Free Web NovelChapter 72: Chapter 68: This is the Correct Way to Solve the Problem
Niu Lianhua favors Sun Liang significantly.
When lecturing on Mathematical Olympiad, she almost only focused on Sun Liang, expressing the meaning that "the rest of you have no hope; you can’t even pass a city-level round."
Normally, it’s true.
Even in the city-level Mathematical Olympiad competition, if you don’t score at least 140, passing is quite impossible.
But expressing it feels depressing!
After leaving the office, Lin Xiaoqing gritted her teeth; her glance at Sun Liang carried a hint of danger.
The expressions of the others weren’t any better.
"Haha, I’ll leave first!" Sun Liang sensed the situation and hurriedly slipped away.
When they got back to the classroom, Lin Xiaoqing found a new target. She took out the Mathematical Olympiad problems she couldn’t solve yesterday and entered the mode of scratching her head and thinking hard.
Niu Lianhua said something that resonated with some people. freewebnoveℓ.com
Although the chances of winning a prize in the Mathematical Olympiad competition are slim, being exposed to difficult questions can help improve math skills and solve normal difficult problems.
The last College Entrance Examination had relatively simple math questions, and many people scored over 140.
According to the logic of Nanjiang Province’s College Entrance Examination that alternates "easy one year, difficult the next," their examination this year will definitely be challenging, particularly in the subjects of mathematics and integrated science.
The previous Monthly Test had very difficult math problems, and most students didn’t pass.
Doing Mathematical Olympiad problems can expand thinking and practice problem-solving methods. It may help with solving normal difficult problems and ultimately improve math scores.
Zhao Yi also decided to try Mathematical Olympiad questions.
There was no evening self-study that day, and Zhao Yi went to a nearby bookstore with Sun Liang after school. Sun Liang skillfully found the Mathematical Olympiad books and even recommended a comprehensive collection to Zhao Yi.
Buy!
Buy!
Zhao Yi bought two exercise books, intending to master all the problems before the competition.
High school level Olympiad math doesn’t have much relation to regular high school math, but it indeed hones the flexibility of thinking. Zhao Yi also hoped to improve his math score further.
Not to say getting a full score of 150, even 145 would be acceptable!
...
After dinner, Zhao Yi tried to do the Olympiad math problems.
Having struggled with a problem for ten minutes, he simply abandoned the conventional logic, opting mostly for causality thinking and a small part of logical thinking instead.
The problem suddenly got much easier.
[Find a four-digit number with the same first two digits as the last two digits, while the number itself is a square of an integer.]
Solution: Let the four-digit number be x; x = 1000a + 100a + 10b + b.
Logical thinking ends here.
Now it’s time for causality thinking. With a and b being digits from 0 to 9, the "Causality Law" gives a = 7, b = 4.
Next step.
Use the "Connection Law" to find the solution process.
Write down the answer.
"Perfect!"
Zhao Yi was satisfied with his evaluation, and immediately looked at the next question: [Prove that the product of four consecutive...]
"Pass!"
"A hundred years of specializing in proofs! Don’t waste time!"
Next question: [Prove that ...]
"Pass!"
Next question: [Find the largest perfect square number so that after removing its last two digits, the remaining number is still a perfect square (assuming that one of the two removed digits is not zero).]
He got stuck.
That’s the limitation of the "Causality Law."
"Causality Law" can find the correct answer among options, but its use is limited to a "finite, smaller is better" condition.
Finiteness is the premise.
Another premise is that there must be a correct option.
In addition, he must be sure that there are correct options inside. Estimations or questions based on vague "None of the above" answers are not valid.
The number of options directly affects energy consumption.
Finding the correct answer from dozens of options consumes much more energy than finding it from ten options. The consumption can be several times higher in different situations.
Zhao Yi took a deep breath, deciding to tackle the problem head-on. Causality thinking can’t always directly provide answers, and there must be some trick to crack the problem.
Read the question again:
[Find the largest perfect square number so that after removing its last two digits, the remaining number is still a perfect square.]
Without an upper limit, the "Causality Law" cannot determine the number of digits.
But ...
"The last two digits definitely exist. So it’s at least a three-digit integer ..."
Using the "Causality Law," he got the digits 6, 8, and 1. After removing the two digits, the last three-digit number is 600.
