A broken car has to walk two miles, one mile up the hill and one mile down the hill. When it goes uphill, the average speed is 15 miles per hour. How fast can you go down the hill in the second mile? 30 miles per hour?

Is it 45 miles? )

B. Amebic protozoa reproduce by simple division, each division takes 3 minutes. Put an amoeba into a container filled with nutritious ginseng liquid. 1 hour later, the container is full of amoebas. If you start with two amoebas instead of one, how long will it take to fill the container? About half an hour, I guess? )

2. Will they meet?

"Where are you calling from?" Bert asked. At the moment, he is in the office at the corner of Merton Street and Spokelous Street, listening to the phone and watching the traffic outside the window.

"At a telephone booth at the intersection of Dale Street and King Street," Ben replied weakly. "Go south for four blocks, and then go east for a few blocks!"

Bert looked at the clock and shouted, "You start now and we'll meet halfway!" " "He put the phone down with a bang. Only then did he realize that he hung up too fast and didn't make it clear how to contact each other.

In fact, there are exactly 70 different routes between two intersections, and the choice between routes has nothing to do with distance.

So, how to understand the meaning of "several" in this sentence?

3. His first job

"ah! Johannes, "Joe met a young man in the street on Sunday and shouted to him," Long time no see, I heard you started working! "

"A few weeks," Johannes replied. "This is a piece-rate job, and I have done quite well. I got more than forty dollars in the first week, and every week after that, I earned 99 cents more than the previous week. "

"What a coincidence!" Joe continued with a smile, "May you continue as always!" "

"I estimate that I can earn 60 dollars a week before long," the young man told Joe. "I have earned a full 407 yuan since I started working. This is really not bad! "

How much did Johannes earn in the first week?

4. After the party.

"They all seemed awake when they left last night," said Bob, who had just returned home from the office.

"I don't think it will be worse than you," his wife firmly believes. "What's the matter?"

Bob smiled faintly. "The four of them have been calling me all day," he told her. "I must solve this mystery. They all took each other's coat and another man's hat by mistake. "

"When you came home, I felt something was wrong," Betty said with a smile. "Go on with your sad story!"

"Well, let me separate: Joe took a guy's coat, and that guy's hat was taken away by Steve; Steve's coat was taken away by another man, who took Joe's hat. "

"What about Ron?" Betty is very interested in this.

"He called first," Bob answered. "He took Togo's hat."

This is a real party! Whose coat and hat did Joe and Steve take?

5. Pinball game

"Come by yourself, but each person only takes 12," said Jim, taking out a dozen marbles from the box. "We have fewer green marbles here than blue ones, and blue marbles are less than red ones. So when everyone takes it, they should take the one with the most red and the one with the least green. But take away every color! "

After Jim did it himself, the other boys followed suit. There are always only three colors of marbles here, and the number of marbles in the box is just enough for everyone to take.

"We all take different methods!" Joe observed the marbles that everyone took out and said. "Only I have four blue ones!"

"So what?" Peter found himself dropping a green marble, so he picked it up. "Let's play!" "

So they started playing marbles.

There are always 26 red marbles here. How many boys are there here?

6. coat color

In a village isolated from the outside world, there lived three people. None of these three people can speak, but they are all smart. The hair of people in this village is either black or red. There are no objects (such as mirrors and lakes) in this village that can see themselves through reflections, so none of them know the color of their hair.

There is a custom in this village: if you know the color of your hair and commit suicide, you can go to heaven happily; If you guess the wrong hair color and commit suicide, you will go to hell in pain. These three people all want to go to heaven, but they all suffer from not knowing their hair color. These three people gather in the square at noon every day, looking at each other, hoping to know their hair colors. It was not until an outsider intervened that this dilemma was broken.

One day, a foreigner entered the village and met these three people in the square. He casually said, "At least one of you three has red hair." Say that finish and left the village. On the same day, after hearing this sentence, all three went home and thought hard. At noon the next day, the three met together in the square. When I went back the next night, two people committed suicide successfully. At noon on the third day, only one person went to the square. The man also committed suicide when he came back.

Excuse me: What color are these three people's hair?

