5 1 Once upon a time, there was a rich man who had 30 children, of which 15 was born by his late ex-wife and the rest 15 was born by his ex-wife. After that, a woman wanted her eldest son to inherit the property, so one day, he said to him, "dear husband, you are going to." Let's arrange our 30 children in a circle, counting from one of them, and let that child stand out every time we arrive at 10, until the last child is left, which child will inherit your property! " The rich man thought, damn, the meaning of this question is quite connotative. Yes, it seems fair, so let's do it ~ However, when the selection process continued, the rich man was dumbfounded. He found that the first 14 child was born to his ex-wife, and the next one to be eliminated was born to his ex-wife. The rich man immediately waved his hand and stopped. Now he counts down from this child. My 15 son can't beat you ~ She immediately agreed to the rich man's motion, and guess who became the heir ~ 52 "There is a pasture where it is known that 27 cows have been raised and all the grass has been eaten in six days; Raise 23 cows and eat all the grass in 9 days. If you have 2 1 cow, how many days can you eat all the grass on the pasture? And the grass on the pasture is growing. " A businessman rode a donkey across the desert of 1000 km to sell 3000 carrots. As we all know, donkeys can carry 1000 carrots at a time, but they have to eat one more carrot every kilometer. Q: How many carrots can a businessman sell? 54 10 box of gold, each box 100 piece, each piece has one or two corrupt officials, and each piece is ground into one dollar. Please weigh not enough boxes at a time. You let the workers work for you for 7 days, and the workers' reward is a gold bar. The gold bar is divided into seven connected parts, and you must pay at the end of each day. If you are only allowed to break the gold bars twice, how can you pay the workers? There are ten bottles of medicine, each bottle 100 tablets (now it seems that it is less than 100 tablets, all of which are 10 tablets with 20 tablets). Anyway, here we are), of which eight bottles each weigh10g, and two bottles each weigh 9g. With a fairly accurate small scale, only once, how to find out the two lighter bottles? 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? 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 three rooms only needed $25, 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 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? There is a train from Los Angeles to new york at a speed of 15km/h, and another train from new york to Los Angeles at a speed of 20km/h ... If a bird starts from Los Angeles at the same time with 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 the bird fly? 6 1 You have two jars, 50 red marbles and 50 blue marbles. Choose a jar at random and put a marble in the jar at random. How can you give red marbles the best chance? What is the exact probability of getting the red ball in your plan? 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? 63 For a batch of lamps numbered 1 ~ 100, all switches are turned on, and the following operations are performed: always turn the switches in the opposite direction by multiples 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, it is a slap 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? 66 Two rings with radii 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? 67 1 yuan a bottle of soda, drink two empty bottles for one bottle of soda. Q: You have 20 yuan money, how many bottles of soda can you drink at most? There are three red hats, four black hats and five white hats. Let 10 people stand in a row from short to high, each wearing a hat. Everyone can't see the color of his hat, but he can only see the color of the hat of the person standing in front. So the last person can see the color of the hats on the heads of the nine people in front, while the first person can't see anyone's hats. Now, start with the last person and ask him if he knows the color of the hat he is wearing. If he doesn't know, keep asking the person in front. Suppose the person in front must know that he is wearing a black hat. Why? 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? Professor Lum said, "I once witnessed a duel between two goats, which led to an interesting mathematical problem. One of my neighbors has a goat, which weighs 54 pounds. It has been king in the nearby mountains for several seasons. Later, a good-hearted man introduced a new goat, which was 3 Jin heavier than it. At first, they lived in harmony with each other. But one day, the lighter goat stood at the top of the steep mountain road and pounced on its competitor. Competitors stand on the mound to meet the challenge, and challengers obviously have an absolute advantage. Unfortunately, both goats died because of the violent collision. Now let's talk about the wonders of this topic. George abercromby knows a lot about raising goats and wrote a book. He said: "Through repeated experiments, I found that the momentum is equivalent to the impact of a 30-pound object falling from a height of 20 feet, just enough to break the goat's skull and kill it. "If he is right, how quickly can the two goats get close to each other and then break their skulls? Can you work it out? 7 1 It is said that someone gave the proprietress of a restaurant a difficult problem: this person knew that there were only two spoons in the shop, which could scoop 7 ounces of wine and 1 1 ounce of wine respectively, but forced the proprietress to sell him 2 ounces 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? It is known that each plane has only one fuel tank, and planes can refuel each other (note that there is no tanker). A tank of oil can make an airplane fly half a circle around the earth. Question: How many planes need to be dispatched at least to make at least one plane fly around the earth and return to the airport after taking off? All planes take off from the same airport and must return to the airport safely. Landing halfway is not allowed. There is no airport in the middle. ) 73 Draw 10 straight lines at 9 points, and require at least three points on each straight line? A fork in the road leads to an honest country and a lying country. Two people came, one from an honest country and the other from a lying country. An honest country always tells the truth, and a liar always tells lies. Now you are going to a country that lies, but you don't know which way to go. You need to ask these two people. How should I ask? How many times do the hour hand, minute hand and second hand of a clock completely coincide in a 24-hour day? When are they? How did you work it out?