44th International Mathematical Olympiad_logo
Problems and Solutions

44th International Mathematical Olympiad PRESENTED_BY_Fujitsu
Regulations of the 44th International Mathematical Olympiad
1. General
1.1 The 44th International Mathematical Olympiad (the "IMO 2003") will be held in Japan between July 7 and July 19, 2003.
1.2 These regulations (the "Regulations") govern the running of the IMO 2003.
1.3 IMO 2003 JAPAN which is a committee established by the Mathematical Olympiad Foundation of Japan has overall responsibility for the organization of the IMO 2003.
1.4 The aims of the IMO 2003 are:
- To discover, encourage and challenge mathematically gifted young people in all countries;
- To foster friendly international relationships among mathematicians of all countries;
- To create an opportunity for the exchange of information on school syllabuses and practices throughout the world;
- To promote mathematics generally.
2. Participation
2.1 Participation in the IMO 2003 is by invitation only. Each invited country is entitled to send a team consisting of up to six contestants (the "Contestants"), a Leader and a Deputy Leader to be known collectively as the participants (the "Participants").
2.2 Contestants must not have formally enrolled at a university or any other equivalent post-secondary institution, and they must have been born on or after July 15, 1983
2.3 Observers including family members (the "Observers") may apply to accompany the Participants and the terms under which they can do so are detailed in sub-clause 3.5 below.
2.4 The official program (the "Official Program") as referred to below is the program and outline itinerary for the IMO 2003 and associated events and will be marked "Official Program". IMO 2003 JAPAN reserves the right to amend or revise the Official Program in whole or part. If there is by any chance a significant change, Participants, Observers, Ministry officials in the invited countries will be notified in advance.
2.4.1 The Official Program will contain, among other things, details of accommodation arrangements (inclusive of food) for Participants and Observers at contracted hotels, the main site and the venues for various official events associated with the IMO 2003, including the opening and closing ceremonies, banquet and examination rooms.
2.5 The Official Program for Leaders begins in Tokyo on July 7, 2003 and ends in Tokyo on July 19, 2003.
2.6 The Official Program for Deputy Leaders and the Contestants begins in Tokyo on July 11, 2003 and ends in Tokyo on July 19, 2003.
2.7 Each invited country wishing to participate at the IMO 2003 must confirm its participation by completing and returning Form 1-1. Form 1-1 is the official acceptance form which must be signed by the Minister of Education (or someone equivalent as indicated) and/or the contact person of the invited country and returned to IMO 2003 JAPAN by air mail no later than Feb 1, 2003. Form 1-2, which must be signed by both the Leader and Deputy Leader should also be returned to IMO 2003 JAPAN by air mail no later than May 1, 2003, will confirm that the Leader and Deputy Leader agree to abide by the Regulations for the IMO 2003. Registration may also be completed via the IMO 2003 JAPAN web site but the foregoing requirements relating to Form 1-1 and 1-2 shall apply in any event. Part 1 of Form 2 must be returned to IMO 2003 JAPAN by May 1, 2003 for Leaders, Deputy Leaders and Observers and by June 1, 2003 for Contestants. Part 2 of Form 2 must be returned to IMO 2003 JAPAN by June 1, 2003 in all cases.
2.8 Leaders and Deputy Leaders are responsible for the conduct of the Contestants, and for the avoidance of doubt the Leaders and Deputy Leaders are acting in loco parentis for their Contestants except where IMO 2003 JAPAN has been notified in writing that an Observer has been nominated to act in loco parentis.
2.9 Leaders and Deputy Leaders must ensure that their Contestants know and fully understand clause 5 of these Regulations. They must also make it clear that any Contestant who violates any of these Regulations may be liable to disqualification from the IMO 2003.
In order to avoid any trouble or accident, Leaders and Deputy Leaders must also inform fully their Contestants of the contents of "Guide to Tokyo" and "Important Contest Information For Contestants".
3. Responsibility for Accommodation and Expenses
3.1 IMO 2003 JAPAN will provide accommodation, meals, land based transport between Narita Airport and the accommodation and other necessary transport between the accommodation and other venues on the Official Program for all the Participants and Observers. In order to maintain the integrity of the IMO 2003, the Official Program will be confirmed until arrival.
3.2 Other than in respect of the provision of accommodation, meals and transport as detailed in clause 3.1 and the Official Program, IMO 2003 JAPAN shall not be liable under any circumstances for any costs or expenses whatsoever or howsoever incurred by any Participant or Observer in connection with the IMO 2003 (including without limitation the costs and expenses of insurance, accommodation, meals and transport):
3.2.1 who spends extra days in Japan outside the relevant dates specified in sub-clauses 2.5 and 2.6 above, or;
3.2.2 in respect of transportation to and from Japan (or within Japan prior to arrival at Narita Airport and following departure) incurred by Participants or Observers.
