1 Suppose there is a pond with infinite water. At present, there are two empty kettles with a capacity of 5 liters and 6 liters respectively. The problem is how to get 3 liters of water from the pond with only these two kettles.
Pour from full 6 to empty 5, leaving 65,438+0 liters. Pour this 65,438+0 liter into 5, then 6 is full, and then pour 5. Because there is 1 liter of water in 5 Li, 6 can only pour 4 liters of water into 5 Li, then pour the remaining 2 liters of 6 into the empty 5 Li and fill it up with 6 to 5.
Pour 3 liters into the jar, leaving 3 liters.
Zhou Wen's mother is a chemist in Yulin Cement Plant. One day, Zhou Wen came to the laboratory to do his homework. I want to go out to play when I'm done. "Wait, mom wants to test you on a topic," she continued. "Look at these six laboratories.
The front three cups are full of water, and the back three cups are empty. Can you just move 1 cup and separate the cup filled with water from the empty cup? "Zhou Wen, who loves to think, is a famous cleverness in the school. she
I just thought about it for a while and then did it. Please think about it, how does "cleverness" work?
Let the number of cups be ABCDEF, ABC be full of DEF and empty, and just pour the water in B into E.
Three boys fell in love with a girl at the same time. In order to decide which of them can marry the girl, they decided to duel with pistols. Xiao Li's hit rate is 30%, Xiao Huang is better than him, and his hit rate is 50%.
The top shooter is Kobayashi. He never makes mistakes. His shooting percentage is 100%. Because of this obvious fact, in order to be fair, they decided in this order: Xiao Li shot first, Huang Xiao second and Xiao Lin last. then
And so on until there is only one person left. So which of these three people has the best chance to survive? What strategies should be adopted?
Kobayashi will kill Huang when it's his turn and he's not dead, and then fight rookie Li.
So, Huang will fight Lin, if Lin is not dead, or he will die.
After calculation and comparison (the process is abbreviated), Xiao Li will decide to play Xiao Lin first.
So after calculation, Xiao Li has 873/2600≈33.6% vitality;
Huang Xiaoyou 109/260≈4 1.9% vitality;
Kobayashi has 24.5% vitality.
Oh, so Xiao Li's first shot will be shot into the air. Of course, whoever is alive will be hit in the future.
As always, Lin was beaten first, and Xiao Lin killed Huang first. The road to go is very narrow!
Finally, the survival rate of plum, yellow and forest is about 38: 27: 35;
A rookie has a great chance to survive and find a beautiful woman.
Li Xian shot an empty gun (if he works in the forest together, he will suffer the most). Huang will choose Lin to shoot (if you don't fight, you will be finished first). Lin will choose the yellow shot (after all, the hit rate is high). Li He is tied with 0.3:0.280.4.
0.3:0.60.6 lin li vs. 0.73 probability success rate.
0.3:0.40.7*0.4 probability lin li vs 0.3:0.7 * 0.6 * 0.70. 7 * 0.6 probability success rate 0.64.
There are two prisoners in a cell. Every day, the prison will provide this cell with a can of soup for two prisoners to share. At first, these two people often argue, because some of them always think this is right.
Fang has more soup than himself. Later, they found a way to kill two birds with one stone: one person divided the soup and let the other person choose first. In this way, the dispute was settled. However, now there is a new prisoner in this cell.
Now it's three people sharing the soup. New ways must be found to keep the peace between them. What should I do? Press: Psychological problems, not logical problems.
Let Party A divide the soup, then Party B and Party C choose the soup for themselves in any order, and leave the remaining bowls to Party A ... In this way, the sum of B and C must be the maximum they can get. Then mix their soup.
Divide the soup again according to the method of two people.
Put n round coins of the same size on a rectangular table. Some of these coins may not be completely on the table, and some may overlap each other; When you put another coin, its center is
When you are on the desktop, the newly put coins must overlap some of the original coins. Please prove that the whole desktop can be completely covered by 4n coins.
In order to make the newly placed coin not overlap with the original coin, the distance between the centers of the two coins must be greater than the diameter. That is to say, for any point on the desktop, the distance to the nearest center of the circle is less than 2, so the whole desktop can be used.
