Smart question research

Whether looking for a job or taking an exam as a civil servant, a common interview or written examination question is a smart question. Some of these questions are relatively simple, some are difficult, some are a skill, and some require mathematical knowledge derivation, in any case, it is absolutely beneficial for a person to exercise his or her own thinking ability. This article provides a list of common intellectual questions for your research and study.

【Rope]

1. A rope (uneven thickness, different lengths) is ignited from one end, and it takes one hour to burn it all out. How can I use this rope to measure it for half an hour? (Elementary)

2. There are some ropes (uneven thickness and different lengths), but each rope is burned for an hour after being ignited. How can I use these ropes to calculate the time for 45 minutes, how long is the computing time of 1 hour and 15 minutes? (Intermediate)

(Analysis) this type of questions is relatively simple. Because the rope is bidirectional, only the two ends of the rope need to be ignited at the same time, 1/2 hours can be obtained. This method implies that one rope can be ignited at one time as a reference, one is bidirectional ignition, and the other is unidirectional ignition. After the first rope is burned, it takes 45 minutes to ignition the other end of the second rope. Likewise, it can be calculated as 1 hour and 15 minutes.

【Plotting]

1. Five rows of ten coins. How can I arrange four coins in each row? (Elementary)

2. five Yuan coins of the same size. What should we do if we need to contact each other? (Elementary)

3. Nine points in matrix form in three rows and three columns. How to draw four straight lines through all nine points. (Intermediate)

4. Draw 10 lines at 9 points. Each line must have at least 3 points. How can we arrange these 9 points? (Intermediate)

(Analysis) These questions often need to be constantly tried and pondered before they can be made. It is generally necessary to use special graphics (for example, question 1 is a five-star arrangement) or break the normal plane (for example, question 2 requires three-dimensional consideration ).

【Category]

1. Assume that 100 table tennis balls are arranged, and two people take the ball into their pockets in turn to get 100th Table Tennis Winners. The condition is: each time you take the ball, you must take at least one, but not more than five. Q: If you are the first person to take the ball, how many should you take? In the future, how can we guarantee that you can get 100th table tennis balls? (Intermediate)

2. Take some of the 16 coins A and B in turn. Each time, The number can only be one of 2, 4. Who finally took the coin and lost. Q: Does A or B have a strategy to win? All of them are smart. (Advanced)

3. It is said that five pirates once snatched 100 gold coins and they passed a plan to determine who to choose:

1. draw lots to determine the numbers of each person (1, 2, 3, 4, 5 );

2. First, the allocation scheme will be proposed by 1, and then five people will vote. If more than half of them agree, the scheme will be passed; otherwise, the scheme will be thrown into the sea to feed sharks;

3. after the death of the first day, the second day will propose a scheme, and four people will vote. If and only when more than half agree, the scheme will be passed, otherwise, they will be thrown into the sea to feed sharks on the 2nd;

4. and so on ......

According to the story above, the following question is raised:

We assume that every pirate is a very intelligent person and can judge their own gains and losses rationally to make the best choice, so what allocation scheme should the first pirate propose to prevent him from being thrown into the sea to feed sharks, and the benefits can be maximized?

(Analysis) classification questions often require reverse thinking, and these two questions are no exception.

For question 1, make sure that you can get the last ball. In the last round ("one round" is defined as the other party and the other party taking the ball one time in sequence), the remaining six values should be obtained, the other party takes X, and you can win the remaining 6-X ,..., Push forward one by one. The 100 table tennis balls can contain 100/6 = 16 rounds, and the remaining 100% 6 = 4 rounds. Therefore, you can get the answer: You get 4 balls first, then the other party gets x balls, and you get 6-x balls. This ensures that you get 100th balls.

For question 2, similar to question 1, you need to determine the number of coins that B Takes (assuming B wins) for the number of coins that a takes ). If you use the reverse push method, you must have one remaining. At this time, let a take it. In the last round, you can have three or six remaining items. In this way, a takes one, B Corresponds to 2; A gets 2; B gets 1; A gets 4; B gets 2 ,..., In turn, the 16 coins can be up to 16/3 = 5 rounds, and the remaining 16% 3 = 1.

