# Reason - examples - page 35

1. Triangles
Hanka cut the 20 cm long straws into three pieces each piece had a length in cm. Then, with these three pieces, she tried to make a triangle. a) What circuit has each of the triangles? b) How long can the longest side measure? c) How many different trian
2. Sweater
Dana confuses sweater and wool has a choice of seven colors. In how many ways she can choose from three colors to the sleeves?
3. In the orchard
In the orchard, they planted 25 apple trees, 20 pears, 15 plums and 40 marbles. A strong late frost, however, destroyed a fifth of all new trees. Unfortunately, it was all the trees of one kind of fruit. What is the probability that the plums have died out
4. The florist
The florist had 200 roses in the morning. During the day, more than half sold it. From the remaining roses, it will tie the bouquet. If a bouquet of 3, 4, 5 or 6 roses are bound, one always remains. How many roses from the morning shipment sold?
5. Subsets
How many 19 element's subsets can be made from the 26 element set?
6. Peaches
There are 20 peaches in the pocket. 3 peaches are rotten. What is the probability that one of the randomly picked two peaches will be just one rotten?
7. Dinning room
How many different combinations can we choose if there are 3 soups, 5 kinds of main dish and 2 desserts in the dining room?
8. Desks
A class has 20 students. The classroom consists of 20 desks, with 4 desks in each of 5 different rows. Amy, Bob, Chloe, and David are all friends, and would like to sit in the same row. How many possible seating arrangements are there such that Amy, Bob, C
9. Progression
12, 60, -300,1500 need next 2 numbers of pattern
10. Six-digit primes
Find all six-digit prime numbers that contain each one of digits 1,2,4,5,7 and 8 just once. How many are they?
11. Clock's gears
In the clock machine, three gears fit together. The largest has 168 teeth, the middle 90 teeth, and the smallest 48 teeth. The middle wheel turns around its axis in 90 seconds. How many times during the day do all the gears meet in the starting position?
12. Rectangles
How many different rectangles with sides integers (in mm) have a circumference exactly 1000 cm?
13. Bridge cards
How many bridge hands are possible containing 4 spades,6 diamonds, 1 club, and 2 hearts?
14. Marriage sttus
In our city, there are 3/5 of the women married to 2/3 of the men. Find what part of the population is free.
15. Find two
Find two consecutive natural numbers whose product is 1 larger than their sum. Searched numbers expressed by a fraction whose numerator is the difference between these numbers and the denominator is their sum.
16. Beds
At the summer camp, there are 41 chalets. Some rooms are 3-beds, some 4-beds. How many campers from 140 are living in 3-bed?
17. Square into three rectangles
Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.
18. Clothes
Danka and Janka collect clothes. Danka had 9 more than Janka, so she gave her 7. Which now has more cloth and how many?
19. Symbols
If 2*3 = 60 ; 3*4 = 120 and 4*5 = 200, what is 2*5?
20. Hectares
The tractor plows the first day of 4.5ha, the second day 6.3ha and the third day 5.4ha. It worked whole hours a day, and its hourly performance did not change and was the highest of the possible. How many hectares did it plow in one hour (what is it perfor

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