Fortune-telling in Zhanqian Shopping Center

Two interesting stories about mathematics.

Pigeon hole principle and computer fortune telling

Computer fortune-telling looks mysterious. As long as you report the year, month, day and sex of your birth, a so-called character and destiny will appear on the screen when you press the button. It is said that this is your "destiny".

It is easy for us to use the pigeon hole principle in mathematics to explain its absurdity. Pigeonhole principle, also known as Pigeonhole principle or Dirichlet principle, is a special method to prove the existence in mathematics. For the simplest example, if three apples are put into two drawers in any way, 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 two drawers. Use the same reasoning.

Principle 1 If more than n objects are put into n drawers, at least one drawer has more than two objects.

Principle 2 If there are more than mn objects in N drawers, at least one drawer has more than m+ 1 or m+l objects.

If calculated in 70 years, the number of combinations with different sexes according to the date of birth should be 70× 365× 2 = 5 1 100, and we regard it as the number of drawers. The existing population of China is 1 1 100 million. Think of it as the number of things. Because1.1× = 2 1526× 51/kloc-0+21400, according to principle 2, there are more than 21526 people, although they

The so-called "computer fortune-telling" is nothing more than storing the manually compiled fortune-telling sentences one by one in their cabinets in advance like a Chinese medicine cabinet. Who wants to tell fortune, that is, according to the different combinations of birth date, date and gender, according to different codes, mechanically take out the so-called fate sentence from the computer cabinet. This kind of activity, which gives the ancient superstitious undead a halo of modern science, is a blasphemy against science.

Using mathematics skillfully to see reality

Two advertisements were reported in the newspaper. There are prizes for sales in a commercial building: first prize 10000 RMB 1, first prize 1000 RMB 2, second prize 100 RMB 10, third prize 5 yuan 200, and 15% discount for sales in second-class commercial buildings. Please think about it. Which sales method is more attractive? Which commercial building is of great benefit to consumers?

In the face of problems, we can't be clear at a glance. So we made a random survey first. We take 0/6 students in the whole group/kloc-as the survey object. Among them, 8 people are willing to go to A's home, 6 people like to go to B's home, and 2 people think that both schools can go. The survey results show that the sales model of a commercial building in A is more attractive, but is this the case?

In practical problems, there is no limit to the turnover of each group and the number of people participating in the lucky draw. So we think there should be several answers to this question.

1. Kujia Commercial Building has determined that awards should be given to each group. When the number of participants is small, less than 213 (112+10+200 = 213), people will think that the chances of winning the prize are greater and a sales model of a commercial building will attract customers more.

Secondly, if the turnover of each group of a commercial building is relatively large, the preferential margin given to customers is correspondingly small, because the preferential amount provided by a commercial building is fixed, totaling 14000 yuan (10000+2000+1000 =/kloc-).

So from this point of view:

(l) When the turnover of the two commercial buildings is 280,000 yuan, the two commercial buildings will give the same amount of preferential treatment.

(2) When the turnover of both shopping malls is less than 280,000 yuan, the discount of shopping mall B is less than10.4 million yuan, so the discount provided by shopping mall A is still10.4 million yuan, which is a big discount.

(3) When the turnover of both companies exceeds 280,000 yuan, the discount of the second commercial building exceeds 14000 yuan, while the discount of the first commercial building remains at 14000 yuan, and the second commercial building provides great benefits.