Classic articles on mathematical puzzles (1)
Who took the change?
When my sister came back from shopping, she put some small change in the drawer. However, when my sister took money to buy food in the afternoon, she found that there was no change in the drawer, so she called her three sisters and asked them if they had any change in the drawer.
A said:? I took it and went to buy snacks at noon. ?
B said:? I saw A take it. ?
C said: In a word, B and I didn't take it. ?
One of the three people is lying, so who is lying? Who took the change?
Answer: C lied, and A and C both took some. Suppose a lies, then b also lies, which is inconsistent with the meaning of the question; Suppose B lies, then A also lies, which doesn't match the meaning of the question. Then, the liar must be C. Only when both A and C are changed can they satisfy the problem.
(2)
Title:
Sister and brother are playing a game: they put 10 coins on the table and take 1, 2 or 4 coins from them in turn. Whoever throws the last coin loses. Excuse me: What can I do to win?
(3)
Title:
Four couples sit together and chat. Among the four women, A ate three pears, B ate two, C ate four and D ate 1.
Among these four people, A and his wife ate as many pears, B ate twice, C ate three times and D ate four times. Four couples ate 32 pears.
Q: Who is C's wife?
(4)
Every prisoner has an answer board and writes a natural number on it. The warden checked the answer sheet. First, check whether there is the same number. If there is, then everyone who fills in this number will die. Look at the rest of the numbers and choose the smallest one. The prisoner who filled in this number was released, and the rest were all dead. If you are three prisoners, how should you fill in the numbers?
(5)
The U2 chorus must arrive at the concert venue within 17 minutes. On the way, it must pass a bridge. Four people started from the same end of the bridge. You must help them get to the other end. It was dark and they only had one flashlight. At most two people cross the bridge at the same time, and they must hold flashlights when crossing the bridge, so someone has to carry flashlights to and from both ends of the bridge. You can't send out the flashlight if you throw it away. Four people walk at different speeds. If two people go together, the slower one shall prevail. It takes 1 minute for Bono to cross the bridge, 2 minutes for Archie, 5 minutes for Adam and 10 minute for Larry to cross the bridge. How do they cross the bridge in 17 minutes?
(6)
There are five ladies in a row. All the ladies wear different clothes, have different surnames, keep different pets, drink different drinks and eat different fruits. Miss Qian wears red clothes, Miss Weng keeps dogs, Miss Chen drinks tea, the lady in green clothes stands on the left, the lady in green clothes drinks coffee, the lady who eats watermelon keeps birds, the lady in yellow clothes eats, the lady standing in the middle drinks milk, and Miss Zhao stands on the far left. The lady who keeps fish eats next door, the lady who eats oranges stands next to the cat, the lady who eats apples drinks champagne, Miss Jiang eats bananas and Miss Zhao stands. Excuse me, which lady keeps snakes?
Selected articles on mathematical puzzles 1. Which number is the smallest?
There are four numbers A, B, C and D, which have the following relations: the sum of A and B is greater than the sum of C and D, the sum of A and D is greater than the sum of B and C, and the sum of B and D is greater than the sum of A and C. Can you know which of these four numbers is the smallest from these conditions?
2. do the problem.
The teacher assigned two homework questions to 60 students in the class, of which 40 were right in the first question, 365,438+0 were right in the second question, and 4 were wrong in both questions. So, can you figure out the number of people who answered both questions correctly?
solve problems
My brother asked his sister to help him solve a math problem. Multiply a two-digit number by five to get a three-digit number, and the sum of the units of the three-digit number and the hundred-digit number is exactly equal to the number in the tenth place. After reading it, my sister was very anxious and felt that she could not get a clue. Can you help her get the answer to this question?
4. The color of the headscarf.
A group of people went for an outing together. Some of them are wearing blue headscarves, others are wearing yellow headscarves. In the eyes of people wearing blue headscarves, there are as many blue headscarves as there are yellow headscarves, while in the eyes of people wearing yellow headscarves, there are twice as many blue headscarves as yellow headscarves. So how many people wear blue headscarves and how many people wear yellow headscarves?
5. Divide the jelly.
Xiaohong's mother bought a lot of jelly. There are 48 jellies. Xiaohong's mother said to Xiaohong: If you can divide these jellies into four parts, so that the first part adds 3, the second part subtracts 3, the third part multiplies 3 and the fourth part divides 3, and the results are consistent, then you can eat these jellies. Xiaohong thought for a long time and finally came up with this problem. Do you know how to divide the smart ones?
