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Chapter 4 Thinking has more than one correct answer

§01 Change thinking and change life
Instead of running aimlessly behind others, it is better to stop and use your brain to make a turn in your thinking.There is more than one correct answer, and there is more than one path to success. Another method may be closer to success.

To be a caring person who is good at thinking——

Children, when we decide to do something, please slow down, calm down and think about whether we can do it better.Success always favors those who are good at thinking and ready to meet it.Therefore, we have to think more, observe more, and flexibly change our learning strategies, often getting unexpected results.

There is a strange small village that has no water source except rainwater. In order to solve this problem, the elders in the village decided to sign a water delivery contract so that someone can deliver water to the village every day.Two people were willing to accept the job, so the elders of the village gave the contract to both of them.

One of the two people who got the contract was named Ed. He immediately took action, running between the lake and the village 1 km away every day, using his two buckets to fetch water from the lake and transport it back to the village. The fetched water is poured into a large, sturdy cistern built by the villagers.Although it is quite a hard job, Ed is very happy because he can keep making money.

The other guy who got the contract was Bill.Oddly enough, Bill has disappeared since signing the contract and hasn't been seen for months.This made Ed even more excited, because he had no one to compete with, and he earned all the water money.

What did Bill do?He made a detailed business plan and used it to find four investors who started a company with him. Six months later, Bill returned to the village with a construction team and an investment.It took a full year for Bill's construction team to build a high-capacity stainless steel pipeline from the village to the lake.

At this time, Bill was thinking: If this village needs water, other villages with similar environments must also need water.So he rewrote his business plan and began selling his fast, high-capacity, low-cost, and sanitary water delivery system to villages across the country and around the world.He only earns 1 penny per bucket of water delivered, but he can deliver hundreds of thousands of buckets of water every day.Whether he works or not, hundreds of thousands of people consume hundreds of thousands of buckets of water, and all of this money flows into Bill's bank account.Apparently, Bill had not only developed a pipe for water to flow to the village, but he had also created a method for money to flow to his wallet.

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Reading Tip: Who is smarter, Ed or Bill?
Classic statement: Bill not only developed a pipe to get water to the village, but he also created a way to get money to his wallet.

Learning Proverbs: Change your thinking to learn, which can help you absorb knowledge more efficiently.

Dare to question the teacher's answer——

Children, you and your classmates may not have any doubts about the knowledge taught by the teacher and the knowledge in the textbooks.In fact, learning also includes daring to question inherent knowledge and asking questions.Only by not being superstitious, fearing authority, and having a questioning attitude can we find the truth.

§02 The taste of apples

The students asked Socrates how to stick to the truth, and Socrates asked everyone to sit down.Holding an apple, he walked slowly past each student's seat, and said as he walked, "Students, please concentrate and pay attention to the smell in the air."

Then, he returned to the podium, lifted the apple up and shook it left and right, and asked, "Has any of the students smelled the smell of apples?" A student raised his hand and stood up and replied, "I smell it, it's a fragrance! Socrates asked again: "Which other students smelled it?" The students were silent.

Holding the apple again, Socrates walked slowly past each student's seat, and told them as he walked, "Students, please concentrate and take a good sniff of the smell in the air."

After returning to the podium, he asked again, "Do you smell apples?" This time, most of the students raised their hands.

After a short pause, Socrates walked among the students for the third time and asked each student to sniff the apple.After returning to the podium, he asked again, "Students, do you smell apples?"

As soon as he finished speaking, all but one student raised their hands.The student who didn't raise his hand looked around and raised his hand hastily.His demeanor caused a burst of laughter.Socrates also laughed, "What smell do you smell?" The students replied in unison: "Smell!"

The smile on Socrates' face disappeared. He held up the apple and said slowly: "Unfortunately, this is a fake apple and it has no taste at all."

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Reading Tip: Why do the students smell the aroma of apples?

Classic sentence: Unfortunately, this is a fake apple with no taste at all.

