Seems a Little Stressful

It is universally acknowledged that IQ encompasses indicators such as observation, memory, imagination, judgment, reasoning ability, and logical thinking.

Therefore, most IQ tests are related to Math, as it encompasses the aforementioned indicators.

Westerners place more emphasis on logical thinking. An old saying in Western academia goes: "Logic is invincible because defeating logic requires using another form of logic."

The organizing committee's intention in setting this logic question is clear: to achieve results in the International Mathematical Olympiad arena, logical ability is essential, and IQ is a prerequisite.

Every time Shen Qi levels up his Math, the System prompts: "Congratulations to the host for leveling up Math to level X. The host's observation, memory, imagination, judgment, reasoning ability, and logical thinking in the field of Math have significantly improved compared to the previous level."

Shen Qi has already leveled up his Math to level 5, the professional level. Even if he only possesses junior high school Math knowledge, he is confident in cracking this prerequisite logic question.

However, a level 5 Math level + junior high school Math knowledge cannot crack Integral Calculus or Differential Equation problems, as this involves knowledge reserves from university Algebra.

Shen Qi's understanding of this System is that it assists him in continuously raising his intellectual ceiling, but the filling of the knowledge base requires him to constantly accumulate knowledge in daily life through reading, attending classes, and other methods. These complement each other. Without looking at those profound Math theories intellectually, they are difficult to understand.

Back to the first prerequisite logic question. (A few words were missing from yesterday's Chapter 46 question, and the conditions were incomplete. It has been updated. Patient students can go back and take a look.)

The three conditions Shen Qi deduced from the short story in the question are:

1. Tom, Jerry and Thomas' numbers are all greater than 0;

2. These three numbers are all different from each other;

3. Any one number is not twice any of the other numbers.

The supporting clues for deducing these three conditions are that the three people can see the numbers of the other two, but cannot see their own number; in the first round of questions, none of the three can give an answer; in the second round of questions, Tom and Jerry still cannot deduce their respective numbers, but Thomas, who answers last, gives the correct answer: the number on his forehead is 144.

Shen Qi assumes he is Thomas. He arrives at the answer of 144 in the second round of questions, so he must exclude one of the above three conditions.

If 144 is the difference between Tom's (x) and Jerry's (y) numbers, an equation can be written, namely x-y=144.

At this time, x and y are both not 0, and x is not equal to y, which satisfies condition 1 and condition 2.

Then, to negate the 3rd condition, another equation needs to be written, namely x+y=2y, solving for x=y. This condition is not valid, otherwise the correct answer could have been obtained in the first round, so Thomas' 144 is not the difference between the two numbers, but the sum of the two numbers.

That is, x+y=144.

Similarly, assuming conditions 1 and 2 are both valid, to make condition 3 invalid, then x-y=2y.

Combining the two linear equations gives a system of equations:

x+y=144

x-y=2y

Shen Qi can calculate the result mentally: x=108, y=36.

Working backward, Shen Qi replays the story scene in his mind:

Tom has 108 on his forehead, Jerry has 36 on his forehead, and Thomas has 144 on his forehead. In the first round of questions, none of the three can guess their own number. In the second round of questions, Thomas, who answers last, gives the answer of 144...

"That's right, that's the logic." Shen Qi writes 108, 36 on the exam paper.

The prerequisite has been met, and 7 points are in hand.

Next, it's time to show his skills.

The second question is a Plane Analytic Geometry problem.

The perpendicularly intersecting x and y axes are old friends to all students. Whether you know them or not, they have always been there, witnessing the changes of the times, the rise and fall of events.

Passersby come and go in the coordinate system, and Mathematicians throughout history have devoted their lives to leaving their great names in this world of one horizontal and one vertical line.

What catches Shen Qi's eyes are two ∞-shaped curves, one large and one small, with the large one enclosing the small one. It has a special name, Cassini Oval.

Don't think it's useless. If you think so, you definitely won't get 7 points.

Shen Qi must find the constant between the two ovals. It cannot be too long, nor should it be too short. Too large and it's easy to have problems, too small and you won't get the breakthrough point.

Analytic Geometry is a combination of Geometry and Algebra. Calculating constants must rely on Geometry methods, and vice versa.

Shen Qi uses the Lemniscate to launch an attack on the Cassini Oval, but he clearly underestimated the almost rogue defensive posture of the Cassini Oval.

The Cassini Oval is ever-changing, exhibiting different properties in the hands of different problem setters.

