Answer Summary:

1. There are two incense sticks that are unevenly distributed. The time it takes for the incense to burn out is one hour. How can you determine a period of 15 minutes?

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

2. A manager has three daughters. The sum of the ages of the three daughters is equal to 13. The sum of the ages of the three daughters is equal to the manager’s own age. A subordinate already knows the manager’s age, but still cannot Determine the ages of the manager's three daughters. At this time, the manager said that only one daughter has black hair. Then the subordinate knew the ages of the manager's three daughters. What are the ages of your three daughters? Why?

Answer: The ages of the three girls should be 2, 2, and 9. Because there is only one child with black hair, that is, she is the only one who has grown up, and the other two are still in childhood, that is, less than 3 years old, with light hair. Combined with this, the age of the manager should be at least greater than 25.

3. Three people went to stay in a hotel and stayed in three rooms. Each room cost $10, so they paid the boss $30 one day. The next day, the boss thought the three rooms only cost $25. Yuan was enough, so I asked the boy to return $5 to the three guests. Who knew that the boy was greedy, so he only returned $1 to each person, and secretly took $2 for himself. In this way, each of the three guests spent nine yuan, so the three I spent $27 per ticket, plus my little brother ate up another $2, the total was $29. But when the three of them paid $30 a ***, where was the remaining $1?

Answer: The 30 yuan paid per day includes 27 yuan (25 yuan for the boss + the younger brother embezzled 2 yuan) and 1 yuan will be returned to each person (***3 yuan), and you will get 27 and 2 yuan Adding them up is purely confusing.

4. There were two blind men. They each bought two pairs of black socks and two pairs of white socks. The eight pairs of socks were made of the same fabric and size, and each pair of socks had a piece of trademark paper. Connected. Two blind men accidentally mixed up eight pairs of socks. How can each of them retrieve two pairs of black socks and two pairs of white socks?

Answer: Open each pair of socks, each person takes one pair, there are no left and right socks, and finally get two pairs of black socks and two pairs of white socks.

5. A train leaves Los Angeles and goes straight to New York at a speed of 15 kilometers per hour, and another train goes from New York to Los Angeles at a speed of 20 kilometers per hour. If a bird starts from Los Angeles at the same time as two trains at a speed of 30 kilometers per hour, encounters another car and returns, flying back and forth on the two trains until the two trains meet, what will this bird do? How far did the bird fly?

Answer: Convert the bird’s flight distance into time. Suppose the distance between Los Angeles and New York is a, the time when the two trains meet is a/(15+20)=a/25, and the bird’s flight speed is 30, then the bird’s flight distance is a/25*30= 6/5a.

6. You have two jars, 50 red marbles and 50 blue marbles. Randomly select a jar and randomly select a marble and put it into the jar. How do you give it? The biggest chance of selecting a red pinball? In your plan, what is the exact probability of getting a red ball?

Answer: Put a red ball in one jar, and 49 red balls and 50 blue balls in another jar. The probability is close to 75%.

This is the maximum probability that can be achieved. .

In fact, as long as there are <50 red balls in one jar and no basketball is placed, and the remaining balls are placed in the other jar, 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 pills have the weight of the uncontaminated pills + 1. You only weigh them once. How do you determine which jar contains the pills? Contaminated?

Answer: Take 1 pill from can No. 1, 2 pills from can 2, 3 pills from can 3, and 4 pills from can 4. Weigh the 10 pills and calculate the ratio

The weight usually indicates the size of the can of medicine that has the problem.

8. You have a bucket of jelly, including yellow, green, and red. Close your eyes and grab two jelly of the same color.

How many do you need to grab to be certain that you have two jellies of the same color?

Answer: 4

9. For a batch of lights numbered 1 to 100, with all switches facing up (on), perform the following operations: For multiples of 1, dial in the opposite direction. Turn the switch once; turn the switch once in the opposite direction when it is a multiple of 2; turn the switch once in the opposite direction when it is a multiple of 3... Question: The last number is the number of the light in the off state.

10. Imagine you are in front of a mirror. May I ask why the image in the mirror can be reversed left and right, but not up and down?

Answer: The axis of mirror symmetry is the central axis of a person

11. A group of people are having a dance party, and each person wears a hat on his head. There are only two kinds of hats, black and white, and there is at least one black one. Everyone can see the color of everyone else's hats, but not their own. The host first asked everyone to see what hat others were wearing, and then turned off the lights. If anyone thought they were wearing a black hat, they would slap themselves in the face. When I turned off the lights for the first time, there was no sound. So the lights were turned on again, and everyone watched it again. When the lights were turned off, there was still silence. It wasn't until the lights were turned off for the third time that the sound of slaps could be heard. How many people wear black hats?

Answer: There are three people wearing black hats. Suppose there are N people wearing black. When N=1, black people wearing black can be sure that they are black when they see that others are white. So there should be a sound when the lights are turned off for the first time. It can be concluded that N>1. For each person wearing black, he can see N-1 black hats, and thus assumes that he is white. But after waiting for N-1 times and no one hits him, every black person will know that he is also black. So when you turn off the lights for the Nth time, N people will hit you.

12. There are two rings with radii of 1 and 2 respectively. The small circle goes around the circumference of the big circle inside the big circle. How many times does the small circle rotate by itself? If it is outside the big circle, how many times will the small circle rotate by itself?

Answer: No matter inside or outside, the small circle rotates twice. The distance experienced by the small circle and the big circle is equal.

13. A bottle of soda costs 1 yuan. After drinking, two empty bottles are exchanged for one bottle of soda. Question: You have 20 yuan. How many bottles of soda can you drink at most?

Answer: 39 bottles, starting from the second bottle, which is equivalent to buying 2 bottles for 1 yuan.