Learn the proverbs: Only when you dare to stick to your true feelings can you get closer to the truth, otherwise the fake apples will be fragrant.

Learning should be diligent, and specific problems should be solved in detail——

Little Euler is a child who loves to use his brain. He can connect theory with practice, and he is good at solving specific problems with the theoretical knowledge he has learned.He can think that a square with a certain perimeter has a larger area than a rectangle. This principle is suitable for fences, and it has received immediate results.

§03 Euler intelligently reforms the sheepfold
Euler is a famous mathematician. He has made great achievements in several branches of mathematics such as number theory, geometry, astronomical mathematics, and calculus.However, this great mathematician was not liked by his teachers at all when he was a child, because he was a student who liked to ask strange questions, so he was expelled from school.After returning home with nothing to do, Euler helped her father herd the sheep and became a shepherd boy.While herding sheep, he reads books, and there are many mathematics books in the books he reads.

Dad's sheep raising gradually increased, reaching 100.The original sheepfold was a bit small, so Dad decided to build a new sheepfold.He measured a rectangular piece of land with a ruler, 40 meters long and 15 meters wide. He calculated that the area was exactly 600 square meters, and each sheep occupied an average of 6 square meters.When he was about to start construction, he found that his materials were only enough for a 100-meter fence, which was not enough.If the sheepfold is 40 meters long and 15 meters wide, its circumference will be 110 meters (15+15+40+40=110).My father felt very embarrassed. If we want to build according to the original plan, we need to add another 10 meters of materials; if we reduce the area, the area of ​​each sheep will be less than 6 square meters.

But little Euler told his father that there is no need to shrink the sheepfold, and there is no need to worry that each sheep's territory will be smaller than the original plan. He has a way.The father agreed to let his son try it.

Little Euler ran to the sheepfold that was about to start work.Taking a wooden stake as the center, he shortened the original 40-meter side length to 25 meters; he ran to the other side, extended the original 15-meter side length, and increased it by 10 meters to 25 meters.With such a change, the originally planned sheepfold became a square with a side length of 25 meters. Then, little Euler said to his father confidently: "Now, the materials are enough and the area is enough."

The father built a fence according to the sheepfold designed by Euler. The 100-meter-long fence was really enough, no more, no less, all used up; the area was also enough, and it was a little bigger.Father is very happy.

His father tried to get Euler to meet Bernoulli, a great mathematician. Through the recommendation of this mathematician, Euler became a student at the University of Basel in 1720. In this year, Euler was 13 years old. Is the youngest student at the university.

good way to learn
Reading hint: When the perimeter is constant, what shape has the largest area?
Classic sentence: My father set up a fence according to the sheepfold designed by Euler. The 100-meter-long fence is really enough, no more, no less, all used up.

Learning Proverbs: Diligent brains, diligent hands, the problems encountered in the study will be easily solved.

Different thinking creates a different future——

Children, active thinking can make our study easy and enjoyable, and proper use of divergent thinking will help us achieve good grades.

§04 Gaussian Calculus
In 1785, 8-year-old Gauss was in the first grade in a primary school in rural Germany.

The math teacher is from the city. He has a prejudice, always thinking that rural children are not as smart as urban children.However, he still has very strict requirements for children's studies. He hates students who don't pay attention in class and like to make small movements, and often beat them with a pointer.But children love to listen to his class, because he often tells some very interesting knowledge.

One day, he came up with an arithmetic problem.He said: "You do the math, 1 plus 2 plus 3, what is it equal to 100? Anyone who can't figure it out is not allowed to go home for dinner." After speaking, he sat on a chair and looked at the students below.

In less than a minute, little Gauss stood up, held up a small slate and said, "Teacher, I figured it out..."

Before little Gauss finished speaking, the teacher said impatiently: "No! Recalculate!"

Little Gauss checked it quickly, and said loudly: "Teacher, that's right." Then he got off his seat and put the small slate in front of the teacher.

