After a spell of training at Grafton Hall, the team left for Auckland Airport and then for Amsterdam. The journey was rather cumbersome with the destination inconveniently located at roughly the other end of the world. We make several stops between our flights to satisfy Stephen’s craving for Burger King (and for our planes to refuel – but that’s beside the point). Finally, we arrive disorientated at Schiphol Airport where we were greeted by the Dutch leader Johan. While he arranged for us to travel to Texel – the place where the joint Dutch-NZ training will be held – we bid goodbye to Chris and remind him of our general distaste for weird combinatorics, which I’m sure he took full heed of. Then we proceed to travel for a long time on the metro to get to our ferry. Many of us note the picturesque views of cobbled streets dotted with neat, colourful houses. We also scan the rustic landscape, which is quite deceptive in its similarity to NZ – save for the occasional occurrence of a windmill. Eventually, we trudged onto the ferry taking us to Texel.

For the next few days, we trained with the Dutch team sitting through 2 mock tests and sampling some nice problems from the 2010 shortlist. We also take time to explore the local town, which looks like something from a fairy tale. But other than that, it’s not very interesting. The weather, might I add, is also not very interesting. Like the countryside, it too seemed to be mimicing the Auckland weather. It did not take a liking to us during our interview on the beach by the Dutch media. In having to avoid showing our frozen faces, the Dutch national TV allowed our feet instead to make a cameo appearance.

Novotel is where we were staying in the final build up to the IMO. It’s a very warm accommodation – made all the more cozy by the vehement outside weather. After meeting our guide Marlisa, the NZ contestants settled into their allocated rooms and were given neat packs loaded with goodies. We later meet up with other teams such as the Australian team. Generally there is a consensus that this year’s IMO was very well managed and the catering staff very helpful. Indeed, they had even arranged to have the opening ceremony only a brief stroll from our stay – which I’m sure caused no sleep loss or worry. There is also, however, a slight disappointment shared by some teams about the cuisine. The food given seems to have its lineage in Indian culture as opposed to Dutch – and so many teams have taken a liking to the stack of instant noodles present in the dining hall.

After the opening ceremony, the NZ team proceeded to make many photos- to use the Dutch saying – with other teams. Especially popular (as always) was the DPRK delegation. But soon the weather soured and loitering outside was deemed impractical. We hurriedly retreated back to the hotel – the contest is the next day.

Day One of the IMO this year was notorious for its inclusion of the windmill problem. The windmill problem was arguably one of the hardest problem 2s ever to grace the cover of the IMO. It was also one of the most loathed for many strong teams weren’t able to solve it at all. Many displeased contestants noted the disproportionate difficulty of problem 2 and 3 in that 3 was much easier than 2, and those who did make the right choice to skip 2 ended up scoring dramatically higher than those who valiantly carried on with faith in the jury to sort the problems in the right order of difficulty. After the exam, a French contestant condemned the windmill problem on the IMO ’11 Facebook page – he got a lot of likes. Also this year, the invigilators screened contestants with metal detectors before entrance into the hall. So I’d like to remind next year’s team to get rid of its habit of bring guns to a maths exam – at least before the IMO anyway.

Day Two bore fewer surprises save for the lack of easy to medium geometry. Indeed, this year the jury broke the lengthy decade long tradition of having an easy and a medium geometry problem on the exam. On the whole the NZ team fared very well with 2 silvers, 2 bronzes and 2 HMs – although the same could not be said of me. We again captured our 29th placing from last year. It must be mentioned that this year’s IMO helped to produce the most successful IMO contestant ever – Lisa Sauermann with her final mound of many golds, a silver and a perfect score. Also congratulations must go to Madelon from the Dutch team for gaining the highest score in her team for her silver medal.

