Summary of Intellectual problems (1)

1. There are two uneven distribution of incense, incense burning time is one hours, you can use what method to determine a period of 15 minutes?
A : incense A lit a side, incense B lit at both ends. When incense B burns, the time has passed for 30 minutes. And then the other end of incense a also lit. From then on to a burn out time is 15 minutes.

2. A manager has three daughters, the age of three daughters equals 13, the age of three daughters is multiplied by the age of the manager, one of the subordinates knows the manager's age, but the manager is still unsure of the age of three daughters, when the manager says only one daughter's hair is black, Then the subordinate knew the age of the manager's three daughters. What is the age of three daughters, please? Why?
Answer: The age of three women should be 2, 2, 9. Because only one child black hair, that is, only she grew up, the other two or early age is less than 3 years old, hair is pale. The age of the re-union manager should be at least greater than 25. And because the light knows the product cannot determine the age of the girls, the product is not unique.

3. There are three people to live in hotels, three rooms, each room $ million, so they pay the boss of the total, the next day, the boss felt that three rooms only need $ $ to be enough so called the younger brother returned to three guests, who knows little brother greedy, only return each person $, he secretly took the $ 2, so that is equal to the three guests each each spent nine yuan, so three people altogether spent a $27, plus the younger brother took the money, a total of $29. But when they were three, they paid a total of $ $.

A: A typical swap concept. In fact 3 people only paid 27 yuan, the boss got 25 yuan, the younger brother took 2 yuan.

4. There were two blind people, each of them bought two pairs of black socks and two white socks, eight pairs of socks cloth, the size is identical, and each pair of socks have a trademark paper attached. Two blind people accidentally mix eight pairs of socks together. How can each of them get back two pairs of black socks and white socks?

A: Take each pair of socks apart one person.

5. A train left Los Angeles at 15 km/h to New York and another train from New York to Los Angeles at a speed of 20 kilometres an hour. If a bird, at 30 kilometers per hour and two trains at the same time, starting from Los Angeles, met another car back, followed by two trains back and forth, until two trains meet, excuse me, this bird flew how long?

A: The railway in Los Angeles to New York is a kilometer long. The two trains met with a A/(15+20) hour, the time when the birds flew. So the distance the bird flies is the speed x time =30XA/35=6/7 Los Angeles to New York Railroad long.

6. You have two cans, 50 red marbles, 50 blue marbles, randomly select a jar, randomly pick a ball into the jar, how to give the red pinball the biggest selection opportunity? What is the exact odds of getting the red ball in your plan?

A: a jar put 1 red, the other left, the odds are 50%x1+50%x49/99=75%

7. You have four cans loaded with pills, each pill has a certain weight, the contaminated pill is not contaminated by the weight of +1. Weigh only once, how can you tell which pot's medicine is contaminated?

A: 1th can take 1 pills, 2nd can take 2 pills, 3rd cans take 3 pills, 4th cans take 4 pills, weighing the 10 pills, heavier than normal weight is the number of cans of medicine there is a problem.


8. You have a bucket of jelly, which has yellow, green, red three species, close your eyes, grab two of the same color jelly. How many can you grab to make sure you have two jelly of the same color?

A: 4. Quantity > color type. The color must be repeated.

9. For a number of 1~100, all switches facing up (on) the lamp to do the following *: Generally 1 in multiples of the opposite direction dial a switch, 2 multiples of the opposite direction and Dial a switch, 3 multiples of the opposite direction and dial a switch ... Q: The number of the lamp that was last turned off.

A: There are 10 lights out, respectively, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100th. Because: each prime number can be divisible by 1 and itself, so the light of the prime is bright. Set a composite to be divisible by n, and N must be an even number. For a composite that is not a certain number of squares, it will be switched n times, that is, even several times, the lamp remains bright, and for the square number listed above, it is switched only N-1 times, so the lamp is off.

10. Imagine you in front of the mirror, ask, why the image in the mirror can be reversed around, but not upside down?

A: The mirror is perpendicular to you in the mirror, but it just turns 180 degrees in the horizontal direction.

11. A group of people had a ball and each wore a hat on their heads. The hat is only black and white, with at least one black. Everyone can see the color of other people's hats, but they can't see their own. The moderator first let everyone see what other people wearing the hat, and then turn off the lights, if someone thinks they are wearing a black hat, hit himself a slap. The first time off the light, no sound. Then turn on the lights, we see again, turn off the lights are still silent. It was not until the third time that the light was turned off that the sound of the slap was popping. How many people are wearing a black hat?

A: There are three people wearing a black hat. Suppose there are n people wearing black, when the n=1, wearing black see others are white can affirm themselves as black. So the first time to turn off the lights should be sound. Can judge N>1. For everyone who wears black, he can see the N-1 top Black hat, and thus assume that he is white. But waiting for N-1 times no one has beaten themselves, every black man can know that he is also black. So the nth turn off the lights there are n people beating themselves.

