I have

1. Mr. S, Mr. P, and Mr. Q know that there are 16 playing cards in the drawer of the table: A, Q, 4 of hearts, J, 8 of spades. , 4, 2, 7, 3, K, Q, 5, 4, 6, A, 5 of diamonds. Professor John picked out a card from these 16 cards, and told Mr. P the value of this card, and told Mr. Q the suit of this card. At this time, Professor John asked Mr. P and Mr. Q: Can you infer what card this card is from the known points or suits? So, Mr. S heard the following conversation: Mr. P: I don’t know this card.

Mr. Q: I know you don’t know this card.

Mr. P: Now I know this card.

Mr. Q: I know it too.

After listening to the above conversation, Mr. S thought for a while and then correctly guessed what the card was.

Excuse me: What is this card?

2. A manager has three daughters. The sum of the ages of the three daughters is equal to 13. The sum of the ages of the three daughters is equal to the manager’s own age. A subordinate already knows the manager’s age, but still cannot Determine the ages of the manager's three daughters. At this time, the manager said that only one daughter has black hair. Then the subordinate knew the ages of the manager's three daughters. What are the ages of your three daughters? Why?

3. Three people went to stay in a hotel and stayed in three rooms. Each room cost $10, so they paid the boss $30 one day. The next day, the boss thought the three rooms only cost $25. Yuan was enough, so I asked the boy to return $5 to the three guests. Who knew that the boy was greedy, so he only returned $1 to each person, and secretly took $2 for himself. In this way, each of the three guests spent nine yuan, so the three I spent $27 per person, plus my little brother ate away $2, the total was $29. But when the three of them paid $30 a ***, what about the remaining $1?

4. There are two blind men. They each bought two pairs of black socks and two pairs of white socks. The eight pairs of socks were made of the same fabric and size, and each pair of socks had a trademark paper. Connected. Two blind men accidentally mixed up eight pairs of socks. How can each of them retrieve two pairs of black socks and two pairs of white socks?

5. A train leaves Los Angeles and goes straight to New York at a speed of 15 kilometers per hour, and another train goes from New York to Los Angeles at a speed of 20 kilometers per hour. If a bird starts from Los Angeles at the same time as two trains at a speed of 30 kilometers per hour, encounters another car and returns, flying back and forth on the two trains until the two trains meet, what will this bird do? How far did the bird fly?

6. You have two jars with 50 red marbles and 50 blue marbles. Randomly select a jar and randomly select a marble and put it into the jar. How to give the red marble the maximum Chances of selection? In your plan, what is the exact probability of getting a red ball?

7. You have four jars containing pills. Each pill has a certain weight. The contaminated pills are the weight of the uncontaminated pills + 1. You only weigh them once. How to determine which jar contains the pills? Contaminated?

8. Perform the following operations on a batch of lights numbered 1 to 100, with all switches facing up (on): for every multiple of 1, turn the switch once in the opposite direction; for multiples of 2, turn the switch once in the opposite direction. Switch; in multiples of 3, flip the switch in the opposite direction... Q: The last number is the number of the light in the off state.

9. Imagine you are in front of a mirror. May I ask why the image in the mirror can be reversed left and right, but not up and down?

10. A group of people had a dance, each wearing a hat on his head. There are only two kinds of hats, black and white, and there is at least one black one. Everyone can see the color of everyone else's hats, but not their own. The host first asked everyone to see what hat others were wearing, and then turned off the lights. If anyone thought they were wearing a black hat, they would slap themselves in the face. When I turned off the lights for the first time, there was no sound. So the lights were turned on again, and everyone watched it again. When the lights were turned off, there was still silence. It wasn't until the lights were turned off for the third time that the sound of slaps could be heard.

How many people wear black hats?

11. There are two rings with radii of 1 and 2 respectively. The small circle goes around the circumference of the large circle inside the large circle. How many times does the small circle rotate by itself? If it is outside the big circle, how many times will the small circle rotate by itself?

A bottle of soda costs 12.1 yuan. After drinking, two empty bottles are exchanged for one bottle of soda. Question: You have 20 yuan. How many bottles of soda can you drink at most?