The last leg of the IMO consisted of excursions and sightseeing opportunities. We must have our guide Marlisa to thank for her expertise in guiding us in and out of Amsterdam. Particularly notable were a 30k long bike ride through the Dutch countryside (under the auspice of good weather for once) and a fun walk through Amsterdam proper where we got a full taste of the many aromas and sights of the liberal city. After a well-organised closing ceremony, the team was ushered to a ‘beach’ in central Amsterdam where the farewell party took place. It was a delightful affair with ample hot food and drinks. Heaps of NZ souvenirs were handed out and we amassed a large pile of Mongolian currency. The weather again did not share the festive mood – but never mind because it was (mostly) warm.

The next day marked our final day in Amsterdam. We bid goodbye to our sprightly guide Marlisa with the presentation of our mascot – the Kiwi. Then back we came from the other side of the world loaded with memories and other stuff.

To finish, I’d like to thank the following people (or organisations) in no particular order: Chris, Ilya, Stephen, Royal Society of NZ, NZMOC, IMO ’11 ’10 ’08 organisation committee for making IMO so cool, Dr Michael Albert, Dr Arkadii Slinko and past volunteers for their invaluable time and efforts. Thank you.

The venue of Kazakhstan offered a particular interest for all of us, and we found it to be (mostly) agreeable and intriguingly exotic. In the competition itself, the New Zealand team put up its best ever performance, gaining two silvers and four bronzes. Outside of the exam room, the atmosphere surrounding the Olympiad was as friendly and exuberant as ever. At no other event in the world do so many like-minded budding mathematicians meet, and so the conversation often and shamelessly turns to maths, and camaraderie abounds….. although this year there was some rivalry between nations brought on by the FIFA world cup. The Dutch are our training partners for the Olympiad, and so out of loyalty we ended up supporting them, to the disgust of the Hispanic nations. But I had better begin my account in the proper place, so here we go…

We arrived in Astana (capital of Kazakhstan) after 30 hours of travel time, and without the company of Scott and Ilya. Scott got stuck in Auckland airport for bureaucratic reasons and was bailed out several days later. Ilya, on the other hand, was delayed in Germany. This proved slightly inconvenient for us, as Ilya was our deputy leader and also the only Russian-speaker among us. Life was extremely interesting for several frantic days. In the meanwhile we embarked on our traditional joint training camp with the Dutch. It was a pleasure to see our old friends Harm, David, Merlijn, Quintijn, and Birgit, and also to meet the rest of the large Dutch contingent. Mealtimes were something less of a pleasure in the rather dubious hotel we were staying in, though I may be biased as I was the one who ended up with food poisoning.

The training camp itself was the standard regimen of mock IMOs and group problem solving. Our leaders also took preventative measures against cabin fever by organising an excursion into Astana, taking our minds off maths for a brief while. By the end of the week Scott and Ilya had arrived, and the hotel’s food hadn’t improved, so we were ready to head off to meet up with the main IMO group. At this point I was also beginning to grow nervous, as my marks had been uniformly bad throughout the training and the Olympiad was growing dangerously near.

We spent a couple more nights in Astana with the other teams whilst registration and the opening ceremony took place. It was also here that we met up with our truly wonderful guide and translator Laura, who would expertly keep us out of trouble for the remainder of our stay. Then we were all escorted off to the exam venue, which was a camp out in the woods, five hours from Astana. The camp, Baldauren, served as maximum-security exam location whilst also offering beautiful scenery and a lake to go boating on. But before we could enjoy these things, we had to deal with the Olympiad itself.

Here I shall omit what could be a rather lengthy account of the various discourtesies we were subjected to at 6.30am on exam day. Suffice to say that the camp’s management appeared to follow some sort of ‘late-to-bed-and-early-to-rise’ policy. The New Zealand team was delighted to hear that a member of the Australian team exercised considerable wrath against the management on all of our behalves.

The exam itself appeared to go well for everyone. Fortuitously, Q.1 was a functional equation, which is a reasonably popular branch of Olympiad algebra that our leaders had thoroughly drilled us in. I solved this question quite quickly, but unfortunately the excitement went to my head, and I failed to produce any more coherent work in the next three hours. Q.2 was geometry – my favourite area – so I had hoped to make more progress with it. Now all chances of getting a medal would depend on the second day.

