In July this year, I had the amazing experience of travelling with the New Zealand Mathematics Olympiad Team to Madrid, Spain, to compete in the International Mathematics Olympiad (IMO) with 98 other countries in what was the 49th annual event of that competition. We left New Zealand on the 6th of July from Auckland Airport, having had several days of training immediately beforehand at the Mathematics Department of Auckland University.
Previously we had been attending trainings most weekends on Sunday mornings in order to advance our skills. Those training us included our Deputy Team leader, Heather Macbeth, who is currently studying at Auckland University, and past team members and past team leaders such as Simon Marshall, who is now attaining his doctorate at Princeton University. In preparation we sat a number of practice exams, each over three hours long, in conditions similar to what we would end up with at the IMO. Furthermore, we listened to a variety of lectures from our instructors in order to learn a number of new theorems and problem solving techniques.
From Auckland airport we had 31 hours of travelling time to endure before arriving to our destination in Spain. The initial long and gruelling flight from Auckland to L.A. took about twelve hours, but having left behind schedule we arrived late and the plane in L.A. had to wait for us to rush to it before it could take off. From there we had a flight of similar length to Munich and henceforth to Madrid. The arrival in Madrid was not without issues itself, however, as two of my compatriots’ baggage had been lost in the caverns of Los Angeles airport and didn’t arrive until a few days later.
Initially, we travelled directly to our first lodgings in Madrid. These were a number of rooms at a hostel for Universidad Carlos III de Madrid where we would spend our first week in Spain. The purpose of this initial week was to recover from the jetlag, acclimatise to the heat and spend seven days training with the Dutch team so that our scores on the test could be improved. Our hostel itself was on the outskirts of Madrid, and in order to go into the city centre, a reasonably long ride on the metro was required.
Our training began right away, as we were instructed we were to have some ‘fun’ problem solving the night we arrived. Our mathematical performance was severely limited by the amount of sleep, or lack thereof, we had received on our plane flights, whereas the Dutch team had to brave just two hours in the air from Amsterdam. For the remainder of the week we trained every day from nine in the morning until six in the evening, with breaks for necessary meals. This included a ‘mock’ IMO every second morning, problem solving in pairs the remaining mornings, and lectures in the afternoon.
For fun we would play soccer against the Dutch in the evenings, play cards, watch movies on people’s laptops or just sit around and discuss things. While it may seem like the time available for any relaxation was severely limited, because of the time of year and location of Spain in the time zone, it remained light until ten thirty at night and so we were able to have some fun in the midst of intense calculation. One of the more interesting things about the accommodation itself was the student cafeteria style take on Spanish cuisine. While a little salty, and despite the disagreement of much of the team, I managed to enjoy it, especially breakfast.
It was evident throughout the mock tests that the results of the IMO depended greatly on how one felt on the day. Over the three mock exams we sat (each four and a half hours) the scores for individuals fluctuated widely from day to day, and as we would find out later on, as would our scores on the actual IMO exam.
Despite the incessant testing, there was some relief to be had. One of the final days before we moved our accommodations was designated a day for ‘playing tourist’ in downtown Madrid. Luckily enough for most of us, we had never been there before, and so the role of tourist fit quite nicely. After taking the metro into the centre city we had free reign to explore the barrios of the city for a brief time before we met back together as a group and found lunch at the most authentic places we could find. Given that we were in a mainly tourist area however, this ended up being relatively formulaic in taste, but the atmosphere still gave as a fantastic sense of Spain (well the Madrid region anyway), as did the difficulties in communication.
We continued to travel around the city and saw many of the huge Cathedrals from long ago and also those built in Franco’s time in power, each having a differing flavour. Furthermore we saw the grand palace, which is as grand as the name suggests, and the Museo Arqueologico Nacional, which contains many amazing artefacts and historical records. It showed us what had occurred over the space of several thousand years of Spanish history in the course of several thousand seconds. Along the way we visited historic sites such as the Placa Mayor. To finish the day off we went on a row boat ride in the centre of the Parque Del Retiro in the centre of Madrid – a sprawling green park in the midst of the city – before heading back to our lodgings.
