1. Hou, the master of crosstalk, has a good personal relationship with the famous mathematician Hua.

One day, two masters were drinking and chatting. You came and went, chatting happily. Hou Wenhua asked, "Under what circumstances 2+3 equals 4?" China can't understand at the moment. Just as he was deep in thought, Hou Linbao said, "As long as the mathematician is drunk, won't the problem be solved?"

Hua couldn't help laughing: "What a humorous master, trying to make fun of me …" He said to Hou: "Please buy a catty of orange juice in the street and bring a packet of fried rice flowers. A catty of orange juice is 44 cents, and I only give you 44 cents here. I don't buy expensive ones, I don't do what I lack! "

Hou came back soon after accepting the task. He gave Hua a catty of orange juice and a packet of fried rice flowers. How did Hou Linbao finish the task? It turned out that Hou made a detour to ten grocery stores, each of which bought only one or two pieces, beat a catty of orange juice, and bought a packet of fried rice flowers with the remaining 40 cents.

2. Han Xin was a general in the Han Dynasty, and he used to think when he was a child.

Legend has it that one day, two oil sellers in the street quarreled endlessly. Han Xin passing by just glanced at him out of curiosity. He finally understood that the two men were partners in selling oil. Because of disagreement, they are going to divide the remaining ten catties of oil in the barrel equally and go their separate ways, arguing over the uneven distribution of oil.

Han Xin looked at it carefully. They don't have a scale at hand, only a 3 kg oil gourd and a 7 kg crock. They turned the oil drum upside down, but both sides were always dissatisfied, so they quarreled.

Is there any way to accurately divide the oil? Han Xin faced two oil sellers and the oil drums, oil pots and oil gourds in front of him, thinking silently. Suddenly my eyes lit up and I said loudly, "Stop arguing, you can split it equally without a scale!" " "Say that finish, he gave directions to the oil seller. According to Han Xin's method, they divided it again, and they were all satisfied.

Solution: First, wrap the oil gourd three times in a row, * * * 9 kg. After the 7 kg crock is filled, there are 2 kg left in the oil gourd. Then pour all 7 Jin of the crock into the oil drum, and then the oil drum is 8 Jin of oil. Then pour all 2 Jin of oil in the oil gourd into the crock. Finally, fill the oil drum with an empty gourd (3 kg) and pour it into the crock. In this way, the oil left in the oil drum and the oil in the crock are exactly 5 Jin. Both sides have their own points, and it happens that everyone's income is exactly the same.

Mathematics has vitality because it is interesting. Mathematics is interesting because of its enlightenment to thinking.

The following is a story about the origin of probability theory.

Earlier, there were two great French mathematicians, one named bhaskar and the other named Fermat.

Pascal knew two gamblers and they asked him a question. They said that after they made a bet, it was agreed that whoever won the first five games would get all the bets. After gambling for a long time, A won four games and B won three. It's getting late, and they don't want to gamble any more. So, how should this money be divided? Do you divide the money into seven parts, four for those who win four games and three for those who win three games? Or because the first time I said five innings, no one arrived, so one person got half?

Neither of these points is correct. The correct answer is: the person who wins four games gets 3/4 of the money, and the person who wins three games gets 1/4 of the money.

Why? Suppose the two of them bet another game, and either A wins or B wins. If A wins five games, all the money should go to him. If A loses, that is, A and B win four games each, and the money will be divided equally. Now A's winning or losing probability is 1/2, so his money should be 1/2×1/2×1/2 = 3/4. Of course, B should get1.

Through this discussion, an important concept in probability theory-mathematical expectation began to take shape.

Among the above problems, mathematical expectation is an average, that is, how to calculate the uncertain money in today's future. This requires multiplying the money that A may get by the winning or losing probability of 1/2, and then adding them up.

Probability theory has developed since then, and today it has become a very widely used subject.

Grandpa Hua is a famous mathematician who died in China. He was born in a family that opened a grocery store. He was sickly since childhood, but eventually he became a generation of mathematicians with strong perseverance and lofty pursuit.

When he was a teenager, Hua especially liked mathematics, but his math performance was not outstanding. 19 years old, an excellent article shocked the famous mathematician Xiong Qinglai at that time. From then on, under the guidance of Mr. Xiong Qinglai, he embarked on the road of studying mathematics. In his later years, for the sake of national economic construction, he applied pure mathematics to industrial and agricultural production and struggled for the construction of the motherland for life!