3.3 All Participants and Observers are responsible for obtaining full accident, health and travel insurance. It is the Leader's responsibility to confirm that this condition has been met for all members of his or her team.
3.4 IMO 2003 JAPAN expects to offer opportunities to Participants and Observers for excursions and cultural trips but will be under no obligation to do so.
3.5 In reference to sub-clause 2.3 above the deadline for receipt of an application to observe the Participants is May 1, 2003. Since extra accommodation is limited, no guarantee is given that such applications will be successful. For those applications that are notified as successful, full payment must be made in cleared funds of the following charges by June 1, 2003. Any application received without the following charges will be rejected. Basically, no refund is allowed.
3.5.1 Observer A: 360,000 (three hundred and sixty thousand) Japanese yen for a single bedroom per person accompanying the Leaders and residing at the contracted hotels near the Leaders' site (for 12 nights).
3.5.2 Observer B: 300,000 (three hundred thousand) Japanese yen for a single bedroom per person accompanying the Deputy Leaders and the Contestants and residing at the contracted hotels near their sites (for 8 nights).
3.5.3 Since only single bedrooms are available at the Leaders' and Deputy Leaders' sites, if the Leaders and Deputy Leaders bringing their family members prefer a twin bedroom, it is possible to choose one at the contracted hotels. In this case, the Leaders and the Deputy Leaders will be asked to pay 150,000 (one hundred and fifty thousand) Japanese yen for their own accommodations (in addition to the payment for the accompanying family members).
3.5.4 Consideration will be given to applications from Observers wishing to attend and observe the IMO 2003 for only part of the period of the Official Program and in such cases the charges, accommodation and all other relevant arrangements that will apply will be those separately confirmed by an officer of IMO 2003 JAPAN.
4. Proposals for Problems
4.1 Each participating country other than the host country is expected to submit up to six proposed problems, with solutions, to be received by the Problem Selection Committee no later than February 15, 2003. The proposals should be sent by air mail (not by e-mail, for security reasons).
4.2 The proposals should, as far as possible, cover various fields of pre-university mathematics and be of varying degrees of difficulty.
4.3 The proposals must only be written in English, French, German, Russian or Spanish. The proposals and solutions should be accompanied by their English versions.
5. Contest Regulations
5.1 The contest element of the IMO 2003 will take place in Tokyo on July 13 and 14, 2003 (the "Contest"), under the direction of the Chief Invigilator appointed by IMO 2003 JAPAN. On each day of the Contest the examination will start in the morning and last for 4 and a half hours. Each of the two examination papers will consist of three problems.
5.2 The problems will be given to each Contestant in his/her own language. On request a Contestant may receive the problems in one other language, provided that the Jury (as defined in 6.1) has approved the relevant translation.
5.3 Each Contestant must work independently and submit solutions in his/her own language. The solutions must be written on answer forms provided by IMO 2003 JAPAN. Contestants must write on only one side of each answer form.
5.4 The only instruments permitted in the Contest will be writing and drawing instruments, such as rulers and compasses. In particular, books, papers, tables, calculators, protractors, computers and communication devices will not be allowed into the examination room.
5.5 The Jury, Observers and any others who have sight of the problems and solutions before the examinations shall do their utmost to ensure that no Contestant has information, direct or indirect, about any proposed problem. They must also ensure that all Contest problems and solutions are kept strictly confidential until after the entire Contest has finished. They will be barred, except for the case of emergency, from having any external communication with Contestants, Deputy Leaders (and accompanying Observers) until the time of the conclusion of the examination. IMO 2003 Japan will provide proper assistance in case of an emergency.
5.6 The total number of prizes will not be more than half the total number of Contestants. The numbers of first, second and third prizes will be approximately in the ratio 1:2:3.
5.7 Special prizes may be awarded for solutions considered outstanding by the Jury.
5.8 The prizes will be awarded at the Closing Ceremony. Each Contestant, who has not received a first, second or third prize will receive a Certificate of Honorable Mention if he/she has received seven points for at least one solution.
5.9 Each Contestant shall receive a Certificate of Participation.
6. Jury Regulations
6.1 The "Jury" will consist of all Leaders, together with a Chairman. A Leader may be replaced by his/her Deputy Leader in an emergency (subject to the prior approval and consent of the Chairman of the Jury). Members of the IMO Advisory Board who are not already members of the Jury, members of the Problem Selection Committee and the Chief Coordinator (as defined in clause 7 below) may also attend meetings of the Jury as observers. Observers may attend meetings of the Jury only with the permission of the Chairman of the Jury, but will not be entitled to speak or vote. However, they may exceptionally speak at the explicit request of the Chairman of the Jury. Deputy Leaders may attend, as observers, meetings of the Jury held after the Contest.
