There was a general named Han Xin in the Han Dynasty of our country. Every time he assembled his troops, he only asked his subordinates to count from 1 to 3, 1 to 5, and 1 to 7, and then report the remainder of each team's count, so that he would know how many people were there. His ingenious algorithm is called Guigu calculation, also called partition calculation, or Han Xin's strategy. Foreigners also call it "Chinese remainder theorem". In the Ming Dynasty, the mathematician Cheng Dawei summarized this algorithm in poetry. He wrote:
Three people walking together at seventy, five trees with twenty-one plum blossoms,
Seven sons are reunited in the moon It's half, divide it by one hundred and five and you'll know.
The meaning of this poem is: multiply the remainder obtained by dividing by 3 times 70, plus multiply the remainder obtained by dividing by 5 multiplied by 21, plus multiply the remainder obtained by dividing by 7 multiplied by 15, the result is greater than Just subtract multiples of 105 from 105, and you will know the number you are looking for.
For example, in a basket of eggs, the number of three and three places is 1, the number of five and five places is 2, and the number of seven and seven is 3. There must be 52 eggs in the basket. The formula is:
1×72×21+3×15=157
157-105=52 (pieces)
Please calculate the following according to this algorithm topic.
Xinhua Primary School ordered a number of "China Youth Newspapers". If there are three and three lands, the remainder is 1; if there are five and five lands, the remainder is 2; and if there are seven and seven lands, the remainder is 2. , the remainder is 2. How many copies of China Youth Daily has Xinhua Primary School ordered?
Puchoko’s Interesting Questions
Puchoko was a famous mathematician in the former Soviet Union. In 1951, he wrote the book "Primary School Mathematics Teaching Methods". There is an interesting question below in this book.
The store sold 1,026 meters of cloth in three days***. The sales on the second day were twice as much as the first day; the sales on the third day were three times as much as the second day. How much rice cloth was sold in each of the three days?
This question can be thought of like this: Consider the number of meters of cloth sold on the first day as 1 share. You can draw the following line graph:
The first day is 1 portion; the second day is 2 times the first day; the third day is 3 times the second day, that is, the first day 2×3 times.
The number of meters of cloth sold on the first day can be calculated by using a comprehensive formula:
1026÷(l+2+6)=1026÷9=114 (meters)
And 114×2=228 (meters)
228×3=684 (meters)
So the cloth sold in the three days are: 114 meters, 228 meters, and 684 meters.
Please use this method to do a question.
Four people donated money for disaster relief. B’s donation is twice that of A, C’s donation is three times that of B, and D’s donation is four times that of C. They donated 132 yuan. How much do each of the four people please donate?
Newton's Problem
The great British scientist Newton once wrote a mathematics book. There is a very famous problem in the book about cows grazing on the pasture. Later, people called this kind of problem "Newton's problem".
The "Newton problem" is this: "There is a pasture. It is known that 27 cows are raised, and the grass is eaten up in 6 days; 23 cows are raised, and the grass is eaten up in 9 days. If 21 cows are raised, , then how many days will it take to eat all the grass on the pasture? And the grass on the pasture will continue to grow."
The general solution to this type of question is: consider the grass that a cow eats in one day. 1, then there are:
(1) The grass eaten by 27 cows in 6 days is: 27×6=162
(This 162 includes the original grass of the pasture and 6 (2) The grass that 23 cows eat in 9 days is: 23×9=207
(This 207 includes the original grass and grass in the pasture. Grass that grows new in 9 days)
(3) Grass that grows in 1 day is: (207-162) ÷ (9-6) = 15
(4) Pasture The original grass on the farm is: 27×6-15×6=72
(5) The new grass that grows every day is enough for 15 cows to eat. Subtract 15 from the 21 cows, leaving 6 cows to eat the original. Grass on the pasture:
72÷(21-15)=72÷6=12 (days)
So if you raise 21 cows, it will take 12 days to eat all the grass on the pasture. .
Please do the math.
There is a pasture. If you raise 25 sheep, you can eat all the grass in 8 days; if you raise 21 sheep, you can eat all the grass in 12 days. If we raise 15 sheep, how many days will it take to eat all the growing grass on the pasture?
Answer: The God of Meteor Shower - Trial Period Level 7-29 20:57
1. Write 789 ( ) times in a row, the number formed can be divisible by 9, And this number is the smallest.
2. There are 6 boxes of goods in the store, weighing 15, 16, 18, 19, 20, and 31 kilograms respectively. Two customers bought 5 of them. It is known that the weight of goods purchased by a customer is twice that of a customer. Ask: How many kilograms does the remaining box of goods in the store weigh?
3.
