(Assuming that the flour weight of each steamed stuffed bun is m, mark each steamed stuffed bun as cage A, B, C, D and E..
As long as you take/kloc-0 steamed bread from cage A, 2 steamed buns from cage B, 3 steamed buns from cage C, 4 steamed buns from cage D and 5 steamed buns from cage E, if all steamed buns are ok, the total weight should be 25M, that is, the total weight must be divisible by 25.
Now put these steamed buns on the scale and check the weight reading, because each steamed bun is missing 10g.
So add 10, 20, 30, 40, 50g to the current weight reading to see if the result is divisible by 25.
If 10G is divisible by 25, then cage A is made by an apprentice.
If 20G is divisible by 25, then the B cage is made by an apprentice, and so on.
If the current weight reading can be divisible by 25, the E cage is made by the apprentice)
2. One page of a book has been torn off, and the sum of the remaining page numbers is exactly 1002. Q:
(1). How many pages does this book have?
(2). Which page was torn off?
(Let's talk about the formula of summation first, which is convenient. This is an arithmetic series. Let * * n pages (1, 2, 3, 4, ..., n), then the sum of page numbers is n(n+ 1)/2, and the torn page is n(n+65438+).
Let's start with page 44. The total number of pages obtained from the formula is 990. This is less than 1002, so it is not suitable.
Say ***45 pages. According to the formula, the sum of page numbers is 1035, which is greater than 1002. Then 1035- 1002 = 33, so these 45 pages are in line with the meaning of the question.
Further down, on page ***46, the sum of page numbers obtained by the formula is 108 1, which is also greater than 1002, but108/-1002 = 79, but 79.
As can be seen from the above, less than or equal to 44 or greater than or equal to 46 is not the meaning of the question, only 45 is the meaning of the question.
So the answer to this question is: this book has 45 pages, and the torn page is 16, 17).
3.( 1): It takes 8 hours for a ship to travel 360km in downstream water and 8 hours for a ship to travel184km in upstream water, so how long does it take for a ship to travel170km in still water?
(2) The ship is sailing 165km, with a speed of 28km per hour and a water speed of 5km. How many hours does it take to sail?
(3) The speed of the ship in still water is 25km/h, the speed of the river is 5km/h, and the ship travels back and forth between Port A and Port B for 4 hours. How many kilometers are AB apart? How many hours does it take to go upstream?
Legal summary:
Downstream velocity = still water velocity+current velocity
Countercurrent velocity = still water velocity-current velocity
Still water velocity = (downstream velocity+countercurrent velocity) ÷2
Water velocity = (downstream velocity-countercurrent velocity) ÷2
( 1)
The speed of the ship in still water: [(360 ÷ 8)+(184 ÷ 8)] ÷ 2 = 34 km/h.
Sailing 170km takes 170÷34=5 hours.
(2):
165(28+5)= 5 hours
(3):
Distance between the two places: (25+5) × 4 = 120km.
Countercurrent sailing needs 120÷(25-5)=6 hours.
I really don't know how far the primary school problem is ...................................................................................................................................................................
Activity 1:
(1) Guess the riddle of age
A asked B's age, and B replied:
"My age is divided by 3, leaving 2.
Age divided by 5 leaves 4,
Age divided by 7 leaves 1. "
Can you guess B's age?
Tip: First list the numbers that meet the condition of "age divided by 7, and the remainder is 1". After investigating 5 and 3, you can get a solution.
Activity 2: Find the hidden number combination.
Question (1): Choose four numbers from the five numbers 0, 4, 5, 6 and 8 to form a four-digit number that can be divisible by 2, 3 and 5 at the same time.
Question (2): Find two prime numbers less than 30 and make their sum 30.
Tip: This is an open question, and there are many possibilities for the answer.
Activity 3: Saw wood or wire.
Question (1) has two pieces of wood, the length of which is 30 cm and 80 cm respectively. Now cut them into small pieces of the same length, and there can be no surplus. How many centimeters per piece?
Question (2) There are three iron wires with lengths of 120cm, 180cm and 240cm respectively. Now we have to cut them into wires of the same length, without any redundancy, and make the wires as long as possible. How long is each wire? How much can you cut?
Question (3) Xiao Ming wants to use a rectangular piece of paper with a length of 48cm and a width of 42cm to cut out several paper cranes with the same area and no remaining area. How many paper cranes can be produced here at least?
Activity 4: Erase the number game.
The cardboard says 100 natural numbers 1, 2, 3, … 100. Party A and Party B take turns to cross out one number at a time until two numbers remain. If the remaining two numbers are mutual, Party A wins, otherwise, Party B wins. B row first and then row. Who has a winning strategy? Analyze the reasons.
Tip: To strengthen students' understanding and mastery of prime numbers, you can play games first, and then organize students to analyze and summarize.
Activity 5: Paving the floor
What is the side length of the smallest square paved with 30 cm and 40 cm squares respectively?
Activity 6:
Party A, Party B and Party C check the information. Party A goes once every six days, Party B once every eight days and Party C once every nine days. If everyone was in the Internet cafe on April 15, 2006, how long will it be next time?
Activity 7:
There is a rectangular piece of white paper with a length of 136 cm and a width of 80 cm. If you cut it into several squares of the same size, so that their areas are as large as possible, and there is no paper left, what is the side length of each square?
Activity 8 Background knowledge of this topic:
In ancient mathematics in China, this kind of problem was called "Han Xin's point soldier".
"All three peers are seventy years old and thin.
Five trees and twenty clubs (read four tones),
Seven sons reunited in the first half of the first month,
Divide by 105. "
In Japan, this problem is called "subtraction of one hundred and fifty" or "calculation between one hundred and fifty", which was recorded in the Edo-era math book "Dust Robbery".
Extended Problem (2): Building blocks
Xiao Ming takes out pieces from the box with 100 pieces and groups them. If each group has 3 blocks, the result is 1 block; 5 pieces in each group, and the result is 1 piece. How many pieces are there in the box?
One, 29.
2, 1.4560, 6540, 5460, 4650, 6450, 5640, 4680, 8640, 8460, 4860, 6480, 6840.
2.23,7; 19, 1 1; 13, 17。
Three, 1. 10cm, 2cm, 5cm.
2.60cm, ***9 yuan.
3.36.
Fourth, ellipsis.
V. 120cm.
Sixth, June 26th, 2006.
Seven or eight centimeters.
Extended problems, 106, 12 1, 136, 15 1, 166,18/kloc-0.