2. A manager has three daughters, and their ages add up to 13, which is equal to the manager's own age. A subordinate knows the manager's age, but still can't determine the age of the manager's three daughters. At this time, the manager said that only one daughter's hair was black, and then the subordinates knew the age of the manager's three daughters. What are the ages of the three daughters? Why?
3. Three people went to a hotel and stayed in three rooms. Each room cost $65,438+00, so they paid the boss $30. The next day, the boss thought that $25 was only enough for three rooms, so he asked my brother to return $5 to three guests. Unexpectedly, my brother was insatiable, and only returned 1 USD each, and secretly took it away by himself. But at the beginning, the three of them paid 30 dollars, so 1 dollar?
4. There are two blind people. They all bought two pairs of black socks and two pairs of white socks. Eight pairs of socks are made of the same cloth, the same size, and each pair of socks is connected with trademark paper. Two blind people accidentally mixed up eight pairs of socks. How can each of them get back two pairs of black socks and two pairs of white socks?
5. One train leaves Los Angeles for new york at a speed of 15km/h, and the other train leaves new york for Los Angeles at a speed of 20km/h ... If a bird starts from two trains at a speed of 30 km/h, meets another train and returns, and flies back and forth in turn until the two trains meet, how long does it take for the bird to fly?
6. You have two cans, 50 red marbles and 50 blue marbles. Choose a jar at random and put a marble in the jar at random. How can we give red marbles the best chance to be selected? What is the exact probability of getting the red ball in your plan?
7. You have four jars containing pills, and each pill has a certain weight. The contaminated pill is the uncontaminated weight+1. You only weigh it once. How do you know which jar is polluted?
8. You have a bucket of jelly, including yellow, green and red. Close your eyes and grab two jellies of the same color. How many can you catch to make sure you have two jellies of the same color?
9. For a batch of lamps numbered 1 ~ 100, all switches are turned on, and the following operations are carried out: rotate in the opposite direction every multiple of 1; A multiple of 2 toggles the switch in the opposite direction again; A multiple of 3 turns the switch in the opposite direction again ... Q: Finally, the number of lights in the off state.
10. Imagine you are in front of the mirror. Excuse me, why can the image in the mirror be upside down, but not upside down?
1 1. A group of people are dancing, and everyone is wearing a hat. There are only two kinds of hats, black and white, and there is at least one kind of black. Everyone can see the color of other people's hats, but not their own. The host first shows you what hats others are wearing, and then turns off the lights. If someone thinks he is wearing a black hat, he will slap himself in the face. The first time I turned off the lights, there was no sound. So I turned on the light again and everyone watched it again. When I turned off the light, it was still silent. I didn't get a slap in the face until I turned off the light for the third time. How many people are wearing black hats?
12. Two rings with radii of 1 and 2 respectively. The small circle goes around the big circle. How many times does the small circle turn by itself? If it is outside the big circle, how many times does the small circle turn by itself?
13. If one beer can be exchanged for every three empty beer bottles, how many bottles of beer can someone drink if he buys 10 beer?
Known as the most difficult interview question in the world!
Source: Zuo An Date of Reading: 20 10-05-2 1 Answer:
1. A Xiang lights one end and item lights both ends. By the time incense B burned out, it was already 30 minutes. Then ignite the other end of incense A, and the time from this time to burning A is 15 minutes.
2. The three girls should be 2 years old, 2 years old and 9 years old. Because only one child has black hair, that is, only she has grown up, and the other two are still very young, that is, less than 3 years old, with light hair. The reorganization manager should be at least 25 years old.
3. Typical concept of stealing. In fact, three people only went out of 27 yuan, the eldest got 25 yuan and the younger got 2 yuan.
4. Unpack each pair of socks, one for each person.
5. Suppose the length of the railway from Los Angeles to new york is one kilometer. Then it took A/( 15+20) hours for the two trains to meet, which is the time for birds to fly. So the distance a bird flies is the length of the railway from L.A. to new york, and the speed × time =30×A/35=6/7.
6. 1/2 probability. Choose the ball first, then the jar. This jar has no effect on the color of the ball.
