Several smart questions

1. There are two unevenly distributed fragrances. The burning time is one hour. How can you determine a 15-minute period?

 

 

2. There were two blind people who both bought two black so and two white so. The eight pair of so were of the same quality and size, and each pair of so was associated with a trademark paper. The two blind people accidentally mixed eight pairs of so. How can they retrieve black and white so pairs?

 

 

3. One train departs from Beijing to Guangzhou at an hourly rate of 150 kilometers. The other train departs from Guangzhou to Beijing at an hourly rate of 200 kilometers. It is assumed that the distance from Beijing to Guangzhou is 3000 kilometers. If there is a beast that starts at a speed of 300 kilometers per hour and two trains at the same time, it departs from Beijing and flies along the railway. When it hits another car, it turns around, in turn, the two fire workshops flew back and forth until the two trains met each other. Could you tell me how long the beast ran together?

 

 

4. There are two cans, 50 red balls and 50 blue balls. Please split these 100 balls into two. Then let others randomly select a jar and randomly select a small ball in the jar. How can I assign these balls to the jar to maximize the probability of selecting a red ball?

 

 

5. There are four cans containing pills, each containing a certain weight. The contaminated pills are not contaminated with the weight + 1. How can I determine which jar of medicine is contaminated once?

 

 

6. For a batch numbered 1 ~ 100, all turn on (on) the light to perform the following operations: All the multiples of 1 turn back one switch; 2 multiple turn back one switch; turn another switch in the opposite direction in multiples of 3 ...... Q: It is the number of the light that is turned off.

 

 

7. A group of people wear a hat on their heads. There are only black and white hats, and at least one black hat. Everyone can see the colors of others' hats, but not their own. The host will show you what hats others wear on their heads and turn off the lights. If someone thinks they are wearing black hats, they will slap themselves in the face. Turn off the light for the first time and there is no sound. Then we turned on the light and watched it again. When the light was turned off, it was still silent. It was not until the third time that the light was turned off that there was a slap in the face. How many people are wearing black hats?

 

 

8. 1 RMB for a bottle of soda. After drinking, you can change two empty bottles to one. Q: How many bottles of soda can you drink if you have 20 RMB?

 

 

 

 

Refer:

 

1. First, ignition the First Incense on both ends, and ignition the second incense on one end. Wait until the first incense is burned out (30 minutes ). Then, the other end of the second root incense is ignited. Then, from this moment to the second end, it will be 15 minutes.

 

Pair of so, remove the trademark, and take one of them.

 

3. Formula for constant speed: distance = speed X time. Because the two trains are relatively moving, calculate the time they need to meet, multiply by the speed of the animal.

 

4. Put one red ball in one jar, 49 red balls and 50 blue balls in the other. The probability of the selected red ball is 0.5 + 0.5*0.49 = 0.745.

 

5. Take 1 medicine for bottle 1, 2 medicine for bottle 2, 3 medicine for bottle 3, and 4 medicine for bottle 4.

 

6. The answer to this question is that a lamp numbered with a full digit will go off, that is, the lamp numbers 1, 4, 9, 16, 25, 36, 49, 64, and 81,100 will go off.

Analysis: Determine whether the n-th lamp is extinguished ~ In N, the number of N's approx. (1) can be an odd or even number. If it is an odd number, the N number is extinguished. If it is an even number, the N is open. If n is a prime number, then n has only 1 and N divisor, that is, the number of divisor is an even number. If n is a combination and not a complete Gini number, then N can be decomposed into k N1 * N2 forms, where n1 <N2, therefore, the approximate number of N is 2 K, which must be an even number. If n is the total number of workers, then N can be used as a factor decomposition and decomposed into k N1 * N2 forms (N1
<N2), and can also be decomposed into T * t forms (because n is the total number of workers ). Then the number of N approx. Is 2 * k + 1, which is an odd number.

 

 

7. 3 people.

Analysis: the key condition is that there must be at least one black hat. (1) if only one person is wearing a black hat, the person will immediately know, so the first time the light is turned off, he should have slapped himself. (2) If two people wear black hats, they can see the other party's black hats but cannot determine whether they are black hats. Therefore, the first time they turn off the lights, they won't slap themselves in the face. Since they didn't hear a slap in the face, they know that there are more than one black hat, so the only possibility is that they also wear a black hat, so the second time they turn off the light, both of them will slap in the face. (3) If three people wear black hats, both of them will see the other two wearing black hats. When they switched off the light for the first time, they were not sure whether they were wearing a black hat. They knew that if only two were wearing a black hat, the second time they switched off the light, someone would be slapped. But when no one slapped the light for the second time, three people thought that if only two people wore black hats, they would have slapped themselves when the light was switched off for the second time, therefore, there must be more than two people wearing black hats. The only possibility is that they also wear black hats. 4 or above can be pushed. The conclusion of this question is that some people slapped the light on the first few times, so there would be some black hats.

 

8. 40 bottles. You need to borrow a bottle temporarily.