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.