1. There are two unevenly distributed incense, and the burning time is one hour. What method can you use to determine the time of 15 minutes?

Answer: light two incense sticks at the same time. The first incense is at both ends, and the other incense is only at one end. When the first incense sticks out (this is 3/4 of the total length), light the other end of the second incense, and the time from lighting to extinguishing at the other end is 15 minutes!

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?

A: The ages of the three girls should be 2, 2 and 9. Because only one child has black hair, that is, only she has grown up, and the other two are still very young, that is, less than 3 years old, with light hair. The reorganization manager should be at least 25 years old.

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?

Answer: ***30 yuan includes 27 yuan (25 yuan gave it to the boss+younger brother embezzled 2 yuan) and everyone paid back 1 yuan (* * * 3 yuan). 2 yuan plus 27 is totally confusing.

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?

Answer: every pair of socks is taken apart, and each person takes a pair, and there are no left and right socks. Finally, two pairs of black socks and two pairs of white socks were taken back.

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?

Answer: Convert the flight distance of birds into time calculation. Let the distance between LA and new york be a, the time when two trains meet is a/( 15+20)=a/25, and the flying speed of birds is 30, then the flying distance of birds is a/25*30=6/5a.

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?

Answer: One jar contains a red ball, and the other jar contains 49 red balls and 50 blue balls. The probability is close to 75%.

This is the maximum probability that can be achieved.

In fact, just put a jar

Put the remaining balls in another jar, and the probability of taking out the red ball is greater than 50%.

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?

Answer: Take pill 1 from tank 1, pill 2 from tank 2, pill 3 from tank 3 and pill 4 from tank 4. According to 10 pills, the ratio is positive.

There is something wrong with the medicine in the jar as heavy as usual.

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?

A: Four.

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.

Answer: when the square root of a number is an integer (that is, a complete square number), it faces down and the other faces are up.

So the numbers 1, 4, 9, 16, 25, 36, 49, 64, 8 1, 100 are facing down.

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?

A: The mirror symmetry axis is the central axis of human beings.

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?

There are three people wearing black hats. Suppose there are n people wearing black. When N= 1, the person wearing black will like to see everyone else is white.

Make yourself black. So when the lights are turned off for the first time, there should be a sound. It can be concluded that N> 1. For everyone who wears black, he thinks he is white when he sees the black hat of N- 1. But after waiting for N- 1 times and no one hits himself, every black person can know that he is black. So when the lights were turned off for the nth time, n people hit themselves.

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?

A: No matter inside or outside, the small circle turns twice. Small circles and big circles experience the same distance.

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?

Answer: 39 bottles, starting from the second bottle, equivalent to 1 yuan to buy 2 bottles.