That afternoon, we met up with Ilya and May (our excellent team manager). IMO regulations restrict the team leaders and deputies from seeing their students during coordination; IMO tradition, on the other hand, stipulates that every year the deputies stage a revolt and do so anyway. This occurred without mishap. We talked over the scripts, and it appeared that everyone did well.

The second day dawned undisturbed. I was optimistic. There is always an ‘easy’ geometry problem at the Olympiad, and seeing as so many people seemed to have difficulty with Q.2, I was betting that the easiest problem today (Q.4) would be geometry as well. It was. I am ashamed to admit, this one took me over three hours to solve because I bungled an early step. Eventually I found my error and went ahead to solve the question. Now I could reasonably hope to get a medal, provided nothing had gone horrifically wrong.

The pressure was now off, and so we were taken on a series of tours and activities. The papers now had to be marked and coordinated by the leaders. We had not seen any of our leaders for a while, and so we were on tenterhooks, keeping ourselves informed through the reports of the British team. Over the next few days, we found our marks to be 15, 16, 16, 16, 21, 22. At Olympiad level, these are truly excellent marks all round, particularly Tom and Malcolm on 21 and 22. The real question was where the medal cutoffs would lie.

So, whilst we listened to concerts, explored the steppes, drank fermented mare’s milk, visited small towns and historical museums, and rambled through forests and mountains, our minds were perpetually engrossed in speculations about the cutoffs. When they were finally announced to be 15, 21, and 27 for bronze, silver, and gold, respectively, our shrieks of hyperactive joy and hysteria were unparalleled among all other teams. Of course there is a certain pure joy in maths for maths’ sake, but for every team member to win a medal is an incredible and exhilarating result. After that, the remaining days spent in Kazakhstan passed in a blur of euphoria.

It must be mentioned, huge thanks go to our team leader Dr Chris Tuffley and deputy leader Ilya Chevyrev, who provided mathematical training and fought valiantly to justify our marks in coordination; to the team manager May Meng for her role in organising the team, assisted most ably by Alan Parris; and to the many other volunteers and helpers who contributed to the training of the team for 2010.

In closing, I would only add that the International Mathematical Olympiad is a truly exceptional event. It offers a level of challenge and stimulation that is unparalleled at high school level competitions, and it develops mathematical skills that any undergraduate (and many postgraduates) would envy. The Olympiad offers keen students a taste of real mathematics, which is to say, pure exploratory problem solving. The work that the lecturers and organisers do to sustain this program is incredibly valuable, and for many high school students provides a welcome enrichment to the standard mathematical curriculum. Additionally, at the IMO itself, a lucky six New Zealand contestants will have earned the chance to meet with other mathematicians of equal or greater ability. This is a wonderful opportunity for further mathematical stimulation and enjoyment. I offer my personal highest recommendation for the New Zealand Mathematical Olympiad Committee, and I will be delighted to contribute to their work in the future.

For me, the journey had begun 18 months earlier, when I attended my first January camp. There, I was exposed to the fascinating world of Olympiad mathematics, as a competition which is hugely popular worldwide and remarkably different from that encountered in high school. From there, I was determined to practice and learn with the hope of eventually being selected for the New Zealand team. Indeed, I was quite disappointed in not being selected for the team in that year, however I gained invaluable experience through being picked for the training squad, attending numerous lectures with the rest of the squad, and completing various assignments and tests. This year, after exceeding many of my expectations in the selection exams, I was selected in the team of six to represent New Zealand at the IMO 2010.

Despite this being my first IMO, I had set myself the lofty goal of returning with a medal, which I felt, given the preparation I had put in, I was capable of achieving. On the 27th June, we departed Auckland Airport (albeit without our team member, Scott, who had encountered visa issues and would rejoin us later in Astana), and after 30 hours of travel via Dubai and Almaty, we arrived in Astana. Given the somewhat dubious view which Kazakhstan is often afforded, I was eager see what awaited us. We were greeted by two Kazakh guides and promptly driven to Hotel Daniyar, where we would stay and train with the Dutch team for a week, in the hope of acclimatising and improving our problem solving abilities. The drive to our accommodation revealed a modern and clean city, dotted with majestic architecture – unusual and unique to say the least. Apparently, Astana was chosen by President Nursultan Nazarbaev to be the new capital of Kazakhstan in 1998, and since then, significant investment has been made with the hope of transforming Astana into one of the world’s leading cities.