13. There are 3 red hats, 4 black hats and 5 white hats. Let 10 people stand in a line from shortest to tallest and put a hat on each of their heads. No one can see the color of the hat they are wearing, but they can only see the color of the hats of those standing in front. (So ??the last person can see the color of the hats on the heads of the 9 people in front, but the person at the front can’t see any hats. Now starting from the last person, ask him if he knows the color of the hat he is wearing. If he answers If you don’t know, continue to ask the person in front. Assume that the person in front must know that he is wearing a black hat. Why? 14.10 boxes, each with 10 apples. The apples are 9 taels each, and the others are 1 jin each. You are required to use a scale and weigh it only once to find the box containing 9 taels per piece.

Press 1 for each of the 15.5 prisoners. -No. 5 catches mung beans in a sack containing 100 mung beans. It is stipulated that each person catches at least one, and the people who catch the most and the least will be executed. Moreover, they cannot communicate with each other, but they can touch them while catching. Find out the number of remaining beans. Ask who among them has the highest chance of survival. Tips:

1. They are all very smart people. 2. Their principle is to save their lives first. , kill more people

3. It is not necessary to divide all 100 pills

4. If there are duplicates, they will be counted as the largest or smallest, and they will be executed together

16. Suppose there are 100 ping pong balls arranged in a row, and two people take turns to put the balls into their pockets. The person who can get the 100th ping pong ball is the winner. The condition is: the person who takes the ball must get at least 1 each time, but The maximum number cannot be more than 5. Ask: If you are the first to get the ball, how many should you get? How can you get the 100th ping pong ball in the future?

17. Lum? The professor said: "I once witnessed a desperate duel between two goats, which led to an interesting mathematical problem. One of my neighbors had a goat that weighed 54 pounds and had been weighing in the nearby mountains for several seasons. Then some bad guy introduced a new goat that was 3 pounds heavier than it. At first, they got along well with each other, but one day, the lighter goat stood on the steep side. On the top of the mountain road, it pounced on its rival, who stood on the mound to meet the challenge. Unfortunately, the challenger had the advantage of being on top. Unfortunately, both goats died due to the violent collision.

Now let’s talk about the wonder of this topic. George Abercrombie, who has done a lot of research on raising goats and has written books, said: “Through repeated experiments, I found that momentum is equivalent to a self. A single impact from a 30-pound object dropped from 20 feet would be enough to crush a goat's skull and kill it. "If he's right, then the two goats would have to have at least a certain closing speed to hit each other. Damn it? Can you figure it out?

18. It is said that someone posed a problem to the proprietress of the wine shop: This person knew that there were only two ladles for scooping wine, one that could scoop 7 taels and 11 taels respectively. He had two taels of wine, but he insisted on the landlady selling him 2 taels of wine.

The smart landlady was unequivocal. She scooped wine into the wine vat with these two spoons and poured it back and forth. She actually measured out 2 taels of wine. Can you do it?

19. Already Know: Each plane has only one fuel tank. The planes can refuel each other (note that they are mutual, there is no tanker). One tank of fuel can allow one plane to fly half a circle around the earth. Question: In order for at least one plane to fly around the earth once How many planes are needed to return to the airport where we took off? (All planes take off from the same airport and must return to the airport safely. Landing is not allowed. There is no airport in between)

20. Why are the sewer covers round?

21. To draw 10 straight lines on 9 points, each straight line must have at least three points?

22.12 balls and a scale. Now we know that only one weight is different from the others. How can we find the ball by weighing it three times? What about 13? (Note that this question does not indicate whether the ball is light or heavy, so careful consideration is required)

23. A fork in the road leads to the honest country and the lying country. Two people came, one was known to be from an honest country, and the other was from a liar country. An honest country always tells the truth, and a liar country always tells lies. Now you are going to Lie Country, but you don’t know which way to go. You need to ask these two people. What should I ask?

24. If you have an infinite amount of water, a 3-liter bucket and a 5-liter bucket. The shapes of the two buckets are uneven up and down. How can you accurately weigh 4 liters? of water?

25. You have a bucket of jelly, including yellow, green, and red. Close your eyes and grab two of the same color. How many do you need to grab to be certain that you have two jellies of the same color?

