Niu Lianhua is particularly fond of Sun Liang.

She explained the Mathematics Olympiad, almost exclusively for Sun Liang alone, and the meaning expressed could be understood as, "The rest of you have no hope, and you can't even pass a pass in the city." ”

Normally, it's true.

Even if you don't get 140 points in the city-level Olympiad competition, you don't have to think about passing the test at all.

But it's depressing to show it!

After walking out of the office, Lin Xiaoqing gritted her teeth, she looked at Sun Liang's gaze, with a hint of danger.

The eyes of the others were not very good.

"Haha, I'll go first!" Sun Liang saw that the situation was not right, and hurriedly flashed people.

After returning to the classroom, Lin Xiaoqing found a new goal, she took out the Olympiad math problems that she didn't do yesterday, and entered the scalp grabbing mode of hard thinking.

Niu Lotus has a little bit to say in the hearts of several people.

There is not much chance of participating in the Olympiad to win prizes, but it is also helpful to improve the level of mathematics and do normal problems by getting in touch with difficult Olympiad problems.

The questions in the last college entrance examination were relatively simple, and there were many people with more than 140 points in mathematics.

According to the logic of the college entrance examination in Nanjiang Province 'one year is simple, one year is difficult', their college entrance examination questions this year will definitely be difficult, and the subjects that improve the difficulty lie in mathematics and science.

Last month, the math paper was very difficult, and most students failed the exam.

Doing Olympiad questions can expand your thinking, exercise, and think about difficult problems, which may be helpful for doing normal problems, and improve your math scores.

Zhao Yi also decided to do Olympiad problems.

There was no evening self-study on this day, and after he and Sun Liang got out of school, they rode to a nearby bookstore together. Sun Liang found the Olympiad book and recommended a complete set of Olympiad exercises to Zhao Yi.

Buy!

Buy!

Zhao Yi bought two exercise books, planning to find out all the questions before the Olympiad competition.

The high school Olympiad has little to do with high school math, but doing the Olympiad can really exercise the flexibility of thinking, and he hopes to improve his math score again.

Not to mention that the exam has a perfect score of 150, a score of 145 is also acceptable!

......

After dinner, Zhao Yi tried to do the Olympiad problems.

After struggling with a question for ten minutes, he simply gave up his normal way of thinking logically and switched to mostly causal thinking and a small part of logical thinking.

The topic is immediately simple.

[Find a four-digit number with the same first two digits and the last two digits, and the number itself is equal to the square of an integer.] 】

Solution: Let the four-digit number be x, x=1000a+100a+10b+b.

This is the end of logical thinking.

The following is the causal thinking time, a and b are both numbers between 0 and 9, and using the law of cause and effect, a = 7 and b = 4 are obtained.

Next.

Use the Law of Liaison to derive the process of solving the problem.

Write down the answer.

“Perfect！”

Zhao Yi made a satisfactory evaluation, and immediately looked at the next question, [Test the multiplication ...... of four consecutive natural numbers]

“Pass！”

"100 years of professional proofing!

Next Question, [Verification ......]

“Pass！”

In the next question, [find the largest perfect square number, and after crossing out the last two digits of it, you still get a perfect square number (assuming that one of the two numbers crossed out is not zero). 】

Stuck.

This is the limitation of the Law of Cause and Effect.

The Law of Cause and Effect can find the correct answer among the options, but the use limit is 'finite, the fewer the better'.

Limited is the premise.

Another premise is that there must be the right options.

In addition, he himself had to make sure that there were the right options in it, and that the questions he created were not valid by 'guessing' or the vague 'none of the above'.

The number of options is directly related to energy consumption.

Finding the right answer in dozens of options can easily consume several times more energy than finding the answer in ten options, and it will consume more for different situations.

Zhao Yi took a deep breath and decided to fight the question, causal thinking cannot be a direct answer, there must be some skills to solve the problem.

Read the question again:

[Find the largest perfect square number, and after crossing out the last two digits of hers, you still get a perfect square number.] 】

There is no upper limit to this problem, so it cannot be determined by the Law of Cause and Effect to determine how many digits it is.

But......

"The latter two definitely exist. So, at least a three-digit integer......"

Using the Law of Cause and Effect, the numbers 6, 8, and 1 are obtained respectively, and the last two digits are crossed out, and the last three digits are 600.

