It is generally believed in the world that IQ includes indicators such as observation, memory, imagination, judgment, deduction ability, and logical thinking ability.

Therefore, most of the IQ test questions are related to mathematics, and mathematics includes the above indicators.

Westerners attach great importance to logical thinking ability, and the old saying in Western academia is: "Logic is invincible, because overcoming logic also requires the use of another logic." ”

The meaning of the organizing committee to set this logic question is very clear, if you want to achieve results in the IMO arena, logical ability is a must, and IQ is the threshold condition.

Every time Shen Qi upgrades his mathematics level, the system will prompt: "Congratulations to the host for upgrading to a certain level in mathematics, and the host's observation, memory, imagination, judgment, deduction ability, logical thinking ability and other indicators in the field of mathematics have been significantly improved compared with the previous level." ”

Shen Qi has upgraded the mathematics level to the professional level of level 5, if he only reserves the mathematics knowledge of junior high school, he will also have a certain degree of confidence in solving this threshold logic problem.

However, the mathematics level of level 5 + junior high school mathematics knowledge cannot solve the integral or differential equations, which involves the knowledge reserve of college algebra.

Shen Qi's understanding of this system is that the system assists him to continuously improve the upper limit of intelligence, but the filling of the knowledge base needs to rely on his own continuous accumulation in daily life, through reading books, listening to lectures, etc. This is mutually reinforcing, and it is difficult to understand intellectually without looking at those esoteric mathematical theories.

Back to the threshold logic of the first question. (Yesterday's title of chapter 46 missed a few words, and the conditions were not fully written, but it was updated later.) If you are patient, you can go back and see)

Shen Qi deduced the three conditions based on the short story:

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

2. These three numbers are not equal in twos and twos;

3. No one number is twice as many as the others.

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 numbers, in the first round of questions and answers, none of the three can give answers, and in the second round of questions and answers, Tom and Jerry still cannot deduce their respective numbers, but Thomas, who answered lastly, gave the correct answer, and the number on his forehead was 144.

Shen Qi assumes that he is Thomas, and I came up with an answer of 144 in the second round of questions and answers, then one of the above three conditions must be excluded.

If 144 is the difference between the numbers of Tom (x) and Jerry (y), you can make an equation that x-y = 144.

In this case, x and y are not 0, and x is not equal to y, that is, condition 1 and condition 2 are satisfied.

Then to negate the third condition, we need to list another equation, that is, x+y=2y, and solve x=y. This condition is not true, otherwise the correct answer can be obtained in the first round, so Thomas's 144 is not the difference between two numbers, but the sum of two numbers.

i.e. x+y=144.

In the same way, if conditions 1 and 2 are both true, and to make condition 3 not true, then x-y=2y.

Simultaneous two linear equations to obtain a system of equations:

x+y=144

x-y=2y

Shen Qi's mental arithmetic can calculate the result, x=108, y=36.

Pushing back, Shen Qi reversed the story scene in his mind:

Tom has a 108 on his head, Jerry has a 36 on his head, and Thomas has a 144 on his head. In the first round of Q&A, none of the three could guess their numbers. In the second round of Q&A, Thomas, who was the last to answer, gave an answer of 144......

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

The threshold has been entered, and 7 points are in hand.

Now it's time to show off your powers.

The second problem is a plane analytic geometry problem.

The x-axis and y-axis of the intersection of the cross are old friends of all students, you will or not, they have always been there, witnessing the changes of the times and the ups and downs.

Visitors in the coordinate system come and go, and mathematicians throughout the ages have spent their lives leaving their great names in this horizontal and vertical world.

What caught Shen Qi's eyes were two ∞-shaped curves, one large and one small, the big one encasing the small one, and it had a special name, Cassini Oval Line.

Don't think it's useless, because if you do, you won't get a 7.

Shen Qi must find the constant between the two eggs, it can't be too long, it shouldn't be too short, it's too big and it's easy to have problems, and too small to get the problem.

Analytic geometry is a combination of geometry and algebra, and the calculation of constants must rely on geometric methods and vice versa.

Shen Qi made a double offensive against Cassini's oval line, but he obviously underestimated Cassini's almost rogue defensive stance.

