One or two

One or two

1. There are five girls sitting side by side in the subway car. A sits at the same distance from B and C, D sits at the same distance from a and C, e sits between her relatives and friends. Who are e's relatives and friends?
Answer: e sits between a and B. A and B are her relatives and friends
2. There are 692 infantry in a certain fortress. Every four of them stand in a horizontal row. The distance between each row is 1 meter. They walk forward 1 meter and walk 86 meters per minute. Now they have to pass the 86 meter long bridge. How many minutes does it take from the first row to the last row?
Answer: three minutes
3. A farmer raises nine sheep, seven pigs and five cows. In terms of price, two sheep can be exchanged for one pig and five sheep for one cow. He wants to divide these cattle, sheep and pigs among his three sons. Not only will no one share the same number of livestock, but also the same value. Can you come up with a distribution plan?
The first son is divided into one cow, five pigs and one sheep; the second son is divided into two cows, one pig and four sheep; the third son is divided into two cows, one pig and four sheep
4. The distance between the two cars is 1500 meters. Suppose that the car in front is moving at a speed of 90 km / h and the car behind is chasing at a speed of 144 km / h, how far is the distance between the two cars in one second of collision?
Answer: 15 meters apart
5. There are two companies, company a and company B, to recruit managers. Company a's annual salary is 100000 yuan, but it is not raised once a year, and each time it is raised 20000 yuan; company B's salary is 50000 yuan for half a year, and it is raised once a half a year, and each time it is raised 5000 yuan?
Answer: going to company B makes more money
6. Romonosov, a famous Russian mathematician, borrowed the Book Principles of mathematics from his neighbor. The neighbor said to him, "if you help me chop firewood for 10 days, I will give you the book and another 20 rubles." as a result, he only split firewood for 7 days. After the neighbor gave the book to him, he paid another 5 rubles. What is the price of the Book Principles of mathematics?
Answer: the price of the book is 30 rubles
7. There are 1000 grams of 15% alcohol in the bottle. Now pour 100 grams and 400 grams of alcohol a and B into the bottle respectively, and the alcohol concentration in the bottle will be 14%. It is known that the concentration of alcohol a is twice that of alcohol B. how to calculate the concentration of alcohol a?
Answer: 20%

Two interesting stories about Mathematics

Drawer principle and computer fortune telling
"Computer fortune telling" seems very mysterious, as long as you report your birth year, month, day and gender, a button, the screen will appear so-called character, destiny sentence, it is said that this is your "destiny"
We can easily explain its absurdity with the drawer principle in mathematics. The drawer principle is also called pigeon cage principle or Dirichlet principle. It is a special method to prove the existence in mathematics. Take the simplest example, put three apples into two drawers in any way, Then there must be two or more apples in one drawer. This is because if there is at most one apple in each drawer, there are at most two apples in the two drawers
Principle 1 put more than n objects in n drawers, then at least one drawer has 2 or more objects
Principle 2 put more than Mn objects into n drawers, then at least one drawer has m + 1 or more than m + L objects
If we calculate by 70 years, the number of different combinations according to the year, month, day and sex of birth should be 70 × 365 × 2 = 51100, which we regard as the "drawer" number. China has a population of 1.1 billion, which we regard as the "object" number. Because 1.1 × = 21526 × 51100 + 21400, according to principle 2, there are more than 21526 people, although they have different origins, experiences, talents and opportunities, But they have exactly the same "fate", which is ridiculous!
The so-called "computer fortune telling" is just to store the artificially made fortune telling sentences one by one in their respective cabinets in advance, just like the traditional Chinese medicine cabinet, That is to say, according to the different combinations of the date, day and gender of birth, the sentences of so-called destiny are mechanically taken out from each "cabinet" of the computer according to different codes. This kind of activity of putting the halo of modern science on the ancient superstitious dead is a blasphemy to science
Using mathematics skillfully to see reality
Two advertisements have been reported in a newspaper. A commercial building implements prize sales: one special prize of 10000 yuan, two first prizes of 1000 yuan, ten second prizes of 100 yuan, five third prizes of 200 yuan. B commercial building implements 95% discount. Please think about it. Which kind of sales method is more attractive? Which commercial building offers more benefits to the seller?
We can't see the problem at a glance. So we first made a random survey. Among the 16 students in the whole group, 8 are willing to go to a's house, 6 like to go to B's house, and two think it's OK to go to both. The survey results show that the sales mode of a commercial building is more attractive, but is that the case?
In practice, there is no limit on the turnover of each group of prize setting sales and the number of participants in the lottery. Therefore, we think there should be several answers to this question
1、 When the number of participants is less than 213 (1 102 + 10 + 200 = 213), people will think that the probability of winning the prize is higher, and the sales mode of Kujia commercial building is more attractive to customers
2、 If the turnover of each group of commercial building a is large, the margin of discount to customers is correspondingly small. Because the amount of discount offered by commercial building a is fixed, the total amount is 14000 yuan (10000 + 2000 + 1000 + 1000 = 14000). Assuming that the discount offered by both commercial buildings is 14000 yuan, the turnover of commercial building B can be 280000 yuan (14000 △ 5% = 280000)
Therefore, it can be concluded that:
(l) When the turnover of the two commercial buildings is 280000 yuan, the two commercial buildings offer the same amount of discount
(2) When the turnover of two commercial buildings is less than 280000 yuan, the discount of commercial building B is less than 14000 yuan, so the discount of commercial building a is still 14000 yuan, which is more favorable
(3) When the turnover of both businesses exceeds 280000 yuan, the discount of commercial building B is more than 14000 yuan, while the discount of commercial building a is still 14000 yuan, the benefit of commercial building B is great

Interesting things about Mathematics
The shorter the better, about 50 words

There is an old story in India: when the king lost the game with the chess player, the chess player asked to put a grain of wheat in the first frame, two grains in the second frame and four grains in the third frame. That is to say, all the frames were filled according to the method of compound interest increase. The king thought that at most a bag of wheat could be used to kill the chess player, but the result was invented, It's not enough to pay for the wheat produced all over the world
Formula F = P * (1 + I) n (power)