Soon afterwards it was time for the 49th International Mathematics Olympiad to officially commence. We were picked up from our current lodgings by bus and taken to where we would be staying for the duration of the competition. We also met our guide Juan who would prove invaluable and a lot of fun for the rest of our time in Spain. At this point we were split up from our deputy leader, Heather, who stayed with all the other deputy leaders in a four star hotel. Our team leader, Michael Albert, had not been able to see us at all up to this point due to his knowledge of what the problems would be in the exam. While the team leaders and their deputies stayed in veritable luxury, we travelled to another set of university housing; however they were in the centre of Madrid this time as opposed to on the outskirts. While the leaders may have been living in greater luxury, I doubt they had as much fun as we did staying in double rooms at the Universidad Complutense de Madrid.
The competition officially began with the opening ceremony on the 15th of July, which was surprisingly held in a several hundred year old circus. I was lucky enough to get to represent the team by carrying the flag at the ceremony, and after that concluded we were treated to circus acts including fire jugglers and mimes. Afterwards we were all invited to an opening dinner, which was outside and not seated but still very tasty and great fun as we mingled with teams from across the world.
The following two days we had the competition itself, and were under strict instructions by our leaders not to do any mathematics within twenty four hours of the competition. While such advice was well intentioned, few of us were able to resist brushing up a little bit under the nervous pressure, but playing cards acted as a reasonable alternative. The focus of the next day was the competition, for which we travelled by bus to the venue and were seated in a hall with all five hundred and fifty competitors. Each exam lasted four and a half hours and contained three questions worth seven marks. The entire competition was made up of two such exams to make a total of forty two marks for the competition. The questions tested our skills in solving problems in the areas of number theory, geometry, algebra and combinatorics.
After the two gruelling days of tests the organisers held a celebration essentially to signify that we no longer were bound by the pressure of exams. As such they hired a band which played familiar rock songs late into the night and fed us unlimited paella. Finally we got a real chance to associate with our peers and have a bit of fun doing it. Activities we participated in (or in the first case started) were a water fight and a mosh pit (as much as can be had at a mathematics competition). Everyone seemed to have fun, and we spent the majority of the time with the Dutch team with whom we had become friends, as well as our guide and anybody else who was brave enough to approach the New Zealanders.
Over the next few days we had excursions to nearby areas of Spain, and on these trips made friends from the Australian, English, Italian, Hungarian, Filipino, German and Portuguese teams among others, many of whom we still keep in contact with using social networking sites such as Facebook. The first excursion was to El Escorial Monastery near Madrid. This was a huge building, many hectares in size, and we were taken on a tour all around the historic and famous sites within. The rest of the day was spent at a nearby centre of pools and soccer fields, where we swam and competed against other nations in a competitive soccer tournament – we did not arrive back until one the next morning, having left at eight the previous morning, and now very tired.
Following this we went to sleep for a few hours and then hopped on the bus again to go to world heritage sites of Toldeo and Aranjuez. These two picturesque towns were hugely enjoyable places to visit. The excursion the next day was once again to Retiro Parque. This time however, we were not left to roam, but instead completed a number of challenges and scavenger hunt activities, again in competition with the other nations. This continued until the afternoon when we visited the Prado and Museo Renia Sophia, seeing some of the great masterpieces such as Picasso’s Guernica.
At the end of the day we were finally able to meet again with our team leaders and deputy team leaders, who had been away marking our papers. Thus, we all found out our scores at that point, but there was still much apprehension as to what the cut-offs for medals would be.
The following day we were told the medal results as we went to the closing ceremony. All of the students as well as all of the team leaders and deputy leaders attended and we were hosted by the Prince and Princess of Spain. My final score was fourteen, which while it may not seem like much out of forty two, was one mark off a bronze medal, for which the minimum was fifteen. A score of fourteen however, did give me an honourable mention, though it was slightly disappointing not to receive bronze when I had made one silly mistake costing me three marks. After the closing ceremony at which medallists were presented with their awards we returned to the lodgings for the final night.
The next day we returned to the airport, said our farewells and left for Auckland. The flight was once again around 30 hours, however this time we went around the other side of the earth, travelling through Hong Kong on the way back. We arrived back in Auckland having had a fantastic experience and a lot of fun in Madrid.
This experience has been one of the most rewarding of my life and I recommend it to any student with a passion for mathematics, competition and travel.