Contests around the world


Overview. The AMC/US lags behind other countries’ mathematics contest programs in several ways. First, we have a smaller participation, both among schools and among students. Second, other countries have ongoing programs that support their students throughout the year. Many countries have competitions that are not timed, multiple choice events, and some have contests that require teamwork.

Below is a collection of summaries of email messages from friends in other countries about their national contests




Math Challenge for Young Australians:

The Mathematics Challenge for Young Australians targets the top 10 per cent of primary students in Years 5 and 6, and secondary students in Years 7 to 10. Whereas it is directed at all students in this category it may be particularly useful in schools where teachers may be working in isolation and have a handful of talented students spread out over a number of classes.

The Challenge provides materials so that these teachers may help talented students reach their potential. Teachers in larger schools also find the materials valuable, allowing them to better assist the students in their care.

The aims of the Mathematics Challenge to Young Australians include:

  • Encouraging and fostering:
    • a greater interest in and awareness of the power of mathematics;
    • a desire to succeed in solving interesting mathematical problems; and
    • the discovery of the joy of solving problems in mathematics.
  • Identifying talented young Australians, recognising their achievements nationally and providing support that will enable them to reach their own levels of excellence.
  • Providing teachers with:
    • interesting and accessible problems and solutions as well as detailed and motivating teaching discussion and extension materials; and
    • comprehensive Australia-wide statistics of students' achievements in the Challenge.

There are three independent stages in the Mathematics Challenge for Young Australians - the Mathematics Challenge Stage, the Mathematics Enrichment Stage and the AMOC Intermediate Contest.

Mathematics Challenge Stage

The Mathematics Challenge Stage (held during a 3 week period normally including April, but dates for current year may be found here) comprises four problems for those in the primary schools and six problems for the secondary school versions. All but two of the problems are to attempted individually while the other two problems can be discussed in pairs before individual submission of solutions. There are separate problem sets for Primary (Year 5-6), Junior (Year 7-8) and Intermediate (Year 9-10) students.

The problems for the Challenge stage are designed by the Challenge Problems Committee, a voluntary committee of Australian teachers and academics.

Mathematics Enrichment Stage

The Mathematics Enrichment Stage is a six-month enrichment program which commences in April. It comprises (2004) six parallel series of comprehensive student and teacher support notes. Each student participates in one series. These programs are designed for students in upper primary and lower to middle secondary (Years 5 to 10).

The materials for all series are designed to be a systematic structured course over the duration of the program. This enables schools to time-table the program to fit their school year.

The Mathematics Enrichment Stage is independent of the earlier Challenge Stage, however they have the common feature of providing challenging mathematics problems for students, as well as accessible support materials for teachers.

The Newton Enrichment Series

This Series comprisies a number of introductory topics in geometry, counting and numbers. It is suitable for students in Years 5 and 6.

The Dirichlet Enrichment Series

This Series contains mathematics concerned with tessellations, patterns, arithmetic in other bases and recurring decimals. It is suitable for students in years 6 or 7.

The Euler Enrichment Series

This Series comprises elementary number theory, geometry, pigeonhole principle, elementary counting techniques and miscellaneous challenge problems, mainly for Year 8 and outstanding Year 7 students.

The Gauss Enrichment Series

This Series comprises elementary geometry, similarity, Pythagoras' Theorem, elementary number theory, counting techniques and miscellaneous challenge problems, mainly for Year 9 students and those who have already done the Euler Series.

The Noether Enrichment Series

This Series consists of material on problem solving, algebra and number theory. It is designed for students in the top 5 to 10 per cent of Year 9 who have taken the Gauss series in another year, and are not yet ready for the Polya series.

The Polya Enrichment Series

This Series consists of notes on deductive reasoning (Euclidean geometry) and algebra. It was designed specifically for the top 5 per cent of Year 10 students and outstanding students in lower years. Schools have found that this series gives a sound base for students who wish to specialise in Years 11 and 12 mathematics.


