The novel Don Quixote describes a country with strange laws. Every tourist has to answer a question: "What are you doing here?" The answer is right, everything is easy; If you answer wrong, you will be hanged.
One day, a tourist replied, "I came here to be hanged."
The tourists were sent to the king. The king thought hard for a long time: Is his answer right or wrong? Whether to hang him or not. If his answer is right, don't hang him, but in this way, his answer is wrong again! If he says his answer is wrong, he will be hanged, but it just proves that his answer is right. It's really a dilemma!
2. Prophecy of Brahma scholars
One day, Brahma scholar and his daughter Su Ye had an argument.
Su Ye: You are a big liar, Dad. You can't predict the future at all
Scholar: I believe I can.
Su Ye: No, you can't. I can prove it now!
Su Ye wrote some words on a piece of paper, folded it up and pressed it under a crystal ball. She said:
"I wrote a thing that may or may not happen before 3 o'clock. Please predict whether it will happen, and write "Yes" or "No" on this white card. If you make a mistake, will you promise to buy me a car now and not delay it later? "
"Ok, it's a deal." The scholar wrote a word on the card.
At 3 o'clock, Su Ye took out the paper under the crystal ball and read aloud: "Before 3 o'clock in the afternoon, you should write a' no' on the card."
The scholar wrote the word "yes" on the card, and his prediction was wrong: "Writing a word" no "on the card before 3 pm did not happen. But what if he wrote "no" on the card? Not right either! Because writing "no" means that he predicted that what happened on the card would not happen, but it happened like this-he wrote a "no" on the card.
Su Ye smiled: "Dad, I want a red racing car with a bucket seat."
3. An unexpected tiger
The princess wanted to marry Mike, and the king made a condition:
"Honey, if Mike kills the tiger hidden behind these five doors, you can marry him. Mike must open the doors in order, starting with gate 1. He didn't know in advance which room had a tiger until he opened the door. The appearance of this tiger will be unexpected. "
Mike looked at the door and said to himself:
"If I open the doors of four empty rooms, I will know that the tiger is in the fifth room. But the king said that I couldn't know where it was in advance, so the tiger couldn't be in the fifth room. "
"Five have been ruled out, so the tiger must be in the first four rooms. Similarly, the tiger will not be in the last room-the fourth room. "
In the same way, Mike proved that the tiger can't be in the third, second and first room. Mike was so happy that he went to see the door with confidence. To his horror, the tiger jumped out of the second room.
Mike's reasoning is not wrong, but he failed. The appearance of the tiger was completely unexpected, indicating that the king kept his promise. Perhaps Mike's reasoning itself contradicts the king's condition that the tiger is "unexpected". So far, logicians have not reached an agreement on where Mike is wrong.
4, wallet game
Professor Smith has lunch with two students. The professor said, "Let me tell you a new game. Put your wallets on the table and I'll count the money inside. People with less money can win back all the money in another wallet. "
Student A thought, "If I had more money, I would lose it." If he has more money, I will win more money than I do. So winning is more than losing, and this game is good for me. "
Similarly, student B thinks the game is good for him.
How can a game benefit both sides?
5. Where did the dollar go?
In a record store, sell 30 old-fashioned hard records, two for one dollar; The other 30 soft records are all three for one yuan. On that day, these 60 records were sold out. The income of 30 hard records is 15 yuan, and the income of 30 soft records is 10 yuan. Total income 25 yuan.
The next day, the boss took out more than 60 records. He thought, "If 30 records 1 USD sell two, and 30 records 1 USD sell three, why not put them together and sell five records for 2 dollars?" On this day, all 60 records were sold for $2.05. The boss paid some money and found that he only sold 24 yuan, not 25 yuan.
Where did this dollar go?
6. Amazing coding
Mr. Kita, an alien scientist, came to the earth to collect human data and met Dr. Herman.
Herman: "Why not get back a set of Encyclopedia Britannica?" ? This set of books sums up all our knowledge most comprehensively. "
Jita: "Unfortunately, I can't carry such a heavy thing. However, I can code the whole encyclopedia and then just mark this metal bar, which represents all the information in the encyclopedia. " It couldn't be simpler!