We spent almost the entirety of the week leading up to the IMO immersed in mathematics, whether it was mock 4½ hour exams, problem solving sessions or lectures, and these were challenging and stimulating, but at the same time very enjoyable. The Dutch team were great company, and we witnessed their jubilation as the Dutch football team recovered to knock Brazil out of the World Cup. Midway through the week, we had a break from the mathematics and toured the outskirts of the city, where we observed the many statues, monuments and fountains scattered around, saw modern buildings among dilapidated Soviet-style apartments, and we took time out to relax at a park. Other free time which we had during the week was spent playing games with the Dutch and exploring the area around our hotel, where we discovered a small marketplace. Though the lack of English spoken made it difficult to communicate (the main languages spoken being Kazakh and Russian), some of the team improvised with crudely drawn pictures. The week passed quickly by and soon it was time for the IMO proper to begin.

The opening days of the competition leading up to the tests were eventful but not entirely ideal. The first night was spent at the luxurious Hotel Duman, where our team and two others (eight of us) were placed in a double room, along with wooden slats which were to serve as our beds for the night. The Opening Ceremony was held the next day, following which we embarked on a 5-6 hour bus ride spanning 250km to the ‘Island of Children’s Dreams’. Otherwise known as Baldauren, this was where the contest was to be held, and was located in an idyllic natural setting. Unfortunately for us the long bus ride was not idyllic, and, having witnessed the endless plains of Kazakhstan, we arrived at Baldauren at around 9:30pm. It was not until after midnight that we slept, mindful of the exam the next day. Our tiredness was compounded when the next morning, at precisely 6:30am, we were awoken to the loud music of ‘Peer Gynt’ followed by a loud rendition of the ‘IMO Hymn’. Following forceful protests from some other contestants, the music was turned off. Sleep-deprived, tired and still a bit dizzy from the long bus journey, I entered the exam room, hoping for the best.

My exam room (source: IMO 2010 organisers).

The exams themselves were all that I could have hoped for. On each of two days, we sat a 4 ½ hour examination of 3 questions, designed to challenge even the most capable mathematicians. On the first day, I was initially dismayed when confronted by the first question, a functional equation, having never solved one in a competition before. Therefore, I was very pleased when I was able to produce a solution within the first hour or so. This left plenty of time to attack the second question, although it was slightly disappointing not to make too much progress on it. The second day was much like the first – I was able to come up with a full proof for the first question, a geometry one, within the first few hours but was unable to make too much progress into Q5, which was a nasty Combinatorics question. I was ecstatic when one of my teammates announced that I had received 16 points, having scraped partial marks on the 2nd and 5th questions. Furthermore, our team had performed exceptionally well, Malcolm and Tom scoring 22 and 21 respectively, myself, Stephen and Scotty scoring 16, and Ed scoring 15 points. It’s fair to say there were scenes of uninhibited jubilation in hearing the medal cut-offs of 15 for a bronze medal and 21 for a silver medal, as this meant that the entire NZ team had received medals for the first time. The team also ranked 29th in the world – in the top 30% of countries – which is the highest ranking New Zealand has ever had at the IMO.

A concert at Baldauren.

During the days following the examinations, we were treated to various excursions, performances and concerts, and we learnt more about the Kazakh culture and history and their language. While the excursions were at times tiring due to the excessive travel times, they were still fascinating and a lot of fun, and included visits to a zoo and museum in Borovoe (which I’m told is the next Las Vegas) and viewing archaeological sites located deep within the tranquil plains. We also witnessed the Kazakh people’s love for performance, as we were treated to two concerts in the town of Kokshetau and at Baldauren, where we witnessed traditional music and dancing mixed in with a more modern flavour. There was also plenty of time to spend time with the other contestants from the other countries, and the nights were spent playing games, ranging from the ubiquitous Mafia to a crudely organised game of Capture the Flag. One of the highlights of my stay at Baldauren was an outdoor disco, where us unruly mathematicians threw away our inhibitions and displayed our conventional and more unusual dance moves. I must also mention that the male to female ratio at the IMO this year was 10:1 – clearly the IMO is significantly male dominated, and hopefully this ratio will lessen in further years – although almost all the guides this year were female. Our time at Baldauren was concluded early on the morning of Monday 11th July, as World Cup fever engulfed us, and we witnessed the ecstasy of the Spanish fans as Spain scored the late winner in the FIFA World Cup final.

