The International Mathematical Olympiad (IMO) is the World Championship Mathematics Competition for High School students. The first IMO was held in 1959, hosted by Romania, with seven countries participating: Hungary, Bulgaria, Poland, Czechoslovakia, East Germany and USSR. Since then, the participating countries have taken turns in hosting it.The number of participating countries increased to 97 countries from all continents in the 49^th IMO.

When the IMO first began, each country was allowed up to eight participants. In 1982, this was scaled back to four members, but in 1983 the number was increased to six, which is where it still stands. The contestants must be no more than 20 years old and must not have any post secondary-school education. There is no limit to how many times a person may participate in the IMO, provided the individual meets the age and schooling requirements. The usual size of an official delegation to an IMO is (a maximum of) six students, along with the Leader and Deputy Leader. The student competitor writes two contest papers on consecutive days, with three problems on each day. Each question is worth seven marks. Only a whole number of marks are given.

Each invited country can send in up to six problems for consideration for the final competition papers. These submissions are reviewed by the host country's problem selection committee, and a short list of about thirty questions is made. The choice of the questions on the actual competition papers is made by the International Jury. The International Jury consists of the Chief Delegate (Leader) from each participating country, together with the Chairman named by the host country. Decisions are made by a simple majority vote. The official languages of the IMO are English, French, German and Russian. Since Spanish is spoken in a large number of participating countries, it has become an unofficial “official” language. In recent years, English has been the working language of the International Jury, with the other official languages available whenever required.

The International Jury members receive the short list of questions on arrival at the sequestered site. They review these problems and then meet to discuss which problems will be included. An honour system requires delegates to identify any suggested problems that are well known, in text books, or have been used in training programs. Some problems are eliminated as too easy or too hard. After thorough debate, the six problems are chosen, and their wording in all the official languages is agreed. The team leaders translate the problems into all further languages required by their contestants. After that all papers, in all languages, are inspected by all members of the International Jury, to ensure that all translations are appropriate.

Meanwhile, the Deputy Leaders and Contestants have arrived at the venue. The Opening Ceremony is held, and the Contest takes place the following two days. Each Contestant has to solve 3 problems within 4½ hours in each of the two days in his/her own language. After the Contest, the Leaders and Deputy Leaders evaluate the solutions of their contestants and hold coordination sessions in order to ensure that the marking has been done correctly and consistently. During these days, the participants enjoy a varied enternainment programme including excursions and games.

The last day is for the Closing Ceremony, and the Gold, Silver, and Bronze medals will be awarded for excellent performances. The International Mathematical Olympiad is an individual competition. Medals are awarded to at most half of the participating students. Gold, Silver and Bronze medals are awarded in the ratio of 1:2:3, so that about 1/12 of the students obtain a Gold Medal, about 1/6 of the students obtain a Silver Medal and about 1/4 of the students obtain a Bronze medal. In order to encourage more students, and to encourage students to solve complete problems, recent practice has awarded a Certificate of Honourable Mention to any student (not receiving a medal) who obtained full marks for at least one problem.

Team Leaders are kindly asked to send problem proposals for IMO 2010 to the following address:

Prof. Yerzhan Baissalov
The Republican Scientific-Practical centre «Daryn»,
Pobedy avenue 60,
Astana city,
Kazakhstan,
010011.

Date	Leaders	Deputy Leaders	Contestants
Friday 2.07.2010	Arrival
Saturday 3.07.2010	Jury meeting
Sunday 4.07.2010	Jury meeting
Monday 5.07.2010	Jury meeting	Arrival	Arrival
Tuesday 6.07.2010	Opening ceremony
Tuesday 6.07.2010		Departure to the Republican Educational and Practical Center «Baldauren»
Wednesday 7.07.2010	Q & A	First day of contest	First day of contest
Thursday 8.07.2010	Q & A	Second day of contest	Second day of contest
Friday 9.07.2010	Coordination	Coordination	Excursion
Saturday 10.07.2010	Coordination	Coordination	Excursion
Sunday 11.07.2010	Last jury meeting	Last jury meeting	Excursion
Monday 12.07.2010	Excursion
Tuesday 13.07.2010	Closing Ceremony / Farewell Dinner
Wednesday 14.07.2010	Departure

30 June – 1 July 2010 – arrival and survey of places by IMO AB members

IMPORTANT INFORMATION FOR TEAM LEADERS

Jury meetings of IMO 2010 from July 2 to July 5, 2010, will be held in Almaty, another city of Kazakhstan. So we kindly ask team leaders and observers A to come directly to Almaty and, if it is possible, to leave Kazakhstan from Astana.