The teacher looked down and saw that it read: 5050 squarely, and he couldn't help being surprised.He couldn't believe that an 8-year-old child could figure out the correct answer to such a complicated math problem in less than a minute.The teacher asked little Gauss: "How do you calculate?" Little Gauss replied: "I didn't add one by one in the order of 1, 1, and 2. The sum of the two numbers at the beginning and the end is the same: 3 plus 1 is 100, 101 plus 2 is 99, 101 plus 3 is also 98...the numbers one after another are added together, there are 101 50 in total, and 101 multiplied by 101, we get 50."

Little Gauss's answer surprised the teacher, because it was the first time he knew that there was such an algorithm.He looked at little Gauss in surprise, as if he had just met this shabby-dressed son of a bricklayer.

Soon, the teacher specially bought a math book for Gauss to encourage him to continue working hard, and recommended him to the local education bureau so that he could receive free education.

Later, Gauss became a world-renowned mathematician.In memory of him, people called his calculation method "Gauss' theorem".

good way to learn
Reading Tips: How to use "Gauss Theorem" to solve similar math problems?
Classic sentence: He looked at little Goss in surprise, as if he had just met this shabby-dressed son of a bricklayer.

Learning Proverbs: Learning should pay attention to methods, don't just bury your head in learning, and properly use divergent thinking, which can help you broaden your thinking in solving problems.

There is more than one way to solve the problem -

On the road of hard study, don’t get stuck when encountering difficulties, change your angle, change your thinking, use your brain, you will find a bright road, and success is waving to you not far away.

§05 Learn to find new ways

During World War II, a ship full of military supplies secretly departed from a certain port in Japan.The freighter will pass through Shanghai, Fuzhou, Guangzhou, and then through the Strait of Malacca, sailing to Thailand, and then to Myanmar to provide supplies for the Japanese army there.

The freighter was loaded with soybeans looted from the three northeastern provinces of my country.After the Anti-Japanese Organization got the information, they immediately instructed the agents to find ways to sink the freighter.

After receiving the instructions, the secret agents managed to sneak into the Japanese freighter.However, the inspection by the Japanese army was very strict. How could the explosives be transported to the ship without anyone noticing it?
There are many ways to sink the ship, using explosives is the most direct method, but it was very difficult to implement under the circumstances at the time.

So they came up with a good idea, secretly pouring water into the warehouse full of soybeans to make the soybeans expand. When the weight and volume became larger and larger, the ship would sink by itself, without firing a single shot. The gun did the job.

Diversion of thinking will make many problems that originally seemed unsolvable can be easily solved.As long as we use our brains, we will find that there is far more than one way to solve the problem.

good way to learn
Reading tips: Why do soybeans swell when they encounter water?

Classic sentence: As long as we use our brains, we will find that there is more than one way to solve a problem.

Learning Proverbs: We must use our brains flexibly when studying, not be stubborn, and not take dead truth as truth.

Learn to think from another angle——

Children, when you are writing hard to solve a problem, you might as well calm down first, change your angle, think carefully, maybe you will have a flash of inspiration and find a simple and convenient solution to the problem.The correct way of thinking is one of the important learning methods.

§06 Spouts for toothpaste

There is a company in the United States that produces toothpaste. The products are excellent and the packaging is exquisite. They are deeply loved by consumers and maintain a high-speed growth every year.

Records show that the company's annual operating growth rate in the first ten years was 10%-20%, which made the board of directors very happy.

However, when the performance entered No.11, No.12 and No.13 years, it stagnated and maintained the same number every month.

The board of directors was dissatisfied with the performance of the past three years, so it held a meeting of the company's top managers to discuss countermeasures.

During the meeting, a young manager stood up and said to the board of directors: "I have a piece of paper in my hand with a proposal. If you want to use my proposal, you must pay me another [-] dollars!"

The president was very angry when he heard this, and said, "I pay you a salary every month, plus bonuses and rewards. Now that I have called you to a meeting to discuss, is it too much for you to pay another $[-]?"