6.2 Only Leaders may vote in the decisions of the Jury and each Leader will have one vote. A motion shall be carried by a simple majority of those voting. In the event of a tie, the Chairman will have a casting vote.
6.3 The Jury may appoint sub-committees to consider specific matters.
6.4 The meetings of the Jury will be conducted principally in English. The Chairman should request a translation into some of the official languages (French, German, Russian, and Spanish) as needed.
6.5 Before the Contest the Jury will
6.5.1 verify that all Contestants comply with the prescribed conditions for participation;
6.5.2 select the Contest problems from amongst the submitted proposals on the basis of a preliminary selection made by the Problem Selection Committee appointed by IMO 2003 JAPAN;
6.5.3 prepare and approve the official versions of the Contest problems in English, French, German, Russian and Spanish;
6.5.4 approve the translations of the Contest problems into all required languages.
6.6 On each day of the Contest, the Jury will consider written questions raised by Contestants during the first half-hour of the Contest and decide on replies.
6.7 After the Contest, the Jury will
6.7.1 receive and approve a report made by the Chief Invigilator on the conduct of the examinations;
6.7.2 receive a report from the Chief Coordinator on any unresolved disputes which may have arisen during coordination and determine the appropriate scores;
6.7.3 approve the scores of all Contestants;
6.7.4 decide winners of first, second and third prizes;
6.7.5 consider and make decisions on all proposals to award special prizes;
6.7.6 consider matters raised about future International Mathematical Olympiads.
6.8 Any allegation or suspicion of a violation of the Regulations generally shall be reported to the Chairman of the Jury. If he considers there is a prima facie case, he will form a committee to investigate further. The committee will report its findings to the Jury. The Jury will decide whether a violation has occurred and, if it decides that one has, then it will decide what sanction, if any, to apply. Possible sanctions include the disqualification of an individual Contestant or an entire team from the competition. The decision of the Jury will be final.
7. Coordination
7.1 Each problem will be allocated a score out of a maximum of seven points.
7.2 Prior to coordination, Contestants' solutions will be assessed by Leaders and Deputy Leaders in accordance with the marking schemes prepared under the direction of the Chief Coordinator appointed by IMO 2003 JAPAN.
7.3 Each coordination session will involve two Coordinators provided by Japan and representatives of the relevant country. Two representatives, normally the Leader and Deputy Leader, are permitted to participate actively in any one session. With the approval of the Chief Coordinator, one further representative may be present to observe the coordination process but cannot take any active part in it.
7.4 The Leader and the designated Coordinators should agree on the scores for each Contestant. These scores will be recorded on official forms and signed by the Leader and the Coordinators. If the Leader and the Coordinators fail to agree on a score for a Contestant, the matter will first be referred to the head Coordinator for that problem. If there is still no agreement, the matter will be referred to the Chief Coordinator. If the Leader and Chief Coordinator then fail to agree on a score, the Chief Coordinator will report the matter to the Jury with a recommendation as to what the score should be. The Jury will then determine the score.
7.5 If, during a coordination session, the designated Coordinators consider that an irregularity may have occurred, they will immediately refer the matter to the Chief Coordinator. Unless he is satisfied that there is no case to answer, he will report the situation to the Chairman of the Jury.
7.6 For each problem, solutions by Japanese Contestants will be coordinated by the Leader and Deputy Leader of the country which submitted the problem, with the assistance of the head Coordinator for that problem if required.
8. Entire Agreement and Understanding
The Leaders, Deputy Leaders and Contestants acknowledge that these Regulations and the documents referred to herein, constitute their entire agreement and understanding of the parties and supersede any previous discussions or representations made by or on the behalf of IMO 2003 JAPAN in respect of the IMO 2003.
9. Force Majeure
9.1 In these Regulations, "force majeure" shall mean any cause preventing IMO 2003 JAPAN from performing any or all of its obligations which arises from or is attributable to acts, events, omissions or accidents beyond the reasonable control of the party so prevented including without limitation strikes, lock-outs or other industrial disputes (whether involving the workforce of the party so prevented or of any other party), act of God, war, riot, civil commotion, malicious damage, compliance with any law or governmental order, rule, regulation or direction, accident, breakdown of plant or machinery, earthquake, typhoon, fire, flood, storm, or default of suppliers or sub-contractors.
9.2 If IMO 2003 JAPAN is prevented or delayed in the performance of any of its obligations to Leaders, Deputy Leaders and Contestants under these Regulations by force majeure it will have no liability in respect of the performance of such of its obligations as are prevented by the force majeure events during the continuation of such events, and for such time after they cease as is necessary for IMO 2003 JAPAN to recommence its affected operations in order for it to perform its obligations.