A manager has three daughters, and their ages add up to 1.
The age of the three daughters is the same as that of the manager himself. A subordinate already knows the manager's age, but he still can't determine the ages 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 There are 15 girls in a student dormitory. They walk in groups of three every day and ask how to arrange it so that every girl has a chance to walk with other girls in the same group, just once a week.