi,cj))) = ∑∑(δ(Ai,cj) + δ(Bi,cj)) = ∑n(cj), since ......"

Gu Lu explained every step in detail.

Bi Qi's eyes were blazing, and he listened very seriously.

“…… To sum up, the minimum value of the number of separators is equal to 56!"

Gu Lu finished writing the last stroke and rubbed his wrist, which was a little sore.

"Do you understand?"

"Understood. Bi Qi nodded again and again, looking at Gu Lu's eyes, full of admiration.

"Teacher, you are so amazing, I thought about a topic that I couldn't come up with all day, and you made it in a few minutes!"

Bi Qi's kung fu is obviously not at home, but it has already made Gu Lu squint comfortably.

He glanced at Bi Qi, "By the way, Bi Qi, let me ask you, what do you think of your competition tutor?"

"You mean Teacher Gao?" Bi Qi raised his head and pondered carefully, "Teacher Gao's teaching is okay, it can be said that he is conscientious." ”

Bizzie gave a more pertinent assessment.

"That's right. Gu Lu raised his eyebrows and said with a smile, "What about you, Bi Qi, after this period of training, do you think it is possible for you to complete that 'little goal'?"

"That ......" Bi Qi scratched his head a little embarrassed, "It should be no problem to enter the provincial team, but the national team is still more difficult." ”

"Teacher, don't talk about me, let's talk about you. Teacher, what were the 'small goals' you set back then?" Bi Qi said.

He knew that the age gap between Gu Lu and himself was very small, and he must have participated in the National High School Mathematics League back then.

"My little goal. It's more ordinary, just trying to get the IMO gold medal. ”

IMO?Gold Medal?!

A prerequisite for participation in the IMO (International Mathematical Olympiad) is a selection for the national team. Then compete with math geniuses from all over the world, and the best of them will win the gold medal.

Bi Qi swallowed hard, "Teacher, have you achieved that little goal back then?"

Gu Lu didn't speak, just opened the drawer and threw three golden signs on the table.

Bizzie recognized at a glance that this was an IMO special gold medal.

And it's a whole three!

Bi Qi almost fell to his knees on the spot.

Three IMO gold medals, doesn't that mean that Mr. Gu has been ...... since he was in high school?

What kind of immortal strength is this!

Bi Qi hugged Gu Lu's thigh violently.

Gu Lu was startled and shook it hard, but he didn't shake it off.

"What are you doing here?" Gu Lu held his forehead, his face full of helplessness.

"Teacher, let me mess with you!" Bi Qi shouted.

…………