1. There are two incense sticks distributed unevenly. The time it takes for the incense to burn out is one hour. How can you determine a period of 15 minutes?

Answer: Light up two incense sticks at the same time. The first incense is lit at both ends, and the other incense is burned at only one end. When the first incense is burned out (this is the total length of the incense burned out) 3/4), light the other end of the second incense, the time from burning to extinguishing the other end is 15 minutes!

2. A manager has three daughters. The sum of the ages of the three daughters is equal to 13. The sum of the ages of the three daughters is equal to the manager’s own age. A subordinate already knows the manager’s age, but still cannot Determine the ages of the manager's three daughters. At this time, the manager said that only one daughter has black hair. Then the subordinate knew the ages of the manager's three daughters. What are the ages of your three daughters? Why?

Answer: The ages of the three girls should be 2, 2, and 9. Because there is only one child with black hair, that is, she is the only one who has grown up, and the other two are still in childhood, that is, less than 3 years old, with light hair. Combined with this, the age of the manager should be at least greater than 25.

3. Three people went to stay in a hotel and stayed in three rooms. Each room cost $10, so they paid the boss $30 one day. The next day, the boss thought the three rooms only cost $25. Yuan was enough, so I asked the boy to return $5 to the three guests. Who knew that the boy was greedy, so he only returned $1 to each person, and secretly took $2 for himself. In this way, the three guests each spent nine yuan, so the three I spent $27 per person, plus my little brother ate away $2, the total was $29. But when the three of them paid $30 a ***, what about the remaining $1?

Answer: The 30 yuan paid per day includes 27 yuan (25 yuan for the boss + the younger brother embezzled 2 yuan) and 1 yuan will be returned to each person (***3 yuan), and you will get 27 and 2 yuan Adding them up is purely confusing.

4. There were two blind men. They each bought two pairs of black socks and two pairs of white socks. The eight pairs of socks were made of the same fabric and size, and each pair of socks had a piece of trademark paper. Connected. Two blind men accidentally mixed up eight pairs of socks. How can each of them retrieve two pairs of black socks and two pairs of white socks?

Answer: Open each pair of socks, each person takes one pair, there are no left and right socks, and finally get two pairs of black socks and two pairs of white socks.

5. A train leaves Los Angeles and goes straight to New York at a speed of 15 kilometers per hour, and another train goes from New York to Los Angeles at a speed of 20 kilometers per hour. If a bird starts from Los Angeles at the same time as two trains at a speed of 30 kilometers per hour, encounters another car and returns, flying back and forth on the two trains until the two trains meet, what will this bird do? How far did the bird fly?

Answer: Convert the bird’s flight distance into time. Suppose the distance between Los Angeles and New York is a, the time when the two trains meet is a/(15 20)=a/25, and the bird’s flight speed is 30, then the bird’s flight distance is a/25*30=6 /5a.

6. You have two jars, 50 red marbles and 50 blue marbles. You can put the marbles in the way you imagined. After placing the marbles, randomly select a jar. A marble is randomly selected and put into the jar. How to give the red marble the greatest chance of being selected? In your plan, what is the exact probability of getting a red ball?

Answer: Put a red ball in one jar, 49 red balls and 50 blue balls in another jar. The probability is close to 75.

This is the maximum probability that can be achieved. .

In fact, as long as one jar contains 50 red balls and no basketballs, and the other jar contains the remaining balls, the probability of taking out a red ball is greater than 50

7. You have four jars containing pills. Each pill has a certain weight. The contaminated pills have the weight of the uncontaminated pills + 1. You only weigh them once. How do you determine which jar contains the pills? Contaminated?

Answer: Take 1 pill from can No. 1, 2 pills from can 2, 3 pills from can 3, and 4 pills from can 4. Weigh the 10 pills and calculate the ratio

The weight usually indicates the size of the can of medicine that has the problem.

8. Xiao Ming and Xiao Hua bought 10 kilograms of honey and put it in a large bottle. They wanted to divide the honey equally. There were only two empty bottles. One contained exactly 7 kilograms and the other contained exactly 3 kilograms. How can we separate the honey in the simplest way? Remember to use the simplest method, that is, the method with the least number of times.

