Quiz

Kangaroo 2020 – Benjamin (grades 6 and 7)

30 problems from the international Kangaroo mathematics competition (19 March 2020), Benjamin category, for grades 6 and 7. The solutions are shown after checking.

Choose one of the five answers for each problem. Problems 1–10 are worth 3 points, 11–20 4 points and 21–30 5 points. A wrong answer loses a quarter of the problem’s points and no answer scores 0. You start with 30 points; the maximum is 150. In the competition the time is 75 minutes. When you finish, click Check answers.

1. One piece has been taken out of the puzzle in the picture. Which piece? (3 points) Figure for problem 1

2. Travelling from Atown to Btown, Anita passes five signposts. One of them is wrong. Which one? (3 points)

3. The big square is made of small white and grey squares. What does it look like if we swap the colours of the small squares? (3 points) Figure for problem 3

4. Mile wants to bake 24 cakes for his birthday. 6 cakes need 2 eggs. Eggs are sold in boxes of 6. How many boxes must he buy? (3 points)

5. Maria reflects the shape in the picture in the two lines drawn. What do the images look like? (3 points) Figure for problem 5

6. Kole has chains of 5 links and chains of 7 links. Joining whole chains he makes longer ones. How many links can his chain NOT have? (3 points) Figure for problem 6

7. Maria has 10 sheets of paper. She cuts some of them into 5 pieces each. Now she has 22 pieces. How many sheets did she cut? (3 points)

8. Sara coloured each region of the figure red, blue or yellow so that neighbouring regions have different colours. The outer ring is blue. How many regions are blue? (3 points) Figure for problem 8

9. Four baskets hold 1, 4, 6 and 9 apples. What is the smallest number of apples that must be moved so that every basket has the same number? (3 points)

10. A dog and a cat walk along the thick path. At the same moment the dog starts from P and the cat from Q. The dog is three times as fast as the cat. At which point do they meet? (3 points) Figure for problem 10

11. The numbers 1 to 10 go in the circles, one in each. Two neighbouring numbers add up to the same as the two diagonally opposite them. Some numbers are already written. Which number goes in place of the question mark? (4 points) Figure for problem 11

12. When Lilko the bat left the cave the digital clock showed 20:20. When he came back and hung upside down, he again saw 20:20 on the clock. How long was he out? (4 points)

13. A dwarf and a troll met. The troll always lies and the dwarf always tells the truth. Both said the same sentence. Which one? (4 points)

14. Maria has 10 white, 9 light grey and 8 dark grey small cubes of the same size. She glued them into one big cube. Which of the cubes shown could be hers? (4 points)

15. The pictures show five routes (thick lines) from X to Y. Which route is the shortest? (4 points)

16. Father kangaroo lives with his three children. They vote on every decision and each has as many votes as his age. Father is 36 and the children are 13, 6 and 4. In how many years will the children win if they always agree? (4 points)

17. Dame has two identical pieces of wire shaped like the first picture. Which shape can NOT be made by putting the two pieces next to each other? (4 points) Figure for problem 17

18. Ana stuck 6 pictures on the faces of a cube (first picture) and showed the cube in two positions. Which picture is opposite the mouse? (4 points) Figure for problem 18

19. The diagram shows the friendships between Ana, Berta, Tsveta, Diana, Elizabeta and Marta. Each number is a girl and each line a friendship. Tsveta, Diana and Marta each have four friends. Tsveta and Diana are both friends of Berta, who has no other friends. Which number is Marta? (4 points) Figure for problem 19

20. Maria poured the same amount of liquid into three box-shaped containers. From the front they look the same, but the liquid stands at different heights. What do they look like from above? (4 points) Figure for problem 20

21. Milan looks at the solid in the picture from above. What did he see? (5 points) Figure for problem 21

22. Three small squares are drawn inside a big square (picture). What is the length marked with the question mark? (5 points) Figure for problem 22

23. Nine counters are black on one side and white on the other. At first 4 show black. Each move turns over exactly 3 counters. What is the smallest number of moves to make all of them show the same colour? (5 points) Figure for problem 23

24. Look at the scales in the picture. What must go on the empty pan of the third scale to balance it? (5 points) Figure for problem 24

25. Ten people each ordered one scoop: 4 vanilla, 3 chocolate, 2 lemon and 1 mango. They were decorated with 4 umbrellas, 3 cherries, 2 wafers and 1 chocolate stick, one per scoop, and no two ice creams are the same. Which combination was NOT served? (5 points) Figure for problem 25

26. A three-digit number is “nice” if its tens digit is greater than the sum of the other two digits. What is the largest number of consecutive nice numbers? (5 points)

27. At a chess tournament Marko has to play 15 games. At some point he had won half of the games played, lost a third and drawn two. How many games does he still have to play? (5 points)

28. Vlade has a square sheet divided into 9 squares (first picture; the top-left one is grey). He folds it like an accordion, first horizontally then vertically, so the grey square is on top. He wants to write 1 to 9 so that after folding they increase from 1 at the top downwards. Which numbers go in a, b, c? (5 points) Figure for problem 28

29. Dejan builds a pyramid of balls: the base is a 3 × 3 square, the middle layer 2 × 2 and one ball on top. There is a dot of glue between every two balls that touch. How many dots of glue are there? (5 points) Figure for problem 29

30. The map shows islands joined by bridges. The postman must visit every island exactly once, starting at “start” and ending at “finish”. He is now on the island in the centre (the green one). Where should he go next? (5 points) Figure for problem 30