On the question of the principle of the drawer, thank you for your help, to be columnar

Each magazine has two choices, 2 * 2 * 2 = 8 choices, because one must be chosen, so none of the three choices should be removed, only 7 kinds, 8 people choose 7 choices, so at least 2 or more than 2 choices are the same.

Counter-evidence: The magazines of the 8 students are not the same.

Three kinds of magazines. There is only one type of c1 3 = 3 kinds of rules (1 is the superscript, 3 is the subscript, the same below).

There are two kinds of rules: c2 3=3 kinds of rules.

There are three kinds of rules: c3 3 = 1 way.

There are a total of 7 types of laws.

If there are 8 students, then the eighth student must have the same regular hair as one of the previous 7 students, so the magazines ordered by the 8 students are not the same.

Then: Explain that two or more of the students must have the same magazine.

There are 3 ways to order one of the three magazines of Oriental Youth, Learning and Play, and We Love Science, two of which also have 3 ways to order, and 1 way to order three magazines, a total of 7 ways to order, and these 7 ways to order them as drawers, and 8 students as apples, then there must be two or more of them ordering the same magazine.

There are ten apples on the table, and if we put those ten apples in nine drawers, no matter how we put them, we will find that there will be at least two apples in one drawer. This phenomenon is what we call the "drawer principle". The general meaning of the drawer principle is:

If each drawer represents a set, each apple can represent an element, and if n 1 or more elements are placed in n sets, there must be at least one set with two elements. The drawer principle is sometimes referred to as the pigeon nest principle ("if there are five pigeon cages and the pigeon keeper has 6 pigeons, then when the pigeons are returned to the cage, at least 2 pigeons are in one cage"). It is an important principle in combinatorics.

Hail 1. Put three apples in two drawers, and there must be at least two apples in one drawer.

2. The common form of the drawer principle is to put all the objects of N+K(K 1) into N drawers in any way, and there must be at least two objects in a drawer.

3. Second, put all the mn+k(k 1) objects into n drawers in any way, and there must be at least m+1 objects in a drawer.

4. Three, put m1 + m2 + ....+mn+k(k 1) objects are all placed in n drawers in any way, then at least m1+1 objects are placed in one drawer, or at least m2+1 objects are placed in the second drawer,......Or put at least mn+1 object four in the nth drawer, and put all m objects in n drawers in any way, there are two cases: When n|m (n|m stands for n divisible m), there must be at least one object high band in a drawer; When n is not divisible by m, there must be a drawer with at least 1 object in it ([x] denotes the maximum integer not exceeding x).

Principle 1: If you put more than N+1 objects in N drawers, there will be at least two items in at least one drawer.

The second drawer principle.

Put (mn 1) objects in n drawers, and one of them must have at most (m-1) objects in one drawer (e.g., if 3 5-1 = 14 objects are placed in 5 drawers, there must be one drawer with fewer than or equal objects to 3-1 = 2).

Put n 1 item into n drawers, at least one drawer with more than 2 items A more general expression of the drawer principle is:

If you put more than kn into n empty drawers (k is a positive integer), then there must be at least k+1 in one drawer. References.

1.n+1 apples into n boxes, one box has at least two apples.

apples into m boxes, n divided by m to get p and q, there is a box with at least p+1 apples.

Solution: If there is no three-point shooting, then at most one shot will score 2 points, then when all 10 shots are 2-point shots, then it is only 2*10=20 points, and there is still one point missing. So there must have been at least one shot that scored a 3-pointer.

ps: You can also take 3 points, 2 points, 1 point, as three drawers, 10 shots as 10 apples, put the apples in the drawer, multiply the number of apples by the drawer score, and then add up to 21, then if there is no apple in the 3-point drawer, and then put all 10 apples in the 2-point drawer, it is not guaranteed that 10*2=21, so there is at least one apple in the 3-point drawer.

Because the results of 6 units are regarded as 6 drawers, 574 points are the objects put into the drawer, and the number of objects is greater than the number of drawers, according to the drawer principle, 574 divided by 6 quotient 95 remainder 4 95 + 1 = 96 points 96 is greater than 92 points Therefore, Cong Cong scored no less than Honghong at least once.

547 divided by 6 is approximately equal to.

According to the second principle of the drawer, I know that I need to add 1, that is.

So Cong Cong said that he scored no less than him at least once.

Proof: 1+29=3+27=5+25=7+23=9+21=11+19=13+17=30

There are 14 numbers on it, which means that the 15 numbers in the question are divided into the above 14 numbers and 15 numbers. When taking nine numbers arbitrarily, because it is necessary to ensure that the sum of two numbers is 30, the most unfavorable principle is used, that is: only one number in the above equation is taken, for example, 1+29, we only take the number 1, or 29, then 14 numbers, take 7 numbers, where the sum of each two numbers is not equal to 30, plus 15, that is, the sum of any two numbers in the 8 numbers is not equal to 30.

Then in the remaining 7 numbers, no matter which number is taken, it can be combined with one of the 8 numbers we started to take to be 30. So, take at least 9 numbers, and the sum of two of them is 30.

Take 8 numbers and set them to 1, 3, 5, 7, 9, 11, 13, 15

Then there must be a 9th number, and one of the 8 numbers adds up to 30.

In the same way, take any 9 numbers, and the sum of two of them must be 30.

400 ÷ 66 = 6……Remainder 4

That is, 400 books, 1 book, 2 books, 1 book, 2 books, one by one, must be distributed in 6 rounds, and the remaining 4 books can also be distributed.

Therefore, at least 6 students received the same number of books.