7. Proof of1= 2

The art of reasoning touches all aspects of our lives, such as deciding what to eat, what kind of map to use, what kind of gift to buy, or proving a geometric theorem. All kinds of skills about reasoning involve solving problems. A small mistake in reasoning may lead to very strange and absurd results. For example, if you are a computer programmer, you will worry that the negligence of a certain step will lead to an infinite loop. Who among us can guarantee that we won't find any mistakes in our explanation, solution or proof? Dividing by zero is a common mistake in mathematics, which will lead to such absurd results as the following proof of "1=2". Can you find out what's wrong?

1=2?

If a=b and a, b > 0, 1=2.

Prove:

1)a, b > 0 is known.

2) a=b is known.

3)ab=bb In the second step, both sides of "=" are the same as "×b"

4)ab-aa=bb-aa Both sides of "=" in step 3 are the same as "-aa"

5)a(b-a)=(b+a)(b-a) In the fourth step, both sides decompose the factors simultaneously.

6)a=(b+a) Both sides of "=" in step 5 are the same as "∫(b-a)"

7)a=2a Step 2 and Step 6 Replacement

8)a=2a Step 7 Add similar items.

9) 1=2 Both sides of "=" in step 8 are the same as "∫"

Author: T. pappas

8. Go for a ride

"What are you up to, Bill?" The professor said attentively. At this time, his friend was drinking the rest of the coffee in one breath and stood up to leave.

"Ready to take three girls to travel by bus!" Bill replied.

The professor smiled: "So that's it! How old are the three beautiful women? "

Bill thought for a moment and said, "Multiply their ages to get 2450, but they are exactly twice as old as you."

The professor shook his head and said, "Very clever, but their age is still a problem."

Bill is still here. He added, "Yes, I forgot to say that I am at least one year younger than the oldest." This makes everything clear!

Of course, the professor knows his friend's age. Excuse me, can you work out their ages?

9. Go to the villa

"Everyone took their family to the villa," Bob said. "It's nice there. It is quiet at night and there is no car horn. "

"But the police go to work as usual," Ryan commented. "Don't you have a policeman there?"

"We don't need the police!" Bob said with a smile, "There is a problem in our driving, which deserves your consideration." What's the situation: before 15 miles, we averaged 40 miles per hour. Then, after walking about nine times, we drove faster. We have been driving very fast for the remaining seventh of the distance. The average speed of the whole journey is exactly 56 miles per hour. "

"What do you mean by' a few tenths'?" Ryan asked.

"The number here is an exact integer," Bob replied. "The speed of the next two trips is also an integer mile per hour."

Bob naturally won't race wildly with his family, although there may be no police on that road!

Excuse me, what is Bob's average speed in the last seventh mile?

10, a friend in need

After lighting the cigar, John leaned back in his chair. He seemed very satisfied with his life. "Yes," he said with a big smile. "Thirty years ago, when we were teenagers together, I never thought that we would have such a good life in the future."

His guest smiled slightly. They were good friends at that time, but that was a long time ago. What is the value of an old friendship when he needs a job badly today? "How are your two brothers?" He asked, "They are all younger than you, aren't they?"

John nodded. "Well done. The youngest Ben owns nearly a million dollars. Ted, the once clever boy, now lives in Washington. Bill, you used to be good at calculating. How about such a question? "

The tycoon scribbled down his question, while Bill waited hopefully for a few minutes: "Ben's age multiplied by the age difference between Ted and me is just smaller than my age multiplied by their age 1. The age here is calculated all year round. "

"That's too bad," Bill shook his head sadly. "I was going to come to work for you, but I didn't expect you to sell me your computing power!"

Bill got the job naturally. However, knowing the ages of those three people will undoubtedly bring you happiness.

1 1, light gambling

"I don't have any change," Hank said, jingling his coins. "How much do you have?"

Ben looked at it and replied, "Exactly five. What's wrong? "

"Do you want to know? How about I want some gambling games? " Hank began to divide the cards as he spoke. "It is stipulated that the loser in the first game will pay one-fifth of the money; The loser in the second game lost a quarter of what he had at that time; The loser in the third game has to pay one-third of what he had at that time. "

So they fought accurately and paid each other. Ben lost in the third game. After paying the money, he stood up and declared, "I think this game puts too much energy into it and pays too little." Until now, the amount between us has always been only seven points. "

This is naturally a small bet, because together they only have 75 cents.

How much money did Hank have at the beginning of the game?