2. 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? (The following questions are worth 5 points each)

3. 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 himself. There is a subordinate. The manager's age was known, but the age of the manager's three daughters was still uncertain. The manager said that only one of his daughters 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?

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?

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?

6. You have two jars with 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 marble the maximum Chances of selection? 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 have the weight of the uncontaminated pills + 1. You only weigh them once. How do you determine which jar contains the pills? 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. Perform the following operations on a batch of lights numbered 1 to 100, with all switches facing up (on): For every multiple of 1, turn the switch once in the opposite direction; for multiples of 2, turn the switch once in the opposite direction. Switch; in multiples 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 were having a dance, and everyone wore a hat on their 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 asks everyone to see what hats others are wearing, and then turns off the lights. If anyone thinks they are wearing a black hat, 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?