Covered with n coins of radius 2.
Double the size of the desktop and coins, then a small desktop with half the length and width of the original desktop can be covered with n coins with a radius of 1. Then, divide the original table into four equal small tables, and then
Each small table can be covered with n coins with a radius of 1, so the whole desktop can be covered with 4n coins with a radius of 1.
A ball and a ruler about 2/3 of the diameter of the ball. How do you measure the radius of the ball? There are many ways to see who is smarter.
Five one-dollar coins of the same size. Require two-phase contact, what should I say?
Put a 1 at the bottom, then two-thirds on 1 and four-fifths on 1.
8 Mr. S, Mr. P and Mr. Q all know that there are 16 playing cards in the desk drawer: spades A, Q, 4, flowers J, 8, 4, 2, 7, 3, diamonds K, Q, 5, 4, 6, A and 5. Professor John here.
Choose a card from 16 cards, tell Mr. P the number of points in this card and tell Mr. Q the color of this card. At this time, Professor John asked Mr. P and Mr. Q: Can you infer this card from a known point or color?
What card is it? 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. listen to
Mr. S thought about the above conversation and correctly deduced what this card was. Excuse me: What kind of card is this?
Box 5
A professor who teaches logic has three students, all of whom are very clever! One day, the professor gave them a question. The professor put a note on everyone's door, telling them everyone's paper.
Everything written on it is a positive integer, and the sum of some two numbers is equal to the third! The professor asked the first student: Can you guess your own number? Answer: no, ask
The second, no, the third, no, ask the first, no, the second, no, the third: I guessed it, it was 144! The professor smiled with satisfaction. Can you guess the numbers of the other two?
After the first round, it means that any two numbers are different. In the second round, the first two people didn't guess correctly, indicating that any number is not twice that of others. Now there are the following conditions: 1. Each number is greater than 02. 220.
Not equal to 3. No number is twice as many as others. Each number may be the sum or difference of the other two, and a third person can guess 144, so one possibility must be ruled out according to the first three conditions. Suppose: it is two numbers.
X-y = 144。 At this time, 1(x, y >；; 0) and 2(x! = y) are satisfied, so denying x+y will inevitably make 3 unsatisfied, that is, x+y = 2y, and the solution is x = y, which is not true (otherwise it can be guessed in the first round).
Not the difference between two numbers. So it is the sum of two numbers, that is, x+y = 144. Similarly, at this time, 1, 2 is satisfied, and 3 must not be satisfied, that is, X-Y = 2Y, and the two equations are simultaneous, and X = 108 and Y = 36 can be obtained.
The order of these two rounds of guessing is actually like this: the first round (1 No.2) and the second round (No.3, 1 No.2). In this way, everyone gets the same information at the end of each round (that is, the first three conditions
)。
Suppose we are C, let's see how C is made: C sees 36 of A and 108 of B, because the sum of the two numbers is the third, so we are either 72 or 144 (I guess this is because
72, 108 is the sum of 36 and 72, and 144 is the sum of 108 and 36. Raise your hand if you don't understand this sentence like this):
Suppose (c) is 72, then B can be seen in the second round. Here is B's idea if C is 72: In this case, B sees A's 36 and C's 72, so he can guess.
Myself, it is 36 or 108 (if you guess this is because 36,36 plus 36 equals 72, 108 is the sum of 36 and 108):
If you assume that your (B) avatar is 36, then C can be seen in the first round. This is C's idea. If B is 36: In this case, C sees A's 36 and B's 36, then he will
You can guess for yourself whether it's 72 or 0 (this will not be explained):
If you assume that your (c) head is 0, then A can be seen in the first round. Here is A's idea if C is 0: In this case, A sees 36 of B and 0 of C, so he can guess.
Himself, is it 36 or 36 (this will not be explained), then he can report 36 at the head. (then push back, push back), now A didn't report him 36 in the first round, C (in B's imagination).
You can know that your head is not zero. If everything else is the same as B's (referring to 36 on B's head), then C can quote his own 72 in the first round. Now C didn't report him 36 in the first round, B (in C's mind)
You can know that your head is not 36. If everything else is the same as C's (referring to 72 on C's head), then B can quote its own 108 in the second round. Now B didn't report his 108, C in the second round.
