IMO ~~~~ International Mathematical Olympiad

Introduction to the IMO Mathematical Competition for High Schools

The International Mathematical Olympiad (IMO) is the world's largest and most influential competition for secondary school students in the discipline of mathematics. It was initiated by the Romanian Roman (Roman) Professor, since 1959 in Romania held the first competition, in addition to the suspension of one year in 1980, an annual session. Only seven or eight countries and regions participated in the first few editions. Initially, the organization was rotated among several participating countries, and by 1980, the International Committee for Mathematical Education created a special IMO Section to seek organizers for IMO each year.

The IMO test questions are not limited to the content of secondary school mathematics; they contain the basic parts of so-called pre-calculus mathematics and even parts of calculus. The test questions have become more difficult as the years have gone by. The difficulty of the test questions lies not in the fact that solving them requires a lot of advanced knowledge, but rather in insight into the nature of mathematics, creativity, and mathematical resourcefulness. The scope of the test questions, although never formally defined, was primarily number theory, combinatorial mathematics, series, inequalities, functional equations, and geometry. In a number of sessions, interesting number theory problems containing the mathematics of the year often appear, showing the humor of mathematicians. Some questions give much wider conditions than just the right conditions to introduce the desired conclusion, while others allow you to introduce only a small portion of a very strong conclusion, and the real purpose of these questions is to test your flexibility and skill, as opposed to the usual types of questions where the right conclusion is introduced by the right conditions. Some of the topics are very different style, novel thinking, only the use of a certain technique can be solved, for such topics, the usual way of thinking is not possible to lead to the correct solution to the problem. Some of the topics of the solution to our revelation, is not limited to a specific problem for the specific skills, but a deep mathematical thinking.

After more than 40 years of development, the functioning of the International Mathematical Olympiad has been gradually institutionalized and standardized, with a set of agreed-upon routines that have been followed by successive hosts.

1. Purpose

To stimulate the mathematical talents of young people; to arouse the interest of young people in mathematics; to discover a reserve army of scientific and technological talents; and to promote the exchanges and development of mathematics education in various countries.

2. Time

Once a year, it will be held in July.

3. Hosting

The host country will take turns to host the event, and the funds will be provided by the host country.

4. Objects

The participants are secondary school students, each team has six students, and two mathematicians are assigned as leaders.

5. Test Questions

Test questions will be provided by each participating country, and then selected by the host country and submitted to the main test committee for voting, resulting in 6 test questions. The host country does not provide test questions. After the test questions are finalized, they are written in the working languages of English, French, German and Russian and translated into the national language by the team leader.6. Examination

The examination is conducted over two days, each day lasting four and a half consecutive hours, and consists of three questions. Six players from the same team are assigned to six different examination rooms and answer the questions independently. Answer sheets are judged by the national leader, who then consults with a coordinator appointed by the organizers, and in case of disagreement, the main examination committee is then called upon to arbitrate. Each question carries 7 points out of 42.

6. Awards

The competition has a first (gold), second (silver), and third (bronze) prizes, in the approximate ratio of 1:2:3; about half of the contestants win awards. The criteria for each award are related to the results of the current examination.

IMO is not a team-to-team competition, so there is no team award, but each team attaches great importance to the rank in which the total team score is placed, and in recent years, the stronger ones are China, Russia, the United States, Germany, and Luo and other countries.

7, the main test committee

The main test committee consists of the leader of each country and the chairman appointed by the host country. This chairman is usually a mathematical authority of that country. The Main Test Committee has six duties:

1) to select the test questions;

2) to determine the marking criteria;

3) to express the test questions accurately in the working language and to translate and approve the translation of the test questions into the language of each participating country;

4) to determine, during the competition, how to answer the students' questions in writing about the test questions;

5) To resolve differences in scoring between individual leaders and coordinators;

6) To determine the number of medals and score lines.

1-20th test questions download:

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Historical development

I. Development of the International Olympiad in Mathematics

In the world, the mathematics competition with number In the world to the content of the competition has a long history: the ancient Greeks have solved the geometric problems of the competition; China's warring states period of king qiwei and general Tian Ji horse race, is actually a kind of countermeasure theory of the idea of the competition; the 16th century in Italy had a stuttering Tartaglia about the stuttering to solve the three equations of the fierce competition; the 17th century, a lot of mathematicians like to put forward a number of problems to challenge the other mathematicians, France's Fermat is the best, he put forward a number of questions to other mathematicians. In the 17th century, many mathematicians liked to propose problems to challenge other mathematicians, and Fermat of France was one of them. His Fermat's Great Theorem (the equation Xn+Yn=Zn has no positive integer solution for integer n ≥ 3; ......) challenged the wisdom of mankind for 300 years; in the 18th century, there was an independent mathematical competition in France; and in the 19th century, the French Academy of Sciences solicited the answers to mathematical puzzles by offering rewards for the answers to the problems, often leading to some important mathematical discoveries. Often important mathematical discoveries were made. Gauss, the Prince of Mathematics, was the winner of the contest, ...... but all these facts are of a localized nature and are limited to adults, whereas mathematical contests aimed exclusively at high school students are a modern fad.

