Rule system

Niu Lianhua is particularly fond of Sun Liang.

She explained the Olympic Mathematics Competition, which was almost only aimed at Sun Liang alone, and what she meant could be understood as, "The rest of you have no hope. You can't even pass a level in the city."

Normally, it is a fact.

Even if the city level Olympiad is less than one hundred and forty in the test, there is no need to pass the level.

But it was depressed when it showed up!

Lin Xiaoqing gritted her teeth after she walked out of the office. She saw Sun Liang's gaze with a hint of danger.

Other people's eyes are not so good.

"Haha, I'm leaving now!" Sun Liang hurriedly flashed people as the situation was wrong.

After returning to the classroom, Lin Xiaoqing found a new goal. She took out the Mathematical Olympiad questions that she hadn't done yesterday, and entered the scalp-scratching mode of contemplation.

Niu Lianhua said something to the hearts of several people.

Participating in the Olympiad is unlikely to win prizes, but getting in touch with difficult Mathematical questions is also helpful for improving mathematics and doing normal problems.

The question of the previous college entrance examination was relatively simple, and there were many people with more than 140 points in mathematics.

According to the logic of Nanjiang Province's college entrance examination of'one year is easy, one year is difficult', their college entrance examination questions this year will definitely be difficult, and the subjects that increase the difficulty are mathematics and science.

The mathematics test paper last month was difficult, and most students failed the exam.

Doing Mathematical Olympiad questions can expand your thinking, exercise, and think about difficult problems, which may help you to do normal problems and improve your math scores.

Zhao Yi also decided to do Mathematical Olympiad.

There was no self-study late that day. After school, he and Sun Liang rode to a nearby bookstore together.Sun Liang was familiar with the Mathematical Olympiad book, and also recommended the Mathematical Olympiad exercise book to Zhao Yi.

buy!

buy!

Zhao Yi bought two exercise books and planned to figure out all the questions before the Olympiad.

Mathematical Olympiad at the high school level has little to do with high school mathematics, but doing Mathematical Olympiad can indeed exercise flexibility in thinking. He also hopes to improve his mathematics.

Not to mention that one hundred and fifty full marks in the exam, one hundred and forty-five points, is also acceptable!

...

After dinner, Zhao Yi tried to do Mathematical Olympiad questions.

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

The question is immediately simple.

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

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

The logical thinking ends here.

The following is the time of causal thinking, a and b are numbers between 0 and 9, using the "law of causality" to get a=7, b=4.

Next step.

Use "Law of Connection" to get the problem-solving process.

Write down the answer.

"Perfect!"

Zhao Yi made an evaluation with satisfaction, and immediately turned to the next question, [Prove the multiplication of four consecutive natural numbers...]

"Pass!"

"Professional doing proofs for one hundred years! No time wasting!"

Next question, [Test Proof...]

"Pass!"

The next question, [Find the largest perfect square number, after you cross out the last two digits, you still get a perfect square number (assuming that one of the two crossed numbers is non-zero).

its stuck.

This is the limitation of the "Law of Causality".

"The Law of Cause and Effect" can find the correct answer in the options, but the usage limit is'limited, the less the number, the better'.

Limited is the premise.

Another prerequisite is that there must be the right options.

In addition, he himself must also make sure that there are correct options in it, and the question established by "guessing" or vaguely "none of the above" is not valid.

The number of options is directly related to energy consumption.

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

Zhao Yi took a deep breath, and the decision and the topic were deadlocked. Causal thinking cannot always get the answer directly. There must be some skills to solve the problem.

Read the question again:

Find the largest perfect square number, after crossing off her last two digits, you still get a perfect square number.

There is no upper limit for this question, and the number of digits cannot be determined by the "law of cause and effect".

but……

"The last two digits definitely exist. Then, at least a three-digit integer..."

Using the "law of cause and effect", get the numbers 6, 8, and 1, cross out the last two digits, and the last three digits are 600.

Let n be the largest square number, a²=n-81

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

Using the "law of cause and effect", the number 4 is obtained.

Guess...40?

40²=1600.

1681=41².

correct!

Use "Law of Contact" to derive steps!

perfect!

...

By combining causal thinking and logical thinking, Zhao Yi asked a dozen questions in a row.

Can't stop at all!

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

Fortunately, most problems can be done.

Zhao Yi found that doing Mathematical Olympiad questions is indeed very useful. In the process of constantly doing the questions, he became more familiar with the use of "Law of Cause and Effect" and "Law of Connection".

Stretched a long way, walked to the room to the living room, took a bite of the apple on the table, and sat down on the sofa.

"Did you finish the questions? Tired?"

Liu Jing helped pick up a glass of water.

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

The "Big Bang" program is being broadcast on the TV, and the two contestants are preparing for a competition to solve the third-order Rubik's Cube.

Zhao Yi came to the spirit.

The two players are called Jia Hongning and Zhou Junkai.

Jia Hongning looks like a popular niche, with black-rimmed glasses on the upper edge, which does have a celebrity posture; Zhou Junkai is like the kind of student who is not good at socializing, and he is also very close to the people dressed up, and a kind smile can also give People like it.

The reduction of the third-order Rubik's Cube is comparable to hand speed.

After the two people's cubes are placed on the table, you can observe them for a few seconds, and the screens are also pointed at the cubes and the players' hands.

Subsequently.

Start!

Huh, Huh, Huh...

Jia Hongning solved the Rubik's Cube in just over nine seconds; Zhou Junkai's hand speed was also very fast, but it obviously took two seconds.

The result of the second round is the same.

Jia Hongning took 11 seconds.

Zhou Junkai is 12 seconds.

The game is a five-game three-win system. In the third round, Jia Hongning completed the Rubik's Cube first and raised his hand excitedly to shout for victory.

Zhou Junkai could only leave with a smile covering up his sadness.

Zhao Zhenxi lay halfway on the sofa and nodded and said, "This Jia Hongning is better than Zhou Junkai, and he gets on a little faster every time."

"That's not necessarily."

Zhao Yi shook his head and said, "I just noticed that in the first round of Jia Hongning's Rubik's Cube, it only takes 17 steps to complete, and Zhou Junkai needs 22 steps."

"In the second round, Jia Hongning needed 19 moves, and Zhou Junkai's had 24 moves."

"The third round of Jia Hongning's is easier, 14 steps, but Zhou Junkai needs 23 steps."

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

Zhao Yi smiled.

Finally, Zhao Zhenxi shook his head, he simply acted as Zhao Yi was joking.

Go back to the room.

When Zhao Yi turned on the computer, he remembered to send the completed algorithm package to Zhang Zhen.

Click to open.

send!

Zhang Zhen, who was opposite, immediately accepted the document, with a surprised expression, "So fast?"

Zhao Yi: "Hurry?"

Zhang Zhen: "You didn't do it all day? Shocked."

Zhao Yi: "Look at it, do you meet the requirements?"

Zhang Zhen: "Okay, right now, wait!"

opposite.

Zhang Zhen opened the file in surprise and saw more than two hundred lines of code inside. He put it into the programming software, made changes to the beginning and end, and then ran it directly.

One time success!

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

no problem!

He was suddenly even more surprised.

The difficulty of this algorithm package is not too high, but even if he is asked to do it, it is impossible to complete it without a whole day.

Design takes time.

It takes time to write code.

It takes more time to debug and modify.

Zhao Yi is a high school student or a third year student, so he should be in class.Even if you don't go to class for a whole day, it's amazing to be able to complete the algorithm package.

"Look again!"

Zhang Zhen opened the code page and looked carefully at the code line by line.