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. The price of each room is $65,438+00, so they pay 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 you give red marbles the best chance? What is the exact probability of getting the red ball in your plan?
7. You have four jars containing pills. 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 lights numbered 1 ~ 100, all the switches are turned up (turned on), and the following operations are done: always turn the switches in the opposite direction once in 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.
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, 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, 1 Yuan, one bottle of soda, two empty bottles for one bottle. Q: You have 20 yuan money, how many bottles of soda can you drink at most?
14。 Suppose there is a car, its fuel tank is just as big as an oil drum, and the car is just right.
Carry a bucket. Suppose a barrel of oil can drive a car 100 km. Now at the starting point, the bus is full.
The starting point is 100 barrel of oil. How far can this car leave the starting point?
15。 Three prisoners will be executed. Now give them a chance to be pardoned.
/kloc-after 0/0 minutes, they will be taken to three isolated rooms, and the prison guards will toss a coin to decide to wear red or blue hats for them. Prisoners can't communicate with each other, but they can see the color of the hats on the heads of other prisoners.
Now prisoners can only guess the color of the hat once, and each prisoner must say "red", "blue" or "over" within 10 second.
(1) If any prisoner breaks the rules, all three prisoners will be beheaded;
(2) If all three prisoners say "Guo", they will all be beheaded;
(3) Any prisoner who says the wrong color of his hat will be beheaded by all;
(4) Otherwise, release it completely.
Now these three prisoners have 10 minutes to discuss what measures should be taken to maximize their chances of being released.
Tip: If all three prisoners guess at random, the probability of success is1/8; If both prisoners say "Guo" and the third prisoner makes a wild guess, the probability of success is 1/2.
Is there a better plan?
16。 Four turtles crawl on the four corners of a square with a side length of 3 meters at a speed of 1 cm per second. Every turtle is crawling in the direction of chasing the turtle in its right corner. How long will it take them to meet in the center of the square?
17。 There are 2000 squares in a row, and two players take turns to write S or O in the squares. Whoever writes SOS in three consecutive lines wins. If you can't write it, it's a draw. Please prove that the person written at the back has a chance to win.
18。 This is a simple and vivid question, which mainly proves that the sum of two sides of a triangle = the third side. Can you find out the mistakes?
19。 Professor Lum said: "I once witnessed a duel between two goats, which led to an interesting math 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 is proficient in raising goats and has written a book. He said: "Through repeated experiments, I found that the momentum is equivalent to the impact of a 30-pound weight falling from a height of 20 feet, just enough to break the goat's skull and kill it." If he is right, how fast must the two goats approach each other before smashing their skulls? Can you work it out?