The RSPC “Daryn” will provide transferring of all team leaders and observers A from Almaty to Astana on July 6, 2010.

February 16^th, Thursday
The online registration procedure starts at the IMO-official site

March 31^st, Wednesday
Last day to accept online the official invitation to participate.

April 30^th, Friday
Last day for the receipt of the problem proposals.

April 30^th, Friday
Last day for the online registration of leaders, deputy leaders and observers.

May 31^st, Monday
Last day for the online registration of contestants.

June 10^th, Tuesday
Last day for the online submission of arrival and departure details.

1. GENERAL

1.1 The 51st International Mathematical Olympiad (the "IMO 2010") will be held in Astana, Kazakhstan from July 2 to July 14, 2010.

1.2 These regulations (the "regulations") govern the running of the IMO 2010.

1.3 The Organizer of the 51st International Mathematical Olympiad is the Republican Scientific – Practical Center "Daryn" (" the RSPC "Daryn"); it has an overall responsibility for the organization of the IMO 2010.

1.4 The aims of the IMO 2010 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 2010 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 9, 1990.

2.3 Observers including family members (the "Observers") may apply to accompany the Participants. The terms under which they can do so are detailed in sub-clause 3.5 below.

2.4 The official programme (the "Official Programme") as referred to below is the programme and outline itinerary for the IMO 2010 and associated events. The RSPC “Daryn” reserves the right to amend or revise the Official Programme in whole or part. If there is by any chance a significant change, Participants and Observers of the invited countries will be notified in advance.

The Official Programme for Leaders begins on July 2, 2010 and ends on July 14, 2010.

The Official Programme for Deputy Leaders and the Contestants begins on July 5, 2010 and ends on July 14, 2010.
The Official Programme will contain, among other things, details of accommodation arrangements (including food) for Participants and Observers and the venues for various official events associated with the IMO 2010.

2.5 Each invited country wishing to participate in the IMO 2010 must confirm participation online (www.imo-official.org/registration) using username and password provided by the RSPC “Daryn” no later than March 1, 2010. This will also confirm that the Leader agrees to abide by the Regulations for the IMO 2010.

Registration of Leaders, Deputy Leaders and Observers must be completed online no later than April 30, 2010.

Registration of Contestants must be completed online no later than May 31, 2010.

Registration of arrival/departure dates of Participants must be completed online no later than June 10, 2010.

2.6 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 the RSPC “Daryn”has been notified in writing that an Observer has been nominated to act in loco parentis.

2.7 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 2010. In order to avoid any trouble or accident, Leaders and Deputy Leaders must also inform fully their Contestants of the contents of "Important Contest Information for Contestants".

3. RESPONSIBILITY FOR ACCOMMODATION AND EXPENSES

3.1 The RSPC “Daryn” will provide accommodation in double rooms as a rule for Leaders, Deputy Leaders and Observers and in shared rooms for Contestants. Furthermore the RSPC 'Daryn' will provide meals, transport between Astana Airport or Astana Main Railway Station and the accommodation site and other necessary transport between the accommodation site and other venues on the Official Programme for all the Participants and Observers. In order to maintain the integrity of the IMO 2010, the detailed Official Programme will not be disclosed until arrival.

3.2 Other than in respect of the provision of accommodation, meals and transport during the Official Programme as detailed in sub-clause 3.1, the RSPC “Daryn” 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 2010. In particular, the RSPC “Daryn” shall not be liable for any expenses derived from:

Spending extra days in Kazakhstan outside the relevant dates specified in sub-clause 2.4 above;

Travel to and from Kazakhstan incurred by Participants or Observers;

Travel within Kazakhstan prior to arrival at Astana Airport or Astana Railway Station or 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 online using username and password provided by the RSPC “Daryn” that this condition has been met for all members of his or her team.

3.4 The RSPC “Daryn” expects to offer opportunities to Participants and Observers for excursions and/or 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 accompany the Participants as Observer is April 30, 2010. 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 May 31, 2010. Any application received without the full payment of the charges will be rejected. No refund will be given.

Observer A accompanying the Leader and residing at or near the Leaders' site: 2200 € (two thousand two hundred Euros) for a single room, 2000 € (two thousand Euros) per person for a double room (for 12 nights).

Observer B accompanying the Deputy Leader and residing at or near the Deputy Leaders' sites: 1200€ (one thousand two hundred Euros) for a single room, 1000€ (one thousand Euros) per person for a double room (for 9 nights).