"Mr. President, please don't get me wrong. If my suggestion doesn't work, you can throw it away without paying a penny," explained the young manager.

"Okay!" The president took the paper, and immediately signed a check for [-] US dollars to the young manager after reading it.

There was only one sentence written on that piece of paper: expand the mouth of the existing toothpaste tube by 1 mm.

The president immediately ordered to replace the new packaging.

This decision has increased the company's No.14 turnover by 32%.

"Looking horizontally, it becomes a ridge and a side becomes a peak, and the distance and height are different." This is true when looking at mountains, and even more so when looking at things.From one angle, thinking with a single mind, we can only see one aspect of things, and from another angle, we will find a different kind of scenery.

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Reading Tips: What are the benefits of enlarged toothpaste nozzles?
Classic sentence: From one angle, if we think with a single mind, we can only see one aspect of things. From another angle, we will find a different kind of scenery.

Learning Proverbs: Learn to be good at thinking about problems from another angle, and you will be able to find simple and convenient solutions to problems.

A loaded ship will not capsize—

Children, only by studying hard can you increase your weight and value, and only when your "value" increases can you stand firm.At the same time, those who are truly knowledgeable and capable will not show off everywhere. Their abilities and accomplishments are reflected in their daily actions.

§07 Add water to the boat
A cargo ship returned after unloading, and suddenly encountered a storm on the vast sea. The old captain decisively ordered: "Open all cargo holds and fill them with water immediately."

The sailors said worriedly: "Filling water into the boat is more dangerous than dangerous. Isn't this asking for a dead end?"

The captain said calmly: "Have you ever seen a tree with deep roots and thick trunk blown down by a storm? It's a small tree without roots."

The sailors dubiously followed suit.Although the storm and waves were still so violent, as the water level in the cargo hold got higher and higher, the freighter gradually stabilized.

The captain told the relieved sailors: "An empty wooden barrel is easily knocked over by the wind. If it is filled with water and loaded with weight, the wind will not blow it down. The ship is the safest when it is loaded. "The most dangerous time is when the ship is empty."

Filling ourselves with "water" makes us bear the weight so that we won't be overwhelmed by the huge waves of society.Everything has two sides, and only by using its advantages and avoiding its disadvantages can it be "victorious".

Just like pouring water into the boat, on the one hand, it has the danger of sinking the boat, but on the other hand, it makes the boat more stable and will not be blown over by the wind. Under the circumstances at that time, the captain took advantage of it, Only then did the ship be saved.

good way to learn
Reading Tips: Why is a heavy boat not easy to capsize?
Classic sentence: Fill ourselves with "water" and make us bear weight so that we will not be overturned by the huge waves of society.

Learning Proverbs: Only by studying hard can we enrich our knowledge, make us more valuable, and always stand in the wind and waves of society and carry the burden forward.

Learn to reverse thinking to solve problems——

It is common knowledge that water can extinguish fire.Fire extinguishes fire, impossible, right?But someone has actually done it, and succeeded.As long as you dare to think, nothing is impossible.Therefore, when any "truth" is used, it must be flexible according to the situation at that time.

§08 Fight fire with fire
Once, a fire broke out on the American prairie, and the fire ruthlessly devoured everything on the prairie with the help of the wind.It happened that a group of tourists were playing on the grassland that day. When they saw the fire, they all panicked.Fortunately, there was an old hunter walking with them. When he saw that the situation was critical, he shouted: "I want you to live and listen to me."

The old hunter asked everyone to pull up the piece of dry grass in front of them and clear an open space.At this time, the fire was getting closer and closer, and the situation was very dangerous, but the old hunter had a plan in mind. He asked everyone to stand on the side of the open space, and he stood on the side close to the fire. Let the people go to the side of this small open space.

Having taken these precautions, the old hunter moved on to the other side of the clearing, where the fire had surrounded the travelers like a high and dangerous wall.He took a bunch of very dry grass and put it on the gun rack and set it on fire, and the dry grass caught fire immediately, and the old man threw the burnt grass into the tall bushes, and then walked to the center of the circle and waited patiently for the result.