Let n be the maximum number of squares, a²=n-81

Analysis: A must be a number followed by 0, and the first non-zero mantissa after the square is 4 or 6.

Using the Law of Cause and Effect, the number 4 is derived.

Guess what...... 40？

40²=1600。

1681=41²。

That's right!

Use the Law of Contact to derive the steps!

Perfect!

......

In the way of combining causal thinking and logical thinking, Zhao Yi came up with more than a dozen questions in a row.

Can't stop!

Among them, there are also questions that cannot be made, and the most annoying ones with letters such as x and y are the most annoying, because even the answers are symbolic representations, and it is impossible to find the answers without getting the steps.

Fortunately, most of the questions can be done.

Zhao Yi found that doing Olympiad problems is indeed very useful, and in the process of constantly doing problems, he became more familiar with the use of "The Law of Cause and Effect" and "The Law of Contact".

He stretched out for a long time, walked to the room to the living room, picked up the apple on the table, nibbled on it, and sat down on the sofa.

"Tired of finishing the question, aren't you?"

Liu Jing helped take a glass of water.

Zhao Yi took a sip and watched TV with his parents.

The program "Brain Bang" is playing on the TV, and the two contestants are preparing to compete in the restoration of the third-order Rubik's Cube.

Zhao Yi came to the spirit.

The two players are named Jia Hongning and Zhou Junkai.

Jia Hongning looks like a popular student, with glasses with black edges on the upper edge, and he does have a bit of a star posture; Zhou Junkai looks like the kind of student who is not good at socializing, and he is also very close to the people, and his kind smile can also give people a good impression.

The third-order Rubik's Cube is restored, and the comparison is hand speed.

When the Rubik's Cube of the two people is placed on the table, you can observe it for a few seconds, and the screen is also aimed at the Rubik's Cube and the player's hand respectively.

Subsequently.

Begin!

Boom, boom, boom......

Jia Hongning only took more than nine seconds to restore the Rubik's Cube, and Zhou Junkai's hand speed was also very fast, but it was obviously two seconds.

The results of the second round were the same.

Jia Hongning took 11 seconds.

Zhou Junkai is 12 seconds.

The game was a best-of-five system, and in the third round, Jia Hongning took the first step to spell the Rubik's Cube, raised his hand and shouted excitedly for victory.

Zhou Junkai could only leave with a smile to hide his sadness.

Zhao Zhenxi half lay on the sofa, nodded and said, "This Jia Hongning is more powerful than Zhou Junkai, and he is a little faster every time." ”

"Not necessarily. ”

Zhao Yi shook his head and said, "I just noticed that the first round of Jia Hongning's Rubik's Cube only takes seventeen steps to complete, and Zhou Junkai's needs twenty-two steps." ”

"In the second round, Jia Hongning needs nineteen steps, and Zhou Junkai's is twenty-four. ”

"In the third round, Jia Hongning's is simpler, fourteen steps, but Zhou Junkai has twenty-three steps. ”

Zhao Zhenxi looked at Zhao Yi blankly, with an expression of 'son, what are you talking about'.

Zhao Yi smiled.

In the end, Zhao Zhenxi shook his head, and he simply thought Zhao Yi was joking.

Back to the room.

Zhao Yi turned on the computer, and then remembered to send the finished algorithm package to Zhang Zhen.

Click on.

Send!

Zhang Zhen on the other side immediately accepted the document, and attached a surprised expression, "So fast?"

Zhao Yi: "Fast?"

Zhang Zhen: "You won't have been doing it all day, will you?" ”

Zhao Yi: "Take a look, do you meet the requirements?"

Zhang Zhen: "Okay, right away, you wait!"

Opposite side.

Zhang Zhen opened the file in surprise and saw more than 200 lines of code inside, he put it into the programming software, made changes at the beginning and end, and directly ran the debugging.

First time!

Then enter some data that is prone to problems, and directly run it to get the sorting.

No problem!

He was even more surprised.

This algorithm package is not too difficult, but even if he is asked to do it, it is impossible to complete it without a whole day.

It takes time to design.

It takes time to write code.

It takes more time to debug and modify.

Zhao Yi is a high school student, and he is still a junior in high school, so he should be in class. Even if you don't have to do it all day, it's quite remarkable to be able to complete the algorithm package.

"Look again!"

Zhang Zhen opened the code page and looked carefully at the lines of the code.