International Mathematics Tournament of Towns


The International Mathematics Tournament of Towns is a mathematics problem solving competition in which towns throughout the world can participate on an equal basis.

Students participate in their own towns which involves minimal transport and administrative costs.

[Konstantinov and Colleagues]

Alexei Sossinsky (Member of the Central Organising Committee), Nikolay Vasiliev (Chairman, Problems Committee and Editor of "Kvant"), and Nikolay Konstantinov (President of the International Mathematics Tournament of Towns and Chairman of the Central Organising Committee), taken in Moscow in 1994.

Format of Tournament

The Tournament is conducted each year in two stages - Autumn and Spring (northern hemisphere time). The southern hemisphere academic year coincides with this structure.

Each stage has two papers, an "O" level and an "A" level, which are spaced roughly one week apart. The A level paper is more difficult, but offers more points. Students and their towns may participate in either stages or levels, or in all levels and stages.

The Tournament is open to all high school students, with the highest age of students being about 17 years old.

Students are awarded points for their best three questions in each paper, and their annual score is based on their best score in any of the four papers for the year.

There are two versions of each paper, known as the Senior and Junior papers. Students in Years 10 and 11 (the final two years of high school in the Russian nomenclature) are classified as Senior participants and therefore attempt the Senior paper. So that Year 10 students are not disadvantaged their scores are multiplied by 5/4. Younger students, in Years 9 and below, attempt the Junior paper. To ensure that the scoring is fair to all levels of students, Year 8 students have their scores multiplied by 4/3, Year 7 students have their scores multiplied by 3/2 and Year 6 students and below have their scores multiplied by 2.

If intending participants are in doubt about the correct year level of students they should contact Professor Konstantinov (see below).

A town's score is based on the average of its best N students, where the population of the town is N hundred thousand (see below for definition of town). There is a minimum of N=5. If a population is less than 500,000 then the score is multiplied by an appropriate compensatory factor.

Students who exceed a certain minimum score are awarded a Diploma by the Russian Academy of Sciences. Local organising committees also present their own awards. The Tournament is managed by a central committee in Moscow, which is a subcommittee of the Russian Academy of Sciences.


The origin of the Tournament dates back to the late 1970s in the USSR. The National (All Union) Olympiad of the USSR previously was based on a system which gave relatively little opportunity to students in the larger republics such as Russia and Ukrainia.

The first Tournament was known as the Olympiad of Three Towns (Moscow, Leningrad and Riga) and was held in the 1979-1980 academic year. Participation quickly grew and the Tournament changed to its current name in the following year.

The Tournament had difficulty in obtaining political recognition in its early years, but its popularity grew and it finally won recognition in 1984 when it became a subcommittee of the USSR Academy of Sciences. The support of the USSR Academy of Sciences allowed the Tournament to become international. This attracted entries initially from Eastern Europe, particularly Bulgaria, where a national committee was formed. In 1988 the city of Canberra entered the 10th Tournament, becoming the first Western and English speaking city to participate.

The Tournament has continued to grow with over 100 towns participating in the recent Tournaments. New towns in recent Tournaments included Buenos Aires and Bahia Blanca (Argentina), Luxembourg (Luxembourg) and Subotitsa (Yugoslavia), which placed 6th in its first attempt. Other entries have come from Canada, Colombia, Germany, Greece, Israel, New Zealand, Slovenia, Spain, UK and USA.

Sample Questions

Click here for a selection of problems from past Tournaments.

How to Enter

The Tournament is open to towns throughout the world. A town is defined by its greater area. For example, London may be defined as a number of smaller cities or boroughs, such as Westminster, however Westminster could not enter alone as it is considered part of "greater" London. Smaller sections of a large city combine their marks with the city as a whole, and the best marks are counted towsrds the city, or town, score.

Small towns may have no academic or administrative support. While academic and administrative support is not compulsory it is advisable. Strict definition of populations do not exist. If a student lives in the country, he or she may have an attachment to a nearby town and enter as part of that town's team.

A town anticipating entry should contact one of the three names below for general enquiries. These contact names will also supply the rules of conduct and question papers. Local organisers should then schedule the paper into their timetable according to the rules. They should make their own assessments and choose the best scores for final assessment in Moscow (I.e. at least one for each hundred thousand of population with a minimum of five).

These scripts should be sent to Professor Konstantinov, in Moscow (address listed below) together with a declaration that proper examination procedures were used; a list of names; schools; school years; and locally assessed scores for all students who attempted the paper. This should be posted by air mail within a week of the date of the A level paper.

National Committees

If people wish to enter a new town in a country already participating they should do so through the national committee of the country. If a single town participates from within a country, the town committee is in effect the national committee. If a second town participates from within a country a national committee should be formed to act as the sole communication point between the country and the central committee.

Entry Fees

The Central Committee in Moscow faces several costs in organising the Tournament, including postage, printing and employing University students to assess submitted scripts. The charge each year is $US 50 per city, plus an additional US$ 3N, where N is the population in hundreds of thousands with a minimum of 5.

Currently the method of payment is being changed. The organisers are establishing a bank account to which electronic transfers should be possible. No notification of entry is needed before the scheduled date.

Further Information

Further information can be obtained from either:


Books containing past problems and solutions may be obtained from the Australian Mathematics Trust. (Go to book shop.)


Problems Committee

Also Available:
  • Australian Mathematics Trust