Cassini's oval line is ever-changing, and it shows a different nature in the hands of different writers.

Shen Qi postponed the offensive, and the weapon he sacrificed --- nunchuck, which could not kill the monster Cassini ovoid line in front of him.

Not to mention that you can't die, people's oval lines won't bleed at all.

The seventy-two changes of Cassini's oval line will inevitably have a true body, find the true body of this monster, and kill him before he can go to the West Heaven to obtain the true scriptures.

If one trick doesn't work, change another trick.

Shen Qi directly threw out the combination of the family's bottom of the magic weapon, the strongest cp of the catenary line + rotary wheel line.

For Shen Qi at this stage, the second hovering weapon is the top magic weapon he can refine, and unless he has to, he will not easily use this kind of big killing move of seconds and seconds, because this consumes too much mana, and he can't stand it if he uses too much brain.

There's no way, this is an IMO arena, and Shen Qi can't care so much.

The catenary + spiral line combination spell that was enchanted by Shen Qi has a powerful physical attack and a spell attack that cannot be reduced, and under such a mixed attack, Cassini's oval line finally revealed a flaw, it revealed its true body, but it was just a mechanical curve.

"You abrasive little vixen, you think that if you put on a cowhide, you will become a powerful bull demon king? Goblin, eat my old Shen!"

Shen Qi pulls out the last trajectory and gives the constant b^2 of the fixing point and spacing of Cassini's oval line.

"Whew, it's so brain-burning, it's so tired. ”

Two and a half hours passed, and Shen Qi, who had solved two questions in a row, had dry lips and was desperately thirsty in his mouth.

"Rest, rest for a while. ”

Shen Qi took a small sip of mineral water to moisten his lips, he didn't dare to drink too much water for fear of peeing.

Twenty contestants were arranged in this classroom to compete in the same field, Shen Qi's seat was in the last row, and he observed the situation of the other contestants, most of them were in a daze, and there was nothing to love.

Each contestant has a small national flag on their exam table, the flag of their respective country.

Shen Qi found that there were only a few players who were not in a daze, they were American players, Russian players, and Kazakhstan players.

"Is this an American?" Shen Qi noticed that the American player in front of him on the left had darker skin, curly black hair, and very obvious South Asian features, most likely of Indian origin.

"The deputy team leader is right, the United States is poaching talents everywhere and bringing doctrines. Shen Qi knows that the U.S. Olympiad team is a strong team, a strong competitor of the Chinese Olympiad team, and the Indians are very good at mathematics and worthy of attention.

Let's look at the two handsome Russian players and Kazakhstan players, both of them are white, among which the Russian brother is more distinctive, he is probably a left-hander, holding a pen in his left hand and quickly answering on the scroll.

Left-handers are generally smarter and deserve attention. If Russia and Kazakhstan are not separated, their former Soviet Union or CIS Olympiad team may be the first in the world, and the Chinese Olympiad team will be the challenger rather than the defender in front of them.

Shen Qi felt the pressure, masters, all masters!

He wants to win the team championship and, more importantly, the IMO individual championship.

The overall strength of the Chinese Olympiad team is very strong, but it may not be able to solo the Russian brother alone, as well as Indians or other ethnic groups naturalized to the United States, and there seem to be Chinese Americans in the American Olympiad team.

Shen Qi didn't dare to relax, and immediately entered the solution of the third question after a short rest.

……

……

True - This chapter says:

Some students said that they could not understand the relevant mathematical theories in this book.

I am writing a novel, and most of the quotations in the text are the most concise parts of the various mathematical theories, and if they are elaborated in the main text, it will inevitably affect the reading fluency.

My original intention in writing this book was to describe some basic subjects in an interesting and not boring way, and I never wanted to write it as an academic paper. I'm going to write about how to calculate the diameter of a circle, which side is sin equal to which edge is better than which side, and so on, I'm sure you don't want to read it.

The author's level is limited, and it is inevitable that there will be omissions in the writing process, and there may be bias in the exposition of some theories.

If some theories are cited, I try to list the sources of the theories at the end of the chapter. Interested students can check on their own.

The references covered in the title of this chapter are:

IQ Test Question Bank

High School Mathematics Compulsory Textbook

University textbook "Analytic Geometry"