26. It is said that those who can answer this question within 20 minutes have an average annual salary of more than 80,000 US dollars. This is a very interesting reasoning question.

Detailed introduction:

In the United States, it is said that people who can answer this question within 20 minutes have an average annual salary of more than 80,000 US dollars. This is a very interesting reasoning question. According to statistics, people in the United States who can answer this question within 20 minutes have an average annual salary of more than $80,000. Five pirates grabbed 100 gems, each of which was the same size and priceless. They decided to divide it like this: 1. Draw lots to decide your own number (1, 2, 3, 4, 5) 2. First, No. 1 proposes a distribution plan, and then 5 people vote. If and only if half or more than half of the people agree, the distribution will be carried out according to his proposal, otherwise it will be thrown into the sea to feed the sharks. 3. If No. 1 dies, No. 2 will propose a distribution plan, and then the four of us will vote. If and only if half or more than half of the people agree, the distribution will be carried out according to his proposal, otherwise it will be thrown into the sea to feed the sharks. 4. And so on... Conditions: Every pirate is a very smart person who can rationally judge the gains and losses and make choices. Question: What distribution plan does the first pirate propose to maximize his profits?

27. In 24 hours a day, how many times do the hour, minute and second hands of the clock completely overlap? What time are they? How did you figure that out?

28. It takes ***1 hour to burn an uneven rope from beginning to end. Now there are several ropes made of the same material. How can we use the rope-burning method to time one hour and fifteen minutes?

29. In the dark night, four travelers came to a narrow bridge without guardrails. No one would dare to cross the bridge without the help of a flashlight. Unfortunately, the four people each brought only one flashlight, and the bridge was only narrow enough for two people to cross at the same time. If they cross the bridge alone, the time required for the four people is 1, 2, 5, and 8 minutes respectively; and if two people cross the bridge at the same time, the time required is the time required for the slower person to walk alone. time. The question is, how to design a plan to allow these four people to cross the bridge as quickly as possible.

There are 2 counterfeit coins among the 30.8 gold coins, and the 6 real gold coins weigh 500 grams each

One of the counterfeit coins is 100 grams lighter, that is, 400 grams

Another counterfeit currency weighed 100 grams, that is, 600 grams.

A scale without a scale, only weighing it four times to find two counterfeit coins, and you have to tell which one is heavier and which one is lighter.

31. Strange villages

There are two strange villages in a certain place. The people in Zhangzhuang lie on Mondays, Wednesdays and Fridays, and the people in Li Village lie on Tuesdays, Thursdays and Saturdays. On other days they tell the truth. One day, Wang Congming from out of town came here, saw two people, and asked them questions about dates. Both people said: "The day before yesterday was the day I lied." If the two people asked are from Zhangzhuang and Licun respectively, then what day of the week is this day?

32. Little monkey moving banana problem

There are 100 bananas next to a little monkey. It has to walk 50 meters to get home. Each time it can move up to 50 bananas, ( If there are too many, it will be crushed to death). It eats one banana every 1 meter it walks. How many bananas can it carry at most to your home? Tip: He can put the banana down and walk back and forth, but he must ensure that he can eat bananas every meter he walks. You can also walk n meters, put down some bananas, and walk back with n bananas to move 50 more bananas.

33. Water pouring problem

There are three cubes without lids. Regardless of the thickness of the container, the volumes are 1*1*1, 2*2*2, and 3*3*3. .

Requirements: 1. Use these three boxes to hold 13 cups of water

2. Each cup can only be filled with water once

3. No water should be wasted Dropped.

What is the method?

34. Wine sharing problem

(1)

There is an 8-liter bottle A cup full of wine and two small cups. Two people, A and B, want to share the 8 liters of wine equally. The way to make both people feel it is fair is for A to divide the wine equally into two small cups until he thinks he can choose no matter what. Until you don’t suffer any loss in any cup. Then let B choose the one he thinks is the most cost-effective among the two small cups. Give the remaining cup to A. Now there are two 8-liter glasses filled with wine and 4 small glasses. How should the four people ABCD divide them so that everyone feels fair?

