Smart question study 2

【It Ideology]

1. There are 1000 bottles of water, one of which is toxic. Mice will die 24 hours after they taste a little poisonous water, how many mice at least can identify the bottle of water from 24 hours? (Intermediate)

2. There are three types of medicines, weighing 1g, 2g, and 3G respectively, and put them in several bottles. Now we can determine that each bottle contains only one of them, in addition, each bottle contains enough pills. Can you know what kind of medicine is filled in each bottle once?

What if there are four types of medicines? What about Category 5? What about N classes )? (Advanced)

If there are m bottles containing N kinds of medicines (m, n is a positive integer, the quality of each medicine is different, but the quality of each medicine is known )? Can you know what each bottle of medicine is once?

(Analysis) this type of questions is suitable for IT users, because they need to use concepts or ideas in computers.

For question 1, binary is required. At least 10 mice were used, SO 2 ^ 10 = 1024> 1000. The method is: Numbers rats and water, respectively 1 ~ 10 and 1 ~ 1000. Each number of water corresponds to a 10-bit binary number. For example, if the number of water is 100, it corresponds to binary 0001100100, where the 3, 6, and 7 bits are 1, then the water should be marked as 3, 6, and 7 mice. Finally, count the numbers of dead mice. For example, the numbers of dead mice are 3, 6, 7, the water numbered 100 is toxic. That is to say, there is a one-to-one correspondence between the death combination of rats and the serial numbers of water through the binary idea.

For question 2, if there are three types of medicines, we can take one in the first bottle, 10 in the second bottle, and 100 in the third bottle, which is called the total weight, the numbers in one place represent the weight of the first type of medicine, and the numbers in ten represent the weight of the second type of medicine ,....

If there are more medicines and the cost of this solution is too high, we can consider the heaviest medicines and then adopt the corresponding base. For example, the three types of medicines, the heaviest of which is 3 GB, can be 4 hexadecimal instead of decimal, that is, three medicines, each type take 4 ^ 2, and then weigh, the resulting decimal weight is converted to 4-digit ,....

【Aircraft Refueling Problems]

Each plane has only one fuel tank, and the planes can refuel each other (note that there is no fuel dispenser). A box of oil can be used for an airplane to fly around the Earth for half a lap. How many planes should be dispatched to bring at least one plane around the Earth back to the airport when it was flying? (All planes take off from the same airport and must return to the airport safely. stopover is not allowed. There is no airport in the middle) (difficult)

(Analysis) you can find the answer to this question on the Internet. In my opinion, the best answer to this question should be five planes. For details, see http://blog.sina.com.cn/s/blog_48ef377d0100089h.html.

The analysis logic of this question should be gradually increased from the beginning until the minimum number is found. At the same time, we should note that (1) this question allows reverse plane response (2) the fuel tank of each airplane is fixed in hours.

【Coin flip]

Four coins are placed on a disc, and the positive and the negative are uncertain (not four are facing up) and arranged in a square shape. With your eyes blindfolded, you can flip any number of coins each time (you cannot touch the front and back sides ). After each flip, the disc will rotate several 90 degrees at random. Then you flip the coin, 8. How many times do you have to flip the game if you want to stop it? (Very difficult)

(Analysis) This question is very difficult, but last year (2010) a senior engineer met during an interview with a company. For the answer, see http://www.cublog.cn/u2/63316/showart_2236291.html. This question is actually an issue of state transition of an automatic machine. It is known that the initial state and the end state allow the constructor to convert the state.

【Probability questions]

1. You have two cans, 50 red balls and 50 blue balls. You can randomly select one and put a ball in the jar. How can you give the biggest chance to select a red ball? In your plan, what is the exact chance of getting a red ball?

2. There is a 10-storey building with a diamond placed in front of each elevator door. These diamond are very different. One person takes the elevator from the 1st floor to the 10th floor. The elevator opens a door every time it reaches the 1st floor. How can I get the biggest diamond? There is only one time (that is, the elevator door cannot be entered)

3. Three young men fell in love with a girl at the same time. They decided to fight with Shou Qiang to decide who could marry the girl. Alex's hit rate is 30%. Chris is better than him. the hit rate is 50%. The best gunner is Bob. He never makes a mistake and the hit rate is 100%. Due to this obvious fact, for the sake of fairness, they decided in this order: Alex shot first, Chris second, and Bob the last. Then it repeats until they have only one person left. Who has the greatest chance to survive these three individuals? What policies should they adopt?

