He frowned, took out two pencils from his pocket, held a short pencil in his hand, straightened his arm, aimed his eyes at both ends of the pencil and looked at the other end of the elephant. Then change the grip of the long pencil, aim at both ends of the pencil, and ask for twenty steps, just to see the beginning and end of the elephant again. He measured the lengths of the two pencils to be 8cm and 16cm respectively, and the arm length was 40cm. Every step is 50cm, and the length of the elephant will soon be 4 meters. Xiaohua was very surprised and asked how San Xiao worked it out.
2. It takes 6 seconds on the fourth floor. How many seconds does it take to run to the eighth floor at the same speed?
3. A group of children are brother and sister, and the two chat casually. The younger brother said that he had one more brother than his sisters. So, how many brothers does my sister have than my sisters?
Xiaoming poured water into a water tank with a bottom area of 24x 18cm and a height of 30cm, accounting for two thirds of its volume. He is a curious boy and wants to know the volume of the lead block he just bought. After the lead block was put into the water tank, the water level rose to 22 cm. What is the volume of lead block? 5. Two boys each ride a bicycle and start riding in a straight line from two places 20 miles apart (1 mile+1.6093 km). At the moment they set off, a fly on the handlebar of one bicycle began to fly straight to another bicycle. As soon as it touched the handlebar of another bicycle, it immediately turned around and flew back. The fly flew back and forth, between the handlebars of two bicycles, until the two bicycles met. If every bicycle runs at a constant speed of 10 miles per hour and flies fly at a constant speed of 15 miles per hour, how many miles will flies fly?
answer
The speed of each bicycle is 10 miles per hour, and the two will meet at the midpoint of the distance of 2O miles after 1 hour. The speed of a fly is 15 miles per hour, so in 1 hour, it always flies 15 miles.
Many people try to solve this problem in a complicated way. They calculate the first distance between the handlebars of two bicycles, then return the distance, and so on, and calculate those shorter and shorter distances. But this will involve the so-called infinite series summation, which is very complicated advanced mathematics. It is said that at a cocktail party, someone asked John? John von neumann (1903 ~ 1957) is one of the greatest mathematicians in the 20th century. ) Put forward this question, he thought for a moment, and then gave the correct answer. The questioner seems a little depressed. He explained that most mathematicians always ignore the simple method to solve this problem and adopt the complex method of summation of infinite series.
Von Neumann had a surprised look on his face. "However, I use the method of summation of infinite series," he explained.
6. A fisherman, wearing a big straw hat, sat in a rowboat and fished in the river. The speed of the river is 3 miles per hour, and so is his rowing boat. "I must row a few miles upstream," he said to himself. "The fish here don't want to take the bait!"
Just as he started rowing upstream, a gust of wind blew his straw hat into the water beside the boat. However, our fisherman didn't notice that his straw hat was lost and rowed upstream. He didn't realize this until he rowed the boat five miles away from the straw hat. So he immediately turned around and rowed downstream, and finally caught up with his straw hat drifting in the water.
In calm water, fishermen always row at a speed of 5 miles per hour. When he rowed upstream or downstream, he kept the speed constant. Of course, this is not his speed relative to the river bank. For example, when he paddles upstream at a speed of 5 miles per hour, the river will drag him downstream at a speed of 3 miles per hour, so his speed relative to the river bank is only 2 miles per hour; When he paddles downstream, his paddle speed will interact with the flow rate of the river, making his speed relative to the river bank 8 miles per hour.
If the fisherman lost his straw hat at 2 pm, when did he get it back?
answer
Because the velocity of the river has the same influence on rowing boats and straw hats, we can completely ignore the velocity of the river when solving this interesting problem. Although the river is flowing and the bank remains motionless, we can imagine that the river is completely static and the bank is moving. As far as rowing boats and straw hats are concerned, this assumption is no different from the above situation.
Since the fisherman rowed five miles after leaving the straw hat, he certainly rowed five miles back to the straw hat. Therefore, compared with rivers, he always paddles 10 miles. The fisherman rowed at a speed of 5 miles per hour relative to the river, so he must have rowed 65,438+00 miles in 2 hours. So he found the straw hat that fell into the water at 4 pm.