From the Australians about the US’s American Math Competitions: 

It was the model for our own very successful event and I would have thought the format was very suitable for your country and that the paper had very serious respect, not only in your country but also from an external viewpoint. Your competition enriches the teaching of mathematics in your country by providing students the opportunity of showing a talent for handling an unexpected situation rather than been tested on immediate recall. It is an opportunity for really being able to discover a student's talent for mathematical thinking and problem solving.


The only negative comment I would make is the use of calculators being permitted. Our feeling is that a paper like this should be a test of mathematical thinking, and that the use of calculators in such contests leads to expectations by students that they might be useful, in fact disadvantaging them by the distraction caused. There is of course a use for calculators in the class room, but we do not think this is an appropriate occasion.



Canada .

  Our structure differs significantly from that of the AMC.  In essence, our view is that students need more than just multiple choice or fill in the correct number.  We run the traditional contests in Grade 7/8 and 9-11.  These contests are multiple choice and are written by approximately 90K students in each of these two divisions.  We have introduced contests in grades 9-11 which are 75 minutes in length and are in essay form.  The idea is to get kids to think about writing solutions to problems and presenting written solutions.  Of course, as you know, we have our grade 12 Euclid contest,  which is 2.5h in length which consists of written questions (with some fill in the blanks).  Again, the philosophy is our desire to have kids write out solutions to problems rather than just select by multiple choice.  Our hope is that kids develop their problem solving skills over a period of time.  We are not trying to select just the very best kids but our objective is to see kids develop over time.  For our written contests, we have established marking centres throughout the country and we also have teachers create the contests themselves.  The contests are finalized by University faculty but most of the work is done by the teachers themselves.  I should just mention that we also have teachers mark these written contests. 



  We are now offering a Grade 5/6 paper which is not really timed (up to the discretion of the teacher) and is done three times per year.  There are three sets of problems provided free of charge on the Web that teachers can access and then use in their class.  We provide certificates for the kids at both the participation level and at the excellence level.  I feel very happy with this approach because it is taking the emphasis out of just competing and is putting the onus on learning. We do not produce National Summaries but provide detailed solutions for teachers so that they can work with the kids. 




In addition to timed individual competitions in the form of math exams, we have another nationwide competition. It is called Team Maths Challenge. Materials are offered

to schools to select their teams. The schools then compete in very many regional and then one national final. Some schools from continental Europe also participate.


The format is: two children from each of two consecutive years (I think grades 8 and 9 in American notation) comprise a team and work together against teams from other schools. There is lots of running about and changing seats, and noise.


The problems involve hands on questions (manipulating

geometric shapes, spotting patterns and so on). In the national final there is also a poster competition; the kids are invited in advance to become expert on a particular (often

geometric) topic (e.g. the centres of a triangle). On the day of the final they manufacture a poster which incorporates what they have learned, together with their answers to three questions which we give them on the topic when they arrive. As well as being educationally splendid, this keeps the kids busy and quiet while the administration of the main part of the competition is being organized (e.g. 40 teams, each with a teacher and the teachers have to be trained on the rules and how to administer the event, so the time is invaluable).



The competition director is Jacqui Lewis

Jacqui Lewis <>


UK is similar - except that the outfit (which seems determined to keep

me outside) still has a monopoly.



Multiple choice first round for large numbers:


Primary (Grades 4-5): new, informal and growing (multiple choice) -

around 100 000 and likely to grow to 250 000


Grades 6-7: around 290 000 from 65% of schools


Grades 8-10: around 260 000 from 60% of schools


Grades 11-12: around 60 000




Second round


Grades 4-5: multiple choice for around 1500


Grades 6-7: 2 hour written for around 1500


Grade 8: 2 hour written (6 questions) for around 600

Grade 9: 2 hour written (6 questions) for around 600

Grade 10: 2 hour written (6 questions) for around 600


Grades 11-12: BMO1 3.5 hour written (5 questions) for around 900 BMO2 3.5 hour written (4 questions) for around 100



Bits and pieces for the IMO squad.

One other summer school for Grades 9-10 (and some 11s)


At senior level things are not healthy, since the system is being

dominated by "Birds of Passage" (from PR China).  But no one will

Admit this.  There is a clear drift back towards selecting kids from

privileged schools (which I had reversed).