The team with our guide, Laura, during an excursion in the forest.

The Bayterek Tower and United Buddy Bears exhibition.

On our return to Astana, we had a brief excursion into the Astana city centre, where first we viewed the United Buddy Bears exhibition, and then finally had the chance to travel up the centrepiece of Astana – the Bayterek Tower. This lollipop-shaped monument offers spectacular views across the entire city, and also features a gilded handprint of President Nazarbaev, which we were told to place our hand on and make a wish. It had become blindingly clear to us that President Nursultan Nazarbaev had a huge influence in this city – an oligarch whose decisions were always honoured. The IMO concluded with the Closing Ceremony which was again held at the majestic Palace of Independence. There we were presented with our medals; which was a proud moment not only for me, but for the entire team. After the farewell banquet, we said our goodbyes to the many of the other teams, as well as to our guide, Laura, with whom we had become such good friends. After a sleepless but fun-filled night, it was time for us to leave. The IMO had come to an end.

From left, Stephen, Scotty, Tom, Malcolm, Ed and Robert (source: Chris Tuffley).

This trip was a truly life-changing experience; the memories from it will stay with me forever. Having not been widely travelled myself, the IMO experience was a huge eye-opener for me – I learnt about the culture and people of Kazakhstan, made many friendships with amazing people from all over the globe, and realised that there are countless opportunities available for students, both in New Zealand and internationally. Representing NZ has been a huge honour, and the team performing with such distinction was incredibly rewarding for all of us. The mathematics involved has been great fun to learn and develop, and it has been very rewarding to see a goal, which I set years ago, being realised. I would certainly recommend any student who has a passion and love for mathematics, who is longing for a challenge (given that school mathematics may not always be challenging or stimulating) to get involved in the mathematical Olympiad programme – the IMO trip is worth it in itself. Thanks and appreciation must go to our team leaders Chris and Ilya, to our team managers, May and Alan, as well as all those who have generously given their time in supporting and training not only the NZ team, but all of the students involved in the Olympiad programme. I am also very grateful to my parents and the Royal Society of New Zealand for their continued support and assistance in funding.

My journey in Olympiad mathematics is not over yet, and I hope that I will have the opportunity to represent NZ at the IMO next year in Amsterdam. Hopefully it will be yet another enjoyable and successful year!

On the evening of July the 6th, the New Zealand International Mathematical Olympiad (NZIMO) team, consisting of Jingcheng Bian, Ben Kornfeld, Heyang Li, John Bernard Ong, Tom Yan and myself, accompanied by our Deputy Leader Heather Macbeth and Team Manager May Meng, left the Auckland International Airport to attend the 49th IMO in Madrid, Spain.

This year’s IMO being in Madrid meant that we would be able to enjoy the wonderful Spanish summer, but it also meant that we had to fly for 31 hours to the opposite side of the world. We had been training hard throughout the year, finishing countless numbers of assignments, sitting the Asia-Pacific Mathematics Olympiad, attending many lectures and most importantly the “Maths Battle” against the last year’s team members. To top off this preparation for the 2008 IMO, from the day of our arrival in Madrid, we undertook a week long training session with the Netherlands IMO team. Our training sessions were very intense – full-on mathematics from 9am until 9pm, only interrupted by lunch and dinner breaks. Our preparation included sets of mock tests, lectures, problem solving in pairs and discussion sessions. This was often very tiring – especially since we were still suffering from jetlag. In the evening sessions we often found it hard to keep ourselves awake.

