Iq

1. February 28th at 19 o'clock you set the mechanical alarm-clock at 8 o'clock in the morning and go to bed. How many hours will you sleep, if we suppose that you fall asleep immediately after setting the alarm-clock?

2. Before entering the flat, you notice that there's water flowing out under the door. After you enter the flat, you can see that someone forgot to close the water-tap. There's a lot of water on the floor, the phone doesn't work and there's noone near you. At disposal, you have: a vacuum cleaner, a hose (10 metres long), an empty bath, a bucket, a rag and a basket. How do you start to solve this situation? 3. There's water dripping into an empty glass. Each minute, the number of drops in the glass doubles. The glass is full in an hour. How long did it take to fill the cup up to one half?

4. There are two men and three hats in a dark room. Two of the hats are white, one is black. Both men are aware of this fact. Each of the men puts one hat on his head, but they don't know what colour it is. They leave the room - one after another - and go out to the light. The second man can see the colour of the first man's hat, but can't see the colour of his own hat. The first man sees neither the colour of his hat, nor the colour of the second man's hat. They both don't know the colour of the hat, left in the room. After a while, the second man says that he doesn't know what colour his hat is. The first man immediately answers that his hat is white. How did he find it out?

5. A dying man left following last will for his pregnant wife: - If a boy is born after my death, he gets 2 thirds and mother 1 third of the inheritance. - If a girl is born after my death, she gets 1 third and mother 2 thirds of the inheritance. How is the inheritance divided, if: a). two boys b). two girls c). a girl and a boy are born?

6. Peter, David and Paul said following sentences: Peter: "David is a liar, Paul always tells the truth." David: "Peter is truthful." Paul: "David is a liar, Peter is truthful." Two of these men always tell the truth, one of them sometimes tells the truth and sometimes lies. Which of these men is a liar?

7. A car leaves from Prague to Brno. An hour later, the second car leaves from Brno to Prague. Both cars have the same speed - 100 kilometres per hour. Which car - when they meet - will be closer to Prague, if we suppose that the distance between Prague and Brno is 200 kilometres?

8. There are two kinds of groups in a room. People from the first group always tell the truth, people from the second group always lie. A visitor comes into the room and meets three people. To learn, which one is a liar, he asks 'A': "Are you a liar, or truthful?" Unfortunately, 'A' answers unintelligibly. That's why the visitor asks 'B': "What does 'A' say?" 'B'

answers: "'A' says that he is a liar." And 'C' says: "Don't believe 'B', he lies." Which group do 'B' and 'C' belong to? 9. Joseph and John meet. One of them says: "Either I am a liar, or John is truthful." What is Joseph and what is John?

10. 'A', 'B' and 'C' meet. There's someone who always tells the truth and someone who only lies. 'A' says: "We all are liars." 'B' says: "One of us is an honest man." Who tells the truth and who lies? 11. If John gives Joseph one crown, they both will have the same amount of money. If Joseph gives John one crown, John will have nine times more money than Joseph. How much money does each of them have? 12. In the castle, there was found a document, where following was stated: "The treasure is buried in a place, where the shadow of the lime tree top falls exactly at 3 o'clock." At digging, no treasure was found. Name the reason, why they couldn't find it.

13. There are three bags on the table - in each of them, there are two marbles of the same size and weight. The marbles are blue and white. In the first bag, there are two blue marbles, in the second bag, there are two white marbles and in the third one, there is one blue and one white marble. The legends on the bags are: white and white, blue and blue, white and blue. None of the legends is identical with the bag's contents. Without looking, you can reach only into one bag and draw out only one marble. According to the colour of the drawn marble, determine what marbles occur in individual bags.

14. Brother says: "I have as many brothers as sisters." Sister says: "I have three times more brothers than sisters." How many brothers and how many sisters are there?

15. A man is 48 years old. He asks the other man how old he is. The asked man answers: "I am twice as old as you were, when I was as old as you are today." How old is the other man?

16. The flower-pot along with clay weigh 1,1 kg. The clay itself is 1 kg heavier than the flowerpot. How much does the flower-pot weigh? 17. The day before yesterday I was 50 (years old). Next year, I am 53. How is it possible? 18. One man tells to the other one: "I'm twice as old as you were when I was as old as you are now. When you are as old as I am now, we'll be together 63 years old." How old is the first and how old is the second man? 19. Girl says: "If I had one more sister, I would have as many brothers as sisters. If I had one more brother, I would have twice as many brothers as sisters." How many sisters and how many brothers are there?

20. Sister tells his brother: "I have as many brothers as sisters." Brother tells his sister: "I have twice as many sisters as brothers." How many sisters and how many brothers are three?