7. Take out 1 capsules from the No.2 tank, 2 capsules from the No.3 tank and 4 capsules from the No.4 tank, and weigh out 1 capsules. If it is heavier than normal weight, there is something wrong with the medicine in tank 2.
8. Four. Quantity > color category. Colors must be repeated.
9. There are 10 lights, namely 1, 4, 9, 16, 25, 36, 49, 64, 8 1, 100. Because every prime number can be divisible by 1 and itself, the prime number light is on. Let a composite number be divisible by n, and n must be an even number. For the composite number other than one party, it will be switched on and off for n times, that is, even times, and the light will remain on; The square number listed above was only switched N- 1 times, so the light went out.
10. The mirror symmetry axis is the central axis of human beings.
1 1. Three people are wearing black hats. Suppose there are n people wearing black. When N= 1, the person wearing black can determine that he is black when he sees that everyone else is white. So when the lights are turned off for the first time, there should be a sound. It can be concluded that N> 1. For everyone who wears black, he thinks he is white when he sees the black hat of N- 1. But after waiting for N- 1 times and no one hits himself, every black person can know that he is black. So when the lights were turned off for the nth time, n people hit themselves.
12. No matter inside or outside, the small circle turns twice.
13. After drinking 10 bottles, you can exchange 9 empty bottles for 3 bottles of beer (there are 4 empty bottles after drinking). After drinking these three bottles, you can exchange them for 1 bottle of beer (there are two empty bottles after drinking).
At this time, he has two empty bottles. If he can borrow an empty bottle from the boss first, he can make up three empty bottles and exchange them for a beer. After drinking this bottle of wine, he can return the empty bottle to the boss.
So he can drink10+3+1+1=15 bottles at most.
Interview question: test your intelligence!
Source: Zuo An's study date: 20 10-05-2 1
Puzzle 1 (pirates divide gold coins)
After five pirates robbed 100 gold coins, they discussed how to distribute them fairly. Their agreed distribution principle is: (1) draw lots to determine everyone's distribution sequence number (1, 2, 3, 4, 5); (2) Pirates who draw lots. 1 Propose a distribution plan, and then five people will vote. If the plan is agreed by more than half of the people, it will be distributed according to his plan, otherwise 1 will be thrown into the sea to feed sharks; (3) If 1 is thrown into the sea, No.2 puts forward the allocation plan, and then four people are left to vote. If and only if more than half of the people agree, they will be allocated according to his proposal, otherwise they will be thrown into the sea; 4 and so on. Assuming that every pirate is extremely intelligent and rational, they can make strict logical reasoning and rationally judge their own gains and losses, that is, they can get the most gold coins on the premise of saving their lives. At the same time, assuming that the results of each round of voting can be implemented smoothly, what distribution scheme should the pirates who have drawn 1 put forward to avoid being thrown into the sea and get more gold coins?
Puzzle 2 (guessing cards)
Mr. S, Mr. P and Mr. Q know that there are 16 playing cards in the desk drawer: hearts A and Q, 4 spades J, 8, 4, 2, 7, 3 flowers K, Q, 5, 4 and 6 diamonds A and 5. Professor John chooses a card from 16 card, tells Mr. P the number of points in this card, and tells Mr. Q the color of this card. At this time, Professor John asked Mr. P and Mr. Q: Can you infer what this card is from the known points or colors? 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. Sir: Now I know this card. Mr. Q: I know that, too. After listening to the above conversation, Mr. S thought about it and correctly deduced what this card was. Excuse me: What kind of card is this?
Puzzle 3 (rope burning problem) It takes 1 hour to burn an uneven rope from beginning to end. Now several ropes are made of the same material. How to time an hour and fifteen minutes by burning rope?
Problem 4 (Table Tennis Problem)
Suppose there are 100 ping-pong balls arranged together, and two people take turns to put the balls in their pockets. The winner is the person who can get the100th table tennis. The condition is: the person who holds the ball must take at least 1 at a time and not more than 5 at most. Q: If you are the first person to take the ball, how many should you take? How can I take it in the future to ensure that you can get the100th table tennis?
Puzzle 5 (Drink soda) 1 Yuan for a bottle of soda. After drinking two empty bottles, change one bottle of soda. Q: How many bottles of soda can you drink at most if you have 20 yuan money?
