Känguru der Mathematik 2023

Holger writes the numbers up to 40 in the table in the same way as shown. Which of the pieces A to E can he then cut from the table?

• (A)

• (B)

• (C)

• (D)

• (E)

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?

• 31

• 51

• 74

• 711

• 800

Which of the shapes cannot be split into two triangles using a single straight line?

• (A)

• (B)

• (C)

• (D)

• (E)

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?

• 9

• 10

• 11

• 12

• 13

Anna has five discs of different sizes. She wants to use 4 of them to build 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?

• 4

• 5

• 9

• 12

• 20

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

• M, N, Q, P

• N, M, P, Q

• N, Q, M, P

• N, M, Q, P

• Q, N, M, P

Alice has four jigsaw pieces. Which two can be fitted together to form a hexagon?

• 1 and 2

• 1 and 3

• 2 and 3

• 2 and 4

• 1 and 4

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 centre. Which numbers can be seen at the same time?

• 4, 6 and 12

• 1, 5 and 10

• 2, 4 and 9

• 3, 6 and 9

• 5, 7 and 12

Jan sticks these three pieces of paper on top of a black circle. Which picture can he not obtain?

• (A)

• (B)

• (C)

• (D)

• (E)

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

• ◻♡

• ◻◻

• ♡♡

• ◊◻

• ♡◊