The three-digit hundreds, tens, and ones digits are 5, a, and b respectively. Repeat it 99 times to become: (5ab5ab...5ab) 99 5ab. If the resulting number is divisible by 91, what is the three-digit number 5ab?
(1) Answer: 3 times, which is smaller than the answer given by the person just now!
(2) Answer: 20 is added up and divided by 2, the remainder is 2, and then Divide these six numbers by 2 one by one. The remainder is 2, which is the weight of the remaining box!
(3) Answer: 546 because 2 5ab can be divided by 91 (5ab5ab=5ab times 5ab 1001), after 98, only the last 5ab is left, try again and you will have the answer!
2000 Primary School Mathematics Olympiad Test Questions
Preliminary (A) Paper
< p>1. Calculation: 12-22+32-42+52-62+…-1002+1012=________.2. A two-digit number is equal to the sum of the square of its single digit and the tens digit. This two-digit number is ________.
3. Five consecutive natural numbers, each number is a composite number. The minimum sum of these five consecutive natural numbers is ________.
4. There are several red and white balls. If a red ball and a white ball are taken out each time, and there are no red balls, there are still 50 white balls left; if a red ball and a red ball are taken out each time,
3 If there are no white balls, there will be 50 red balls left. Then there are _________ in this pile of red balls and white balls.
5. A young person’s age this year (2000) is exactly equal to the sum of the numbers in the year of birth, then the young man’s age this year is ________.
6. As shown in the picture on the right, ABCD is a parallelogram with an area of ??
72 square centimeters. E and F are the midpoints of AB and BC respectively.
Then the area of ??the shaded part in the figure is _____ square centimeters.
7.a is a 2000-digit integer composed of 2000 9s, and b is a 2000-digit integer composed of 2000 8s. Then the sum of the digits of a×b is ________.
8. Four consecutive natural numbers. From small to large, they are multiples of 3, multiples of 5, multiples of 7, and multiples of 9. The sum of these four consecutive natural numbers is the smallest
< p>is____.9. The charging standard for electricity in a certain district is as follows: each household uses less than 10 kilowatt hours of electricity per month, and is charged at 0.45 yuan per kilowatt hour; if it exceeds 10 kilowatt hours, it does not exceed
The part with 20 degrees is charged at 0.80 yuan per degree; the part with more than 20 degrees is charged at 1.50 yuan per degree. In a certain month, user A pays 7.10 yuan more for electricity than user B
, and user B pays 3.75 yuan more than user C. Then users A, B, and C pay *** yuan for electricity (electricity consumption All charges are based on whole degrees).
10. A car and a large truck met on a narrow road 9 kilometers long. They had to reverse before they could continue to pass. It is known that the speed of the car is three times that of the big truck. The speed of the two cars in reverse is their own speed. The distance that the car needs to reverse is 4 times that of the big truck. If
the speed of the car is 50 kilometers per hour, then it will take at least ________ hours to pass through this narrow road.
11. There are 110 fifth-grade students in a certain school. They participate in activity groups for Chinese, mathematics, and English. Each person participates in at least one group. It is known that 52 people participate in the Chinese group
and 16 people only participate in the Chinese group; 61 people participate in the English group and 15 people only participate in the English group; 63 people participate in the mathematics group < /p>
There are 21 people who only participate in the math group. Then there are ________ people participating in all three groups.
12. There are 8 steps. Xiao Ming walks up from bottom. If he can only cross one or two steps at a time, he may have ________ different ways to go up.
Answer: Bad Lazi - Xiucai Level 2 7-31 14:00
1. Dongsheng Village will build a rectangular parallelepiped reservoir with a planned water storage of 720 tons. It is known that the length of the pool is 18 meters, the width is 8 meters, and the depth is at least how many meters? (1 cubic meter of water weighs 1 ton.)
2. The length of a classroom is 8 meters, the width is 6 meters, and the height is 4 meters. The roof and walls of the classroom should be painted. Excluding doors, windows and blackboards, the area is 26 square meters. How many square meters will be painted?
3. A garment factory originally used 3.8 meters of cloth to make a uniform. After improving the cutting method, each set saves 0.2 meters of cloth. The cloth used to make 1,800 sets of uniforms, how many sets can now be made?
4. Two cars, A and B, are traveling towards each other from a place 516 kilometers apart. Car B stops for repairs after driving for 6 hours. At this time, the distance between the two cars is 72 kilometers. Car A maintains its original speed. After another 2 hours of driving, we met Car B. Find the speed of car B.
5. Use iron sheets to make an uncovered rectangular sink 5 decimeters long, 4 decimeters wide and 3 decimeters high.
How much iron sheet is needed at least?
6. The picture below is a bar chart of the output of five agricultural products on a state-owned farm last year. Answer the questions below.