The Kangaroo Tests turn 30: Can you solve the problems?

BarcelonaAlmost always when you talk to one of the students who has obtained the best grade in the science entrance exam or who has excelled in high school or university, at some point in the conversation the word ends up appearing kangaroo. Also, when math teachers are asked how they've motivated their students, the response often includes a phrase: "There are tests that are given every year..." It's impossible to separate the educational success of many brilliant Catalan students from the Cangur tests. It's an international math competition that celebrates its thirtieth edition in Catalonia this Thursday, with more than 100,000 students registered. Hundreds of schools, institutes, and even universities collaborate, providing space for "the competition for the greats."

To celebrate these three decades, the Catalan Mathematical Society (SCM), which is the parent organization of the Cangur tests in Catalonia and the Valencian Community, has made public some of the problems that Catalan students have solved. The ARA has collected 10 at the end of this piece so you can test yourself.

One of the public schools currently participating in the tests organized by the Catalan Mathematics Society is Ernest Lluch in Barcelona. "We've been doing this for many years, and that encourages those entering the first year of compulsory secondary education to see that older students want to do it and encourages them to sign up," explains Cuchi Camarillo, a math teacher at the school.

With this momentum and the help of former math teachers from the school who have now retired, they have managed to get the vast majority of their students to sign up for these tests, which are completely voluntary. "It's true that the top 20% of students receive a small reward on their final grade," the teacher laughs. Furthermore, she explains that, paradoxically, the fact that the problems in the Cangur tests are different has led to situations in which students who failed traditional math actually do very well in the international competition. "There are students who have a very well-organized mind, but they don't know how to develop it on a written exam," Camarillo claims.

"Beautiful problems"

To understand the importance of the Cangur tests in Catalonia, we must go back to 1995, when SCM professor Josep Grané discovered the existence of "a math competition with very nice problems," recalls Toni Gomà, one of the driving forces behind the Catalan Cangur tests and responsible for the competition between 2001 and 2007. With the help of some of the teachers involved, a small pilot test was conducted in Catalonia in 1995 with students from the then third year of BUP (currently the first year of baccalaureate). From then on, the competition in Catalan, promoted by the SCM, has spread throughout the Països Catalans to this day.

Several key factors have played a role in achieving the current goal of more than 100,000 students solving math problems in a single day. One of them is the collaboration of the schools and institutes themselves (and their teachers, who voluntarily apply to register for the math competition).

However, when the decision was made to change the day of the competition in 2000—normally held on a Friday afternoon, when it was easy to find free classrooms to take the tests—the lack of space made it necessary to seek a new ally: the universities. Thus, for the past twenty-five years, many of the high school students who participate in the Cangur tests do so directly from the classrooms of various Catalan universities where they will likely end up studying for a degree. Furthermore, the collaboration of the ONCE (National Institute of Statistics and Census) has also been key, helping to translate the math problems into Braille to make the tests more accessible to all students.

Now, thirty years later, there are two facts that demonstrate how special Catalonia's presence is in these tests, in which more than one hundred countries participate simultaneously. Only two participants, despite not being countries, have been allowed to participate in the competition organized by the Kangourou Sans Frontières association: Hong Kong and Catalonia. Furthermore, the proportion of Catalan students participating is the third highest among the hundred participating territories.

Examples of problems

To celebrate three decades of participation in international tests, the Catalan Mathematics Society has published some of the problems that Catalan students have solved over these thirty years. The ARA has chosen 10 for you to test and also to demonstrate the extent to which mathematics can be taught and enjoyed in a variety of ways. (The correct answer to each problem can be found in the caption of each exercise.)