(2)

There are three wine glasses, two of which can hold 8 taels of wine each, and one can hold 3 taels of wine. Now that the two large wine glasses are full of wine, how can the wine be distributed equally among four people using only these three glasses?

35. The classic hat problem (difficult to get, requires a process of jumping in thinking)

There is a cell with three prisoners in it. Because the glass is very thick, the three people can only see each other but cannot hear each other's voices. ”

One day, the king thought of a way and put a hat on each of their heads. He only let them know that the color of the hat was either white or black, but did not let them know what they were wearing. What color is the hat? In this case, the king announced two things as follows:

(1) Whoever can see that the other two prisoners are wearing white hats can be released;

(2) Anyone who knows they are wearing a black hat will be released.

In fact, the king gave them black hats because they were tied up and could not see themselves. That’s it. So the three of them stared at each other without saying anything. But soon, the smart person A used reasoning to determine that he was wearing a black hat. How did he infer?

36. One dollar banknote

Note: The coins in U.S. currency have denominations of 1 cent, 5 cents, 10 cents, 25 cents, 50 cents and 1 dollar. Please continue to read the text. , challenge the limits of your logical reasoning.

A small shop has just opened for business. There are only three male customers and one female shopkeeper in the shop. When the three men stood up to pay the bill at the same time, the following situation occurred:

(1) Each of the four men had at least one coin, but none of them had a face value of 1 cent or 1 cent. Dollar coins.

(2) None of the four people can redeem any coin.

(3) A man named Lou has the largest bill, a man named Mo has the second largest bill, and a man named Ned has the smallest bill. .

(4) No matter how every man pays the bill with the coins he holds, the female shopkeeper cannot find the change.

(5) If the three men exchange coins of equal value among each other, each person can pay his bill without giving change.

(6) When the three men made two exchanges of equal value, they found that none of the coins in their hands had the same face value as the coins they originally held.

As things further developed, the following situation emerged:

(7) After the bill was paid and two men left, the remaining man bought another got some candies. The man could have paid with the coins he had left, but the female shopkeeper couldn't make change with the coins she had.

(8) So the man paid for the candy with a dollar bill, but now the female storekeeper had to give him all her coins.

Now, please don’t worry about how the female shopkeeper had trouble getting change that day. Which of the three men paid for the candy with a $1 note

?

37. Problems with aircraft refueling

Known:

Each aircraft has only one fuel tank, and the aircraft can refuel each other (note that it is each other, there is no refueling) (Aircraft) One tank of fuel can power an airplane to fly half way around the earth.

Question:

In order for at least one plane to circle the earth and return to the airport where it took off, how many planes must be dispatched? (All planes take off from the same airport and must return to the airport safely. Landings are not allowed. There is no airport in between)

38. Coin question (recall question 4, what is the difference?)

16 coins, A and B take turns to take some, and the number taken each time can only be one of 1, 2, or 4.

Whoever takes the coin last loses.

Question: Does A or B have a strategy to ensure they win?

Assume they are all smart

39. Thirteenth Street

Smith lives on Thirteenth Street, the number of the house on this street It's from the 13th to the 1300th. Jones wanted to know the number of the house where Smith lived.

Jones asked: Is it less than 500? Smith replied, but he told a lie.

Jones asked: Is it a square number? Smith replied, but did not tell the truth.

Jones asked: Is it a cubic number? Smith answered and told the truth.

Jones said: If I know whether the second digit is 1, I can tell you the number of that house.

Smith told him whether the second digit was 1, and Jones told him what he thought the number was.

However, Jones was wrong.

What is the number of the house where Smith lives?

40. Sunny and rainy days

For a period of time, if it rained in the morning, it would be sunny at night; If it rained, it must be sunny in the morning. It rained for 9 days in one day, and there were 6 clear nights and 7 clear mornings. How many days did this period last?