In a blink of an eye, a wall of fire rose around the old hunter, and this wall of fire spread in three directions at the same time.A miracle happened. The wall of fire lit by the old hunter did not follow the wind, but faced the fire on the other side. When the two fires finally came together, the fire suddenly weakened and then gradually extinguished.

After the tourists got out of danger, they asked the old hunter for advice on how to put out fire with fire.The old hunter smiled and said: "There is a fire in the grassland today. Although the wind is blowing towards this side, the airflow will still blow towards the flame near the fire. The fire I set is to seize the opportunity and take advantage of this wind." The air flow rushed over there, and the fire burned the nearby grass and trees, so that the fire on the other side could not be burned again, so we were saved."

good way to learn
Read the tip: Why is fire also used to extinguish fire?
Classic sentence: When two piles of fire finally meet one, the fire suddenly weakens, and then gradually goes out.

Learn Proverbs: When encountering a problem, you may wish to use reverse thinking, and you may find the answer.

Breakthrough thinking, don't stick to the rules——

Children, don't act blindly when encountering problems, only by observing clearly can you hit a hit.Sometimes the more complex the problem, the simpler the solution.Don't get stuck in the quagmire of the method and lose the goal. Only when the goal is clear can the most effective solution be found.

§09 Gordias' Knot
In ancient Greece, there is such a story of Gordias' knot.

In the winter of 223 BC, Alexander the Great of Macedon sent troops to Asia.When he arrived in the city of Virginia in Asia Minor, he heard that there was a famous prophecy in the city: Hundreds of years ago, King Gordias of Virginia tied a complicated knot on his ox cart, And declared: Whoever can untie it will become the king of Asia.

Every year since then, many people have come to see Gordias tie the knot.Warriors and princes from all over the world want to untie this knot, but they can't even find the end of the rope, and they don't even know where to start.Alexander was very interested in this prophecy and ordered someone to take him to see this mysterious knot.

Alexander carefully observed the knot. After a while, he still couldn't find the end of the rope. Alexander had to admire King Gordias.At this time, he suddenly thought: "Why don't you use your own method to untie this knot?" So Alexander drew his sword, aimed at the knot, and split the knot in two fiercely. The centuries-old knot was easily untied.

Facing hundreds of years of intractable knots, it is a traditional way of thinking to find out the clues from the headless knots, but this kind of "complex" thinking can't solve the problem, and has caused many people's problems. fail.

Alexander did not stick to the rules, and used the simplest thinking and the most direct method to find the target and act first. Not only did he untie the Gordias knot, but he was destined to become the king of Asia.

good way to learn
Reading tips: Why did Alexander become the king of Asia?
Classic sentence: Alexander drew out his sword, pointed at the knot, and split the knot in two fiercely. This difficult knot that had been preserved for hundreds of years was easily untied.

Learning Proverbs: Learning must break through the limitations of thinking in order to find the most effective solution.

Innovative thinking easily helps the library move——

Children, when you encounter problems in your studies, do you still use conventional methods to solve them little by little?In fact, as long as you think innovatively, you can find new ways to solve problems.Only by constantly innovating can you make continuous progress in learning.

§10 Library moving

According to legend, the old library of the British Library fell into disrepair for a long time, and a new library was built in a new place. After the new library was completed, the books in the old library would be moved to the new library.This was originally a matter for the moving company, and there was nothing to plan. Just load the books on the car, take them away, and put them in the new library.The problem was that the budget required £350 million and the library didn't have that much money.

Seeing that the rainy season is coming, if you don't move immediately, you will lose a lot.For this reason, the curator has thought of many plans, but is still at a loss.

When the curator was distressed, a librarian asked what the curator was worried about, and the curator explained the situation.A few days later, the librarian approached the curator and told him that he had a solution, but it still required £150 million.The curator is very happy because the library has such a big budget.