Let n be the largest square number, a² = n - 81
Analysis: a must be a number with a trailing 0, and after squaring, the first nonzero digit at the end is 4 or 6.
Using the "Causality Law," he got the number 4.
Guess... 40?
40² = 1600.
1681=41².
Correct!
Use the "Connection Law" to deduce the steps!
Perfect!
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With a combination of causal and logical thinking, Zhao Yi posed a series of over a dozen problems.
He just couldn’t stop!
Among them, there were problems that couldn’t be solved, the most annoying ones being those marked with x, y, and other letters. Because even the answers were expressed in symbols, it was impossible to find the answer without obtaining the steps.
Fortunately, most of the problems could be solved.
Zhao Yi found that doing Mathematical Olympiad problems was indeed useful. In the process of continuously solving problems, he became more familiar with the use of "Causality Law" and "Connection Law."
Stretching lazily, he walked into the living room from his room, picked up an apple from the table, took a bite, and sat down on the sofa.
"Done with the problems? Tired, right?"
Liu Jing offered him a cup of water.
Zhao Yi took a sip and joined his parents watching TV.
The show "Brain Power Burst" was on, and two contestants were about to compete in solving 3x3 Rubik’s Cubes.
Zhao Yi perked up.
The two contestants were Jia Hongning and Zhou Junkai.
Jia Hongning looked like a popular young star with black-rimmed glasses, giving him a bit of a superstar vibe; Zhou Junkai looked like the type of student who wasn’t good at socializing, and his friendly demeanor and attire were very approachable, with a kind smile that could win people over.
The 3x3 Rubik’s Cube restoration contest was all about speed.
As the cubes were placed on the table, the contestants had a few seconds to observe them, and the camera focused on both the cubes and the contestants’ hands.
Then...
Begin!
Swish, swish, swish...
Jia Hongning restored his cube in just over nine seconds; Zhou Junkai’s hand speed was also fast but clearly more than two seconds slower.
The result of the second round was the same.
Jia Hongning used 11 seconds.
Zhou Junkai used 12 seconds.
With a best-of-five format, Jia Hongning won the third round, raising his hand in excitement to celebrate his victory.
Zhou Junkai could only leave with a smile that masked his sadness.
Half-lying on the sofa, Zhao Zhenxi nodded and said, "This Jia Hongning is better than Zhou Junkai, always a bit faster."
"Not necessarily."
Zhao Yi shook his head and said, "I just noticed that in the first round, Jia Hongning’s cube only needed 17 steps to solve, while Zhou Junkai’s needed 22."
"In the second round, Jia Hongning’s needed 19 steps, while Zhou Junkai’s was 24."
"In the third round, Jia Hongning’s was even simpler, only 14 steps, but Zhou Junkai needed 23."
Zhao Zhenxi stared blankly at Zhao Yi, as if to say, ’Son, what are you talking about?’
Zhao Yi just smiled.
In the end, Zhao Zhenxi just shook his head, deciding to treat Zhao Yi’s words as a joke.
Returning to his room,
Zhao Yi turned on his computer, remembering to send the completed algorithm package to Zhang Zhen.
Click.
Send!
Zhang Zhen on the other side immediately accepted the file, adding a surprised expression, "That fast?"
Zhao Yi: "Is it fast?"
Zhang Zhen: "You didn’t spend an entire day on it, did you? /Shocked."
Zhao Yi: "See for yourself, does it meet the requirements?"
Zhang Zhen: "Alright, I will check it out right now! Just wait a moment!"
On the other side...
Zhang Zhen was astonished as he opened the file, saw the 200-plus lines of code, and put them into the programming software. After making some adjustments to the beginning and end, he ran it for debugging directly.
It succeeded on the first try!
Even when he inputted some problematic data, it successfully executed the sorting.
No problem!
He was even more amazed.
Although the algorithm package wasn’t too difficult, it would still be impossible for him to complete it without a whole day’s work.
Designing took time.
Writing code took time.
Debugging and modifying took even more time.
Zhao Yi was a high school student, a senior at that. He should be in class. Even if he didn’t go to class and spent the entire day on it, completing the algorithm package would still be impressive.
"Take another look!"
Zhang Zhen opened the code page and carefully scrutinized each line of code.