41 .Three people guessing the number

Three people have a natural number written on their heads. Everyone can see the other two numbers, and they all know that the sum of two of the three numbers is equal to the third one

Now ask:

Does the first person know the number on his head? Answer: No

Does the second person know the number on his head? Answer: No

Does the third person know the number on his head? Answer: No

Does the first person know the number on his head? Answer: No

The second person Does the person know the number on his head? Answer: No

Does the third person know the number on his head? Answer: Yes, it is 144

Question: What should the other two numbers be? How many? (All three people are very smart)

42. Three Elves (The author of the question is a foreign professor. He once asserted that no one will be able to solve this question for a long time. It is indeed a classic Classic)

There are three elves A, B, and C. One of them only tells the truth, and the other only tells lies. Another randomly decides when to tell the truth and when to lie. You can ask three yes/no questions to these three elves, and each question can only be asked to one of the elves (you can ask all three questions to the same elf). Your task is to find out from their answers who is telling the truth, who is lying, and who is answering randomly. The hard part about this puzzle is that the elves will answer with "Da" or "Ja," but you don't know what they mean, only that one word means "right" and the other means "wrong." What are the three questions you should ask?

43. There are 100 people and ghosts, and it is difficult to distinguish them from the appearance. I only know that more than half of them are humans, and the rest are ghosts, and humans only tell the truth, while ghosts may tell the truth or lies. These 100 people (ghosts) all know whether each other is a human or a ghost.

Now you are asked to find one person among these 100 people (ghosts). You can only do this in the following way:

Pick out two people at a time and let them talk to each other. The identity of the other party is revealed, and you make a judgment based on their words.

How many times do you need to find a person as quickly as possible? (Be sure to consider the worst case scenario)

100 people and ghosts, refers to the number of people and the number of ghosts is equal to 100. This question is not a brain teaser

44. A and B both hold a piece of paper in their hands, and write a number on the paper. They only know that these two numbers are continuous natural numbers. Both A and B You can see the other person's number, but you can't see your own number. A asks B: Do you know what the number on my hand is? B says: I don't know. B then asks A back, then do you know what the number on my hand is? What is the number? A also said he didn’t know. A asked B again: Do you know what the number on your hand is? B also said he didn’t know. B asked A again, now you know what is written on your hand. What is the number? A said, I understand. What is the number on the hands of A and B?

45. Three young men fell in love with a girl at the same time, in order to decide who of them can marry This girl, they decided to have a duel with pistols. Xiao Li's hit rate is 30%, Xiao Huang is better than him, his hit rate is 50%, the best shooter is Xiao Lin, he never makes mistakes, his hit rate is 100%. Because of this obvious fact, for the sake of fairness, they decided to go in this order: Xiao Li shot first, Xiao Huang second, and Xiao Lin last. And then cycle like this until they only have one person left. So who among these three has the best chance of survival? What strategies should they all adopt?

46. There is a man who has 240 kilograms of water, and he wants to transport it to drought areas to make money.

He can carry up to 60 kilograms at a time and consume 1 kilogram of water for every kilometer he travels (average water consumption). Assume that the price of water is 0 at the departure point, and then it is proportional to the transportation distance (that is, it is 10 yuan/kg at 10 kilometers, 20 yuan/kg at 20 kilometers...), and assume that he He must return safely. How much money can he make at most?

47. There are several planes in an airport. Each plane can go around 1/3 of the Earth's equator with a full tank of fuel. Fuel can be transferred between planes by air. How many planes can be arranged to take off at least to ensure a safe flight? A plane can circle the earth once and return to the airport without touching the ground, provided that all planes cannot crash and can only land at the airport

48. There are 100 seats on the plane, numbered from 1 to 100 in sequence. There are 100 passengers. They have been assigned seats from 1 to 100. They board the plane in order of numbers and should take their seats. If they find that the corresponding seat is occupied by someone else

, he will choose any of the remaining empty seats to sit. Now if passenger No. 1 is crazy -_-! (the others are not crazy), he will

sit in a random seat among the 100 seats. So what is the probability that the 100th person sits in his seat correctly?

