1. There are two incense sticks distributed unevenly. The time it takes for the incense to burn out is one hour. How can you determine a period of 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 age of the manager. One of his subordinates already knows. The age of the manager, but still could not determine the ages of the manager's three daughters. At this time, the manager said that only one daughter had black hair, and then the subordinate knew the ages of the manager's three daughters. What are the ages of your three daughters? Why?

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 I thought that three rooms only cost $25, so I asked the boy to return $5 to the three guests. Unexpectedly, the boy was greedy, so he only returned $1 to each person and secretly took $2. In this way, each of the three guests had their own money. It cost nine yuan, so the three of them spent $27 each. In addition, the younger brother ate $2 for himself, and the total was $29. But when the three of them paid $30 a ***, where was the remaining $1?

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 cloth and the same size, and each pair There is a label paper attached to the socks. 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?

5. A train leaves Los Angeles and goes straight to New York at a speed of 15 kilometers per hour, and another train runs 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?

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 to give the red pinball the greatest chance of being selected? In your plan, what is the exact probability of getting a red ball?

7. You have four jars containing pills. Each pill has a certain weight. The contaminated pills are the uncontaminated weight + 1. Weigh them only once. , how to determine which jar of medicine is contaminated?

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?

9. For a batch of lights numbered 1 to 100, with all switches facing up (on), perform the following operations: For every multiple of 1, flip the switch in the opposite direction; 2 If it is a multiple of 3, flip the switch in the opposite direction again; if it is a multiple of 3, flip the switch in the opposite direction... Q: 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?

11. A group of people had a dance, each wearing 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 kind of 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 third time the lights were turned off that the sound of slaps could be heard.

How many people wear black hats?

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?

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? ?

14. If every 3 empty beer bottles can be exchanged for one beer, and someone buys 10 bottles of beer, how many bottles of beer can he drink at most? ================================================== ===============================

Answer: 1. Light one end of incense a, and light one end of incense b. Both ends. By the time the incense was finished burning, 30 minutes had passed. Then light the other end of the incense stick. The time from this point until a is burned out is 15 minutes.

2. 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. Typical concept of secret exchange. In fact, the three people only paid 27 yuan, the boss got 25 yuan, and the younger brother got 2 yuan.

4. Take apart each pair of socks and give each person one piece.

5. Let the railway length from Los Angeles to New York be A kilometers. Then it took A/(15 20) hours for the two trains to meet, which is the flight time of the bird. So the distance the bird flies is speed × time = 30 × A/35 = 6/7 the length of the train from Los Angeles to New York.

6, 1/2 chance. Choose the ball first and then the jar. This way the jar actually has no effect on the color of the ball.

7. Take 1 pill from Can No. 1, 2 pills from Can No. 2, 3 pills from Can No. 3, and 4 pills from Can No. 4. Weigh the 10 pills. How much heavier than the normal weight is? There is a problem with the number of cans of medicine.

8, 4. Quantity>Color type. Colors must be repeated.

9. There are 10 lights that are off, namely numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. Because: every prime number is divisible by 1 and itself, so the prime number light is on. Suppose a composite number can be divided by N numbers, N must be an even number. For the sum of squares other than a certain number, it will be switched on and off N times, which is an even number of times, and the light will remain on; for the square numbers listed above, it will only be switched on and off N-1 times, so the light will be off.

10. The axis of mirror symmetry is the central axis of a person

11. There are three people wearing black hats. Suppose there are N people wearing black. When N=1, black people 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 Ngt;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. No matter inside or outside, the small circle turns twice.

13, 39 bottles. Two empty bottles = one bottle of soda (with empty bottles). An empty bottle = soda. Because a bottle of water = 1 yuan. So water = 0.5 yuan. So 20 yuan is equivalent to 40 bottles of water. Because there was an empty bottle left at the end and they were not replaced. So you can drink 39 bottles.

14. After drinking 10 bottles, exchange 9 empty bottles for 3 bottles of beer (there are 4 empty bottles after drinking)

Drink this Three bottles can be exchanged for 1 bottle of beer (there are 2 empty bottles after drinking)

At this time, he has 2 empty bottles. If he can borrow an empty bottle from the boss first, it will be enough. You can exchange 3 empty bottles for a bottle of beer. After drinking the bottle, just return the empty bottle to the boss.

So he can drink up to 10 3 1 1 = 15 bottles