1. A pile of 80 coins, one is not enough. There is a balance. Is there any simple way to find it?

2. A boy and a girl go to two schools two kilometers and one kilometer away from home respectively, and walk home at the speed of four kilometers and two kilometers per hour at the same time after school every day. A puppy runs from the boy to the girl and from the girl to the boy at a speed of 6 kilometers per hour, and so on until he gets home. How many miles did the puppy run? If the puppy runs back and forth between boys and girls at school, where is the puppy at school?

3. Epitaph of Diophantine (linear equation) On the tombstone of Diophantine, a famous algebraic scientist in ancient Greece in the third century A.D., the inscription reads: "Passerby, Diophantine's ashes are buried here. The following figures can tell you how long his life span is. One sixth of his life was a happy childhood. After living for twelve times, a thin beard grew on his cheek. Diophantu is married, but has no children yet. In this way, my life has passed by another seventh. Five years later, he had a child and felt very happy. But fate gave the child a brilliant life, only half of his father's in this world. Since the death of his son, the old man has lived in deep sorrow for four years, ending his earthly career. Please calculate, how old did Diophantine live before he died? "

4. A week in Birmingham

There is a supermarket, a department store and a bank in Boomingham town. On the day I arrived in Birmingham, the bank was already open for business.

(1) But there is not a day a week when supermarkets, department stores and banks are open.

Department stores are open four days a week.

This supermarket is open five days a week.

(4) All three units are closed on Sundays and Wednesdays.

(5) During three consecutive days: On the first day, department stores were closed; The bank closed the next day; On the third day, the supermarket closed.

(6) Another three consecutive days: the first day of bank closure; The supermarket closed the next day; On the third day, the department store closed.

So what day do I arrive in Bloomingham?

5. One, three or four?

There is a coin game, and its rules are: (1) a pile of coins * * * nine. (2) Both parties take one, three or four pieces in turn. (3) Whoever takes the last one wins. Is it certain that one of the two men will win? If yes, how to obtain it?

6. Dream lover

John's dream girl has blonde hair, blue eyes, slim figure and tall. He knows Adele, Betty, Carol and Doris, one of whom is John's dream girl. (1) Only three young ladies have blue eyes and slim figure. (2) Only two are tall people with yellow hair; (3) Only two are thin and tall. (4) Only one has blue eyes and yellow hair. (5) Adele and Betty have the same eye color. Betty and Carol have the same hair color. Carol and Doris are different in stature. Doris is as tall as Adele. Which of these four people is John's dream lover?

7. Hair 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 three people don't 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 color of your hair 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?

;