2023 Kangaroo Math Benjamin Test

Q1. Holger writes the numbers up to 40 in the table in the same way as sho wn . W hich of the pieces A to E can he then cut from th e table ?

3 points

Q2. Matchsticks are arranged to form numbers as shown . To form the number 15 one needs 7 matchsticks . To form the number 8 one needs the same amount . What is the biggest number that one can build using 7 matchsticks ?

3 points

Q4. Nine steps of a staircase arranged in a cylindrical order starting at the bottom and leading all the way to the top can be seen. All steps are equally high . How many steps cannot be seen ?

3 points

Q5. Anna ha s five discs of different sizes. She wants to use 4 of them to b uild a tower. She always has to place a smaller one on top of a bigger one. How many ways are there for Anna to build the tower ?

3 points

Q8. A dark disc with three holes is placed on top of a dial of a watch (see diagram). Then the disc is rotated around its cent re . Which numbers can be seen at the same time ?

3 points

Q10. Franziska writes down three consecutive two - digit numbers . They are in increasing order . Instead of the digits she uses symbols and writes ◻ ◊ , ♡ △ , ♡ ◻ . W hat does Franziska ’ s next number look like ?

4 points

Q11. A terrace is covered with square tiles of different sizes. The smallest tile has a perimeter of 80 cm. A snake lay down along the edges of the tiles (see diagram) . How long is the snake ?

4 points

Q13. Maria, Peter, Richard a nd Tina play football in the classroom. While doing so a window pane broke. When the head mistress wanted to find out who broke the window pane she got the following answers : Maria: „ It wa s Peter . “ Peter: „ It was Richard . “ Richard: „I t wasn’t me . “ Tina: „I t wasn’t me . “ Later is became clear that only one child sp oke the truth . Who broke the window pane ?

4 points

Q14. The sum s of the numbers in the white and in the grey fiel d s should be equall y big . Which two numbers have to be swapped so that the sums are equally big ?

4 points

Q15. The big rectangle is made up of five small rectangles (see diagram). Lukas wants to colour in the small rectangles in red, blue and yellow. Two rectangles next to each other should be coloured in different co lours. How many ways are there for Lukas to do that ?

4 points

Q16. 4 posts are placed a long a 120 m long running track . How many more posts have to be placed so that the running track is split into equally lo ng sections that way ?

4 points

Q17. In a game one is allowed to take (some or all) building blocks from the top of a stack of building blocks , turn them upside down and place them back in the same position within one move (see diagram) . Goran starts with this stack of bui ld ing block s : In the end all building blocks should be ordered according to size like this : What is the minimum number of moves Goran needs to make ?

5 points

Q18. Robert a nd Sonja play a game with the following rules : taking it in turn they can take 1, 2, 3, 4 o r 5 cards from the pile on each move . Whoever takes the last card has lost . At the moment there are 10 cards on the pile and it is Robert’s turn . How many cards should he leave for Sonja so that he can be certain to win ?

5 points

Q19. A rabbit, a beaver and a kangaroo are hav ing a competition. All three begin at the same time from the “ Start ” and hop in the same direction. The beaver always moves one position forwards with each jump. The rabbit always moves two positions forwards with one jump and the kangaroo always three positions . Whoever takes the least am ount of jumps to land exactly in the position labelled „Ziel“ is the winner . W ho wins the competition ?

5 points

Q20. Tina draws shapes into each field of the pyramid. Each field in the second and third row contains exactly the shapes of the two fields below. Some fields are already done. W hich shapes does she draw into the empty field of the bottom ro w ?

5 points

Q21. A tower is made up of bricks that are labelled with the numbers from 1 to 50 from bottom to top. Bob uses these bricks to build a new tower . Each time he takes the two top most bricks off the old tower and places them down on top of the new tower without chan g ing thei r order (see diagram). W hich two bricks lie on top of each other when he is finished with the re - arrangement ?

5 points

Q22. Martin ha s three cards that are labelled on both sides with a number . Martin places the three cards o n the table without paying attention to back or front. He adds the three numbers that he can then see . How many different sums can Martin get that way ?

5 points

Q23. Anna ha s two machines R and S. If she places a square piece of paper in machine R it is rotated 90° in a clockwise direction . (Hin t : Note the marking in the corner !) If she places the piece of paper in machine S, it gets printed on. She wants to produce this pict ure : In w hich order does Anna use the two machines so that this pictur e is made ?

5 points

Q24. Monika wants to find a path through the la byrinth from ‘ Start ’ to ‘ Ziel ’ . She has to stick to the following rules : She is only allowed to move horizontally and vertically respectively . S he has to enter every white circle exactly once but is not allowed to enter a black circle . In w hich direction does Monika have to move forward s when she r eaches the ci rcle marked with x ?

5 points

2023 Benjamin (Grade 5 - 6)

Q1. Holger writes the numbers up to 40 in the table in the same way as sho wn . W hich of the pieces A to E can he then cut from th e table ?

Q2. Matchsticks are arranged to form numbers as shown . To form the number 15 one needs 7 matchsticks . To form the number 8 one needs the same amount . What is the biggest number that one can build using 7 matchsticks ?

Q3. Which of the shapes c annot be split into two triangles using a single straig ht line ?

Q4. Nine steps of a staircase arranged in a cylindrical order starting at the bottom and leading all the way to the top can be seen. All steps are equally high . How many steps cannot be seen ?

Q5. Anna ha s five discs of different sizes. She wants to use 4 of them to b uild a tower. She always has to place a smaller one on top of a bigger one. How many ways are there for Anna to build the tower ?

Q6. Four ribbons M, N, P a nd Q are wrapped around a box. In which order were they wrapped around the box ?

Q7. Alice ha s four jigsaw pieces. W hich two can be fit ted together to form a hexagon ?

Q8. A dark disc with three holes is placed on top of a dial of a watch (see diagram). Then the disc is rotated around its cent re . Which numbers can be seen at the same time ?

Q9. Jan sticks these three pieces of paper o n top of a black circle . W hich picture can he n o t obtain ?

Q10. Franziska writes down three consecutive two - digit numbers . They are in increasing order . Instead of the digits she uses symbols and writes ◻ ◊ , ♡ △ , ♡ ◻ . W hat does Franziska ’ s next number look like ?

Q11. A terrace is covered with square tiles of different sizes. The smallest tile has a perimeter of 80 cm. A snake lay down along the edges of the tiles (see diagram) . How long is the snake ?

Q12. The picture of a digital watch can be seen in a mirror : W hich picture of the watch can be seen in th e mirror 30 minutes late r ?

Q14. The sum s of the numbers in the white and in the grey fiel d s should be equall y big . Which two numbers have to be swapped so that the sums are equally big ?

Q15. The big rectangle is made up of five small rectangles (see diagram). Lukas wants to colour in the small rectangles in red, blue and yellow. Two rectangles next to each other should be coloured in different co lours. How many ways are there for Lukas to do that ?

Q16. 4 posts are placed a long a 120 m long running track . How many more posts have to be placed so that the running track is split into equally lo ng sections that way ?

Q20. Tina draws shapes into each field of the pyramid. Each field in the second and third row contains exactly the shapes of the two fields below. Some fields are already done. W hich shapes does she draw into the empty field of the bottom ro w ?

Q22. Martin ha s three cards that are labelled on both sides with a number . Martin places the three cards o n the table without paying attention to back or front. He adds the three numbers that he can then see . How many different sums can Martin get that way ?