Observer C accompanying the Contestants and residing at their site: 1200 € (one thousand two hundred Euros) for a single room, 1000€ (one thousand Euros) per person for a double room (for 9 nights).
Consideration will be given to applications from Observers wishing to attend and observe the IMO 2010 for only part of the period of the Official Programme and in such cases the charges, accommodation and all other relevant arrangements have to be negotiated with the RSPC “Daryn”.

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 April 30, 2010. Only the Leader may submit the proposals. They should be sent by 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. They should be new and may not have been suggested for or used in any other Mathematics competition.

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 2010 (the "Contest") will take place near Astana on July 7 and 8, 2010, under the direction of the Chief Invigilator appointed by the RSPC “Daryn”. 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 Each Contestant may receive the problems in one or two languages, previously requested on the registration form, 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 the RSPC “Daryn”. 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 are barred, from the moment of their arrival in Astana until the time of conclusion of the second examination, from having any external communication with Contestants, Deputy Leaders and accompanying Observers. In case of an emergency, the RSPC “Daryn”will provide proper assistance. Similarly, Contestants, Deputies and their Observers are barred from contacting Leaders and Observers accompanying the Leaders, during the same period of time. Information about arrivals, delays about arrivals and similar messages are to be directed exclusively to the IMO office and may be forwarded by the office to the Leaders upon request.

5.6 The total number of prizes will not exceed 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. Proposals for such special prizes will be put forward by the Chief Coordinator.

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 Honourable Mention if he/she has received seven points for the solution of at least one problem.

5.9 Each Contestant will 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

verify that all Contestants comply with the prescribed conditions for participation;

select the Contest problems from amongst the submitted proposals on the basis of a preliminary selection made by the Problem Selection Committee appointed by the RSPC “Daryn” of IMO 2010;

prepare and approve the official versions of the Contest problems in English, French, German, Russian and Spanish;

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

receive and approve a report made by the Chief Invigilator on the conduct of the examinations;

receive a report from the Chief Coordinator on any unresolved disputes which may have arisen during coordination and determine the appropriate scores;

approve the scores of all Contestants;

decide winners of first, second and third prizes;

consider and make decisions on all proposals to award special prizes;

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 the RSPC “Daryn” and discussed and agreed upon at the meeting of the Jury.

7.3 Each coordination session will involve two Coordinators provided by the RSPC “Daryn” 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 (Problem Captain) 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 Kazakhstan Contestants will be coordinated by the Leader and Deputy Leader of the country which submitted the problem, with the assistance of the Problem Captain for that problem.

8. ENTIRE AGREEMENT AND UNDERSTANDING

8.1 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 the RSPC 'Daryn' in respect of the IMO 2010.

9. FORCE MAJEURE

9.1 In these Regulations, "force majeure" shall mean any cause preventing the RSPC “Daryn” 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 the RSPC “Daryn” 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 the RSPC “Daryn” to recommence its affected operations in order for it to perform its obligations.

Contest will take place in "Baldauren" which is situated 240 km from Astana."Baldauren" is a national educational and recreational activities Center created on behalf of President of Republic of Kazakhstan, Nursultan Nazarbaev in 2000.

"Baldauren" is located in one of the most picturesque parts of Kazakhstan, in Borovoye resort area on the shore of Lake Shchuchye.


The SNNP "Burabay" was established in August, 2000 and it is under the supervision of the Administration of Presidential Affairs. The territory of SNNP "Burabai" is a part of the Kokshetau steppe, a mixed steppe and forest and hilly upland. The climate is extreme continental here, with hot summers and severe winters. The topography of the territory consists of lowlands, hills and plains.


Burabay (Borovoe) National Nature Park

In the north of Akmola region the SNNP "Burabay" is located. This resort pearl of Kazakhstan is a fantastic mountain land harboring mysterious wonders. Gorgeous pine forests, cliffs formed of neat gigantic natural bricks, and fantastical shapes of peaks resembling sometimes exotic, sometimes Egyptian pointed pyramids separated by serene lakes.

Although Burabay Park does not have any artifacts on its territory, every rock here has its own legend.

Nature has generously scattered precious gifts from its mineral treasury around the Burabay area. Among them is Okzhetpes cliff ("Inaccessible even to Arrows") with a peak resembling an elephant calf, and the creek of the Bun with Zhumbaktas cliff ("Riddle-stone") resembling a mysterious sphinx with severe fearless features.