For question 3, see: http://wenku.baidu.com/view/086e9ce8856a561252d36f4f.html

【Reverse water]

1. Suppose there is a pond with an infinite amount of water in it. There are two empty kettles with 5-litre and 6-litre capacities respectively. The question is, how can we get 3 liters of water from the pond using only the two kettles? (Elementary)

2. If there is an infinite amount of water, a 3 litre bucket and a 5 litre bucket, the shapes of the two buckets are uneven, how can you accurately claim 4 liters of water? (Elementary)

3. How can I accurately produce 2 liters of water if the bucket is 7 liters and 11 liters of water? (Elementary)

4. There are three wine glasses. Each of the two wine glasses can hold 8 or 2 wine glasses and one can hold 3 or 2 wine glasses. Now the two big wine glasses are full of wine. How can we evenly allocate the three cups to four people? (Intermediate)

(Analysis) Formal water pouring problem: infinite amount of water, the capacity of a, B (A <= B) of the water bottle is poured out C (C <= B.

Conclusion: C % *** (a, B) = 0 has a solution, which can be proved by the extended Euclid theorem: There are integers x, y, make AX + by = *** (A, B ).

General Solution: (C-litre water is poured from the kettle with capacity a and capacity B)

Int T = 0;

While (T! = C ){

Do (fill a), Do (pour a B );

T = T +;

If (T> = B ){

T = T-B;

Do (empty B), Do (pour a B );

}

}

For example, question 1:

Clerk a B t (A = 5, B = 6)

Fill a, pour a B 0 5

Fill a, pour a B 4 6 10

Empty B, pour a B 0 4 4

Fill a, pour a B 3 6 9

Empty B, pour a B 0 3 3 (SUCCESS)

【Weighing type]

5. There are a total of 12 balls of the same weight, only one of which is different from the others (unknown weight). I will give you a balance, just called three times, to find the ball with different weights? (Elementary)

6. If a total of 13 identical balls have only one weight different from the others (unknown weight), give you a balance, just three times, and find the ball with different weights? (Advanced)

(Answers and analysis are available online)

【Weird]

1. Two blind people bought two black so and two white so (each so is connected together). If you are not careful, the eight so are mixed together, how can they get their own so?

2. There were 23 coins on the table, with 10 coins facing up. Let's assume that someone has your eyes covered, and your hand cannot touch the front of the coin. Let you use the best way to divide these coins into two heaps, each of which has the same number of front-up coins (you can flip any coin at will ).

3. 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 other people's hats, but they don't know their own colors. 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?

4. There are 3 red hats, 4 black hats, and 5 white hats. Let ten people stand up from the dwarf to the tall, and wear a hat on each of them. Everyone cannot see the color of their hats, but they can only see the hats standing in front of them. (So the last person can see the color of the first nine hats on his head, but the first one cannot see the hats. Now, the last man asked him if he knew the color of his hat. If he replied that he didn't know, he asked him again. Suppose the first person must know that he is wearing a black hat. Why?

(Analysis) this type of question cannot be understood, and the question may have a strange meaning, but after careful analysis of the problem, the result will be obtained.

For question 1, every blind person only needs to take one of all the pair of so.

For question 2, you only need to divide 23 coins into two groups, one group of 10 and the other group of 13, and then flip all the coins in the group of 10.

For question 3, the recursive + Lenovo method can be used. First, assume that only one person is wearing a black hat, then when the light is turned off for the first time, there will be a clear slap in the face (you can think of N people, only you wear a black hat, before the first light is turned off, when you see everyone else wearing white hats, it is easy to think that you only have to wear black hats. Then, immediately give yourself a slap in the face after the lights are turned off ~); Then, let us assume that two people wear black hats (set the two to A and B respectively). Before the first light is turned off, both A and B will see each other wearing a black hat. After the light is turned off, they won't beat themselves. However, before the second light-off, for a, he thought that B didn't beat himself the last time, which means B saw someone with a black hat, while, B sees that everyone except himself is the same, that is, all wearing white hats. A thinks: B must have seen himself wearing black hats. Similarly, B will think like this, so when the lights are turned off for the second time, AB will beat itself ,..., In this case, N people wear black hats if a slap in the face appears after the light is turned off n times.

