Lanjie and Yang Kewei are both science madmen.

One of the attributes of science madman is to seek truth and be pragmatic; the second is to like to invite people to dinner; the third is to help the weak and care for the weak.

Yang Kewei said that his Chinese language was broken, and Lanjie also said that his Chinese language was broken, but Yang Kewei was deeper, so Lanjie invited Yang Kewei for lunch.

I took math test in the afternoon. This math test was average overall, but there was a calculation question that was difficult.

It is known that the box contains red balls and 100 blue balls each. The two colors of balls contain one ball of 1, 3, 3^2,..., 3^99. The sum of the numbers of the two colors of balls is S. For a given positive integer n, if several balls can be taken out from the box and the sum of the numbers of the numbers is n, it is called a ball-taking "n-scheme". Remember the different "n-scheme" numbers as f(n), try to find the values ​​of f(1)f(2)...f(S).

Are you familiar with each other? Are you kind?

This method of setting questions has a strong personal style. Langjie can make a judgment even if he thinks with his toes. The question of red and blue balls is likely to be given by Teacher Han.

Teacher Han is a kind person. Before he sets questions, he will definitely explain relevant knowledge in class.

Teacher Han has focused on explaining a large amount of special skills such as arrangement, combination count, combination identity, probability.

However, even if you listened to all Teacher Han’s courses carefully, you would not be able to solve this red and blue ball question even for a second.

‘So, maybe this question was not given by Teacher Han?’

‘So the teachers in the mathematics teaching group are all keen on the red and blue double color balls?’

‘Teacher Kang, who teaches Class 8 and Class 9, just resigned, so Teacher Kang is developed? Or is it going bankrupt? If it goes bankrupt, Teacher Kang should work harder to repay the debt, and not lose anything. In summary, Teacher Kang must have made a fortune!’

Langjie thought deeply about this math problem. He thought for a full ten minutes but couldn't start writing.

Fortunately, Lanjie completed all the previous questions in just half an hour, and he had plenty of time to solve the red and blue ball problems.

brush!

Yang Kewei suddenly raised his hand.

The math test in the afternoon was still invigilator for Teacher Lu Zhenhua. Teacher Lu walked to Yang Kewei and asked in a low voice: "Yang Kewei, have you finished it? Hand over the paper?"

Yang Kewei did not take the initiative to influence other classmates. He did not make any sound. He nodded slightly with great quality and signaled that he would hand in the paper.

A true male god is not only good-looking, tall, with high exam scores, but also has high personal quality.

Yang Kewei handed over the paper and left, and Teacher Lu exclaimed from the heart: "Kewei, what an excellent student."

'Do you believe Yang Kewei handed in forty minutes?'

‘Whether you believe it or not, I believe it anyway.’

Ranger felt much pressure, and he focused and used all his strength to overcome this math problem.

Time passed by minute by minute, and Lan Jie, who was focused and focused on thinking, suddenly woke up!

What are you thinking about? Ajie, the fancy superficial phenomena that are all traps when you go around the question, and the key to solving the question is the tertiary system!

Second sister, you are so naughty!

Ajie, you are so clever!

Ranger's fast calculation, for each number m in the set A={0,1,...,S   }, it can be represented as a ternary form m=a03a13^2a2...3^99a99, where ai∈{0,1,2},i=0,1,2,...,99.

Based on the logic of ternary system, Ranger quickly calculated the answer, f(1)f(2)...f(S)=2^200-1.

If you check the reverse reversal, the right thing is to reduce one to the power of 200.

‘Fortunately I’m better off.’

Ranjie let out a long sigh. He spent a few minutes checking the previous question, checking it correctly, holding his left hand high.

Teacher Lu Zhenhua walked to Lanjie and asked, "Langjie, do you hand in the paper in advance?"

Ranjie nodded slightly and handed over the person away.

Teacher Lu carefully examined Lanjie's math test paper. After the review, Teacher Lu couldn't help but sigh: "Students with good Chinese scores have good math scores."

Lanjie, who left the examination room, wanted to talk to Yang Kewei about his life ideals, but Yang Kewei was no longer seen.

After taking the math exam, Lanjie can go back to the classroom of Class 2 and 3 for self-study, go home, or play for a while before going home.

The exam will continue tomorrow, so Ranger chose to go home directly.

When passing by the large playground, Lanjie found that the international class in his second year of high school was taking physical education classes.

The liberal arts and science classes in the second year of high school all took the exams these two days, and they all took math this afternoon.

The teaching arrangements of international classes are different from those of liberal arts and science classes, and there is no midterm exam for international classes.

On the track, there were eight girls in the international class running in groups of 100 meters.

Lanjie, who passed by, stopped and watched. He saw eight girls starting and setting off. The girls were heroic, including Yuyouluo, odd and even ponytails, black straight race, running and running, chasing and chasing, and eight girls each showed their magical powers.

The most powerful one is the girl on the 8th lane, she runs so fast.

The running range has just exceeded 50 meters, and the girl in the 8th lane is more than two meters ahead of the second place.

This woman is Zhang Yutong. Her hair hasn't been cut for a long time. She has a long storage and has tied a single ponytail.

After running to the last 20 meters, Zhang Yutong beat all the girls with an absolute crushing advantage.

During the sprint stage, Zhang Yutong's rubber band with her ponytail was loose and fell off. The wind was quite strong at this time, and it must be more than 2 meters above the wind speed.

Hulala!

Zhang Yutong's long hair swayed wildly, and she was like a little madman running wildly in the wind, leading the second place about eight meters when she crossed the line.

"Zhang Yutong is used to beating!"

Lanjie has known Zhang Yutong for more than three semesters, and now he has to re-examine Zhang Yutong.

Zhang Yutong is very good at pushing shot put and is also very strong in sprinting.

Compared with most girls of the same age, Zhang Yutong's upper limbs and lower limb strength are at a higher level.

It can be seen from the naked eye that although Zhang Yutong ran fast, she had not received professional training. She simply beat the other girls with her brute force.

"Zhang Yutong, full marks, you can move freely." The physical education teacher praised it very much.

"Oh, buy Gadisi! Yutong, you run so fast!"

"Yutong, your legs are so long. It turns out that girls with long legs are fast!"

Several girls in the same group were all impressed. A girl took off the rubber band from her wrist and handed it to Zhang Yutong, asking Zhang Yutong to tie her hair.

"Yuxin, thank you." Zhang Yutong took the rubber band and expressed her gratitude. She tied her hair and said very modestly: "Oh, I just ran away casually. Besides, my legs are not long. Compared to Ba, I am a short-legged girl."

Yu Xin didn't react at once: "What's the joke about Eight?"

Yutong explained: "Eight don't even have heads, they all have legs."

Yu Xin laughed wildly: "Puff, it's funny you!"

Zhang Yutong, who was talking and laughing, suddenly realized that Ba was coming, and Ba stared at her not far away.
Chapter completed!