Intelligence logic question (2)

[11] 12 balls and one balance, now know that only one is different from other weights, ask how to name the ball three times to find it. What about 13? (Note that this question does not indicate that the weight of the ball is light or heavy)

When there are 12, you can find out whether it is heavy or light. When there are 13, you can only find out which ball it is.
Compile the ball as ① (2) (4) (6. (When 13 digits are numbered as hour)
Said for the first time: first put ① ③ ④ and ⑤ 7th on both sides of the balance,
(I) if they are equal, it indicates that the special ball is in the remaining four balls.
Perform the second weighing of ① weight and ↓ weight,
If the weight is equal, it indicates that the weight is special. If the weight is equal to the weight of the weight, you can determine whether the weight is heavy or light.
For example, ① weight <weight loss indicates that either the weight loss or the weight loss is light.
The weight and weight are weighed for the third time. If the weight is equal, the weight is light.
For example, ① weight> weight loss indicates that either the weight is light or the weight is heavy.
The weight and weight are weighed for the third time. If they are equal, the weight of the weight is not equal.
(Ii) For example, if the left side is <right side, the left side is light or the right side is heavy.
Perform the second weighing for ① ⑤ and ③ ④
If the weight is equal, it indicates that there is a weight in the 7th and 7th, and the third weighing is done to determine who is the weight in the 7th and 7th
For example, ① ② ⑤ <③ ④ ⑥ indicates that either ① ② has a light or ⑥ is heavy.
Perform the third weighing of ① and ②. If the weight is equal, the weight is equal to or equal to the weight.
For example, ① ② ⑤> ③ ④ it means that either ⑤ is heavy or ③ One of them is light.
Perform the third weighing of ③ and ④. For example, if the weight is equal, the weight of ⑤ is not equal.
(3) on the left and right, refer to (2.
When there are 13 balls, perform the following steps after step 1.
Perform the second weighing of ① weight and ↓ weight,
If the weight is equal, it indicates that the weight is special. When the weight is weighed for the third time, you can determine whether the weight is heavy or not, but the weight cannot be determined.
For more information about regions, see step 1.

 

[12] it takes an hour to burn an uneven rope. How can I use it to determine a half hour? It takes an hour to burn an uneven rope from the beginning to the end. Now there are several ropes of the same material. How can I use the burning method to time the rope for an hour and 15 minutes? (Microsoft pen exam)

1. A rope is burned from both ends and burned out for half an hour.

2. When one piece is burned at one end, one piece is burned at both ends (30 minutes), and the other end is burned at the other end for 45 minutes. Then the third node is ignited from both ends, and the second node is burned at 01:15.

 

[13] There are three types of medicines, weighing 1g, 2g, and 3G respectively, and put them in several bottles. Now we can make sure that there is only one of them in each bottle, 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 )? 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?
Note: of course there is a price. We don't need the medicines we call.
The first bottle took out one piece, the second bottle took out four pieces, and the third bottle took out sixteen pieces ,...... The m is used to take out the power of the n + 1 m-1. Put all these pills together for weighing.

 

[14] the mechanical strange question about monkey ropes is simple at first glance, but it is said that it puzzles Lewis Carol. It is unclear whether this strange question was proposed by the Oxford University mathematical expert known for Alice roaming wonderland. In short, in an unlucky moment, he consulted people on the following questions: A rope goes through a non-friction pulley and hangs a 10-pound weight on its end, there is a monkey at the other end of the rope, and the balance is exactly the same as the weight. How does a weight work when a monkey begins to climb up? "It's strange," Carol wrote. "Many good mathematicians give very different answers. Price believes that the weight will increase and the speed is getting faster and faster. Kelifton (and Harcourt) believes that the weight will rise at the same speed as the monkey, but Samson says the weight will fall! "An outstanding mechanical engineer said," This will not be more effective than a fly crawling on a rope ", A scientist believes that "the rise or fall of weight will depend on the reciprocal of the speed at which the monkey eats an Apple", but he still has to find the square root of the monkey's tail. Seriously, this question is very interesting and worthy of careful consideration. It shows the close relationship between interesting questions and mechanical problems.