You can know that your avatar is not 72, so the only possibility on the C avatar is 144.
10 In a city, a car hit a man and ran away. There are only two colors of cars in this city, blue 15% and green 85%. A man saw it at the scene when it happened. He testified that it was a blue car, but according to the analysis of experts at the scene,
At that time, the possibility of seeing the disease correctly was 80%. So, what is the probability that the car involved in the accident is a blue car?
15%*80%/(85%×20%+ 15%*80%)
1 1 A man has 240 kilograms of water, and he wants to transport it to the arid area to make money. He can carry up to 60 kilograms at a time, and he needs to consume 1 kilogram of water per kilometer (even if it is water consumption). Suppose the price of water is 0 at the starting point, and then
, which is in direct proportion to the transportation distance (i.e. 10km10 yuan/kg, 20km/kg 20 yuan), and assuming that he must return safely, how much money can he earn at most?
F(x)=(60-2x)*x, and when x= 15, there is a maximum value of 450.
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Then something from easy to difficult. If you think about it yourself, the answer is not difficult.
1. There is a very old village. There are two kinds of people in this village, red eyes and blue eyes. These two kinds of people are no different. No one knew what color his eyes were before the baby was born. There is a square in the center of the village where the villagers gather. Now there are only three people living in three places in this village. In this village, there is a rule that if a person can know the color of his eyes and commit suicide at night, he will go to heaven. These three people can't tell each other the color of their eyes in words, nor can they prompt each other what color their eyes are in any way, let alone see the color of their eyes with reflective substances such as mirrors and water. Of course, they are not blind. They can see each other's eyes, but they can't tell him! They can only think with their minds, so they come to the square early every morning, sit face to face, and think about the color of their eyes. Day by day, there is no progress at all, until one day, a foreigner comes to the square and says something that changes their fate. He said that at least one of you has red eyes. Say that finish and left. Hearing this, the three men sat face to face at night before going back to sleep. The next day, they came to the square and sat for another day. That night, the two committed suicide successfully! On the third day, when the last man came to the square, he saw that the two men didn't come and knew that they had succeeded in suicide, so he also went back. That night, he also succeeded in suicide!
According to the above, please tell the colors of three people's eyes and tell the reasoning process!
There is a river. There is a hunter, a wolf, a man and two children in the river. And a woman with two children. If the hunter leaves, the wolf will eat everyone. If the man leaves, the woman will strangle her two children. If the woman leaves, the same as above. There is a boat in the river, only two people can do it (additional conditions: only hunters, both men and women can row.
There are 50 people in the village, and everyone has a dog. There are sick dogs among these 50 dogs (the disease is not contagious). So people must find sick dogs. Everyone can observe the other 49 dogs to judge whether they are sick, but only their own dogs can't. The results obtained after observation shall not be conveyed, nor shall the owner of the sick dog be informed. Once the owner knows that his family is a sick dog, he will shoot his own dog. Everyone has the right to shoot his own dog, but not to kill other people's dogs. The first day, the second day, there were no gunshots. On the third day, there was a burst of gunfire and asked how many sick dogs there were. This practical solution is similar to the problem 1.
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Well, the question is:
198 1 Berlin german institute of logical thinking test questions.
Premise:
There are five houses in a row.
All the houses have different colors.
All the homeowners come from different countries.
All homeowners have different pets; Drink different drinks; Smoke different cigarettes
Tip:
The English live in a red house.
The Swede keeps a dog.
Danes drink tea.
The green house is on the left of the white house.
The owner of the green house drinks coffee.
The owner of Pall Mall cigarettes keeps birds.
Yellow homeowners smoke Dunhill Road.
The host in the middle drinks milk.
Norwegians live in the first house.
Blend smokers live next door to the cat house.
The owner of the horse is smoking next door to Dunhill's house.
Master Lan's master drinks beer.
The Germans slapped the prince.
The Norwegian lives next door to the blue house.
People who only drink boiled water live next door.
Q: Who raises fish?