Ireland's Participation in the 52Nd International Mathematical Olympiad
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Ireland's Participation in the 52nd International Mathematical Olympiad Bernd Kreussler September 22, 2011 From 12th until 24th July 2011, the 52nd International Mathematical Olympiad took place in Amsterdam (The Netherlands). With 564 participants (57 of whom were girls) from 101 countries, this IMO was similar in size to its three predecessors. It was the first time ever that a team from Kosovo participated in the IMO. Senegal and Uruguay sent Observers and plan to participate for the first time next year. The Irish delegation consisted of six students (see Table 1), the Team Leader, Bernd Kreussler (MIC Limerick), the Deputy Leader, Gordon Lessells (UL) and the Official Observer, Mark Flanagan (UCD). 1 Team selection and preparation At five different locations all over Ireland (UCC, UCD, NUIG, UL and NUIM), mathematical enrichment programmes are offered to mathematically talented stu- dents, usually in their senior cycle of secondary school. These classes run each year from December/January until April and are offered by volunteer academic mathe- maticians from these universities or nearby third-level institutions. Like last year, we contacted schools directly and asked them to nominate their best students for the enrichment programmes. This is significantly less efficient than the practice of previous years in which the Department of Education and Skills and the State Examinations Commission provided information which enabled school principals to identify those of their students who were among the best performers in the country in Junior Certificate Mathematics. As a result, participation of good students in the training programme is not as high as it should be. The selection contest for the Irish IMO team is the Irish Mathematical Olympiad (IrMO), which was held for the 24th time on Saturday, 7th May, 2011. The IrMO Name School Year Adam Keilthy Sutton Park School, Dublin 5th Ewan Dalby Col´aisteBhr´ıde,Carnew, Co. Wicklow 6th Padraig Condon St. Gerald's College, Castlebar, Co. Mayo 6th Kieran Cooney CBS Charleville, Co. Cork 6th Vicki McAvinue St. Angela's Secondary School, Waterford 6th Yunwoo Lee Presentation Secondary School, Wexford 5th Table 1: The Irish contestants at the 52nd IMO 1 contest consists of two 3-hour papers on one day with five problems on each paper. The participants of the IrMO, who normally also attend the enrichment classes, sat the exam at the same time in one of the five centres. This year, a total of 50 students took part in the IrMO. The top performer is awarded the Fergus Gaines cup; this year this was Adam Keilthy. The best six students (listed in order in Table 1) were invited to represent Ireland at the IMO in Amsterdam. As in previous years, special training camps for our contestants at the IMO took place in Limerick. Following the good experience of last year, instead of one week- long camp we organised two shorter camps for the students. The first of these was held at MIC Limerick on 8/9 June 2011. As the LC Examinations started on these days, four of the six team members could not participate. The participants included the two team members who did not sit their LC Examinations this year and five of the best students (chosen on the basis of their performance at the IrMO) who will be eligible to participate in future IMOs. The second camp, at which the six members of the Irish IMO team participated, was held at the University of Limerick from 5 to 8 July 2011. The camps were organised as usual in a very efficient way by Gordon Lessells. The sessions with the students were directed by Mark Burke, Mark Flanagan, Eugene Gath, Donal Hurley, Kevin Hutchinson, Bernd Kreussler, Tom Laffey, Jim Leahy, Gordon Lessells, Anca Mustata and Edin Omerdic. A new feature this year was a joint training camp with the Colombian IMO team. The camp was held in the Youth Accommodation and Education Centre at Hanenbos a few miles south of Brussels. The facilities were excellent and very reasonably priced. The venue was organised by the Colombian Leader Maria Losada with help from the Belgian IMO Leader Bart Windels. During the period of the joint camp, classes were organised some together and some separate. Two Colombian trainers, Ivan Contreras and Esteban Gonzalez, and Gordon Lessells conducted the classes. There was also time for relaxation with Table Tennis being popular with members of both teams. The feedback from students about this activity was very positive. 