Puzzle 6 (Divide gold bars) You let the workers work for you for 7 days, and the workers' reward is a gold bar. Gold bars are divided into seven consecutive parts. At the end of each day, you must give them some gold bars. If you are only allowed to break the gold bars twice, how can you pay the workers?
Puzzle 7 (Gui Gu Kao Tu) Sun Bin and Pang Juan are both disciples of Gui Gu Zi; One day, the ghost came up with a problem: he chose two different integers from 2 to 99, told Sun the product and told Pang the sum. Pang said: I'm not sure what these two numbers are, but I'm sure you don't know what these two numbers are either. Sun said: I really didn't know at first, but after listening to your words, I can confirm these two figures now. Pang said, since you put it that way, I know what these two numbers are. What are these two numbers? Why?
Puzzle 8 (Wine Picking Puzzle) It is said that someone gave the proprietress of a restaurant a puzzle: this person knew that there were only two spoons in the shop, and they could scoop 7 taels and 1 1 taels respectively, but forced the proprietress to sell him 2 taels of wine. Smart proprietress is also unambiguous. She used these two spoons to hold the wine, turned it upside down and actually measured out 2 ounces of wine. Can you be smart?
Puzzle 9 (Five Prisoners)-A puzzle that really stumbles hundreds of millions of people. This is an interview question for Microsoft. Five prisoners, according to 1-5, caught mung beans in sacks containing 100 mung beans. It is stipulated that everyone should catch at least one, and those who catch at most and at least should be put to death. And they can't communicate with each other, but when they catch, they can find out the remaining number of beans. Ask them who has the greatest chance of survival: 1. They are all very smart people. 2. Their principle is to save lives first, and then kill 3 100 more. You don't have to share all four. If there is any duplication, it will be regarded as maximum or minimum, and it will be implemented together.
Puzzle 10 (The King and the Prophet) Before going to the execution ground, the king said to the prophet, "Aren't you good at predicting?" Why can't you predict that you will be executed today? I'll give you a chance, and you can predict how I will execute you today. If your prediction is right, I will let you take poison to death; Otherwise, I will hang you. " But the wise prophet's answer made it impossible for the king to execute him anyway. How did he predict it?
Puzzle 1 1 (strange village) There are two strange villages somewhere. People in Zhangzhuang lie on Mondays, Wednesdays and Fridays, while people in Licun lie on Tuesdays, Thursdays and Saturdays. On other days, they tell the truth. One day, Wang Congming from other places came here, met two people and asked them questions about the date. Both of them said, "The day before yesterday was the day when I lied." If the two people asked are from Zhangzhuang and Licun, what is the date?
Puzzle 12 (Who stole the captain's ring? The British cargo ship Elizabeth sailed for Japan for the first time. In the early morning, the cargo ship entered Japanese territorial waters. As soon as Captain David got up, he arranged the entrance and left a diamond ring in the captain's room. 15 minutes later, when he returned to his master's room, he found the ring missing. The captain immediately called the chief officer, sailors, flag bearers and chefs who were on duty at that time for questioning, but these crew members denied having been to the captain's room. Everyone claimed that they were not at the scene. Chief mate: "I broke my glasses. Go back to my room and change a pair. I must have been in my room then. " Sailor: I'm busy salvaging the lifebuoy. Flag-bearer: I hung the flag upside down and I was about to put it back. Chef: I'm repairing the refrigerator. ""Did the ring fly? "David, who likes detective stories at ordinary times, found out the liar according to their respective statements and mutual testimony. Facts have proved that this liar is a criminal!
Puzzle 13 (ball problem) 12 ball and a balance. Now we know that only one is different from the others in weight. How can we find the ball after weighing it three times? Note that this problem does not indicate whether the weight of the ball is light or heavy, so it needs careful consideration. )
Interview question: test your intelligence!
Source: Zuo An Reading Date: 20 10-05-2 1 Reference Answer:
1. Question 1:
1:96 2:0 3
:0 4:2 5:2
First of all, when voting on the proposal of 3, 4 will support 3, because otherwise he will die against 5.
Therefore, if 1 2 dies, the scheme of 3 must be 100, 0, 0, and it will be supported by 3 and 4. At this time, the payoffs of 4 and 5 are 0, so 1 2 can bribe 4 and 5 to get support.