On Friday we took a short break from maths. We toured around Madrid, visited some of the tourist attractions, including Plaza Mayor, Sol and Palacio Real, and shopped around for a day. We experienced Spain’s rich history as well as the distinct culture. It was purely fantastic, especially because I was not very widely travelled, and also because New Zealand, in comparison to Spain, has a very short history. I could feel the Spanish culture everywhere, from architectures and food to more trivial things like cars and fashion.

Madrid street. (Source: Heather Macbeth)

On Monday, it was time to go. Our time to end the mathematical preparation and focus on being in the right state of mind mentally. Our time to be picked up by our IMO guide. Our time to go to the official accommodation site and meet the other contestants.

The Opening Ceremony was next day. Sweating in our long sleeved shirts in 38˚C, we travelled to the Circus, where the ceremony was to be held. Inside the circus was filled up with beautiful decorations, all maths-related, as well as hundreds of people from many different countries. The quality of the performances was outstanding and I thoroughly enjoyed the entire ceremony.

The day after was the doomsday. The first day of the examination. 551 contestants somehow all managed to fit in one massive room at Escuela de Caminos. As we arrived at the exam room very early, we spent about an hour and a half, panicking, worrying and fidgeting. As it neared 9am, I wished the NZ team good luck and took a seat. And then it began.

This was my first IMO, and although I had my hopes and expectations, I knew I wouldn’t be able to perform at a very high level. With nervousness I opened the examination booklet and stared at the questions. They looked extremely difficult, if not nearly impossible. I struggled even with the first question, let alone the other two. I vaguely knew how to approach the first problem, but I couldn’t solve it. I was pretty disappointed with myself because I knew it was an easier problem one than usual. I also did not produce significant amount of working for the other two questions. As I walked out of the room, I tried to keep cheerful and hoped for an improvement from the score I had received during my mock exams.

On the second day, I was determined to redeem myself and perform better. However, the questions were even harder than the previous day’s. To worsen my situation, I had an acute stomach pain from an unknown source, possibly from drinking milk in the morning. I spent most of my time on Question four, which was a functional equation problem. I knew there was a major problem with my solution but I was not able to finish it off. Although I was disappointed with myself, examinations were now well and truly over, and we were now ready to relax, socialise and enjoy.

The next three days were full of excitement. We had a party dinner with the ‘Hey Hey Hey Band’, went on excursions to places such as Segovia, Escorial, Madrid city centre and Toledo and on the last day, watched a Flamenco show. They were really amazing. I experienced even more Spanish culture and by the end I even could sing a song in Spanish and speak some basic Spanish verses.

The Hey Hey Hey Band. (Site: IMO08 archive)

The Closing Ceremony was held on Monday. The Prince of Spain and his wife had attended, and although I did not get a medal, the ceremony was still very spectacular. Sadly, none of the New Zealand team received a medal. However, Ben (who missed out on a Bronze by a mark), Heyang and Jingcheng managed to get Honourable Mentions.

The next day we set off to the Madrid Airport in order to fly back to New Zealand. Saying good-bye to our guide was difficult, as we had become such good friends. Overall, the IMO was an eye-opener for me. I enjoyed every single bit of it – the excursions, great friends I made and the examination itself. I know I did not perform well enough, but I still have gained so much from the trip. IMO has taught me how small New Zealand was, how much harder I had to work and how high the standards are internationally. IMO has provided me with inspirations, motivations, heaps of fun, and most of all, great friends. I must thank Michael Albert (the NZ team leader), Heather Macbeth (the NZ team Deputy Leader) and May Meng (the NZ team manager) for accompanying us to IMO and making it a fabulous occasion. I also would like to thank the Royal Society of New Zealand, NZAMT, Saint Kentigern College and my parents for their support and sponsorship.

 My journey started when I went to Auckland on 2nd/July/2008. I was so excited and very sure I would enjoy this trip. Everything went fine along the first flight from Christchurch to Auckland. I met Heather (our deputy leader) at the bus stop and settled in Grafton Resident Hall (part of Auckland University), room 605, which besides one of my friend Ronald. This room had a very nice view of the outside: I could see the top of One Tree Hill Domain on the right, and some distance old trees in the centre. On the left, there were some buildings which unfortunately blocked my view of the sea.

