“Among any 367 people, there must be people with the same birthday.”

“Pick 6 out of any 5 pairs of gloves, at least 2 of which are exactly the same. For a pair of gloves. ”

“Select any 6 numbers from the numbers 1, 2,...,10, at least 2 of which have different parity.”

The drawer principle is used here. The content of the drawer principle can be expressed in figurative language as:

“Put m things into n empty drawers randomly (m>n), then there must be At least 2 things were put in one drawer. ”

In the first conclusion above, since there are at most 366 days in a year, at least 2 of the 367 people were born on the same day of the same month. This is equivalent to putting 367 items into 366 drawers, with at least 2 items in the same drawer. In the second conclusion, you might as well imagine that 5 pairs of gloves are numbered respectively, that is, there are two gloves each with numbers 1, 2,..., 5, and two pairs of the same number are one pair. Take any 6 gloves. They have at most 5 numbers, so at least two of them have the same number. This is equivalent to putting 6 items into 5 drawers, with at least 2 items in the same drawer. ?

Using the above principle, it is easy to prove: "Among any 7 integers, the difference between at least 3 numbers is a multiple of 3." Because when any integer is divided by 3, the remainder is only 0 and 1 , 2 are three possibilities, so at least 3 of the 7 integers have the same remainder when divided by 3, that is, the difference between them is a multiple of 3.

If there are infinitely many objects discussed in the problem, there is another expression of the drawer principle:

“Put infinitely many things into n empty drawers (n is a natural number), then there must be an infinite number of things put in a drawer. ”

The content of the drawer principle is simple, simple and easy to accept, and it plays an important role in mathematical problems. Many existence proofs can be solved with it. ?

2. The phenomenon of rising and falling limits

Suppose you have 100,000 yuan:

The first situation: after the daily limit on the first day, it is 110,000 yuan. After the limit fell the next day, 99,000 yuan was left.

The second situation: after the lower limit on the first day, the price is 90,000 yuan, and after the upper limit on the second day, it is still 99,000 yuan.

3. The phenomenon of covering positions or fixed investments

Suppose that when the net value of a fund is 10 yuan, you buy 10,000 yuan. In the second month, when the net value of the fund dropped to 5 yuan, you bought another 10,000 yuan.

Excuse me: What is your holding cost? A.7.5 yuan B.6.67 yuan

Correct answer: The holding cost is 6.67 yuan.

This is the charm of fund fixed investment, which can significantly reduce your holding costs.

4. The bee hive is a strict hexagonal column. One end of it is a flat hexagonal opening, and the other end is a closed hexagonal rhombus-shaped bottom, which is composed of three identical rhombuses. The obtuse angle of the rhombus that makes up the chassis is 109 degrees 28 minutes, and all acute angles are 70 degrees 32 minutes, which is both strong and material-saving. The wall thickness of the hive is 0.073 mm, and the error is extremely small.

5. Red-crowned cranes always fly in groups and form a "human" shape. The angle of the "herringbone" shape is 110 degrees. A more precise calculation also shows that half of the angle of the "herringbone" shape - that is, the angle between each side and the direction of the crane group's advance is 54 degrees, 44 minutes and 8 seconds! The angle of the diamond crystal is exactly 54 degrees, 44 minutes and 8 seconds! ?

6. In winter, cats always hug their bodies into a spherical shape when sleeping. There is also mathematics in this, because the spherical shape minimizes the surface area of ??the body and thus dissipates the least heat.

7. Capital-guaranteed asset portfolio

The following two investment products:

Suppose you have 1 million yuan, you invest 800,000 yuan in asset A, and invest 20 Ten thousand to asset B.

In this way, you have created a capital-protected investment portfolio: the worst return is zero, and the best return is 12%.

8. A game with a gambling nature: the person in charge puts 4 balls of different colors, 5 each of red, yellow, blue and white, for a total of 20 balls, into the box Here, participants randomly draw 10 balls from inside. If the combination of the four colors is 5500, you can get a Leica camera; if it is 5410, you will be given a Chinese cigarette; but there are two combinations for which you have to pay him in turn: one is 3322 and the other is 4321 .

As a result, when gamers go there and grab it, it is often 3322 or 4321. This is a very easy math problem to calculate. Liang Changhong, the president of Xi'an University of Electronic Science and Technology, is a mathematician. He organized hundreds of student tests at the school and calculated them on the computer. The results were the same: 3322 and 4321 accounted for the highest proportions, close to 30%; and 5500, Only one in hundreds of thousands.

9. Yield phenomenon: If you buy a stock for 100,000 yuan, it will be 200,000 yuan after it rises 100%; but if it falls another 50%, it will return to 100,000 yuan. You know, it is much easier to fall by 50% than to rise by 100%.

10. The myth of zero and infinity: "0" is also a number that interests me. I think "0" is philosophically speaking, what the Chinese call "nothing".