Answer: 10 catties bottle, 7 catties bottle, 3 catties bottle

Before starting 10 0 0

1. 3 7 0

2 . 3 4 3

3. 6 4 0

4. 6 1 3

5. 9 1 0

6. 9 0 1

7. 2 7 1

8. 2 5 3

9. 5 5 0

一***9 Steps, this method is the least, people who make 10 steps should think about it again.

9. Perform the following operations on a batch of lights numbered 1 to 100, with all switches facing up (on): For every multiple of 1, turn the switch once in the opposite direction; for multiples of 2, turn the switch once in the opposite direction. Switch; in multiples of 3, flip the switch in the opposite direction... Q: The last number is the number of the light in the off state.

Answer: When the square root of the number is an integer (that is, a perfect square number), it faces down, and other numbers face up.

In this way, numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 face down

10. Three hunters took a black bear, and two A brown bear crosses the river.

The boat is very small and can only carry two people, or two bears, or one person and one bear across the river at a time

Three hunters can row the boat. Black bears are hunters Those who have been trained can also row boats.

But once the number of bears exceeds the number of people, the bears will eat people

How to cross the river safely

Answer : The black bear first transported a brown bear across the river. The black bear rowed back and then transported the other brown bear across the river. The black bear rowed back. Two tearful people rowed across the river. One hunter brought back a brown bear, and the other hunter transported the black bear across the river. River, a hunter is bringing back a brown bear, two hunters are rowing across the river, the black bear is rowing back and transporting the two brown bears across the river in two times

11. A group of people have a dance party, everyone wears a hat on their head Wearing a hat. There are only two kinds of hats, black and white, and there is at least one black one. Everyone can see the color of everyone else's hats, but not their own. The host first asked everyone to see what hat others were wearing, and then turned off the lights. If anyone thought they were wearing a black hat, they would slap themselves in the face. When I turned off the lights for the first time, there was no sound. So the lights were turned on again, and everyone watched it again. When the lights were turned off, there was still silence. It wasn't until the third time the lights were turned off that the sound of slaps could be heard. How many people wear black hats?

Answer: There are three people wearing black hats. Suppose there are N people wearing black. When N=1, black people wearing black can be sure that they are black when they see that others are white. So there should be a sound when the lights are turned off for the first time. It can be concluded that Ngt;1. For each person wearing black, he can see N-1 black hats, and thus assumes that he is white. But after waiting for N-1 times and no one hits him, every black person will know that he is also black. So when you turn off the lights for the Nth time, N people will hit you.

12. There are 10 boxes of cans. Each of these 10 boxes contains 20 boxes, and each box weighs 1 catty.

But there is one box with only 9 taels per box.

Now there is only one scale, and it can only be weighed once

We must find the problematic box.

[Premise: You cannot lift it with your hands. Which one is lighter]

Answer: Number the boxes as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Start from No. 1 Take one box, two boxes of No. 2...ten boxes of No. 10. ***There are 55 boxes.

Put the boxes you took out on the scale and look at the number. When it is 10 When the boxes are 1 kilogram each, the number displayed on 55 boxes should be 55 kilograms, and the question says that there is a box with 9 taels per box. Judging from the method of picking up the box just now, if it is No. 1, No. 1 will only take one box. Then the indication number should be 54.9. If it is No. 2, No. 3, No. 4... and No. 10, the indication number is 54.8, 54.7, 54.6, 54.5, 54.4, 54.3, 54.2, 54.1, 54. Look at the last one. You will know which one is lighter by its weight.

13. A bottle of soda costs 1 yuan. After drinking, two empty bottles are exchanged for one bottle of soda. Question: You have 20 yuan. How many bottles of soda can you drink at most?

Answer: 39 bottles, starting from the second bottle, which is equivalent to buying 2 bottles for 1 yuan.

