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China Mathematics Online
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China Olympic Mathematics Network
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The Window of Mathematics in Guangzhou Middle School
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High school mathematics network
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Mathematical China
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Maisi Mathematical Network
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Both websites have the theme of Olympic mathematics:
www.aoshu.cn
www.klsx.net
1. There are 28 children waiting in line. The number from the left 10 is Aihua. What's the number on his right?
2. new york time is HK time minus 13 hours. You have an appointment with a friend in new york, new york time in April 1, and call him at 8 pm. When should you call him in Hong Kong?
A worker can process 90 parts in 5 hours. /kloc-how many workers does it take to process 540 parts in 0/0 hour?
4. How many integers greater than 100 have the same quotient and remainder after dividing by 13?
5. Four rooms, with no less than two people in each room and no less than eight people in any three rooms. How many people are there in these four rooms?
6. The divisor (or factor) of1998 has two digits, which is the largest?
7. In the English exam, Xiao Ming scored an average of 88 points in the first three times. How many points does he get if he wants to average 90 points for the fourth time?
8. There are at most five Sundays in a month. 12 What are the months with five Sundays in a year?
9. Choose six of the ten numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, and fill in the following boxes to make the formula hold. Each box is filled with a number, and the number in each box is different.
□ +□□ =□□□
What is the largest three digits in the formula?
10. A number is six digits, the first four digits are 2857, and the last two digits are unclear, namely
2857□□
But I remember it can be divisible by 1 1 and 13. Please work out the last two figures.
1 1. A school has 5 18 students. If the number of boys increases by 4% and the number of girls decreases by 3, the total number will increase by 8. So how many more boys than girls?
12. Chen Min wants to go shopping three times. 5 yuan, 2 yuan, 1 yuan, how many coins should I bring * * * so that I don't generate any change below 10 yuan at a time?
(There are only three kinds of coins: 5 yuan, 2 yuan, 1 yuan. )
13. The figure on the right is a graph composed of three semicircles, in which the diameter of the small circle is 8 and the diameter of the middle circle is 12.
14. The kindergarten teacher sent some pictures to Class A, Class B and Class C, and everyone can get 6 pictures. If it is only Grade B, everyone can get 15 pictures. If it is only Grade C, everyone can get 14 pictures. If it is Class A, how many photos can each person get?
15. Two people play a game: take turns to count off, and the count off can only be 1, 2, 3, 4, 5, 6, 7, 8. Add up the figures reported by two people. After the number is reported, the plus sign is 123, and the winner will give priority to the number.
16. The page number of the novel must be printed in the font of 1989. 1 How many times does this number appear in the page number of this book?
What are the last four digits of the sum of 17.23: 3, 33, 333, …, 33…3(23 3s)?
18. Arrange the eight numbers 1, 1, 2, 2, 3, 4, 4 into an eight-digit number, so that there is a number between two 1, two numbers between two 2, three numbers between two 3 and two 4. Then, like this.
19. Take at most a few numbers from the natural number 1, 2, 3, …, 2004, 2005, so that the difference between every two numbers is not equal to 4?
20. There is a six-digit telephone number, in which the three digits on the left are the same, and the three digits on the right are three consecutive natural numbers, and the sum of the six digits is exactly equal to the last two digits. What's the phone number?
2 1. If a is a natural number, prove 10 │ (A2005-A 1949).
22. Give 12 different two-digit numbers, and prove that two numbers can be selected from them, and their difference is a two-digit number composed of two identical numbers.
23. Find the smallest three digits of 2 divided by 3, 3 divided by 5 and 5 divided by 7.
24. Let 2n+ 1 be a prime number, and prove that:12,22, …, n2 is divided by 2n+ 1 to get different remainders.
25. The difference between the sum of squares of prime numbers not less than 5 1 will be divisible by 24.
26. There are two kinds of sugar water, A contains 270g of sugar, 30g of water, B contains 400g of sugar, and water100g. Now we want to get100g of 82.5% sugar water. How many grams should we take from everyone?
27. A container contains 65,438+00 liters of pure alcohol. After pouring out 1 l, fill it with water, then pour out 1 l, and then pour out 1 l. What is the concentration of alcohol solution in the container?
28. A few kilograms of 4% salt water evaporated part of the water and became 10% salt water. After adding 300 grams of 4% salt water, it becomes 6.4% salt water. How many kilograms was the original salt water?
29. It is known that a few grams of brine, after adding a certain amount of water for the first time, the concentration of brine becomes 3%, and after adding the same amount of water for the second time, the concentration of brine becomes 2%. Add the same amount of water for the third time to find the concentration of brine.
30. There are three kinds of brines, A, B and C, which are mixed according to the quantity ratio of A to B of 2: 1 to obtain brines with the concentration of 13%; According to the mass ratio of A to B 1: 2, the brine with the concentration of 14% was obtained; According to the mass ratio of A, B and C 1: 1: 3, the brine with the concentration of 10.2% was obtained. What is the concentration of brine C?