I kidnapped an alien civilization

There is only one week before the start of school, and the teachers of Mengcheng No. 1 Middle School have already started to prepare for the new semester.

Teacher Zhang, the head teacher of Class 1 and 3, is sorting out the final grades of last semester in the office.

Song Yiyang: Math 81, Chinese 75, English 90, Zhang Meng: Math 90, Chinese 85, English 86 Chen Shuxian: Math 95, Chinese 92, English 96 If she plans to study abroad, she will not be able to take the college entrance examination. Teacher Zhang is a bit pity.

Yang Hui: Math 75, Chinese 80, English 85 Li Mo: Math 70, Chinese 75, English 73

Calculating the grades of the students, Teacher Zhang was a little worried. The grades of the students in the first and third grades were much worse than those in the grades one and one and the second grade. He knew the reason. When the high school was divided into classes, the school assigned many good seedlings to the first class of senior high school.

This is something Mr. Zhang knew when he took over Class One and Three, and it was also a big hole dug for him by the school's academic affairs director.

Knowing that it was a big pit, he jumped into it without hesitation, because in his opinion, the teacher just taught without discrimination. Good students should be educated well, and poor students should be educated more carefully.

The reality taught him a hard lesson, and then the school announced that every year the head teacher of the class with the best performance in the college entrance examination will be rewarded with a 120-square-meter house.

How much he wants the house, he is still living with his father-in-law and mother-in-law's family. Although the two old people were very kind to him, he had wanted a house of his own for a long time. His wife also murmured in his ear many times, but looking at the house price of more than 10,000 outside, he knew that he couldn't even afford the down payment.

After calming down, Teacher Zhang began to prepare for the start of school. He remembered Li Mo's prank phone call. It seemed that he was going to visit Li Mo's home before school started. There is also Chen Shuxian's house to go, after all, she is the best student.

Hey, look at the report card. As far as the grades of your class are 10 points lower than ours, the house after two years will be mine.

The dean is my cousin!

Old Zhang, you'd better stop worrying about the house, save some brain cells, and live for two more years!

The person who came was Luo Peifen, the head teacher of Class One and One of Senior High School, a 50-year-old woman who put on makeup and powder, and her brother was the director of the school's academic affairs.

Teacher Zhang ignored her and just walked out with the student's materials. He still wanted to take them home to study how to help the students improve.

Woke up feeling refreshed. Although the Collats conjecture has been proven, the thesis has not yet been sorted out. Li Mo didn't even bother to eat breakfast, and started writing his thesis.

Topic: For every positive integer, if it is an odd number, multiply it by 3 and add 1, if it is an even number, divide it by 2, and so on, and finally get 1. The conclusion is established.

Abstract: This paper realizes the proof of the thesis through the method of double reverse induction

text:

n is an even number, n/2 is an even number, ..., always divide 2 to 1; n is an even number, n/2 is an even number, until n is divided by 2 to the X power, it is an odd number. We represent n divided by 2 to the X power as n, which can be equivalent to n being an odd number. (When it is an even number, the number must be decreasing)

. . . . . . . . . . .

n is an odd number, n×2+n×1+1 2n+n+1, this must be an even number, (2n+n+1)/2 n+(n+1)/2, there are two situations here, as If it is an even number, it is an odd number; if it is an even number, cycle ① (the number keeps decreasing when it is an even number), until n+(n+1)/2 is an odd number.

Because: n is an odd number, there is and only (n+1)/2 is an even number 1 n+(n+1)/2 can be an odd number.

n is an odd number, n+(n+1)/2 is an odd number, continue below:

n+(n+1)/2 is an odd number, ×2+×1+1 2n+n+1+n+(n+1)/2+1 is an even number, divided by 2 2n+1+(n+1) /4

Continue the two cases, if it is an even number, it is an odd number, and if it is an even number, cycle ① and ②, (Anyway, the number is decreasing when the number is even)

, until 2n+1+(n+1)/4 is an odd number. Transform to n+(n+1)+(n+1)/4

Because: n is an odd number, n+1 is an even number, and only (n+1)/4 is an even number, and n+n+1+(n+1)/4 can be an odd number.