At the same time, the expected return of 3 is 100, and he will be desperate to oppose 1 2.
And if 1 dies, the scheme of 2 must be 98,0, 1, 1, and it will definitely pass.
Therefore, the optimal scheme of 1 is 96,0,0,2,2, which will definitely pass.
In fact, 98, 0, 0, 1, 1 are also possible, and they may all pass (depending on the mood and cruelty of 4 and 5).
2. The second question:
The first sentence of p means that the number of points is one of a, q, 5 and 4.
Q: The first sentence indicates that the color is hearts or diamonds.
The second sentence of p means it is not a.
The second sentence of q can only be box 5.
Answer: Box 5
3. The third question:
Take three ropes.
First light both ends of the first root and light one end of the second root at the same time. (t=0)
When the first one burns out, light the other end of the second one. (t = 30 minutes)
When the second root burns out, light the two ends of the third root. (t = 45 minutes)
When the third root burns out, t = 75 minutes.
4. The fourth question:
Take four first.
Then if the opponent takes 1 5, I will take 5 1. So in any case, the number of balls left is 6n, N minus 1. Finally, I just got six balls, and then I won.
5. Question 5:
39 bottles
20->； 10->； five
Take four bottles for two bottles, another bottle, this empty bottle and 5-4 empty bottles for another bottle. 20+ 10+5+2+ 1+ 1=39
6. Question 6:
After thinking for a long time, I didn't understand it, so I looked for the answer online. It turned out to be ...
In my answer, I think the gold bars given can be recovered. Obviously, I think workers are idealistic workers. They don't need to eat or spend ... I can't remember ... (Gold bars are divided into 1, 2,4, which is a bit like our paper money only needs 1, 2,5 to handle all the change problems! )
7. Question 7:
It seems to be (4, t), where t = 7, 13, 19, 23, 3 1 37, 43, 53, 6 1 67, 73, 79, 83, 9.
8. Question 8:
Fill up 7, pour it into 1 1, fill it up again, and fill it up to 1 1. At this time, there are 3 left in 7.
Empty 1 1, pour 3 of 7 into 1 1, and then fill 7 into 1 1. At this time 1 1 Yes 10.
Fill it up with 7, and it will be 1 1, and there will be 6 left in 7.
Empty 1 1 again and pour 6 out of 7 into 1 1.
Fill it up with 7 to 1 1. At this time, there are 2 left in 7.
9. Question 9:
The person who made this rule must be a fascist. ...
Wait, let me answer question 10. ...
This question is really difficult. ...
10. Question 10:
"You won't poison me."
1 1. Question 1 1:
It can also be exhaustive.
Monday.
12. Think independently
13. First, it is proved that if there are three balls P 1, P2 and P3 are all satisfied, and P 1 is heavier, or one of P2 and P3 is lighter and has two standard balls, then the one with different quality can be found by using the balance. In fact, if P 1 and P2 are compared with the standard ball, P3 is lighter; If the sum of P 1 and P2 is greater than the standard ball, P 1 is heavier; If P 1 and P2 are smaller than the standard ball, P2 is lighter. Similarly, P 1, P2, P3 satisfy that either P 1 is light or P3 P2 is heavy, and non-standard balls can be found at one time.
Divide into three batches (marked as group A, group B and group C), with 4 in each batch, and weigh two batches of A and B.. If it is balanced, balls with different qualities are in Group C, and they can be found twice (compare two balls with standard balls first; If it is balanced, compare one of the remaining two with a standard ball; If it is not balanced, compare one with the standard ball. If it is unbalanced (it may be assumed that Group A is lighter than Group B), then Group C is the standard ball. Arrange a and b as follows
1234
A○○○
B○○○
Take A 1, A2, B1(Group A') and A3, A4 and B4 (Group B') and weigh them on both sides of the balance respectively. If group A' is lighter than group B', either A 1, A2 is lighter or B4 is heavier. From the previous proof, the third weighing can find out the different quality. If Group A is heavier than Group B, either B 1 is heavier or A3 and A4 are lighter, you can also find the one with different quality. If it is balanced and B2 and B3 are heavier, you can find the heavier two by putting them at both ends of the balance.