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## In the Wonderland of the Integers

further riddles: Trivialities Analogies Geometry Probabilities

1. If we group ourselves in rows of ten people, there is one person less. If we group ourselves in rows of nine people, there is one person less likewise. There would be one person less, also in rows of eight, seven, six, five, four, three and finally two.
How many people are we? (less than 5000)

2. 20 + 20 + 20 + 10 + 10 = 80    In English it results in:
 T W E N T Y + T W E N T Y + T W E N T Y + T E N + T E N = E I G H T Y
Which 8 numerals are represented by the 8 letters E, G, H, I, N, T, W, Y, if this addition is to be correct?

3. 4 + 4 + 4 + 4 + 4 = 20    In Spanish it results in.
 C U A T R O + C U A T R O + C U A T R O + C U A T R O + C U A T R O = V E I N T E
Which 10 numerals are represented by the 10 letters A, C, E, I, N, O, R, T, U, V, if this addition is to be correct?

4. In order to celebrate their wedding day, Mr. Dupont invited his wife into a good restaurant. When leaving the restaurant he realized that only one fifth of his cash remained. He now has just as much centimes as he originally had francs, while he still has one fifth of the initial number of centimes in francs.
How much was the bill?

5. Martina distributes 26 drops to her four little brothers. Everyone eats several drops and one hour later she realized that everyone has exactly the same number of drops left. The oldest one has eaten just as many as the third, the second has eaten half of his allotment and the fourth has eaten as much as all the other three together.
How did Martina distribute the drops?

6. Can the square number of a integer end with three equal numerals, except zero?
If yes call the smallest!

7. Andreas says to Katrin: "I am three times as old, as you were, when I was as old, as you are now."
Katrin replies: "If I will be as old, as you are today, the sum of our ages will amount to 77 years."
How old are both of them?

8. How many brothers and sisters do you are ?
If you ask this question to me, I'll answer that my mother dreamed to have at least 19 children, but that her dream did not come true. My sisters are three times more numerous than my cousins and I have half as much brothers as sisters.

9. The latin test is marked from 0 to 20. Micheal got more than the average, Klaus less. If you subtract a third of the smaller from each of the two notes, the remainder of the larger will be three times as high as the remainder of the smaller.
Which marks did they got?

10. On the racetrack I set all my cash on a first horse, and the sum doubles. Then I set 60 Marks, which I lose on a second horse. Owing to a third horse I double my assets. But with fourth I lose again 60 Marks. With the fifth attempt I double again the sum, which remained for me. The sixth horse on which I set 60 Marks brings the calamity to me: I am broke.
With how much Money I went to the the racetrack?

11. A number out of three numerals increases by 45, if you exchange the sequence of the two right numerals reduces by 270, if you exchange the sequence of the two left numerals.
What happens, if you exchange the sequence of the two outside numerals?

12. In the different classrooms of a school the same number of pupils are accommodated. 6 classrooms were destroyed by a fire. So 5 pupils had to be assigned to each of the remaining classrooms. Later they realized that 10 further classrooms were destroyed through damages caused by water of the fire-brigade. Therefore 15 further pupils had to be divided into each remaining classroom.
How many pupils go to this school?

13. A brother says: "My sister, you have exactly as many brothers as sisters."
A sisters answers: "My brother, you have twice as many sisters as brothers."
How many childrens do they are?

14. The family Müller has more children than the family Meier. The difference of the square number of the two numbers of child is 24. None of the families has a only child.
How many children do each family have?

15. During a rendezvous I told my age to my female company. The girl answered: "When you were as old as I am today, you were three times as old as I was. And when I'll be three times as old as I am today, then we are exactly one century old altogether.".
How old is she?

16. If you ask the old Leonore, with many cats she lives together, then she answers lugubrious: "With four fifth of my cats plus four fifth of one cat".
How cats do she have?

17. Complete the following multiplication by replacing the ?:
 ? ? ? ? × ? 9 - - - - - - - - - ? 7 5 4 7 ? ? ? ? ? - - - - - - - - - 2 5 8 8 6 ?

18. The product of four consecutive integers is 3024.
Which numbers does it concern?

19. Some children divide a bag of marbles. The first child takes a marble and a tenth of those, which remain, afterwards the second child takes two marbles and a tenth of the remainder. Then the third child takes three marbles and a tenth of the remaining marbles, and so on up to the last one, which takes all remaining marbles.
How many children and how many marbles were it, if every child got the same number of marbles?

20. At a conference between Frenchmen and Englishmen 12 persons meet together. More Frenchman than Englishmen appeared. The Frenchmen welcome each other in pairs in their language, then the Englishmen welcome each other in the same way. But the Englishmen do not welcome the Frenchmen and in reverse.
If altogether 31 greetings were exchanged, how many Frenchmen and Englishman participate?

21. With which numeral does the number N = end?

22. With how many nulls does the number "100!" end?

23. Is the following number an integer: N = ?

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