Tournament of the Towns
The Tournament of the Towns is an international competition conducted each year in two stages – Autumn and Spring (northern hemisphere time), managed by a central committee in Moscow, which is a subcommittee of the Russian Academy of Sciences via the Australian Mathematics Trust (see their Tournament of the Towns site). Each stage has two papers, an O (Ordinary) level and an A (Advanced) level, which are spaced roughly one week apart. The A level paper is more difficult, but offers more points. Students may participate in any or all stages or levels. (Note that even the O level paper is quite difficult, and requires a student to have an extra-ordinary talent for mathematics.)
Tournament of the Towns for the ‘Town’ of Perth
The last Tournament of the Towns competition, held at Curtin University, was the Northern Autumn stage for 2004-2005. Then there was a hiatus until 2007. It is now running again but the venue is now UWA. Students are typically invited to participate on the basis of their result in the Australian Intermediate Mathematics Olympiad (AIMO). The competition is used as part of a training strategy for the Australian Mathematics Olympiad (AMO).
The Perth Tournament of the Towns competition is currently being organised and run by: Dr. Greg Gamble of Curtin University.
Training session notes and questions
Below are the notes handed out during the training sessions, but revised since the training sessions, together with the problems of the two training sessions including some of the solutions of the 8 November, 2003 Training Session and all of the solutions of the 22 November, 2003 Training Session. If you would like to see a solution to a problem that’s not there already or have any difficulty with reading or understanding a solution, send Greg Gamble an email. All files below are in PDF format (which requires Adobe’s Acrobat Reader or xpdf or some similar program to read them).
- Glossary ... a list of terms that one should know, in alphabetic order.
- Plane Geometry notes
- Number Theory notes
- Induction notes
Induction problems should be ‘bread and butter’, i.e., where you can get some easy points. Here are a whole bundle for you to try. The solutions are included. Try to do them without looking at the solutions.
- Induction problems with solutions.
- 23 October 2004, Training Session questions.
- 1 May 2004, Training Session questions.
- 24 April 2004, Training Session questions.
- 10 April 2004, Training Session questions.
- 22 November 2003, Training Session questions with solutions.
- 8 November 2003, Training Session questions with some solutions.
- See also ... my Academy for Young Mathematicians site, which has notes with more depth and an extensive supply of Number Theory problems with complete solutions.
Links to related sites/competitions/programmes
- Mathematics Enrichment ... Mathematics Enrichment programme for Year 5 to Year 11 students, held in Terms 2 and 3 of the school year, at Curtin Uni.
- UWA Academy for Young Mathematicians ... for Year 10, Year 11 and advanced Year 9 students, running from March through to November, at UWA
- Mathematics Challenge for Young Australians ... for Years 7 to 10, and advanced Year 5 and Year 6 students, generally run through schools with materials provided by the Australian Mathematics Trust.
- W.A. Mathematical Olympiads ... includes links to WAJO (WA Junior Mathematics Olympiad), held in late October or early November, at UWA
- Australian Mathematics Competition ... five levels in 2005: Years 3 and 4 (middle primary), Years 5 and 6 (upper primary), and Years 7 and 8 (junior), Years 9 and 10 (intermediate) and Years 11 and 12 (senior), held in 2005 on 4 August, through schools.
Frequently asked questions
- How does one become a Tournament of the Towns participant?
Generally one is invited through one’s school, based on having participated in a previous Tournament of the Towns competition, or on performances in a mathematics olympiad competition or the Australian Mathematics Competition and/or participation in one of the above mathematics enrichment programmes.
- How do I find out how I went in a Tournament of the Towns competition?
Each student will have an unofficial result mailed to them within a few weeks of sitting the paper(s). The best scripts (about half of them) are then sent on to Canberra, and the very best of all the scripts received in Canberra are sent on to Moscow.
- When and how do I get my certificate for participating in a
Tournament of the Towns competition?
The certificates take some time to arrive from Canberra. Typically the certificates for one competition arrive at about the time of the following competition, and are then posted on to the schools for distribution. If you have not received a certificate from two competitions ago, ask your teachers at your school who the certificates would have been sent to.
- Does a score of 0 or close to 0 mean I’m just not talented enough?
Definitely not. The questions are difficult. To score anything for a question you must have made substantial headway, and if you didn’t hit on the key idea behind the question, you will tend to get 0. If you managed to get even one question completely out, then you have done well. Give yourself a pat on the back. You were invited to the competition because you had talent. You will find that just by participating you will have learned a substantial amount that will help in future tournaments.
About the Tournament of the Towns
The Tournament evolved from a competition known as the Olympiad of Three Towns (Moscow, Leningrad and Riga) in Russia, that was first held in 1979-1980 to provide an alternative to the International Olympiad for the many talented students who did not have the opportunity to participate in the international competitions. Since then other towns have joined the competition, and the name of the competition changed to its current name in 1980-1981. Today over 100 towns worldwide participate; Australia was first represented when Canberra entered the 10th Tournament in 1988. 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 (for Years 11 and 12) and Junior (for Years up to Year 10) papers. The scores are multiplied by appropriate factors so that the younger students attempting each paper are not disadvantaged.
A town’s score is based on the average of its best N students, where the population of the town is N hundred thousand. For Perth, with a population of around 1.2 million, N = 12.
Students who exceed a certain minimum score are awarded a Diploma by the Russian Academy of Sciences. All participants receive a certificate from the Australian Mathematics Trust.
Please report any inaccuracies in the above to Greg Gamble.