Often appear in the topic of mathematical operation? Most? 、? At least? 、? Maximum? 、? Lowest? We call this kind of problem as the maximum problem. The maximum problem is a very important basic question type in mathematical operation, and it is often investigated in line test. Many times, it is combined with other questions as a complex sentence question, which requires candidates to master it comprehensively. The easy test points of this kind of questions are mainly divided into four categories: the most unfavorable structure (also called pigeon hole principle), sequence structure, multi-set reverse structure and complex maximum problem. Each type of questions has its own characteristics of questions and fixed methods of solving problems, which requires candidates to quickly match questions and solve problems by combining methods.

Example 1(20 12- Zhejiang -56. ) There are cards numbered 1~ 13, each with 4 cards and 52 cards. Ask at least a few cards, and you can guarantee that there must be three card numbers connected.

a . 27a b . 29

C.33 D.37

Answer d

Solution thinking

Step one, mark the quantitative relationship? At least? 、? Promise? .

Step two, according to? At least? 、? Promise? It can be seen that this question is a question of pigeon hole principle, and the answer is the number of all unfavorable situations. The number of three cards to be connected. The most unfavorable situation is that only two cards are connected: 1, 2, 4, 5, 7, 8, 10,1,13, and each number has four cards.

The third step is to touch at least one piece. Therefore, choose the d option.

If two numbers are connected, the number of unfavorable situations is: 1, 3, 5, 7, 9, 1 1, 13, and it is easy to choose the wrong b; If we think that there are two numbers connected, then the number of unfavorable situations is: 2, 3, 5, 6, 8, 9, 1 1, 12, and it is easy to choose the wrong C.

Jianhua Middle School students 1.600, including165,438+080 who like table tennis, 1.360 who like badminton, 1.250 who like basketball and 1.040 who like football.

A.20 people B. 30 people

C.D. 50 people

Answer b

Solution thinking

Step one, mark the quantitative relationship? Both? 、? At least? . The second step, by? Both? 、? At least? It can be seen that this problem is a multi-set reverse construction. The steps to solve the problem are: conversely:1600-1180 = 420 people don't like table tennis. Similarly, 240 people don't like badminton, 350 people don't like basketball and 560 people don't like football. Plus: The maximum number of people who don't like any of the four sports is 420+240+350+560= 1570. Job: So four ball games? Both? Do you like it? At least? There are 1600- 1570=30 people. Therefore, choose option B.