14. In the market, a peasant woman put the eggs laid by the chickens she fed in a basket for sale. A young man on a bicycle accidentally touched her basket. The basket was knocked over and the eggs were broken. The young man wanted to compensate her for the loss and asked: "How many eggs are in the basket?" "I don't remember the correct number," the peasant woman replied, "But I know that when I press 2 eggs from the basket at a time or When I take out 3 pieces at a time, 4 pieces at a time, 5 pieces at a time, and 6 pieces at a time, there is always one left in the basket, but when I take out 7 pieces at a time, there is no one left in the basket.

How many eggs are there in the basket?

Answer: 301. For this question, you must first know the least common multiple of 2, 3, 4, 5, and 6, which is 60, so this number is 60x. 1. And because this number is divisible by 7, x=560x 1=301. Of course, if you say 721, it is also possible, but to consider the actual situation, 301 is more practical.

15. There is a wife. She went shopping with two 50 yuan bills and bought exactly 100 yuan of things. She bought grapes for 22 yuan, apples for 11 yuan, oranges for 30 yuan, peanuts for 15 yuan, garlic for 14 yuan, and washing powder for 8 yuan. But this old man. My wife is a weird person. She only wants change from one of the 5 stores she buys from, and she doesn’t want to change it.

Answer: There are many answers, old lady. First go to a store and use two pieces of 50 yuan to buy apples for 11 yuan and garlic for 14 yuan respectively, and get back 39 yuan and 36 yuan (a piece of 20 yuan, a piece of 10 yuan, a piece of 5 yuan and 4 coins) and (one A piece of 20 is worth 10 yuan each, a piece of 5 yuan and 1 coin)

Then I went to the second store and used a piece of 20 yuan and 2 coins to buy grapes (two pieces of 20 yuan were left) 10 yuan, two pieces of 5 yuan and 3 coins)

I went to the third store and used one piece of 20 yuan and one piece of 10 yuan to buy oranges (left one piece of 10 yuan, two pieces of 5 yuan and 3 coins) coins)

Go to the fourth store and buy peanuts with one piece of 10 yuan and one piece of 5 yuan (leaving one piece of 5 yuan and 3 coins)

Use the last money 8 Yuan (5 yuan and 3 coins left) bought washing powder at the fifth store.

I only had change at the first store, but I didn’t get any change.

16. Three frogs can eat three worms in three minutes. How many frogs can eat 81 worms in twenty-seven minutes?

Answer? : Nine. If three frogs eat three bugs in three minutes, they can eat twenty-seven bugs in twenty-seven minutes. Now they need to eat eighty-one, so they can only multiply the number of frogs by three. .

17. There are three boxes: red, green, and yellow.

Only one box has a prize. There is a note on each box. Three There are three sentences written on the note, only one of which is true.

The red box says: The prize is not in the red box

The green box says: The prize is not in the green box

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The yellow box says: The prize is not in the red box

Which box is the prize in?

Answer: The red box, because only the red box has a prize.

18.1 2 3 4 5 6 7 8 9=100

You can only use addition and subtraction to make these numbers equal to 100

Because there are many answers

So who can solve this problem with the fewest addition and subtraction signs

Answer: 123 45-67 8-9=100

19. Xiao Ming’s son He is the father of my son, so what is my relationship with Xiao Ming

Answer: There are four possibilities. 1. Xiao Ming’s son and I are the same person. So Xiao Ming and I have a father-son or mother-son relationship.

2. Xiao Ming’s son and I are not the same person. Then I am the wife of Xiao Ming’s son, then Xiao Ming and I are the relationship between mother-in-law and daughter-in-law or father-in-law.

20. On a snowy night, you are driving home. Halfway through, you see three people on the road. One is a seriously ill old man, one is the doctor who saved your life, and the other is the doctor in your dream. Lover, they all ask for a ride in your car, but your car can only carry one person. What will you do?

First of all, you need to know: 1. The old man is dying. 2. You really want to repay this doctor. If you miss this opportunity, you don’t know if you can meet him next time. 3. Your loved one will go abroad soon, and you will have no chance to confess your love any further

Answer: The best thing is to ask the doctor to take the old man to the hospital, and stay with your loved one yourself. But everyone has their own choices. This answer can only be said to be the most comprehensive answer, but it may not be the most suitable for you.