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A collection of mathematical puzzles_a collection of difficult questions

The best way to activate advanced mathematics classrooms and awaken students’ interest in learning is to provide them with attractive mathematics stories, games, puzzles, jokes, paradoxes, formulas, poems, etc. What are the mathematical puzzles? This article is my collection of information on mathematical puzzles, for reference only.

Classic Mathematical Puzzles

(1)

Who took the change?

After my sister came back from shopping for groceries , she casually put some change in her hand in the drawer. However, when her sister went to get money to buy groceries in the afternoon, she found that there was no change in the drawer, so she called her three younger sisters and asked them if they were Take the change from the drawer.

A said: "I took it and went to buy snacks at noon." ?

B said: ?I saw A took it. ?

C said: In short, neither I nor B took it. ?

One of the three people was lying, so who was lying? Who took the change?

Answer: C lied, and both A and C took part of it. If A lies, then B also lies, which is inconsistent with the meaning of the question; if B lies, then A also lies, which is inconsistent with the meaning of the question. Then, the liar must be C. Only if A and C both get change can it meet the meaning of the question.

(2)

Title:

The sister and brother are playing a game: they put 10 coins on the table and take turns to take 1, 2 or 4 coins, whoever gets the last coin loses. May I ask: What should I do to win?

(3)

Topic:

Four couples are sitting together chatting. Among the four women, A eats He ate 3 pears, B ate 2, C ate 4, and D ate 1;

Among the four men, A ate as many pears as his wife, and B ate his wife. 2 times as much as his wife, C ate 3 times as much as his wife, and D ate 4 times as much as his wife. The four couples ate 32 pears.

Question: Who is C’s wife?

(4)

Each prisoner is given an answer board and writes a natural number on it. The warden checks the answer board. First check to see if there are the same numbers. If so, then everyone who fills in this number will die. Look at the remaining numbers and choose the smallest one. The prisoner who fills in this number will be released and the rest will die. If there are three prisoners, how should they fill in the numbers?

　(5)

The U2 choir has to rush to the concert venue in 17 minutes, and must cross a bridge on the way. Starting from the same end of the bridge, you have to help them get to the other end, it's dark and they only have a flashlight. At most two people can cross the bridge at the same time, and they must hold a flashlight when crossing the bridge, so someone has to bring a flashlight to and from both ends of the bridge. Flashlights cannot be passed around by throwing them away. Four people walk at different speeds. If two people are walking together, the slower one will prevail. Bono takes 1 minute to cross the bridge, Edge takes 2 minutes to cross the bridge, Adam takes 5 minutes to cross the bridge, and Larry takes 10 minutes to cross the bridge. How can they cross the bridge in 17 minutes?

　(6)

There are five ladies in a row. All the ladies wear clothes of different colors, have different surnames, and have different pets. , drink different drinks and eat different fruits. Miss Qian is wearing red clothes, Miss Weng is raising a dog, Miss Chen is drinking tea, the girl in green clothes is standing on the left side of the white clothes, the girl in green clothes is drinking coffee, the girl in green clothes is raising birds, and the girl in yellow clothes is eating watermelons. Liu Ding, the lady standing in the middle is drinking milk, Miss Zhao is standing on the far left, the girl raising fish is eating Liu Ding next door, the one eating oranges is standing next door to the cat, the lady eating apples is drinking champagne, Miss Jiang is eating bananas, Zhao The lady in blue clothes stood next to the one who drank only boiled water and stood next to the one eating oranges.

Ask which lady keeps snakes? Selected Mathematical Puzzles

1. Which number is the smallest?

There are four numbers A, B, C, and D. They have the following relationships. : 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. Excuse me, can you know from these conditions which number is the smallest among these four numbers?

2. Do the questions.

The teacher assigned two homework questions to the whole class of 60 students. 40 of them got the first question right, 31 got the second question right, and 4 got both questions right. All done wrong. So, can you count the number of people who got both questions correct?

3. Problem solving

The younger brother asked his sister to help him solve a math problem, multiplying a two-digit number 5. The result of the product is a three-digit number, and the sum of the ones digit and the hundreds digit of this three-digit number is exactly equal to the number in the tens digit. After my sister read it, she felt very anxious and felt that she had no clue. Can you help her get the answer to this question?

4. The color of the headscarf.

There is a group of people going for an outing together. Among these people, some of them are wearing blue headscarves, and some are wearing yellow headscarves. A person wearing a blue turban sees as many blue turbans as a yellow turban, while a person wearing a yellow turban sees twice as many blue turbans as yellow turbans. So, how many people are wearing blue headscarves and how many are wearing yellow headscarves?