"Speak out!" the curator was anxious.

The librarian said: "A good idea is also a commodity. I have one condition."

"What condition?" The curator became even more anxious.

"If all 150 million pounds are spent, then it is right that I have contributed to the library. If there is any surplus, the library will give me the remaining money."

"Then what's the problem? I'll give you the remaining money within 150 million pounds, and I'll make the decision right away!" the curator said firmly.

"Then let's sign a contract?" The librarian realized that there was a chance to make a fortune.

Shortly after the contract was signed, the librarian's new relocation plan was implemented. The library was moved without using up even a fraction of the £150 million.

It turned out that the library published an astonishing news in the newspaper: "From now on, the British Library will borrow books from the public for free and unlimited, on condition that they borrow from the old library and return them to the new library."

good way to learn
Reading tips: How do librarians help the library move?
Classic sentence: From now on, the British Library will borrow books from the public for free and unlimited, on condition that they borrow from the old library and return them to the new library.

Learning Proverbs: Learn to innovate in learning, and use divergent thinking correctly, so that you can make continuous progress in learning.

For each question, there are at least two ways to answer it——

Children, do you think there is only one way to solve the problem?In fact, sometimes the answer to a question is not necessarily the only one.So when looking at a problem, we have to open our minds and diverge our thinking.

§11 Measuring the height of a building with a barometer
A physics teacher gave students an exam question: "How to use a barometer to measure the height of a building."

The student's answer is: take the barometer to the top of the tall building, tie the barometer with a long rope, and then put the barometer down from the top of the building until it touches the street, then pull the barometer up to the top of the building, Measure the length of the rope, the length of the rope is the height of the building.

Without even thinking about it, the physics teacher gave the student a zero because it was not his ideal answer.But the student disagreed, and he thought his method was correct.So they called the principal.

The principal knows that the student's answer is correct and should be given full marks, but if the student is given full marks, it proves that the student has a high level of physics, but usually the answers of students with high levels of physics will not have anything to do with physics.

So the principal asked the student to answer the same question in 6 minutes, but he had to use physics knowledge to answer.Without hesitation, the student gave the answer that the physics teacher originally wanted: take the barometer to the roof, let it lean against the edge of the roof, let the barometer fall from the roof, use a stopwatch to record the time it falls, and use the drop to The distance elapsed in time is equal to the acceleration of gravity multiplied by half of the square of the fall time to calculate the height of the building.

After reading the answer, the principal asked the teacher if he would back down.The teacher backed down, and the principal gave the student almost the highest rating.

Just as the principal was about to leave the office, the student said he had another answer, so the principal asked him what kind of answer it was.The student replied: "There are many ways to use the barometer to measure the height of a building. For example, you can record the height of the barometer on the roof of the building and the length of the shadow on a sunny day, and then measure the length of the building's shadow." , you can use the simple proportional relationship to calculate the height of the building.”

"Very well," said the principal. "Any other answers?"

"Also," said the student, "there's one more basic measurement you'll like. Take the barometer and climb up the stairs from the first floor. As you ascend, mark the number on the barometer. Mercury altitude, so you can use the barometer unit to get the height of the building. That's the most direct way."

"Of course, if you still want to get a more accurate answer, you can tie one end of a wire to the barometer, make it swing like a pendulum, and then measure the acceleration of gravity on the street and the acceleration of gravity on the roof, two gravity The difference in acceleration can, in principle, be used to calculate the height of the roof.”

Finally he said, "If I don't limit myself to answering this question with physical methods, I have many other ways. For example, go to the ground floor with a barometer and knock on the door of the administrator. Say the following sentence: 'Mr. Administrator, I have a beautiful barometer. If you tell me the height of this building, I will give you this barometer...'"

good way to learn
Reading Tip: Is there any other way you can know the height of this building?

Classic statement: If you don't limit me to the physical method to answer this question, I have many other methods.

Learning Proverbs: In learning, we might as well try different methods to answer questions.

(End of this chapter)