Team events

(i) for Grades 7-8 (teams of 4) - involving 1200 schools nationwide

(ii) For Grade 11 (teams of 10 - more like ARML) - involving 70

schools (by invitation) nationwide.




National; "Problem solving journal" - once per term for all secondary

ages.  Still small - may not survive, but we will see.


Regional: Take home competitions (old established, but not thriving, in

Scotland; thriving in area around Liverpool).




  • The Kangaroo Math Contest is the largest in the world, with over a million participants each year. Can we have Math Kangaroo at our school?
    Yes! Just view the rules and contact our headquarters.
  • How can my student get prepared to Math Kangaroo next edition?
    Please see our page with past Math Kangaroo problems. They contain links to many interesting sites as well. If Kangaroo problems seem to be too hard, contact us about solutions.
  • Our school is not interested in hosting Math Kangaroo. Where can my student participate in the competition?
    Please visit Our Team page and contact our leader in your area. You will be allowed to enroll your student in any of our locations. If no location is close to your place, talk to your PTA, your parish, your Park District and arrange home for Math Kangaroo in your neighborhood.
  • What is the cost of participation in Math Kangaroo in USA?
    The participation fee for Math Kangaroo 2005 is $20 . Please, be assured that all money from participation fee is spent on awards and on preparing of the competition. We are a not-for-profit organization with 501(c)3 status.
  • What should I do, if I have more questions?
    Please send all your questions and comments to Your concerns will be addressed promptly.



We have two nationwide competitions:


*1) /Mathematik-Olympiade MO/

The "Mathematics Olympiad"(/Mathematik-Olympiade started in 1960/61 in former

East-Germany. It is a yearly organized 4-rounds-competition

(/"School-Olympiad", "Regional Olympiad", State-Olympiad",

"Germany-Olympiad"/).  Students from grade 5 to grade 12/13 are invited

to participate and have to solve specific problems according to their

age. The first round is a home work round. The best participants qualify

for the next round. The problems for these competitions are posed by

central commissions, which involve university-professors and teachers.

The competition was and still is very successful. Since 1995 students of

all 16 German states have participated. *


*(2) /Bundeswettbewerb Mathematik BWM/

The "Federal Mathematics Competition" (/Bundeswettbewerb Mathematik started in the 1970th in

former West-Germany. It is a yearly organized 3-rounds-competition. The

students have to solve the same set of problems in a given year

throughout the state, independent of age. During the first and second

round they work out their solutions at home. The best participants

qualify for the next round. In the last round the students have to stand

through a one-hour mathematical discussion with a university professor

and a high-school teacher. The prize-winners get a prestigious

scholarship of the /Studienstiftung des Deutschen Volkes/. *


Hong Kong

1.      How does the existing AMC structure compare with programs in Russia, other Eastern European countries, and China?



The Hong Kong Competitions do not use multiple choice questions. Contestants have to work out the answers.  Examples:


HK mathematical high achievers selection contest (for Secondary 1 to 3)

HKMHASC website


HK Mathematics Olympiad (for Secondary 4 or below)

Enter  and select activities.


Students will be invited to do AIME as a result of the AMC, and this will lead to the final IMO team. In Hong Kong, there is an open invitation of a separate selection test for any students who are interested to be in the IMO team.


2.      What competition formats are in use anywhere in the world that do not focus on timed individual problem-solving?


In HK, there is a maths competition  sponsored by a commercial organization which does not take the form of timed individual problem-solving. Students get a period of about 3 months to submit their work once started.

The Hang Lung Mathematics Awards is organized by Hang Lung Properties, the Institute of Mathematical Sciences and Department of Mathematics of the Chinese University of Hong Kong, and the Hong Kong Education City in a three-way partnership. It is a biannual competition on mathematical research projects done by teams of secondary school students. It aims to encourage students to discover knowledge, develop scientific creativity, and communicate scholastically.