This situation is similar to the calculation of the speed and distance of objects on the earth's surface. Although the earth rotates in space, this motion has the same effect on all objects on its surface, so most problems about speed and distance can be completely ignored.
7. An airplane flies from city A to city B, and then returns to city A. In the absence of wind, the average ground speed (relative ground speed) of the whole round-trip flight is 100 mph. Suppose there is a persistent strong wind blowing from city A to city B. If the engine speed is exactly the same as usual during the whole round-trip flight, what effect will this wind have on the average ground speed of the round-trip flight?
Mr. White argued, "This wind will not affect the average ground speed at all. In the process of flying from City A to City B, strong winds will accelerate the plane, but in the process of returning, strong winds will slow down the speed of the plane by the same amount. " "That seems reasonable," Mr. Brown agreed, "but if the wind speed is 100 miles per hour. The plane will fly from city A to city B at a speed of 200 miles per hour, but the speed will be zero when it returns! The plane can't fly back at all! " Can you explain this seemingly contradictory phenomenon?
answer
Mr. White said that the wind increases the speed of the plane in one direction by the same amount as it decreases the speed of the plane in the other direction. That's right. But he said that the wind had no effect on the average ground speed of the whole round-trip flight, which was wrong.
Mr. White's mistake is that he didn't consider the time taken by the plane at these two speeds.
It takes much longer to return against the wind than with the wind. In this way, it takes more time to fly when the ground speed is slow, so the average ground speed of round-trip flight is lower than when there is no wind.
The stronger the wind, the more the average ground speed drops. When the wind speed is equal to or higher than the plane speed, the average ground speed of the round-trip flight becomes zero, because the plane cannot fly back.
8. Sunzi Arithmetic is one of the famous Arithmetic Textbooks in the early Tang Dynasty. It has three volumes. The first volume describes the system of counting, the rules of multiplication and division, and the middle volume illustrates the method of calculating scores and Kaiping with examples, which are all important materials for understanding the ancient calculation in China. The second book collects some arithmetic problems, and the problem of "chickens and rabbits in the same cage" is one of them. The original question is as follows: let pheasant (chicken) rabbits be locked together, with 35 heads above and 94 feet below.
Male rabbit geometry?
The solution of the original book is; Let the number of heads be a and the number of feet be b, then b/2-a is the number of rabbits and a-(b/2-a) is the number of pheasants. This solution is really great. When solving this problem, the original book probably adopted the method of equation.
Let x be the pheasant number and y be the rabbit number, then there is
x+y=b，2x+4y=a
Get a solution
y=b/2-a，
x=a-(b/2-a)
According to this set of formulas, it is easy to get the answer to the original question: 12 rabbits, 22 pheasants.
9. Let's try a hotel with 80 suites and see how knowledge becomes wealth.
According to the survey, if we set the daily rent as 160 yuan, we can be full; And every time the rent goes up in 20 yuan, three guests will be lost. Daily expenses for services, maintenance, etc. Each occupied room is calculated in 40 yuan.
Question: How can we set the price to be the most profitable?
A: The daily rent is 360 yuan.
Although 200 yuan was higher than the full price, we lost 30 guests, but the remaining 50 guests still brought us 360*50= 18000 yuan. After deducting 40*50=2000 yuan for 50 rooms, the daily net profit is 16000 yuan. When the customer is full, the net profit is only 160*80-40*80=9600 yuan.
Of course, the so-called "learned through investigation" market was actually invented by myself, so I entered the market at my own risk.
10. The age of the mathematician Wiener. The whole topic is as follows: The cube of my age this year is four digits, and the fourth power of my age is six digits. These two numbers only use all ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. How old is wiener? Answer: this question is difficult at first glance, but it is not. Let Wiener's age be X. First, the cube of age is four digits, which defines a range. The cube of 10 is 1000, the cube of 20 is 8000, and the cube of 2 1 is 926 1, which is a four-digit number; The cube of 22 is10648; So 10 =
Uniformly arranged 1, 2,3,4 1987 natural numbers ... 1986, 1987 form a big circle, counting from 1: every 1 crosses 2 and 3; Cross out 5 and 6 every 4, so that two numbers are crossed out every other number, and then circle. Q: How many numbers are left in the end?
Answer: 663