How did Mr. Kita do it?
Keita: "I first use numbers to represent each letter, number and symbol, and separate them with zeros." . For example, the code of the word cat is 3-0- 1-0-22. I can scan quickly with an advanced pocket computer and turn all the contents of the encyclopedia into a huge number. Add a decimal point before it to make it a decimal point, such as 0,2015015011 ...
Mr. Kita found a point on the metal bar, which divides the metal bar into two parts, A and B, and A/B is exactly equal to the decimal part above.
Kita: "When you go back, measure the values of A and B, and you can work out their ratio." According to the code, your encyclopedia was deciphered. "
In this way, Kita left the earth with only a metal bar, but he has already "returned with a full load"!
7, can't escape.
Mr. Pat went up the hill along a path. He set out at seven in the morning and reached the top of the mountain at seven that night. The next morning, I took the same road, returned to the foot of the mountain at seven o'clock in the evening, and met Klein, the topology teacher.
Klein: "Pat, did you ever know that you passed such a place when you went down the mountain today, and the moment you passed this point was exactly the same as the moment you passed this point when you went up the mountain yesterday?"
Pat: "That's impossible! I walk fast and slow, and sometimes I stop to have a rest. "
Klein: "When you start going downhill, imagine that you have a body body double and start climbing at the same time. The climbing process of double body is exactly the same as when you climbed yesterday. You and this body double are destined to meet. I can't say where you met, but there must be such a thing. "
Pat got it. Are you clear?
8. bugs on rubber ropes
Rubber rope 1 km long, with a bug at one end. Worms crawl along the rubber rope at a steady speed of 1 cm per second; Rubber rope is stretched every 1 sec 1 km. If this continues, will the worm finally come to an end?
At first glance, with the stretching of the rubber rope, the worm is farther and farther away from the finish line. But careful readers will think that the worm will move forward with every stretch of the rubber rope.
If expressed by mathematical formula, the position where the worm is not on the rubber rope at the nth second is expressed as the whole rope. The score is (the derivation process is omitted):
When n is large enough (about e 100000), the value of the above formula exceeds 1, indicating that the worm has climbed to the end.
9, tricky lighting
An electric light that is switched by a button. Suppose you turn on the light for one minute, then turn off the light for half a minute, then turn on the light for 1/4 minutes, then turn off the light for 1/8 minutes, and so on. This process ends in exactly two minutes.
So, at the end of this process, is the light on or off? This question is really difficult!
10, Russell paradox
One day, a barber put up a sign: "I cut my hair for all the people in the village who don't cut their own hair. I only cut their hair for these people." So someone asked him, "Who will cut your hair?" The barber was speechless at once. Because if he cuts his own hair, it belongs to the category of cutting his own hair. However, the sign says he doesn't want this hairstyle, so he can't cut his own hair. If another person cuts his hair, he is the one who doesn't cut his own hair. The sign says that he will cut all those who don't cut his own hair, so he should cut his own hair. It can be seen that no matter what inference is made, what the barber says is always contradictory. This is a famous paradox called "Russell Paradox". This was put forward by the British philosopher Russell, who expressed a famous paradox about set theory in a popular way. 1874, the German mathematician Cantor founded the set theory, which soon penetrated into most branches and became their foundation. By the end of 19, almost all mathematics was based on set theory. At this time, some contradictory results appeared in set theory, especially the proposition of "Russell Paradox" in 1902, which is extremely simple and easy to understand. In this way, the foundation of mathematics has been shaken passively, which is the so-called third "mathematical crisis". Since then, in order to overcome these paradoxes, mathematicians have done a lot of research work, produced a lot of new achievements and brought about changes in mathematical concepts.
1 1, God is not omnipotent.
Prove by reduction to absurdity: if God is omnipotent, then God can be a stone that he can't lift, otherwise God is not omnipotent; But God can't move this stone, so God is not omnipotent, which contradicts the hypothesis. So the original assumption is untenable, that is, God is not omnipotent.