Problems of the 12th Dürer Math Competition

Plenty of mathematics contests are traditionally held in Hungary. From primary schoolers to university students, everybody can find a contest that fits their age and qualifications. These are mostly individual contests where the participants sit down in a room for a few hours, working on the problems quietly. However at the Dürer Competition, there are teams of 3 taking part. For the duration of the contest each team works together to solve the problems, so the contestants can experience the benefits of cooperative thinking. Our experience shows that the majority of students are happier and more relaxed than during an individual contest.

It is a very important goal for us to set interesting problems to show the beauty of mathematics and the joy of thinking to lots of students. We also wish to include as many original problems as possible. In each year, about 150 problems appear on the contest — of course not all can be original, but we invent most of the harder problems on our own.

At this point we definitely have to mention that the organising team traditionally consists of young people, mostly university students studying maths. This dates back to the early years of the competition, and ever since then, we can regularly welcome former competitors as new organisers. The success of the competition depends on this community, consisting of 30 to 70 people. Some of them have been organisers for 10 years already (and still take part enthusiastically, even alongside a full-time job) and some of them take important responsibilities as first-year undergraduates already.

This is the spirit in which we have been organising the contest for 12 years. The competition attracts more and more students and schools with each year. In the 2018–19 academic year, approximately 800 students competed in the high school maths categories.

The following link contains all problems of the 2018–19 Dürer competition in the high school mathematics categories, complete with detailed solutions to the traditional problems and answer keys to the relay round.

Problems and solutions (PDF)