Shen Qi suspends the attack. The weapon he offered, the nunchucks - the Lemniscate, cannot kill the monster in front of him, the Cassini Oval.

Not to mention killing it, the oval doesn't even lose health.

The seventy-two transformations of the Cassini Oval must have a true form. Find the true form of this monster, kill him, and then you can go to the Western Paradise to obtain the true scriptures.

If one move doesn't work, change another.

Shen Qi directly throws out his signature combination magic weapons, the strongest cp of Catenary + Cycloid.

For the current stage of Shen Qi, the two instruments of Catenary and Cycloid are the most top-level magic weapons he can refine. He will not easily use this kind of big killing move that can kill the sky, kill the earth, and kill the air unless it is absolutely necessary, because it consumes too much magic power. His brain can't handle it if he uses it too much.

There's no way, this is the International Mathematical Olympiad arena, and Shen Qi can't control that much.

The Catenary + Cycloid combination magic weapon, which has been enchanted by Shen Qi, possesses powerful physical attacks and unavoidable magic attacks. Under such a mixed attack, the Cassini Oval finally reveals a flaw. It reveals its true form, which is just a mechanical curve.

"You little vixen, did you think you could become the all-powerful Bull Demon King by wearing a leather jacket? Hehe, too naive. Monster, eat my Old Shen's stick!"

Shen Qi draws the last segment of the trajectory and gives the constant b^2 of the fixed point and spacing of the Cassini Oval.

"Phew, so brain-burning, so tiring."

Two and a half hours have passed, and Shen Qi's lips are dry, and his mouth is desperately thirsty after solving two problems in a row.

"Rest, rest for a bit."

Shen Qi took a small sip of mineral water to moisten his lips. He didn't dare drink too much, fearing he'd need to pee.

This classroom accommodated twenty contestants taking the exam simultaneously. Shen Qi's seat was in the last row. He observed the condition of the other contestants; most of them were spacing out, seemingly devoid of hope.

Each contestant's desk was adorned with a small national flag, the flag of their respective country.

Shen Qi noticed that only a handful of contestants weren't spacing out: the United States contestants, the Russia contestants, and the Kazakhstan contestants.

"Are these really Americans?" Shen Qi noticed that the United States contestant in front of him and to the left had a darker skin tone, curly black hair, and very obvious South Asian features, most likely of Indian descent.

"The deputy leader was right, the United States just digs up talent everywhere, pure pragmatism." Shen Qi knew that the United States Olympic Math team was a strong team, a formidable competitor to the China Olympic Math team. People of India descent are quite good at Math, worthy of attention.

Looking at the two handsome Russia contestants and the Kazakhstan contestant, they were all white. The Russia guy was particularly distinctive; he was probably left-handed, using his left hand to rapidly solve problems on the exam paper.

Left-handed people are generally smarter, worthy of attention. If Russia and Kazakhstan hadn't separated, their former Soviet Union or Commonwealth of Independent States Olympic Math team might have been the best in the world. The China Olympic Math team would be challengers rather than defending champions in their presence.

Shen Qi felt the pressure. Experts, they were all experts!

He wanted to win the team championship, and even more so, the International Mathematical Olympiad individual championship.

The overall strength of the China Olympic Math team was strong, but in one-on-one combat, they might not necessarily solo against the Russia guy, as well as the Indian descent or other descents naturalized to the United States. It seemed there were also people of Chinese descent in this year's United States Olympic Math team.

Shen Qi didn't dare to relax. After a short rest, he immediately began working on the third problem.

True-Chapter Comments:

Some students say they don't quite understand the relevant Math theories in this book.

I'm writing a novel. Most of the content quoted in the main text is the most refined part of each Math theory. If I were to elaborate in detail in the main text, it would inevitably affect the reading flow.

The original intention of writing this book was to describe some basic Science in an interesting and not boring way. I definitely don't want to write this book as an academic paper. I want to write about how to calculate the diameter of a circle, which side is sin equal to divided by which side, and I believe you wouldn't be too willing to read that either.

The author's level is limited, and omissions are inevitable in the writing process. There may be biases in the description of certain theories. I also welcome students to criticize and correct me, and offer valuable suggestions.

If I quote some theories, I will try to list the source of the theory at the end of the chapter. Interested students can check it out for themselves.

The references involved in this chapter's topic are:

IQ Test Question Bank

High School Math Compulsory Textbook

University Textbook Analytic Geometry