1 yuan coins, 2 yuan 5 yuan paper money. It costs 10 yuan to buy books. How did you get it?

Solution:

Can be divided into three categories of considerations:

First, there are three payment methods for RMB in one currency: 10 1 yuan coin; 5 2 yuan banknotes; Two 5 yuan notes.

Category II: There are five payment methods for RMB with two denominations:

(1) There is a way to pay with 1 yuan coins and 5 yuan banknotes: 5 1 yuan coins and 1 5 yuan banknotes.

(2) There are four ways to pay with 1 yuan coins and 2 yuan banknotes: 1 2 yuan banknotes and 8 1 yuan coins; 2 2 yuan banknotes and 6 1 yuan coins; 3 2 yuan banknotes and 4 1 yuan coins; 4 2 yuan banknotes and 2 1 yuan coins.

Category III: There are two payment methods for RMB with three denominations: 1 5 yuan note, 2 2 yuan notes, 1 1 yuan coin; 1 5 yuan note, 1 2 yuan note and 3 1 yuan coins.

3+5+2= 10 (species)

Therefore, * * * has 10 ways to hold.

Addition principle is used in this solution. First, divide the problem-solving methods into several categories, how many problem-solving methods are found in each category, and then add them up. The key to solving the problem in this way is how to classify it reasonably, so that it is neither heavy nor leaking.

Ninth lecture, expansion and improvement, exercise 2, (2) Small problems in "Daily Exercise in Olympic Games"

Title:

Make the number of four small circles add up to become the number of big circles in the middle.

Solution:

To make the sum of four numbers 9, the smallest number is 1 (students are not required to consider the case of 0 here), and the number should be less than or equal to 6. We can use addition principle and divide it into four categories:

The number of 1. is 6. There is a filling method: 6, 1, 1, 1.

Second, the number is 5. There is a filling method: 5,2, 1, 1.

The number of 3 is 4, which can be filled in two ways: 4, 2, 2,1; 4、3、 1、 1

The number of 4 is 3. There are two filling methods: 3, 2, 2, 2; 3、3、2、 1

When the number of is 2, the sum of the four numbers is 8, which does not meet the requirements of the topic. )

1+ 1+2+2=6 (species)

Therefore, regardless of the order of the four numbers, * * * has six filling methods.