→ A manager has three daughters, the ages of which add up to 13, and the ages of the three daughters add up to the manager's own age. A subordinate knows the manager's age, but he still can't determine the ages of his three daughters. At this time, the manager said that only one daughter's hair was black, and then the subordinates knew the ages of the three daughters. What are the ages of the three daughters? Why?
→ 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. I didn't expect my brother to be greedy, so he only paid back 1 dollar and secretly took 0 $ by himself. But at the beginning, the three of them paid 30 dollars, so 1 dollar?
There are two blind people. They all bought two pairs of black socks and two pairs of white socks. Eight pairs of socks are all made of the same cloth and the same size, and each pair of socks is labeled 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?
→ Three people share a biscuit (with a knife). How to divide it so that all three people are satisfied? (Rational distribution problem)
→ Table tennis 12, one is not up to standard, I don't know whether it is light or heavy. Weigh the ball three times to find the bad ball. ("Ping-pong" problem)
On one occasion, a jewelry store in the capital of a country was robbed of a diamond worth 5000 dollars by thieves. After several months of investigation, it is certain that one of the four people, A, B, C and D, committed the crime. As a result, the four men were arrested and put on trial as the main suspects. There are some contradictory contents in the confessions of the four people:
I didn't commit a crime: D is the criminal. C:B is the criminal who stole this diamond. D:B set me up on purpose
Now, we know that only one of the four people told the truth. Then ask: Who is the criminal? ("True or False" Question)
You have a bucket of jelly, 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?
→ Perform the following operations on a batch of lamps numbered 1 ~ 100, and turn them all on: turn the switch 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.
Imagine you are in front of a mirror. Excuse me, why can the image in the mirror be upside down, but not upside down?
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?
→ Five pirates robbed 100 jewels, each of which was the same size and priceless. They decided to divide it like this: first, draw lots to decide their own numbers (1, 2, 3, 4, 5); Step 2: First, 1 puts forward the distribution plan, and then five people vote. If and only if more than half of the people agree, they will be distributed according to his proposal, otherwise they will be thrown into the sea to feed sharks. Step 3: After the death of 1, the distribution plan will be put forward on the 2nd, and then four people will vote. If and only if more than half of the people agree, they will be distributed according to his proposal, otherwise they will be thrown into the sea to feed sharks; The fourth step, and so on.
Question: What is the final distribution result?
Tip: The principle of judging pirates: 1. Get as many gems as possible on the premise of saving your life.
2. Kill as many people as possible on the premise of getting the same number of gems.
("Nash equilibrium" problem)
In a remote mountain, there is a village. Here, women are in power, and women have the final say in everything. There are 100 couples in the village.
The village has formed established rules. If a woman finds out that her husband is unfaithful to her, she will not hesitate to kill him and execute him the same day. Of course, she must have definite evidence to prove that her husband is unfaithful. Because of this factor, a woman finds out that a man is unfaithful, and she won't tell the unfaithful man's wife. However, she will tell other people's wives that women will pass this message to each other, so in the end, a man is unfaithful, and all other women know it except his wife.
In fact, every man in the village 100 is unfaithful, but every woman doesn't know that her man is unfaithful because she won't tell his wife what she knows. Therefore, the village has been very stable, and there has never been a case in which a wife killed her husband.
In the village, there is an old lady with high seniority. She is respected, honest and respectable. Because everyone reported the situation in the village to her, she knew everything about the situation in the village. She knows that every man is unfaithful.
One day, the old man said a very common sentence to these 100 women: "At least one of you men is unfaithful." So, this happened in the village: in the first 99 days, the village was calm, but on the first100th day, there was a massacre in the village, and all the women killed their husbands.
Why is this? This is a question about public knowledge.
→ There are two adjacent islands AB in the Pacific Ocean. The residents of island A are honest people, while the residents of island B are liars. When you ask a question, the residents of Island A will tell you the correct answer, while the residents of Island B will give you the wrong answer. One day, a tourist boarded one of the two islands alone. He can't tell whether the island is an island or an island, except that people on this island have both residents and tourists from another island. He wanted to ask the people on the island, "Is this Island A or Island B?" But it is impossible to judge whether the interviewee's answer is correct. The tourist thought for a while and finally came up with a solution. He only needs to ask anyone he meets a word, and he can accurately judge which island it is from the other person's answer. Can you guess the questions asked by tourists? ("Asking for directions")
→ A row of five rooms with five different colors;
There is a person of different nationalities living in each room;
Everyone is drinking a certain brand of drinks, smoking a certain brand of cigarettes and keeping a pet;
No two people smoke the same brand of cigarettes, drink the same brand of drinks or keep the same pet.
Question: Who keeps fish as pets?
Einstein gave the following clues:
English people live in red houses;
Swedes keep dogs as pets;
Danes drink tea;
The green house is next to the white house, on the left of the white house;
The owner of the green house drinks coffee;
People who smoke Bellevue cigarettes raise birds;
People in the yellow house smoke Dunhill cigarettes;
People who live in the middle house drink milk;
Norwegians live in the first house;
Smokers are adjacent to cat owners;
The owner of the horse is adjacent to the person who smokes Dunhill cigarettes;
People who smoke BlueMaster cigarettes and beer;
Germans smoke prince cigarettes;
Norwegians live next door to people who live in blue houses;
People who smoke mixed cigarettes are adjacent to people who drink mineral water.