There are 14 lakes on the territory of the park, each of which has an area of more than 1 km, and there are a great many smaller lakes. The river network is sparse and consists only of small rivers, springs and temporary channels. The largest lakes are Bolshoye Chebachye and Maloye Chebachye, Shchuchye and Borovoye.

Plant life on park territory is represented by forest, steppe, meadow, marsh and salt marsh species. The flora comprises about 800 species. There are 305 vertebrate animal species.

On the territory of SNNP "Burabay" are 35 permanent recreation facilities. The current landscape of the park is represented by steppe, lake, forest and forest and steppe and lowlands.

Borovoye (Burabay) Lake is situated in the territory of the Shuchinsky district of Kokshetau oblast in the eastern foothills of Kokshe Mountain. Its territory is 10.5 sq. km, length is 4.5 km, width is 3.9 km; average depth is 4.5 m, and maximum depth is 7 m. The shore line is 13.6 km and water area is 164 sq. km. The bowl of the lake is almost round, and its bottom level; the southern shores are rocky, and the eastern shores are sandy. The water in the lake is soft and still, and one can see to the deepest bottom of the lake. Borovoye Lake is separated by mountain ranges from the closest lakes (Big and Small Chebiache, Shuche, Kotyrkol, Zhukei, etc.). The island "Zhumbaktas" is situated in the northwestern part of the lake at a height of 20 m above the water. The cliffs and capes of the northwestern and southern coasts (Kyzyltas, Gorky, etc.) create a unique landscape. The shores are overgrown with pine and birch forests.


The combination of mountains, pine forests and lakes creates special climate conditions in the natural boundary. Medicinal health resort complexes (sanatoriums "Borovoye" and "Okzhetpes"; rest house "Blue Gulf", etc.) are some of the best in the country and built on the eastern coast between the Sarybulak and Gromotukha rivers. There are medicinal mud and mineral springs. The beauty of the nature of Borovoye is proclaimed in Seifulin's poem "Kokshetau" and in Mukanov's novel "Botagoz".


The legend of Borovoye
There are many legends and stories about Borovoye. "When God was creating the world, one of the nations received the lands rich of forests, another got fertile fields with large rivers, and the third got the beautiful mountains and blue lakes. But the Kazakh ended up with only feather-grass steppe.


This offended him and he asked God to endow him with some natural beauty. God took the mountains, rocks, beautiful pine and deciduous forests, blue lakes with pure water, and emerald fields covered with grasses and flowers from his korzhyn and spread them with a bountiful hand into the boundless steppes. It was the appearance of Borovoye; of one of the most picturesque places in Kazakhstan, which for its beauty and rare harmonic combination of mountains, forests, lakes, and unique flora and fauna received the poetic name "The pearl of Kazakhstan".


Borovoye is also the name of a health resort, which is situated in the Shuchinsky district of Kokshetau Region, 20 km from the station of Borovoye Resort (in the town of Shuchinsk). From the north it is surrounded by the Kokshetau Mountains at a height of 974 m above sea level, covered with birch forests. In the neighboring of the resort are such interesting rocks and cliffs as: "Okzhetpes", "Sphinx", "Cow", "Sleeping knight", and "Knight". The first private health resort was opened here in 1910. Average temperature in January is -16'C, in July is +19'C. Atmospheric precipitation is up to 400 mm, with about 2000 sunny hours per year. The main medicinal remedies here are fresh air and picturesque views.


Borovoye Lake is the beauty and pride of this area, featuring a variety of sanitariums, camping sites and resorts, with crowded shores and all the attributes of resort life: restaurants, beaches, stores and dance halls. Across the small mountain isthmus you can get from Borovoye Lake to Bolshoe Chebach Lake. It is perfect for lovers of unhurried and "wild" recreation, who prefer camping and contact with nature. From the top of Mt. Sinyukha ("Kokchetau", 961 m), the highest in the vicinity, opens a panoramic view of the lake, as big as a sea, stretching almost to the end of the horizon. The Burabai National Park system also contains the big Lake Shchuchye and many smaller lakes.


One can not be help but mention the lakes of Borovoye. There are many Lakes Shychie, Borovoye, Big and Small Chebachie, and Koturkul glitter on the green atlas of the forest.


The small lakes Svetloye, Karasye, Gornoye, Lebedinoye can be seen from the Kokchetau Cliffs. The visiting card of Borovoye is the Blue Bay on the lake of the same name. Right out of the waters of the bay, Mount Zhumbaktas (Mystery, Sphinx) soars.