6 million participants in total enjoy the highly imaginative tasks, over 50,000 in Switzerland. The aim of the competition is to support mathematical education in schools, to awaken and consolidate the joy of working with mathematics. The range of interesting tasks on offer is intended to encourage independent work in
the classroom.

Category Junior (year 9 and 10)

(1) This morning Marie-Luise was in a hurry. She even had to run so as not to miss her underground. Two stops later she got off and walked to school as usual. One of the following speed-time diagrams fits Marie-Luise's way to school. Which one? 

(2) Once I met the headmaster's 6 daughters whose ages are 6 consecutive natural numbers. 1 asked each of the 6 sisters: "How old is your oldest sister?" Then, I added the 6 numbers from their answers. Which of the following numbers is definitely not the sum that I got?

(A) 95 (B) 125 (C) 167 (D) 205 (E) 233

(3) Feodor has drawn a closed line on a cuboid. What does the net of this cuboid definitely not look like?

Kangaroo, Mathematical Olympiad... Are you wondering why there are several math competitions for students? Apart from the general procedure, the big difference lies in the tasks, which are different in the Mathematical Olympiad and the Kangaroo. For comparison: Here are three Olympic math problems. Examples of tasks from the olympic disciplines of number theory, algebra, geometry and combinatorics can be found here. Different types of tasks can appeal to different talents.

Category Student (year 11 to 13)

(4) The cylinder shown is 15 cm high and the circumference of its base is 30cm. The path shown from A to B on the surface of the cylinder always runs vertically upwards or horizontally, i .e. parallel to the base. What is the length of this path?

(A) 45 cm (B) 55 cm (C) 60 cm (D) 65cm (E) 75 cm

(5) The average ( i.e. the arithmetic mean) of five numbers is 24, the average of the three smallest of these numbers is 19, and the average of the three largest is 28. What is the third largest of these numbers?

(A) 20 (B) 21 (C) 22 (D) 23 (E) 24

(6) The numbers from 1 to 11 are to be written in the hexagons. The sum of the three numbers in the hexagons around a black dot should be the same for all six dots. Three numbers have already been written in. Which number must be written in the hexagon with the question mark?

(A) 1 (B) 3 (C) 5 (D) 7 (E) 9

Are you interested in taking part in Kangaroo with your pupils? The competition will take place on March 21, 2024. Here you can find information about the competition, instructions on how to register and the homepage of the International Kangaroo Association "Kangourou sans Frontières".The competition lasts 45 to 75 minutes depending on the category and can be completed on paper or online (both under supervision). Only notepaper may be used as an aid. Do you know any students who might be interested in the Mathematical Olympiad tasks? It starts again after the summer vacation. You can find all the information here.

Solutions

(1) E (2) D (3) E (4) E (5) B (6) E

The sample problems and more information as a PDF