5. Divide the jelly.

Xiaohong’s mother bought a lot of jelly. There were 48 jelly pieces in one piece. Xiaohong’s mother said to Xiaohong: If you can divide these jelly into 4 parts and make the first part Add 3, subtract 3 from the second portion, multiply by 3 from the third portion, and divide the fourth portion by 3. The result is the same, then you can eat these jelly. Xiaohong thought about it for a long time and finally figured it out. Are you smart enough to know how to divide it?

6. Buy books.

Xiaohong and Xiaoli went to Xinhua Bookstore to buy books together. They both wanted to buy the book "Comprehensive Exercises", but they didn't have enough money. Xiaohong was short of 4.9 yuan, and Xiaoli was short of 0.1 yuan. Two people combined their money to buy a book, but the money is still not enough. So, what is the price of this book?

Answers to the complete collection of logical thinking training questions:

1. C is the smallest. From the meaning of the question, we can get (1) A, Bgt; C, D; (2) A, Dgt; B, C; (3) B, Dgt; A, C. Agt;C can be known from (1) (2), Bgt;C can be known from (1) (3), and Dgt;C can be known from (2) (3). Therefore, C is the smallest.

2. According to the question, let us first assume that the two-digit number is AB and the three-digit number is CDE, then AB*5=CDE.

Step 1: It is known that CDE is divisible by 5, and the units digit can be found to be 0 or 5.

Second step: If the last digit E=0, since E C=D, so C=D.

Step 3: According to the question, the quotient of CDE/5 is two digits, so the hundreds place is less than 5.

Step 4: Because C=D was obtained in the previous step, therefore, when C=1, 2, 3, 4, D=1, 2, 3, 4, CDE=110, 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 8 such numbers in this question.

3. There are 15 people who got both questions right. 40 31(604)=15.

4. Since everyone cannot see the headscarf on their head, so there appear to be the same number of people wearing blue headscarves, indicating that there is one more blue headscarf than yellow headscarf. Suppose there are yellow headscarves There are X number, then, there are X 1 blue headscarves.

And for every person wearing a yellow turban, there are twice as many blue turbans as there are yellow turbans. In other words, 2(X1)=X 1, the solution is X=3. So, there are 4 blue turbans and 3 yellow turbans.

5. The four copies are 12, 6, 27, and 3 respectively. Assume that these four portions of jelly are all This way you will know how much each portion is. A simplified version of mathematical puzzles

1. Mathematical brainteasers: losing money

There were originally 10 copper coins in Xiaohong’s pocket, but they all fell. What’s left in Xiaohong’s pocket? What's left?

Answer: There is only one hole left

2. Mathematical brain teaser: the hour and minute hands coincide

The hour hands of the customs clock coincide with each other throughout the day and night How many times do minutes overlap?

Answer: 23

3. Math brainteaser: Ferry

A small boat has to ferry 37 people, and only 7 people can be carried at a time , how many times can it be crossed?

Answer: six times, because each time a rower has to come back

4. Math brainteaser: cat eats mouse

There are five mice in a mouse hole. A cat enters the hole and eats one mouse. How many mice are left in the hole?

Answer: None

5. Mathematical brain Sharp turn: What eggs can’t be eaten

What eggs can’t be beaten or cooked, let alone eaten?

Answer: Zero eggs from the exam

6. Mathematics brainteaser: Who lost?

Xiao Wang went to the Internet cafe to open a membership card. It cost 20 yuan to open the card. Xiao Wang didn't find any change, so he gave the network administrator a 50 yuan note. The network administrator found back 30 yuan and gave it to him. Little Queen, Xiao Wang found 20 yuan. After giving the network manager 20 yuan, the network manager returned the previous 50 yuan to him. Who lost?

Answer: The network manager lost 30 yuan.

7. Math Brainteaser: Buying a Shirt

Xiao Ming brought 100 yuan to buy a 75 yuan shirt, but the boss only gave him 5 yuan. Why?

Answer: Xiao Ming only gave the boss 80 yuan

8. Math brainteaser: take medicine on time

The doctor gave you three pills and asked you to take half of each pill. How long does it take to eat one pill in an hour?

Answer: One hour

9. Mathematical brain teaser: Floods cover the bridge

On the Yellow River There are two bridges, one high and one low. Both bridges were submerged by three consecutive floods. The high bridge was flooded three times, but the low bridge was flooded only once. Why?

Answer: After the water receded, the high bridge was exposed but the low bridge remained flooded

10. Math Brainteaser: Buying Hats

Two pairs of father and son went to buy hats. Why did they only buy three hats?

Answer: Grandparents and grandsons