# Reason + natural numbers - examples

1. Dance group
The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group?
2. Last page
Two consecutive sheets dropped out of the book. The sum of the numbers on the sides of the dropped sheets is 154. What is the number of the last page of the dropped sheets?
3. The King
The King wants to divide his sons equally. He has 42 rubies and 45 diamonds. How many sons and how will they share them?
4. Brick weight
The brick weighs 2 kg and a half bricks. How much does one brick weigh?
5. Monkey
Monkey fell in 23 meters deep well. Every day it climbs 3 meters, at night it dropped back by 2 m. On what day it gets out from the well?
6. Diophantus
We know little about this Greek mathematician from Alexandria, except that he lived around 3rd century A.D. Thanks to an admirer of his, who described his life by means of an algebraic riddle, we know at least something about his life. Diophantus's youth l
7. Z9-I-4
Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Fi
8. Z9–I–1
In all nine fields of given shape to be filled natural numbers so that: • each of the numbers 2, 4, 6 and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in the cir
9. Birthdate
Jane on birthday brought 30 lollipops and 24 chewing gum for their friends. How many friends has, if everyone receives the same number of lollipops and chewing gums? How much chewing gum and lollipops got any friend?
10. Camel
Camel owner wants to get out of the city into oasis. He bought 3000 bananas, which wants to sell in oasis. However oasis from the city divided 1,000 kilometers of desert. Camel can carry at one time up to 1000 bananas, and for every kilometer traveled, ea
11. Chocolates
In the market have 4 kinds of chocolates. How many ways can we buy 19 chocolates?
12. Chocolate
How many times should be broken chocolate consisting of 10 × 12 pieces to get the 120 parts?
13. Octahedron - sum
On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also.
14. Pension or fraud
Imagine that your entire working life working honestly and pay taxes and to Social Insurance (in Slovakia). You have a gross wage 730 Euros, you pay social insurance (you and your employer) monthly € 263 during 44 years and your retirement is 354 Eur.
15. Exhibition
The teacher paid for 280 Kč for 4.A students for admission to the exhibition. How many students were on the exhibition?
16. Rectangle diagonals
It is given rectangle with area 24 cm2 a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
17. Euler problem
Someone buys a 180 tolars towels. If it was for the same money of 3 more towels, it would be 3 tolars cheaper each. How many were towels?
18. Rectangle
The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
19. Basements
In the first basement is more flies than the spiders, the second vice versa. Each basement had spiders and flies together 100 feet. Determine how many could be flies and spiders in the first and second basement. PS. We only need, when you write how many.
20. Elections
The elections attended a total 4818 voters. First day 39 men more than women, the second day 21 women more than men. How many women attended elections?

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