49. Once, a ship encountered a storm at sea. In order to reduce the weight of the boat, the option presented to the 25 passengers was to throw some of them overboard. In this way, the ship and the remaining people might still be saved. No one wants to jump into the sea automatically. There were 11 religious people among the passengers, and one of them came up with an idea. He asked all 25 people to sit in a circle, and then counted "1, 2, 3" in sequence. It was stipulated that the person who reported "3" would be thrown into the sea. The final count showed that 14 people were thrown overboard. The rest are these 11 believers. So, how did he arrange the positions of these remaining ones

50. There is a bacterium that divides into 2 in 1 minute, and then divides into 2 again in 1 minute. The total number of divisions is 4. In this way, it takes 1 hour for one bacterium to divide into a full bottle. If the same bacteria divides from 2, it will take several minutes to divide into a bottle

51. A mechanic went to the warehouse to pick up gasoline. The custodian pointed to a row of six oil barrels on the shelf and said: "These six barrels contain gasoline, diesel, and engine oil respectively. You are not allowed to look inside the barrels, and you are not allowed to smell them. Just look at the quantities marked on the barrels. The quantities are: 15 liters, 16 liters, 18 liters, 19 liters, and 20 liters. Liter, 31 liters. He also told you that the engine oil is only half of the diesel, and there is only one barrel of gasoline left." If it were you, which bucket should you carry? Why carry that bucket?

52. One day, a valuable diamond was stolen from a jewelry store. After investigation, it was found that the perpetrator must be among A, B, C and D. As a result, these four major suspects were interrogated. The confession obtained during the interrogation is as follows:

A: I did not commit the crime.

B: Ding is a criminal.

C: B is the criminal who stole the diamond.

Ding: I was not the one who committed the crime.

It was verified that only one of the four people’s confessions was false. So, which of the following is the correct result of solving the crime?

(A) A committed the crime.

(B) B committed the crime.

(C) C committed the crime.

(D) Ding committed the crime.

(E) A, B, C, and Ding committed the crime together

53. An ancient king and his five generals Zhang, Wang, Li, Zhao, and Qian We went hunting together, and everyone's arrows were engraved with their own surnames. While hunting, a deer fell down with an arrow, but it was unknown who shot it.

Zhang said: "Either I shot it, or General Li shot it."

Wang said: "It was not General Qian who shot it."

Li said: "If it was not shot by General Zhao, then it must have been shot by General Wang."

Zhao said: "It was neither me nor General Wang who shot it. "

Qian said: "It was neither shot by General Li nor General Zhang.

"

The king asked someone to bring the arrow that had hit the deer, looked at it, and said, "Only two of your five generals' guesses are true." "Based on what the king said, which of the following is true?

(A) General Zhang shot the deer.

(B) General Wang shot the deer.

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(C) General Li shot the deer.

(D) General Zhao shot the deer.

(E) General Qian shot the deer. /p>

54. There is a pasture with 27 cows and it is known that the grass will be eaten in 6 days; if 23 cows are raised, the grass will be eaten in 9 days. If 21 cows are raised, how many days will it take to finish the pasture? What about when all the grass is eaten?

55. There are 23 coins on the table, 10 of them face up. Suppose someone blindfolds you and yours. You can't find the reverse side of the coins with your hands. Let's use the best method to divide these coins into two piles, with the same number of coins facing up in each pile.

56. Two hollow balls, the same size. The weights are the same, but the materials are different. One is gold and the other is lead. The surface of the hollow sphere is painted with the same color. Now it is required to use a simple method to indicate which one is gold and which one is lead without damaging the surface paint.

57. There is a large watermelon. Use a fruit knife to cut it flatly. The total number of cuts is 9 knives. How many parts can it be cut into at most and how many parts can it be cut at the minimum?

58.100 people answered five test questions. 81 people answered the first question correctly, 91 people answered the second question correctly, 85 people answered the third question correctly, 79 people answered the fourth question correctly, 74 people answered the fifth question correctly, and three or three questions were correct. The people above the question are considered to have passed. So, among these 100 people, at least how many people have passed?

59. Now there are 100 horses and 100 stones. There are three types of horses, large horses. , medium-sized horses and small horses. One big horse can carry 3 stones at a time, and two small horses can carry one stone. How many large horses and small horses are needed? ( The key to the problem is that it must be exactly 100 horses)

60. A ball and a ruler whose length is about 2/3 of the diameter of the ball. How do you measure the radius of the ball? There are many methods? , see whose one is more clever.