For question 4, see: http://www.oursci.org/archive/magazine/200111/011111.htm

【Optimization]

1. A monkey has 100 bananas on the side. It takes 50 meters to get home. Each time it moves 50 bananas at most, it eats one for every 1 meter walk, how many bananas can be moved to the house at most.

2. 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?

3. There is a 100-storey building with two identical glass pawns in your hands. Dropping the pawns from a certain layer of the building will break down. Use the two glass pawns in your hands to find an optimal strategy to find out the critical layer.

(Analysis) such questions need to be answered based on the specific situation using simple mathematical knowledge.

For question 1, because the monkey can only move 50 at a time, he needs to return a trip in the middle to fetch the remaining bananas. If a monkey returns at least 50 bananas in the middle of the journey, the optimal condition is that at least 50 bananas need to be stored in the middle of the journey and then go home without hesitation (no return ). Obviously, if (50-2 x) + (50-x)> = 50 and x <= 16.6 is obtained, X takes 16. At this time, the monkey can take 16 bananas home.

For question 2, recursive methods can be used. For $20, you can buy 20 bottles of soda, use these 20 empty bottles for 10 bottles of soda, and then use these 10 empty bottles for 5 bottles of soda, then use these five empty bottles for 2 bottles of soda, then use these three empty bottles for 1 bottle of soda, and then use the remaining two empty bottles for 1 bottle of soda. Finally, borrow an empty bottle, change a bottle of soda, and change the empty bottle back. A total of 20 + 10 + 5 + 2 + 1 + 1 + 1 = 40 bottles. Two other ways of thinking: solution 2: Let's take a look at how many bottles of soda can be consumed for 1 RMB at most. Drink 1 Bottle and 1 empty bottle, borrow one empty bottle from the merchant, and change 2 to 1 bottle to continue drinking. After drinking, return the empty bottle to the merchant. That is, a maximum of two bottles of soda can be consumed for 1 RMB. Of course, you can drink up to 40 bottles of soda for $20. Solution 3: two empty bottles for one bottle of soda, we can see that pure soda is only worth 5 cents. Of course, you can drink up to 40 bottles of pure soda for $20. Of course, N yuan can drink up to 2N bottles of soda.

This topic can be promoted to: 1 yuan a bottle of soda, after drinking two empty bottles for a bottle of soda, then N yuan, you can buy 2n bottles of soda.

Question 3 is actually a search problem on an ordered array. However, because there are only two pieces of glass that are available, the binary search method cannot be used. The solution to this problem is: first, there is still a glass pawn in the layer X. If it is broken, the other glass pawn will be used from 1 ~ X-1 layer test, find the critical layer; if the X layer is not broken, then in the x + (x-1) = 2x-1 layer is still a glass pawn, if broken, then, the x + 1 ~ 2x2 layer to find the critical layer ,..., In this way, we can get the expression: x + X-1 +... + 1> = 100, you can get x = 14, that is:

First from 14 layers (broken 1-13)

Then I threw it from layer 27 (15-26 broken)

Then I threw it from 39 layers (I tried 28-38)

Then I threw it from layer 50 (40-49 broken)

And then from the 60-layer drop (Broken 51-59)

Then I threw it from 69 layers (I tried 61-68)

Then I threw it from layer 77 (I tried 70-76)

Then, I threw it from layer 84 (dismounted trial 78-83)

And then from the 90-layer drop (broken down the trial 85-89)

Then, I threw it from the 95 th layer (I tried 91-94)

Then I threw it from layer 99 (96-98 broken)

Finally, from Layer 3