Where maths problems are solved as a team

151 maths enthusiasts poring over tricky number puzzles at tables, running back and forth to have their solutions checked, discussing, puzzling and laughing as a team. On the other side, mathematicians from the Institute of Mathematics, who check these solutions, distribute new tasks and join in the fun.

This was the picture on 13 March 2026 at the international mathematics competition Náboj at the University of Würzburg, in which students have to solve challenging problems from algebra, geometry, combinatorics and number theory together. In addition to mathematical understanding, creativity and logical thinking are required. Teamwork is also important - a key skill that also plays a central role in excellent research.

Solve as many problems as possible in two hours

Náboj is an international maths competition for teams of up to five members from a school. Each team starts with six tasks. As soon as one is solved correctly, it is given a new, slightly more difficult task. The aim is to solve as many problems as possible within 120 minutes. Some of these tasks were created by members of the Institute of Mathematics.

An example: The task is to find the sum of the digits of a seven-digit number in which all digits are different and not equal to zero and the number is divisible by each of its digits. One possible solution: The seven-digit number is 9867312, its sum of the digits is 36. The detailed solution can be found here (only in German).

There are two categories in the competition:

• Juniors: Teams whose members are in year 11 or less.
• Seniors: Teams that can be made up of pupils from the same school.

Across Germany, the 2026 competition took place at the universities in Hamburg, Leipzig, Paderborn, Passau, Tübingen and Würzburg. Internationally, students from Austria, Switzerland, the Czech Republic, Germany, Estonia, Spain, Great Britain, Hungary, Morocco, Poland, Portugal, Romania, Singapore, Slovenia, Slovakia, Sweden and Uzbekistan took part. A total of 1,986 teams competed with almost 10,000 participants.

31 teams puzzle at the University of Würzburg

A special feature of the Náboj competition is that it takes place at the same time worldwide. This means that the teams can already see how they compare to other teams in Germany and internationally during the competition. This provides additional excitement and motivation. At the same time, it is a challenge for the organising team from the Institute of Mathematics at JMU: the entire schedule has to be coordinated internationally.

31 teams competed at the Würzburg site, mainly from the region. However, some also travelled a long way to take part. The best schools were honoured at the final award ceremony by Professor Frank Werner, Managing Director of the Institute of Mathematics. In his welcoming address, Werner expressed the hope of seeing as many of the participants as possible again at another event or as students at JMU.

The senior team from Wirsberg-Gymnasium Würzburg was particularly successful this year, coming 3rd in Germany. In the junior category, Gymnasium Veitshöchheim won by a very narrow margin.

Discovering enthusiasm for maths

The competition in Würzburg was organised by a team from the Institute of Mathematics led by Dr Theresa Lechner. In addition to the mathematical challenge, the main focus for her is on having fun: "It's fantastic to see how the young people puzzle, laugh and discover their enthusiasm for maths - I'd love to join in the puzzling myself!"

This is also confirmed by the feedback from the participants and from the schools. One teacher wrote afterwards that her teams had really enjoyed taking part - and definitely wanted to take part again next year.

Further information on the competition, tasks, solutions and all results can be found at maths.naboj.org/en/en/

Contact

Dr Jan Bartsch, Institute of Mathematics, jan.bartsch@uni-wuerzburg.de