Where is the one yuan?
Three people stayed in a hotel, and the price per person per day was 10 yuan. Everyone paid 10 yuan, and the total was the boss 30 yuan. Later, the boss gave a discount of 5 yuan and asked the waiter to return it to them. As a result, the waiter embezzled 2 yuan, and each of the remaining 3 yuan returned 1 yuan, which means that each person spent 9 yuan's money. Three people spent a total of * * * 27 yuan, plus 2 yuan, a corrupt waiter, spent a total of * * * 29 yuan. Where did the dollar go?
Divide apples
There are five students in Xiaomi's family Xiaomi's father wants to entertain six children with apples, but there are only five apples at home. What shall we do? I have to cut the apple, but I can't cut it into pieces. Xiaomi's father wants each apple to be cut into three pieces at most. This has become another topic: divide five apples equally among six children, and each apple is not allowed to be cut into more than three pieces.
How did Xiaomi's father do it?
Ma Xiao Hu cooked chicken
During the Spring Festival, Xiao Mahu, a professional chicken farmer, stood in the yard, counted the total number of chickens, and decided to stay and give them to the People's Liberation Army 1/2 and the nursing home 1/3. After he sent the chickens away, he heard the chickens crowing in the room, only to know that there were 10 chickens missing. So I counted the chickens inside and outside the room again, and there was nothing wrong, no more, no less, just 1/2 left. Little careless and strange. What's the problem? Do you know how many chickens Xiao Mahu counted in the yard?
How many guests came one day and Xiao Lin was washing dishes at home. Xiao Qiang saw it and asked, "Why do you wash so many bowls?" "
We have guests at home. ""How many people came? " Kobayashi said, "I don't know. I only know that each of them uses a rice bowl, two people share a soup bowl, three people share a vegetable bowl, four people share a big wine bowl, and one * * uses 15 bowl. "Do you know how many guests are here?
It is said that there are 243 beads of the same shape, one of which is slightly heavier. How many times does it take to find this bead with a weightless balance?
Divide pears
There is a box of pears in the box. The first person took half and most of the pears, the second person took the remaining half and most of the pears, the third person took the second half and most of them, the fourth person took the second half and most of them, and the fifth person took the second half and most of them. At this time, the pears in the box had just been eaten, and everyone had no pears in their hands. How many pears are there in the box?
How to group
Divide the class into 15 groups during the summer vacation. There are six students in the class, namely Zhao, Qian, Sun, Li and Zhou. How to divide each group into different surnames?
Skillfully calculate the week
October 1st this year is Monday. What day is October 1st next year? Please write a simple algorithm?
Who runs fast?
He and Xiao participated in the 100 meter race. As a result, when Xiao Wei ran to the finish line, Kobayashi only ran 95 meters. Xiao Lin asked to run again. The starting line of Xiao Wei is 5 meters behind Kobayashi's. If everyone runs at the original speed, will they reach the finish line at the same time?
Train crossing the bridge
The railway bridge of Nanjing Yangtze River Bridge is 6772 meters long, and the freight train is 428 meters long, traveling 20 meters per second. How long does it take for the whole train to cross the bridge?
Unlocking problem
Try to open the 10 lock with the same key. How many times can you tell which key matches which lock?
What is this three-digit number?
There is a three-digit number, ranging from 400 to 500. One digit is 3 larger than the hundredth digit, and ten digits are 5 smaller than one digit. What is this three-digit number?
Calculate age
Xiaoming's father is 50 years old and Xiaoming is 22 years old. Will Xiaoming's father be twice as old as Xiaoming after too many teenagers?
How many floors does this building have?
Teacher Wang recently moved into the teachers' dormitory. One day, Mr Wang stood on the balcony and looked down. There are three balconies below and five balconies above. What floor did you say Mr. Wang lived on? How many floors are there in the teachers' dormitory?
How many athletes are there?
With a loud noise, the athletes who participated in the 1500m final rushed out of the starting line and ran along the circular track. Lin Lin also participated in the final. There are five athletes running in front of Linlin and five athletes running behind Linlin. How many athletes participated in the1500m final?
Who caught the fish?
Xiao Ming, Xiao Fang and Xiao Li go fishing together. When they got home, there were 15 fish in their car. Everyone catches the same number of fish. This pile of fish has 1 big fish weighing 5 kg, five weighing 4 kg, four weighing 3 kg, three weighing 2 kg and two weighing 1 kg. One * * * is 45 Jin. No one can remember who caught the big fish. Xiao Fang only remembers that he caught two 1 kg fish in one net. Who caught that big fish weighing 5 Jin?
Find a pattern
Please carefully observe the number rule in each line below, and then fill in a number in brackets to make it conform to this rule.
( 1) 1,5,9, 13,( ),2 1,25
(2) 1,3,9,27,( )243,729
(3) 1,8,27,64,( )2 16,343
(4) 1,2,4,7,( ) 16,22
(5) 1,2,6,24,( )720,5040
(6) 1,3,7, 15,( )63, 127
(7) 1,2,5, 10,( )26,37
(8) 1,4,9, 16,( )36,49
(9) 1, 1,2,3,5,8,( )2 1,34
( 10)2,3,5,7,( ) 13, 17
( 1 1)3 12,423,534,645,( )
( 12) 122 1,2332,3443,4554,( )
( 13) 1232 1,23432,34543,45654,( )
College mathematics problems
Now I'll introduce you to a math problem in college. When students hear that this is a university problem, they should not be afraid. In fact, if you use your head and think in another way, you can work it out. Here's the question.