The modern mathematical competitions for secondary school students (hereinafter referred to as secondary school mathematics competitions) originated in Hungary. 1894, to commemorate the President of the Mathematical Society, Evos, as the Minister of Education, the Mathematical Society passed a resolution: to hold a mathematical competition named after Evos, participated in by students in high school, held in October of each year, each time out of the three questions, limited to four hours to complete, allowing the use of any reference book, the test questions often have the content of higher mathematics, and the solution to the problem, but not the answer. the content of higher mathematics, while the solutions were entirely elementary. Under the leadership of Evos, this mathematical competition played a great role in the development of mathematics in Hungary, many successful mathematicians and scientists are the winners of the Evos competition, such as 1897 Foyle, 1898 Von Karmen and so on. After Hungary, Romania organized a competition in 1902 by the Journal of Mathematics. No other country systematically organized a major event of this kind for the next 30 years.

It was not until the 1930s that the Soviet Union organized a wider range of mathematical competitions involving a larger number of secondary school students, and the mathematical competitions for secondary school students in 1934 and 1935, sponsored by the Universities of Leningrad and Moscow, took the lead in adopting the name "Mathematical Olympiad". The analogy between intellectual competitions and sports competitions, which also emphasize the spirit of participation in the pursuit of perseverance, has gradually become a worldwide **** knowledge, and today, many countries and regions have mathematical competitions called "Olympiads".

In 1949, Bulgaria hosted a mathematics competition;

In 1950, Poland hosted a mathematics competition;

In 1951, the former Czechoslovakia hosted a mathematics competition;

In 1956, China hosted a mathematics competition;

This was followed by East Germany (1961), Vietnam (1962), the former Yugoslavia (1962), and the Netherlands (1962). Yugoslavia (1962), the Netherlands (1962), Finland (1962), Mongolia (1963), Great Britain (1965), Finland (1965), Israel (1968), Canada (1969), Greece (1969), the former West Germany (1971), and the United States (1972) ...... < /p>

Circumstances show that since the 1950s there has been a world-wide boom in the organization of secondary school mathematics competitions, which both prepared the way for the birth of the International Mathematical Olympiad (IMO) and provided the impetus for the development of the International Mathematical Olympiad (IMO).In 1956, following the activism of Prof. Roman of Romania, a plan for the development of an IMO in the countries of Eastern Europe was formalized. The 1st IMO kicked off in July 1959 in Bra?o, the ancient capital of Romania. At that time, 52 students*** participated in the competition, coming from seven countries in Eastern Europe: Romania, Bulgaria, Hungary, Poland, the former Czechoslovakia, the former German Democratic*** and State and the former Soviet Union. Each country had eight team members, and the former Soviet Union sent only four. This is the math competition across national boundaries, but from the first to the fifth, the participating countries are limited to a few countries in Eastern Europe, in fact, only regional and not much international.

Since the 1960s, the International Mathematical Olympiad has expanded to become a truly global secondary school mathematics competition, and in 1967 it was joined by teams from Western European countries such as England, France, Italy, and Sweden. After 1974, the United States also actively involved in this activity. The President of the United States has received and encouraged the U.S. Mathematical Olympiad teams that have achieved good results. The most famous U.S. military colleges (such as West Point) for many years has been for the Mathematical Olympiad U.S. team to provide training places. 1986, China's first official team to participate in the International Mathematical Olympiad. In the late 1980s, the International Mathematical Olympiad grew into a very large-scale event, thanks to the inclusion of teams from many countries in Asia, Latin America, and Africa. Japan, which emphasizes strict basic training in mathematics education, was constrained by a nearly harsh entrance examination system, making it difficult to conduct Mathematical Olympiads. However, since the 31st International Mathematical Olympiad in 1990, Japan has been actively participating in this worldwide event. By 1997, the International Mathematical Olympiad had grown into a large-scale event with 460 participants from 82 teams. Due to the high number of bidders, the annual International Mathematical Olympiad has been scheduled for 2006, which shows the importance and support for this event worldwide. The style of the Mathematical Olympiad tends to be more adaptable to a wider range of teams and competitors. The promotion of mathematical explorations that appeal to a wider range of participants will be a trend for the future.