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

n+2(n+1)+(n+1)/4+(n+1)/8 is an odd number, ×2+×1+1

10n+8+(n+1)/8 is an even number, divided by 2 5n+4+(n+1)/16

2n+4(n+1)+(n+1)/2+(n+1)/4+n+2(n+1)+(n+1)/4+(n+1)/8+ 1

n+4(n+1)+(n+1)/16

Infinite loop until (n+1)/2 gets x power=1

So far the proof is complete.

It can be determined from this that for every positive integer, if it is an odd number, multiply it by 3 and add 1, if it is an even number, divide it by 2, and so on, and finally get 1. This conjecture is completely correct.

Author: Li Mo Mengcheng No. 1 High School, Class No. 1 and No. 3

The primary study paper writing function in his head is really easy to use, and Li Mo almost finished it in one go. Checked again carefully to make sure there was nothing wrong.

He took out the piggy bank he had hidden under the bed, counted it carefully, and there was 205.6 yuan left. He took out 20 yuan, and there was 185.6 yuan left. He was going to print and mail the thesis.

The money in the piggy bank is what he usually saves from the few meals. I was going to buy a new basketball.

His annual New Year's money was confiscated by Li Mo's mother in the name of safekeeping. The New Year's money was sent to relatives' children, so Li Mo didn't complain too much.

There was a knock on the door, and Li Mo opened the door, only to see Li Mo's mother outside with a fruit plate.

Son, you are tired from studying, eat some fruit.

Li Mo took a step back, he was frightened by this super treatment.

Mom, come in and sit. Li Mo moved the only chair in the room over.

Mom doesn't sit down, just to see that you have been studying for the past few days? Have you been stimulated by something?

Study is more important than physical health. Why don't you take a break and play golf in the afternoon? Li Mo's mother asked softly.

Li Mo couldn't laugh or cry, it was his mother who forced him to study with sticks all day long, and now it was this mother who persuaded him to go out to play.

It's okay, mom, I'm in good health. I want to review all the books before school starts. Li Mo doesn't have much time to go out and play now. He read two more books today and got 20 points. Seeing the points credited, Li Mo felt like playing a game.

It feels so good!

Li Mo had already used up one of the two cans of coffee obtained by the lottery, and he wanted to keep the remaining one. He found that it was a magic weapon to explode the liver.

Before dinner, Li Mo finished reading two more history books. He earned 20 points.

Today, Li Mo's father came back a little early, and it was rare for the family to sit together for dinner.

I heard from your mother that you have been studying these past few days? Li Mo's father asked after hesitating for a long time.

Well, I'm going to review it before school starts. Li Mo made an excuse.

Today, the manager Chen in the factory, that is, the old Chen who used to live next door, gave me a ticket to the city planetarium. He wants you to take her daughter to visit tomorrow. Li Mo's father hesitated and said.

Since you still want to read, I'll call and resign for you.

I? Chen Shuxian? City Planetarium? Li Mo was a little confused.

Ahem. Don't refuse! Li Mo's mother hurriedly stopped her when she heard Lao Li's words, regardless of being almost choked on the porridge.

Think about who that old Chen is, your immediate boss. I heard from Chen Shuxian's mother that Lao Chen is going to be promoted again. Who like you has been in the workshop all his life, and if you offend him, you will have good fruit to eat?.

Chen Shuxian is so good at studying, it's a great thing to be able to learn from others together.

Besides, the tickets for the City Planetarium cost more than one hundred?

How can such a good thing not go.

Li Mo's mother swallowed the porridge and spoke like a machine gun.

Lao Li looked at Li Mo. Wondering about his decision.

Okay, I'll go to Chen Shuxian's house to pick her up early tomorrow morning. Li Mo said, taking the ticket.

Reading does not feel that the spring is deep, and every inch of time is an inch of gold. It's not Taoists who come to make people laugh, Zhou Qing and Confucius are pursuing it.

Without the addition of extraterrestrial coffee, Li Mo felt very tired after reading for two hours after dinner. Lying on the bed, looking at the picture of Kobe on the wall, he knew that he was getting farther and farther away from the NBA.