Weights increase at the same speed as monkeys because they are of the same quality and stress.

 

[15] Two hollow spheres have the same size and weight, but different materials. One is gold and the other is lead. Hollow Sphere surfaces are painted in the same color. It is now required to use a simple method to identify which is gold and which is lead without damaging the surface paint.

The rotation speed indicates that the density and quality of the golden ball are the same. Therefore, the actual volume of the Golden Ball is small. Because the outer radius is the same, the inner radius of the Golden Ball is large, so the inertia of the Golden Ball is large, under the same external torque, the angle acceleration of the Golden Ball is small, so it turns slowly.

 

 

[16] Three bulbs in the house, three switches outside the house, one switch only controls one lamp, and the other cannot see how to enter the house only once, so you can know which switch controls which lamp? Si Zhan ~

Temperature, open one first, close after a long enough time, open another, enter the room to see, bright for later, touch hot for first open, the remaining one is OK.

Four switches: Set the four switches to ABCD. Open AB first. After a long time, turn off B and open C. Then enter the room. The light is hot and bright, and the light is a. Only B is hot, only light is not hot for C, light is not hot for D.

 

[17] Five monkeys found a pile of peaches by the sea and decided to divide them equally the next day. in the early morning of the next day, the first monkey first came, and its left and right points were inseparable. Then, one monkey was thrown into the sea, which could be divided into five portions. It took one of its own portions and went away. the second, and fifth monkeys encountered the same problem. In the same way, they both threw away one and split it into five portions. how many peaches are there at least?
There are at least 3121 peaches.
The first monkey threw away one and took 624 and the remaining 2496;
The second monkey threw away one and took 499 and the remaining 1996;
The third monkey threw away one and took 399 and the remaining 1596;
The fourth monkey threw away one and took 319 and the remaining 1276;
The fifth monkey threw away one and took 255 and the remaining four heaps, each with 255.
If positive and negative values are not considered,-4 is a solution.
Considering that five monkeys are required, it is assumed that the number of monkeys is equal to n.
The solution of the question: 5 ^ n-4
This topic is entitled 5 ^ 5-4 = 3121.

Set a total of a peach, and then B = (4/5) (4/5) (4/5) (4/5) (4/5) (A-1)-1) -1)-1)-1)-1), that is, B = (1024a-8404)/3125; A = 3B + 8 + 53 * (B + 4)/1024, if 53 and 1024 are not correlated, B = 1020 can have an approximate solution. A = 3121 is obtained, and X is used to obtain the equation.
4/5 {4/5 {4/5 [4/5 (x-1)-1]-1}-1} = 5N
Expand
256x = 3125n + 2101
Therefore, x = (3125n + 2101)/256 = 12n + 8 + 53 * (n + 1)/256
Because 53 and 256 are not correlated, we can judge that n = 255 has a solution. X as an integer, equal to 3121.

 

[18] Mr. Zhang and Mr. Xiaoqiang are both students of Mr Zhang. Their birthdate is m month N. Both of them know that Miss Zhang's birthdate is one of the following 10 groups, mr. Zhang told James about m and John about N. Did she know that his birthday was that day?
March 4 March 5
June 4
September 1
December 1 December 2
James said: If I don't know, I'm sure I don't know either.
Xiaoqiang said: I didn't know either, but now I know.
James said: Oh, I know.
Determine the day of Miss Zhang's birthday Based on the conversation above.

9.1

 

[19] if you ask a worker to work for you for seven days, the reward for the worker is a golden stripe. Gold bars are evenly divided into seven connected segments. You must pay at the end of each day. How do you pay your workers if you only break the gold bars twice?

Divide the gold bars into three segments: 1, 2, and 4. First day 1, second day 2, third day 1 + 2 ...... The Seventh Day is 1 + 2 + 4.

 

[20] 10 boxes of gold, 100 RMB per box, one or two RMB per block. There are corrupt officials who need to pay for each block in a certain box. Please name the box that finds the bulk at a time

Take 1 for the first box, 2 for the second box, and N for the nth box, and then put them together to see how much money is missing, if n is missing, it indicates the nth box.