12. Two rings, the radius is 1 and 2, the small circle in the circle around the circle round Monday weeks, asked the small circle itself to turn a few weeks? If the outside of the great circle, the small circle itself to turn for several weeks?

answer ; Both inside and outside, the small circle turns two laps. Because the circumference of a circle is twice times the circumference of a small circle.

13.1 yuan a bottle of soda, after drinking two empty bottles for a bottle of soda, asked: You have 20 yuan, you can drink up to a few bottles of soda?

answer : 39 bottles. Two Empty bottles = one bottle of soda (with empty bottles). An empty bottle = soda. Because the bottle + water = 1 yuan. So water = 0.5 yuan. So 20 yuan is equivalent to 40 bottles of water. Because there is only one empty bottle left to change. So I can drink 39 bottles.

14. Two rooms think can not see, a room has three switches, respectively control the other room in the three lights, asked: only to enter two rooms only once, how to determine which switch is the control of which lamp?

answer : through the temperature. That is: first open the Switch 1, open 10 minutes, then turn off, turn on the switch 2, into the room with a lamp, with the hands of the light of the two light bulbs, the heat is switch 1 control, no heat is switch 3 control, the light is switch 2 control

15. There is a person is blue-green blindness, that his eyes see blue reaction is green, see green reaction is blue, but this person's consciousness is blue as green, green as blue, that is, he saw blue things, or will say is blue. But he himself does not know what is different from other people, ask: What kind of way can you let him know that he is different from others?

A: optically, blue + red = purple, green + red = yellow, so, give him red eyes, let him look blue, he will say is "yellow", and the normal person should say the purple. (self-made answer, unofficial)

16. One day a young man bought a present from the boss of Wang. This gift cost 18 yuan, the price is 21 yuan. The result of the young people out of 100 yuan to buy this gift, Wang Boss no change, had to find the neighborhood for 100 yuan change. Looking for young people 79 yuan, but the neighborhood found 100 yuan is counterfeit money, Wang boss helpless also the neighborhood 100 yuan.
Question: How many dollars did boss Wang lose in this transaction?

answer : Enter: 100+100 (FALSE)

out: 79+18+100

Into-out =79+18=97

17. How many points on the earth make it a mile south from that point, a mile east, and a mile north, just back to the beginning?

answer:"North Pole" is a traditional answer, in fact, there are other answers to this question. In fact, there are infinitely many points to meet the requirements. All the miles from the Antarctic point 1 + 1/(2π) are satisfying, and a mile south will take you to the South Pole 1/(2π), a mile east, just a week after the latitude circle, and then north to the original road back to the starting point. In fact, this is still not the whole point of satisfying the requirements. From Antarctica point 1 + 1/(2kπ) is possible, where k can be any positive integer.

18. Consider a two-player game. The game is on a round table. There are enough coins for each player. They need to take turns placing coins on the table, each time it is necessary and can only place a coin, requiring the coin to be placed entirely on the table (not part of the outside of the desk), and cannot overlap with the original coins. Whoever has no place to put the new coin will lose. Is there a winning strategy for the pioneers of the game or the followers? What is this strategy?

Answer: the forerunner places a coin in the center of the table, and the future coin is always placed in the position relative to the place where the following person had just put it. In this way, as long as the person can put, the forerunner must have a place to put. Pioneers win.

Both 19.A and B were on two islands. B is sick, and a has the medicine that B needs. C has a boat and a lockable box. C is willing to carry things between A and B, but things can only be placed in boxes. As long as the box is not locked, C will steal everything in the box, no matter what is in the box. If A and B each have a lock and can only open the key of their own lock, how should a be delivered to B?

Answer: A put the medicine in the box and lock the box with your own locks. b After getting the box, add a lock on the box. After the box is shipped back to a, a takes off its own lock. When the box is transported to B, B takes off his lock and gets the medicine.

20. A couple invited N-1 to a party (so there was a total of 2N people at the party). Everyone shook hands with all the people they didn't know. Then, the host asked the rest of the people (a total of 2n-1 individuals) each held a few hands, the answer is all different. Assuming everyone knows their spouse, how many hands did the hostess hold?

Answer: The number of handshakes can only be from 0 to 2n-2 this 2n-1 number. Apart from the male master, there are altogether 2n-1 individuals, so each number happens once. One of them (0) did not shake hands, and a man (2n-2) and all the other couples shook hands. These two people must be a couple, otherwise the latter will shake hands with the former (thus the former handshake number is no longer 0). Apart from the couple, one person (1) shook hands with (2n-2) only one person (2n-3) and a couple other than (0). These two people must be a couple, otherwise the latter will shake hands with the former (thus the former handshake number is no longer 1). And so on, until the person who has held N-2 times and the person who has held the N-time hand is paired. At this point, all but the male owner and his spouse are paired with each other. According to the rule of exclusion, the last remaining person to shake hands is the hostess of the N-1.

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Summary of Intellectual problems (1)