For each competition, there will be Gold, Silver, Bronze, and Honorable Mention awards with a total award amount of HK$1,200,000. (US$1 = HK$8) Prizes for each winning team will be given out in the forms of team member scholarships, teacher leadership award, school development grant, and MSc tuition scholarship for teachers. Projects submitted for competition will be seriously reviewed in several stages by internationally acclaimed scholars.



Concerning the 1st question, the most important difference may be the fact that the Australian and the Canadian programs are run independently of their mathematical associations.  In the USA, the MAA controls the entire process, and most importantly, the budget.  Therefore, the AMC ends up supporting other MAA programs with moneys collected from the high schools. 


Concerning Question 2, I want to emphasize that until recently, there were no multiple choice problems on competitions in Central and Eastern Europe or the former Soviet Union, whose teachers were proficient enough in mathematics to grade essay-type solutions to olympiad-level problems, if they were given appropriate instructions for doing so.  Unfortunately, the situation is changing fairly speedily, partially due to the political pressures towards americanization in the field of education.  Therefore, if we wish to learn from those countries, we should do so soon.


With respect to competitions with less time pressure, let me call your attention to Hungary's High School Mathematics Journal (KöMaL), which was primarily responsible for training that small country's many excellent mathematicians since 1894.  I wrote about it in the preface of the book C2K, available through the MAA,o where I also wrote a bit about my attempts to introduce a similar vehicle for competitive learning in the USA.  Of them, only the USAMTS survived, and I am happy to report that it is doing well.  But I need not tell you so, since you were a great help to me throughout the years, and you are still working with it.





New Zealand

and click

on problem Challenge or National Bank Junior Math Competition to see

what competitions we run from here. These are the only ones produced in

New Zealand for students in all schools.





Polish Mathematical Olympiad. In Poland, we have only one great math competition except

the PMO: it's called 'kangur' /kangaroo/.

it has many levels and consists of about 30 problems. for each problem, student has only to tick which of the three possible answers is correct.

do you want me to give some further details about kangur or PMO?





The Tournament of Towns

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.


South Africa

The competitions in which I am involved are of the timed 5-option mcq model, just like AHSME, the Australian and Canadian competitions. We have an "Inter-Provincial Mathematics Olympiad" rather like ARML, which is very successful. We choose our Olympiad teams via a Talent Search and program of mathematical camps, as you do, but our entire annual budget is a fraction of yours.  Our funding has been largely corporate, but governmental funding is starting to play a more important role.  Given the economic realities in South Africa, we do not charge entrance fees, so funding from outside is always an issue.

We can claim to be better than the USA in just two areas:  we have had more girls in our IMO teams (three last year) than the USA.  No, I don't know if there is a secret formula for this. 






Po Leung Kuk
Primary Mathematics World Contest

Po Leung Kuk is a renowned welfare organization and school-sponsoring body in Hong Kong. It runs various types of schools including 24 kindergartens, 29 primary schools, 5 special schools, 15 secondary schools and 1 sixth-form college. Each year, Po Leung Kuk sponsors the Primary Mathematics World Contest (PMWC) in Hong Kong that attracts participants from around the world. The 6th PMWC held in July 2002 attracted 40 teams from countries that included China, Japan, Taiwan, Singapore, Thailand, Malaysia, the Philippines, Macau, Bulgaria, Cyprus, South Africa, India, Mexico and the United States.

The PMWC aims to:

·    provide an opportunity for the exchange of information of primary school mathematics education throughout the world.

·    foster friendly relations among primary school students from different cities.

·    discover the mathematics potential of gifted primary students among different cities.

A team consists of a team leader, a deputy team leader and a maximum of four student contestants. To be eligible to participate in the contest, the students must be age 13 or under as of September 1 and have not enrolled at a secondary institution or its equivalent. A qualifying test is sent to schools throughout Texas in November (contact us for a copy). Mathworks selects four students from the pool of qualifying test entrants. For information regarding a qualifying test, contact the Mathworks office. The selected team members attend the Junior Summer Math Camp at Texas State University-San Marcos for two weeks in June in preparation for the July competition. All expenses including room, board and travel will be covered.