How are the International Mathematical Olympiad exams constructed?

Each IMO session, the International Council will vote to select 6 problems from 25-30 problems selected from proposals by participating countries.

From March every year, countries and territories participate in the International Mathematical Olympiad.(International Mathematical Olympiad - IMO)are requested to send exam questions to the host country, up to6 problems.

BThe host country's exam selection committee will shortlist the problems.(short list), including the best songs, no duplicatestopici IMOprevious years, or national exams of participating countries and territories. These questions do not require advanced math knowledge, are not too difficult or too easy, but candidates must use all their reasoning ability and learned math knowledge.

Mr. Nguyen Khac Minh, an expert from the Department of Quality Management (Ministry of Education and Training, in charge of Math Olympiad) said that the short list includes 25-30 entries, covering all 4 subjects: Algebra, Combinatorics, Geometry and Arithmetic. Each subject has from 6 to 8 entries.

NIn recent years, the exam of each IMO consists of 6 problems. The selection of 6 problems from the short list is the job of the International Jury of each IMO. The President of the International Jury and the secretaries are from the host country. The remaining members are from the Council of Heads of Delegations of the IMO.

IMO exam consists of 6 questions, at easy - medium - difficult levels.

The evaluation of the short-listed problems to select the 6 problems is carried out in the meetings of the International Council. After discussion and evaluation, the heads of delegations will vote to select the 6 problems.

According to the regulations, the 6 problems must have 3 levels: easy, medium and difficult, each level has 2 problems. The voting for the 6 problems is conducted in the following way: after discussion, the heads of the delegation propose easy pairs of problems (not all heads of the delegation are required to propose), ensuring that the two problems in the pair do not belong to the same subject, then vote to choose a pair according to the principle of majority winning over minority.

The International Council will then do the same to select the medium pair, then the difficult pair. For each pair, the selection is done through several rounds of voting, ensuring that in the final round there are only 2 pairs facing off. Before each round, the heads of delegations are allowed to express their opinions and lobby for votes for this pair or another.

According to Mr. Minh, in recent years, the above-mentioned method of selecting papers has revealed a major drawback: it can create a significant imbalance between the number of papers in each subject. This can cause an imbalance for candidates, because most of them are only strong in a few subjects.

Teachers Le Ba Khanh Trinh, Nguyen Khac Minh, Le Anh Vinh (from left to right) at the 2017 International Mathematical Olympiad.

In order to overcome this situation and from the viewpoint that the medal “dispute” mainly occurs in 4 easy and medium level problems, at IMO 2013 held in Colombia, the International Council unanimously voted to stipulate that the 4 easy and medium level problems in the IMO exam must belong to all 4 sub-disciplines. This decision forced the voting method of 6 exams to change.

Specifically, from 2013 to present, 6 problems in each IMO are voted on by the method that after discussing the professional quality, the delegation leaders propose a list of easy problems, then vote to choose one problem. Then do the same to choose the average problem of the subject.

After choosing one easy and one medium problem in each subject, the heads of delegations voted to choose the easy pair. The medium pair was derived from the easy problem, by applying the axiom "4 easy and medium problems must belong to all 4 subjects".

Voting to choose an easy or medium problem in each category, or to choose a pair of easy problems, is done in the old way, that is, voting in many rounds, in the final round there are only 2 problems or 2 pairs facing each other...

"In the above mentioned method of constructing exam questions, for each subject, a problem can be proposed as both an easy problem and an average problem. Even after being selected as an easy problem, that problem can still be proposed again when voting for an average problem. Thus, easy and average problems in a subject do not necessarily have to be different. This is accepted by the heads of delegations because there is no definition of what is difficult and what is average," said Mr. Minh.

The test is translated into the candidate's native language.

After the IMO exam consisting of 6 problems was determined, the team leadersThe questions will be translated into their own language so that candidates can solve the problems in their mother tongue. The team leaders will be completely isolated from the candidates to avoid cheating.Each problem is worth a maximum of 7 points. Candidates must solve these 6 problems over 2 consecutive days, 3 problems each day within 270 minutes.

After the end of 2 days of exam,The contestant's exam will be marked in parallel by the judges and the contestant's head of delegation. The two sides will then consult to come up with the final result. The judges and the head of delegation can both argue with each other's marking methods to get the most accurate score for the contestant's exam. If the two sides cannot reach an agreement, the head of the jury will decide. The final solution is for all the heads of delegations to vote together. The exam of the host country's contestant will be marked by judges from the countries whose exam papers were selected.

As the person in charge of selecting, training, and leading the delegation for decades, Mr. Minh said that Vietnam has not recently submitted any problem proposals to IMO. "I have not compiled specific statistics, but I remember that in 1987, Vietnam submitted a proposal, and one of the submitted papers was used in the IMO exam," said Mr. Minh.

Determining gold, silver and bronze medals

According to IMO regulations, gThe awards include gold, silver and bronze medals, awarded according to the total points achieved by the contestants. The number of contestants awarded medals accounts for about half of the total number of participants. The points for classifying medals will follow the principle of the ratio of contestants winning gold, silver and bronze medals of 1:2:3. Those who do not win medals, but fully solve at least one problem (7 points) will be awarded a certificate of merit.

"The leaders of the delegations will meet to decide on the medal points because there may be many points that satisfy the above conditions," said Mr. Minh.

In addition to medals and certificates, the IMO Organizing Committee also awards special prizes for "extreme creativity" or "generalization of the problem posed in the problem". These prizes were popular in the 1980s but have been less frequently awarded recently.The most recent person to receive a special prize from the Organizing Committee was Iurie Boreico, a candidate from Moldova, in the 2005 exam. Candidate Le Ba KhanhPresentationof Vietnam received this award in the 1979 competition.

The International Mathematical Olympiad is a math competition for high school students. From its inception until 1981, each country sent a team of 8 members, but in 1982 it was reduced to 4. From 1983 until now, the IMO regulation has been a maximum of 6 members.

According to VNE