2 The events After arriving in Amsterdam on the evening of Tuesday, 12 July, Mark Flanagan and I were driven to the Conference Hotel Koningshof in Veldhoven near Eindhoven in the south of The Netherlands. As usual, the Jury was kept separated from the contestants until after the end of the second exam. The Jury of the IMO, which is composed of the Team Leaders of the participating countries and a Chairperson who is appointed by the organisers, is the prime decision making body for all IMO matters. Its most important task is choosing the six contest problems out of a shortlist of 30 problems provided by a problem selection committee, also appointed by the host country. This year's Chairman of the Jury was Professor Hans van Duijn, Rector of the TU Eindhoven. He led the Jury meetings in a pleasant yet efficient way. There was more time than usual, until Wednesday afternoon, to study the 30 short- listed problems without being spoiled by the official solutions. Even in this early phase, the presence of Mark as an Observer was very useful. 2 During a number of meetings between Thursday and Sunday, the Jury chose the six contest problems and approved all translations and the marking schemes. The working conditions at the hotel, a former monastery, were excellent. The formulation of the contest problems in the five official languages (English, French, German, Russian and Spanish) and the translation into 50 further languages was finished on Saturday evening. The most remarkable thing to report about the problem selection process is the following. During the past 15 years, there were always two geometry problems chosen for the contest. Not so this year, even though there was a large pro-geometry group in the Jury. The final vote, between a second geometry problem and the combinatorics problem which became contest problem 2, was as close as possible with a margin of one vote only. The six Irish contestants, accompanied by Gordon Lessells, arrived in Amsterdam by train from their training camp in Belgium on the evening of Saturday, 16th July. All contestants were accommodated in the Hotel \Novotel" in Amsterdam. The Opening Ceremony took place on Sunday afternoon in the \RAI Theatre", a short walk from \Novotel". The organisers improved the traditional parade by grouping the teams by continent and interrupted it accordingly by short speeches and music from the \World Orchestra". It was widely agreed that this was a pleasant ceremony. The two exams took place on the 18th and 19th of July, starting at 9 o'clock each morning. There were three venues for the exams and the conditions were reported to 1 have been excellent. On each day, 4 2 hours were available to solve three problems. During the first 30 minutes, the students were allowed to ask questions if they had difficulties in understanding the formulation of a contest problem. The Q&A session on the first day of contest with 36 questions was relatively short, whereas the 189 questions from 72 countries on the second day constituted an unusually long one. The most frequently asked question was whether the order of weights matters in Problem 4 (of course, it does). After the first scripts arrived late Monday evening, it soon became apparent that Padraig solved Problem 1, except for a small arithmetical error which cost him an Honourable Mention. After the final Q&A session on Tuesday morning the Leaders and Observers moved to Amsterdam to stay in the same hotel as the contestants and Deputy Leaders. Most of our contestants went to the latest Harry Potter movie so that we did not see them until dinner time. We used the afternoon and evening to prepare coordination of the first three problems which was to start at 9 a.m. on Wednesday morning. Most of this work was done before the scripts of the second day were available in the evening. The scripts of the second day contained an interesting surprise: Ewan devised a very novel recursion for Problem 4 which (as we could show) could be completed to form a solution different from any of those found by the Problem Selection Committee or the Jury. Unfortunately, he didn't provide a clean proof of it and also didn't complete the solution. He only scored 2 points for this problem. During the process of completing Ewan's solution, Mark with his combinatorial knowledge was extremely helpful. He discovered that the numbers in Ewan's double recursion are known as bifactorial numbers. To get the coordinators to agree about the 2 points for Ewan's attempt, it was necessary to show how the solution could be 3 completed. The availability of the helping hand of an Observer was vital to achieve this. The purpose of the coordination, during which the representatives of each country meet experts appointed by the host country, is to achieve equal standards in marking the scripts of the students. This year's high level coordination was conducted by a well prepared team of about 80 experts, 20 of whom had already participated as coordinators in the IMO 2009 in Bremen. During the two days of coordination, excursions and other activities were organised for the students.