(Analysis) for such problems, data probability calculation is generally used to obtain the results.

For question 1, you need to break your mind and do not always think about putting the two jars in the same request. If you want to maximize the probability of getting a red ball, it is best to make the full red ball in one can (the probability of getting a red ball from this can is 1), and the other can have as many red balls as possible, so I got the answer: put a red ball in one jar, and put all the remaining balls in another jar. In this way, the probability of getting a red ball is 1/2 + 1/2*49/100.

Question 2 is a difficult Probability Calculation Problem. This model is transformed from the "secretary problem" in the game theory. It was also one of Microsoft's candidates. The problem with the secretary is as follows: I want to hire a secretary with N people for an interview. After each interview, you have to immediately decide whether to hire him or not. If you decide not to hire him at the time, he will not come back. During the interview, you will always be able to clearly understand the suitability of the job seeker and compare it with everyone before. Q: Why is the most appropriate strategy to be selected as a secretary? The basic solution strategy is as follows: for certain integer r, the first R people will not be hired in the first interview, among the subsequent N-R people, if anyone is better than the person interviewed earlier, hire him.

What is the value of R? The answer is r ≈ N/e ≈ 0.20.n (which can be derived from the probability formula), where E is the basis of the natural logarithm. The success rate of using this R value is 0.20.n. In the elevator question, the number of floors n = 10, r ≈ 3.68, and the nearest integer is 4. That is, the first four layers are not selected, but the maximum size of the diamond we have seen is noted down. From the very beginning, we will choose the one with the most similar size as the diamond.

For question 3 (online answer http://wenku.baidu.com/view/1d816c4fe518964bcf847c60.html ),

Set: A -- Alex, B -- Chris, c -- Bob

Only AB relative

A is likely to survive

30% + 70% × 50% × 30% + 70% × 50% × 70% × 50% × 30% + ...... = 0.3/0.65

B is likely to survive

70% × 50% + 70% × 50% × 70% × 50% + 70% × 50% × 70% × 50% × 70% × 50% × + ...... = 0.35/0.65

It should be equal to 1-0.3/0.65.

Only ac-relative

A is more likely to survive than 30%.

C is 70% likely to survive.

Only BC relative

B is more likely to survive than 50%.

C is 50% likely to survive.

Three-person comparison

There are three situations for a to survive.

1. A kills C, B does not die a, and a does B again. The probability is 30% × 50% × 0. 3/0. 65.

2. A kills C, B kills C, and a kills B. The probability is 70% × 50% × 0. 3/0. 65.

3. A: C: B: C: 70% x 50% x 30%

Therefore, the likelihood of a's survival is 0.105 + 3/13 ≈ 0.336 or more than 1/3, Which is lucky.

B can survive in three situations

1. A kills C and B kills a with a probability of 30% x 50%.

2. If a kills C, B kills C, and AB kills a, the probability is 70% × 50% × 0. 35/0. 65.

3. If a kills C, B cannot kill a. If AB is relative, B kills a. The probability is 30% × 50% × 0. 35/0. 65.

Therefore, the likelihood of B's survival is 0.15 + 3.5/13 ≈ 0.419 or more than 1/3, which is very lucky.

There is only one case for C to survive.

1. A: C: B: C: 70% x 50%

Therefore, the likelihood of c Survival is 0.245 or less than 1/3, which is unfortunate.

The sum of the likelihood of ABC survival is exactly 1.

【Ring Problem]

The radius of the two rings is 1 and 2 respectively, and the circle is centered around the circumference of the circle for one week. How many weeks have the circle itself been rotated? What if the circle itself turns around for weeks outside the circle?

(Analysis) This question is relatively simple. The distance of a circle rotation depends on the circumference of the circle center. When the circle is outside, the radius of the trajectory is 3. When the circle is inside, the radius of the trajectory is 1.

Original article, reprinted Please note:Reposted from Dong's blog

Link:Http://dongxicheng.org/brain/intelligence-problems-2/

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