Tournament of Towns



The Tournament is open to all high school students (both gymnasium and nine-year school in Sweden).

The Tournament is conducted each year in two stages - Autumn and Spring. Each stage has two papers, an "O" level and an "A" level, which are spaced roughly one week apart. All papers possess equal rights. The A level paper is more difficult, but offers more points. Towns may participate in either stages or levels, or in all levels and stages. A student may participate in any of these papers irrespective of his/her participation or results in previous papers.

All the towns try to hold the sitting in one day that is recommended by the Central Jury (usually in October and in March), but holidays can cause a delay. Local managers of the Tournament must be sure the students aren't able to receive problems prior the competitions. All participants from the town have the sitting in the same place. They submit their solutions in writing. Students doing the 0-level version are given no more than 4 hours, those doing the A-level version - 5 hours. Calculators, reference books and even collections of mathematical problems are allowed!

There are two versions of each paper, known as the Senior and Junior papers. Students in two last Years, say 11th and 12th Year of education (that corresponds to 2nd and 3d Year in gymnasium in Sweden) are classified as Senior participants and therefore attempt the Senior paper. All other students get the Junior paper.

The local jury tests the papers in one or two weeks, notifies about preliminary results, discusses and explains the solutions. It must also select the best papers, translate (if necessary) to some international mathematical language and send the papers to the Central Jury for final testing and for determining the result of the town in the competition. The Central Jury determines the final results of the academic year (usually - next Autumn). It issues diplomas and publishes the list of awarded students and results of towns in the annual report in Russian and in English.

Student's Result

The result of the academic year is taken to be the maximum of the results of all papers during this Year.

Each paper include from 4 to 7 problems with the maximum grade for each of the problems is shown in brackets [ ] in the text of the problem. Each paper (contestant) is graded by taking the sum of the three best grades obtained in solving the individual problems (the sum can be then multiplied by the age coefficient, see below).

Some problems includes questions a), b), that are graded separately. Then the result for the problem is the sum of results for the questions, and this sum is still considered to be one problem.

The age coefficient is used to encourage the younger participants that solve the same problems as elder ones. To get the result the sum of three best problems is multiplied: by 5/4 for Year 11 students, by 4/3 for Year 9 students, by 3/2 for Year 8 students and by 2 for Year 7 and younger.

Central Jury in Moscow tests the best papers. Central Jury can raise the grade for some problems and even give the whole variant the raising coefficient.

The Central Jury decides how many points is awarded with a diploma (usually 11-12 and more) and issues those diplomas. It also decides how many points are sufficient for a student to get an invitation to a Summer Conference (usually 18-20 points).

Grade for a city

The final grade for a city equals the average score of the best grades of the officially competing participants from that city. The number of the officially competing participants equals to the city population divided by 100000, but not less then 5 (20 for Stockholm). For smaller cities (population <500000) this grade is multiplied by the coefficient K, calculated according to the formula K=1+(500-N)/800, where N is the city's population in thousands.