This is the fourth question in the final examination paper of the 15th "Spring Cup" primary school students' mathematics competition in Beijing, and it is also the question that the contestants lose the most points.
Get a = 1, b+e = 9, (e≠0), c+f = 9, d+g = 9.
In order to calculate the maximum number of such four digits, conditions A, B, C, D, E, F and G are different from each other. It can be seen that there are seven ways to choose B (B ≠ 1, 8,9) and six ways to choose C (C ≠ 1, 8,9). So according to the principle of multiplication, there can be at most four digits like (7×6×4=) 168.
After answering the question 1, if we think further, it is not difficult to think of the following question.
Question 2: There are four cards with the number 1 written on both sides. The first one is 0 and 1, and the other three are 2 and 3, 4 and 5, 7 and 8 respectively. Now take out three cards at random and arrange them in a row. How many different three digits can a * * * make up?
This question is the preliminary examination question of the 14th "Spring Cup" mathematics competition for primary school students in Beijing. The solution is:
After that, 10 digit b can take the six digits of the other three cards; The last number c can be the four numbers of the remaining two cards. To sum up, a * * * can form different three digits * * (7× 6× 4 =) 168.
Is it a coincidence that the scores of two counting questions in the "Spring Cup" competition for two consecutive years are 168?
Careful readers can easily find that as long as we deal with the question 1 a little, it can become the equivalent form of question 2. In other words, 1 and 2 are essentially just two different formulations of the same question.
The equivalent form of the question 1 is as follows:
Now four cards are constructed, with numbers written on the front and back. The first one says 0 and 9,
The good thing is that three cards are randomly selected from these four cards and arranged in a line, so how many different three-digit numbers can be formed. To solve practical problems, we must carefully examine the questions, understand the meaning of the questions, deeply and carefully analyze the quantitative relations in the questions, and find the breakthrough through the comparison, transformation and reorganization of conditions, so as to solve the problems smoothly.
Exercise 1:
1. A toy factory puts 630 toys into 5 plastic bags and 6 paper bags respectively, and there are as many toys in one plastic bag as in 3 paper bags. How many toys are there in each plastic bag and paper bag?
The department store shipped 300 pairs of sports shoes in two wooden cases and cartons respectively. If there are as many sports shoes in two cartons as in one wooden box. How many pairs of sports shoes are there in each wooden box and carton?
3. xinhua primary school bought two tables and five chairs and handed them over to 195 yuan. As we all know, the price of each table is four times that of each chair. How much is each table?
4. Uncle Wang bought 3 Jin of litchi and 4 Jin of longan, and paid 156 yuan. As we all know, the price of 5 kg litchi and 2 kg longan is equal. How much is litchi and longan per kilogram?
Exercise 2:
1. Weight of a barrel of oil180kg. Half of it is used, and there is still 100 kg in the bucket. How much does the oil and barrel weigh?
A basket of pears weighs 38kg. Half sold, 20kg left in the basket. How much do pears and baskets weigh?
A basket of apples weighs 35 kilograms. Give half to the children in kindergarten first, and then half to the children in grade one. The remaining apples are 1 1 kg. How much does this basket of apples weigh?
There is some oil in the oil drum. If the oil is doubled, the oil drum will weigh 38 kilograms. If the oil quadruples, the oil and oil drums will weigh 46 kilograms. How many kilograms of oil are there in the oil drum?
Exercise 3:
1. There are 5 boxes of tea. If 200g is taken out of each box, the remaining tea leaves are exactly the same as the original 4 boxes of tea leaves. How many grams are there in each box of tea?
There are 6 baskets of pears, and each basket has the same number of pears. If you take out 40 pears from each basket, the sum of the remaining pears is exactly the same as the original two baskets. How many pears are there in each basket?
There are as many oranges in five wooden boxes. If you take out 60 oranges from each box, the sum of the remaining oranges is exactly the same as the original two wooden boxes. How many oranges are there in each box?
A food store has the same 5 boxes of biscuits. If 20kg is taken out of each box, the total number of biscuits left is exactly equal to the weight of the original 3 boxes of biscuits. How many kilograms are there in each box of biscuits?
Exercise 4:
1, a timber factory produces a batch of desks. Originally planned to produce 60 sheets a day, in fact, 4 sheets were produced more than originally planned. Results The task was completed 1 day ahead of schedule. How many desks were originally planned to be produced?
The TV factory has received a batch of production tasks. It is planned to produce 90 sets per day, which can complete the task on time; Actually, five more units were produced every day, and the task was completed 1 day in advance. How many TV sets are there in this batch?
Xiaoming read a story book. He planned to read 12 pages every day, but actually he read 8 more pages every day. As a result, he finished reading it two days in advance. How many pages does this story book have?
4. build a highway. It was originally planned to build 60 meters a day, but actually it was built 15 meters more than the original plan, and it was completed four days ahead of schedule. How many meters did a * * * make?