6. Buy books.
Xiaohong and Xiao Li go to Xinhua Bookstore to buy books. They both want to buy the book Comprehensive Exercise, but they don't have enough money. Xiaohong is short of 4.9 yuan and Xiaoli is short of 0. 1 yuan. They bought a book with their money, but the money is still not enough. So, what's the price of this book?
Training logical thinking training questions daquan answer:
1.c is the minimum value. ( 1)A，B >； c、D； (2)A、D & gtb、C； (3)B, D> A, C. A >: C from (1)+(2), B > from (1)+(3); C, d > is known from (2)+(3); So, c is the smallest.
2. According to the stem, we assume that two digits are AB and three digits are CDE, so AB*5=CDE.
Step 1: It is known that CDE is divisible by 5, and it can be concluded that each bit is 0 or 5.
Step 2: If the last digit E=0, C=D, because E+C = D. ..
Step 3: According to the meaning of the question, the quotient of CDE/5 is two digits, so the hundred digits are less than 5.
Step 4: Since C=D was obtained in the previous step, when C = 1, 2,3,4, D = 1, 2,3,4, CDE =1/kloc-0,220,330,440.
Step 5: If E=5, when C = 1, 2, 3, 4, D = 6, 7, 8, 9, CDE = 165, 275, 385, 495.
So there should be eight such numbers in this question.
There are 15 people who answered both questions correctly. 40+3 1(604)= 15。
4. Because people can't see the headscarf on his head, it seems that there are as many people wearing blue headscarfs, that is to say, there is one more blue headscarf than yellow headscarf. If there are x yellow headscarfs, there are X+ 1 blue headscarf. And everyone who wears a yellow headscarf thinks that the blue headscarf is twice as big as the yellow headscarf. In other words, 2(X 1)=X+ 1, and the solution is X=3. So there are four blue headscarves and three yellow headscarves.
5. The four copies are 12, 6, 27 and 3 respectively. Suppose these four jellies are all X, then the first one is X+3, the second one is X3, the third one is 3X, and the fourth one is X/3, and the total is 48, so X=9. So we can know how much each one is.
Mathematical puzzles simplified 1, mathematical brain teaser: losing money
Xiaohong had 10 copper coins in his pocket, but they were all dropped. What's left in Xiaohong's pocket?
Answer: There is another hole.
2, math brain teaser: the hour hand and the minute hand coincide.
How many times does the hour hand coincide with the minute in a day and night of the customs clock?
Answer: 23
3, math brain teaser: ferry
A boat has to ferry 37 people, and only 7 people can be ferried at a time. How many times can it be completed?
Answer: Six times, because every time a rower comes back.
4, math brain teaser: cats eat mice
There are five mice in a mouse hole. The cat went into the hole and ate a mouse. How many mice are left in the hole?
Answer: No.
5. Math brain teaser: Which eggs can't be eaten?
What eggs can't be broken, boiled or eaten?
Answer: I have zero eggs in the exam.
6. Math brain teaser: Who lost?
Xiao Wang went to an Internet cafe to open a membership card and asked for 20 yuan. Xiao Wang didn't find any change, so he gave the stationmaster a card from 50 yuan. The stationmaster asked 30 yuan to give the little queen, and Xiao Wang gave 20 yuan's change. After giving it to the stationmaster 20 yuan, the stationmaster returned the former 50 yuan to him. Who lost?
Answer: The webmaster lost 30 yuan.
7, math brain teaser: buy a shirt
Xiaoming bought a shirt from 75 yuan on 100, and the boss only gave him 5 yuan. Why?
Answer: Xiao Ming only gave money to his boss, 80 yuan.
8, math brain teaser: take medicine on time
The doctor will give you three pills every half hour. How long will it take to complete?
A: One hour.
9. Math brain teaser: The flood flooded the bridge.
There are two bridges on the Yellow River, one high and the other low. Both bridges were flooded three times in a row. Gao Qiao was flooded three times, while the short bridge was only flooded 1 time. Why?
A: After the water receded, Gao Qiao was exposed, and the short bridge was always flooded.
10, math brain teaser: buy a hat
Two fathers and sons went to buy hats. Why did they only buy three?
Answer: It's three grandparents and grandchildren.
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