Grandpa Hua carefully cultivated the younger generation, so that young mathematicians can thrive and stand out. After work, he also does not forget to write some popular science books for his friends for many years. The following is an interesting math game that Grandpa Hua once introduced to his classmates:

A teacher wants to tell his three students which is smarter. He used the following methods: show them three white hats and two black hats in advance, then tell them to close their eyes, put on their hats respectively and hide the remaining two hats. Finally, tell them to open their eyes, look at other people's hats and say the color of their hats.

The three students looked at each other, hesitated for a moment, and said in unison that they were wearing white hats.

Smart reader, think about it. How do they know the color of the hat? "

In order to solve the above problems, let's first consider the problem of "two people 1 black hat and two white hats". Because the black hat only has 1. If I wear them, the other person will immediately say that he is wearing a white hat. But he hesitated, which showed that I was wearing a white hat.

In this way, the problem of "three people, two blacks and three whites" will be solved. Suppose I wear a black hat, then the two of them become a question of "1 black hat and white hat", and they can answer it right away, but they all hesitated for a while, which shows that I wear a white hat and the three of them have the same thinking, so they all took out their own white hats.

Look here. Students may clap their hands and say it is wonderful. Grandpa who came to China later complicated the original problem. How to solve the problem of "n people, n- 1 black hat and several (not less than n) white hats"? In the same way, it is easy to solve. He also warned us that being good at "retreating" complex problems, "retreating enough" and retreating to the most primitive place without losing importance are the secrets of learning mathematics well.

Everyone is familiar with the story of "Cao Chong called an elephant", but few people know the story of "salvaging an iron cow".

This happened a long time ago in the Song Dynasty.

There is an eye-catching official "notice" posted at the gate of Yongji County, which reads: The Yellow River overflowed and the pontoon bridge outside the city was destroyed. Eight iron cows tied to the bridge on both sides of the river were also involved in the water. In order to rebuild the pontoon bridge and contain the flood, anyone who has the ability to fish out the iron cows one by one will be rewarded with 1200 silver …

Before the notice, a bunch of people looked up and talked. People often say that "there must be a brave man under the four rewards", but "one thousand two hundred pieces of silver" is a huge sum of money, but it is not a brave man. An iron cow weighs thousands of kilograms. There were no modern cranes at that time. Who has so much power to drag the iron cow up? What's more, the iron cow is still underwater! Someone said, "Unless the water recedes, ask hundreds of people to carry it ..."

"there is a flood at present, and there is no iron cow to stop it ... how can we wait until the river dries up?"

The government is worried and the people are impatient. The notice was posted for many days, and no one dared to disclose the list and make a phone call. One day, a thin monk in a big cassock suddenly appeared. After reading the notice carefully for several times, he opened his sleeve, reached out and took it off, folded it up and took it away calmly. The onlookers looked at the thin bald monk in surprise. Someone asked with disdain, "Master, did you disclose the list just to catch the iron cow?" Do you need to ask this? The monk did not answer. Someone asked curiously: "1 how many kilograms of iron cows, and tens of thousands of kilograms of eight iron cows." Master, is there a fairy to help you catch it? " The monk smiled faintly and said, "The iron cow was washed away by the water, so I will let the water come up again." This mysterious answer makes everyone more unpredictable.

On the day when the iron cow was salvaged, the crowd of onlookers was dark. I met the bald monk, hired several assistants, supported two wooden boats, and sure enough, I fished out the iron cows one by one. Later, people learned that this monk was the famous engineer Huai Bing.

Can you know how Huai Bing fished the iron cow out of the water?

Monks are pregnant with soldiers by:

Fill two wooden boats with sediment until the weight makes the side of the boat slightly higher than the water surface. Tie a thick board horizontally between the two boats and row them to the water surface where Tieniu sank.

Then, please ask someone who is good at water to dive into the water with a rope, and tie one end of the rope firmly to the iron cow, and the other end tightly to the wood between the two ships.

Finally, people were asked to throw the sediment from the boat into the river, so that the weight of the boat was reduced. With the buoyancy of the water, the ship's side gradually rose out of the water, so that the iron cow was hung by the rope on the wood and hung in the water. In this way, Tie Niu was dragged to the place where the new pontoon bridge was built.