There is a 22-digit number, and its unit number is 7. When you multiply this 22-digit number by 7, its product is still a 22-digit number, but the single-digit number 7 is moved to the first place, and the arrangement order of other 2 1 digits remains unchanged. What is this 22-digit number?
Tip: If the number is expressed in letters, the formula is: abcdefghijklmnopqrstu 7× 7 = 7abcdefghijklmnopqrstu.
Monks play chess.
There was a monk in ancient India who was very proficient in chess, and the king happened to like playing chess. One day, the king called the monk to his palace to play games with him. The king said to him, "I heard that you are good at playing chess, so I invited you to play chess with me." Don't dare to hit me just because I am the king, you should show your real skill. If you beat me, I can promise you anything. The monk said, "Since your Majesty allows me, I dare to play a few games with your Majesty. But if I beat you, I only have one small request. " The king said, "as I said just now, you can make any conditions, and I will meet your requirements." The monk said, "My request is very simple. Isn't there 64 squares on this chessboard? I win you a set, you give me the first box of one grain of rice, win two sets, give me the second box of two grains of rice, win three sets, give me four grains of rice, give me four sets of eight grains of rice, ... each set is twice as big as the last set until this sixty-fourth box. " The king smiled and said, "It's not easy. There is a lot of rice in our national treasury, even less than nine Niu Yi hairs. " Monk Gao Kun said, "Your Majesty, don't go back on your word." The king said, "It's a deal." So they played a game of chess. As a result, the monk won 30 sets Guess how many meters the king should give the monk? "
Han Xin ordered the soldiers.
Han Xin was a famous general of Han Dynasty in China. He once commanded thousands of troops and knew his soldiers like the back of his hand. He had a unique method of counting soldiers, which was later called "Han Xin Point Soldiers". his
Here's the method. After the troops were assembled, he asked the soldiers to report 1, 2, 3- 1, 2, 3, 4, 5- 1, 2, 3, 4, 5, 6 and 7 three times, and then reported the remainder of each time to him to let him know the actual situation of the troops. His calculation methods are also called "ghost valley calculation", "partition calculation" and "pipe cutting" in history, while foreigners call it "Chinese remainder theorem". Someone summed up the solution to this problem with a poem: Seventy-three people walked together, five trees and twenty-one branches, and seven children got together in the middle of the month, only after 105 did they know. This means that the first remainder is multiplied by 70, the second by 2 1 and the third by 15. Add up the results of these three operations and divide by 105, and the inexhaustible remainder is the number (that is, the total). For example, if three 3-site reports are 1, five 5-site reports are 2, and seven 7-site reports are 3, the total is 52. The formula is as follows:
1×70+2×2 1+3× 15= 157
157÷ 105= 1……52
Here is a question for the students. Please use the "Han Xin's Point Troop Method" to calculate.
Xiaohong helped Aunt Zhang release ducks in the summer vacation, but she always couldn't count how many. She first
Three or three, there are three left; She counted five more, leaving only four. She counted seven more, leaving only six. She still can't figure out how many ducks are in a * * *. Children, please help Xiaohong figure out how many ducks Aunt Zhang Er has fed.
Strange numbers
The math teacher asked his students, "will there be such a six-digit number?" Multiply it by 1, 2, 3, 4, 5, 6, and the product of six digits is the same, but the arrangement order is slightly different? "
Will there be such a strange number? The students find it hard to believe.
"yes. There are six such figures. Now I'll write it down. Multiply yourself by 1-6 and look at these six interesting products. This is a very interesting thing. " The math teacher has finished.
Write six numbers on the blackboard.
You must want to know six figures, right?
Interesting natural number
The sum of five consecutive natural numbers is 350. What are these five natural numbers?
Buy groceries
Xiaohei came back from the vegetable market and told his father that he had bought four dishes: four cucumbers, three tomatoes, six potatoes and five peppers. "Cucumber is 6 cents each and pepper is 9 cents each," Xiaohe said to his father. "A * * * spent 1 yuan 70 cents."
"This account is wrong," Dad said with a smile. There must be a calculation error. "
"You don't know how much potatoes and tomatoes are worth, so how do you know you are wrong?"
"Do it again, you must be mistaken." Dad said positively.
Xiaohe calculated it carefully and it was really wrong. Strange, how did dad know?
Bottom hole worm
A bug accidentally fell into the well. It's climbing every day. Unfortunately, it can climb 3 meters every day and slide down 2 meters at night. But the bug insisted on climbing. This well is 20 meters from the bottom to the wellhead. Insects began to climb up from the bottom of the well in the early morning. How many days will it take to climb out of the wellhead?
A few nines
Both Mingming and Shen like math very much. One day, Mingming asked Shen, "What do you like best?"
"I like 9 best."
"From 1 to 100, how many times did you say' 9'?"
"ah! ..... this is "difficult", "this is to be counted clearly"
"One minute" clearly means.
Children, please tell me how many 9s there are from 1 to 100 in one minute.