Nowadays, although not every country in the world participates in every edition, most economically and culturally developed countries are among them, and the IMO has become the most influential subject competition in the world. It is also recognized as the highest level of secondary school mathematics competition.

Although, the International Mathematical Olympiad teams continue to increase, the scale of the competition continues to expand, but before 1980, there is no unified international body responsible for the organization and coordination of work. Initially, it was essentially the first few Eastern European countries to participate in the international competitions that bore the organizational work and the required costs in turn. As the number of new entrants increased, the burden could not be placed on a small number of countries, and in 1976 Austria became the first Western country to host the IMO. This was followed by the United Kingdom, which hosted the 21st IMO in 1979, but the failure of the 1980 IMO to take place because of the financial difficulties of the original host, Mongolia, and the lack of an international coordinating organization for the IMO to make potential hosts and participants aware of the situation, made it clear that there was a need to establish an international body to coordinate the organization of each year's IMO. 1980 saw the establishment of an international body to coordinate the organization of each year's IMO. Committee decided to set up an IMO Sub-Committee (formally established in April 1981), which was responsible for determining the hosts for each session. The tradition of the IMO has thus continued uninterrupted since 1981 and has been gradually standardized.

II. The Statutes of the International Olympiad in Mathematics stipulate:

1) The host country of the annual IMO is rotated among the participating countries (or regions), and the time is set in July; the host country pays for the necessary funds; the host country is the chairman of the whole event, and the main examining committee composed of the leaders from each country presides over the event; the exam questions and solutions are provided by the participating countries, with 3 to 5 questions from each country (or not); the host country does not provide exam questions; the host country does not provide exam questions, and the exam questions and solutions are provided by the participating countries. ), the host country does not provide the test questions, but the host country will form a selection committee to evaluate and select the test questions provided by each country, mainly considering whether the test questions are duplicated with the previous test questions, and categorize the test questions according to Algebra, Number Theory, Geometry, Combinatorial Mathematics, Combinatorial Geometry, etc., to determine the difficulty of the test questions (A, B, C level), and select about 30 questions. If there is a new solution to these questions, it is also required to provide an answer other than the original solution, translated into English for the selection of the main test members.

2) Each corps organizes a team of no more than 8 members, including no more than 6 players (students from secondary schools or schools of the same level), and 1 leader and 1 deputy leader, and the examination is divided into two days and two tests, each test has 3 questions, and each test is 4.5 hours long, with 7 points for each question, so that each contestant's maximum score is 42 points.

3) The official language of IMO is English, French, German and Russian, while the participating countries need about 26 languages, at that time, each leader will translate the examination paper into his/her own language, and approved by the Coordination Committee. The answer sheets are first judged by the main and deputy team leaders of each country, and then in consultation with the Coordination Committee (each coordinator is responsible for the grading of one test question), and in case of disagreement, the main test committee will arbitrate, and the consultation is carried out in an atmosphere of trust and friendship.

4) The number of prizes for IMO is about half of the number of participants, and the judging is based on the score bands of the first, second and third prize winners in the ratio of 1:2:3 on an average.In addition, the Main Examination Committee may give special prizes to students for very nice (meaning simple and ingenious ideas, original) or mathematically meaningful answers to a particular test question.

5) The Main Test Committee

The Main Test Committee consists of the team leaders of each country and a chairman appointed by the host country. This chairperson is usually a mathematical authority in that country. The main test committee has six responsibilities:

A) selecting the test questions;

B) determining the criteria for scoring;

C) expressing the questions accurately in the working language and translating and approving translations into the languages of the participating countries;

D) determining how to answer written questions about the questions during the competition;

E) resolving individual problems and problems in scoring. differences in scoring between leaders and coordinators;

F) determining the number of medals and score lines.

According to IMO rules, the host of each edition must extend an invitation to all the countries that participated in the previous edition, while new participants should indicate their willingness to participate to the host, who will then extend an invitation.

The spirit of IMO is the Olympic spirit: "It is not winning that counts, but participating." Accordingly, since the 24th edition in 1983, although each team (6 people as a group) counts its total points and knows in which order it is placed, the Organizing Committee does not award prizes to the team winners because IMO it is only a competition of individuals, not of teams.