The Grafton Hall had a lot of facilities: a pool table and a table tennis table, along with the SKY TV and a computer room. My favourite activity at Grafton Hall was the pool: it is such a good sport to play with people you just meet. I played a lot of pool and some table tennis with Ronald; he seemed to be better than me. Anyway we had a lot of fun. By the way, the food in Grafton Hall is wonderful; there are some much options for each meal. I had toast or cereal for breakfast, there were over 15 options. For lunch, for the convenience, I usually packed my own lunch. For diner, there were 2 to 3 different and good dinners to choose. I just totally loved it.

Grafton Hall. (Source: Thomas Li)

During my stay in Auckland, the weather has never been good for a whole day. It always rained and then stopped. The good thing was the rain tended to stop when I was going outside. Therefore, I did a lot of exploring around Auckland. I went Queen St twice, and enjoyed the busy streets. Also, I went to Albert Park a few times; just relax myself after the maths training.

It was a maths trip, so maths was always the first priority. From 3rd/July and the next two days, we had a training camp in University of Auckland. In the morning, it was 3 hours problem session to tackle 3 problems with IMO question 1 difficulty. I found it to be the right level of difficulty for me, and found it very enjoyable and rewarding after solving them. In each of the afternoons, we first went over the problem, then a few lectures on some of the interesting maths topics.

Lectures in Auckland. (Source: Thomas Li)

2. Flying to Madrid

6 July

It was time for the NZ IMO team to travel to Madrid, Spain. We flied to Los Angles (USA) first, then to Frankfurt (Germany), and finally to Madrid. Jed’s dad delivered me to the airport. Everyone in our team got there with 3 hours to spare. We checked in, got our ticket, and got on the plane at 7 pm. We were flying with Air New Zealand; they provided us with a wonderful service. There was a TV in front of each one of us, there were games, movies and TV shows. I watched 2 movies, the best one was “21”. When we got to LA, we had to go through some of the toughest security checks. Luckily we were from New Zealand, they took easy on us. We got on the next flight just in time. When we got to Frankfurt, we had 2 hours to spend, I went to buy some post cards and some Germany Chocolate, and they tasted so well.

7 July

“Yes, we are in Madrid. No, my luggage is lost in LA.”

It turned out they were dropped in LA, and it would arrive one day late.

3. Training with the Dutch

Our training started in the evening. We were going to train together with the Dutchs. Even though English was not their first language, but they could speak it well enough for maths.

Spanish living pattern is slightly different from New Zealand. Their dinner is very late, around 9 pm. Their lunch is late as well, which is the most important meal of the day. Since it is summer there, there are so many different fruits available there, which I have not seen in New Zealand before. Water melon is much fresher and cheaper here. Spanish bread is very hard, our team member decide to call it “brick”. It is uneatable without having it with water or juice. Some of the Dutch team members even played soccer with this type of bread.

8 July

From 8th/July and the following 5 days, everyday was a hard training day. We got up at 8am and had breakfast. The morning problem session ran from 9am to 1:30pm. Then it was one hour for lunch, and half an hour break. From 3 to 4 pm, it was discussion about the problems, and then it followed one hour of training session in our own team. Half an hour break, then it was a 3 hour lecture that went to 8:30pm, some time even 9pm. Then it was dinner, and went to sleep. Even though it was a bit tough, I learnt a lot of mathematical skill that could be used for this IMO, and also for the rest of my life.

Mock exam in Madrid. (Source: Heather Macbeth)

11 July

11th of July was a bit of an exception: we had a day not doing maths. We went to central Madrid (Sol). On that day, we took the subway about 9 times, it was so cool. Subway is a much faster transportation system. How could people in a large city live without it? When we were in central Madrid, we went to the amazing Royal Palace with two beautiful cathedrals: one small restaurant and one royal museum, to take 45 minutes boat riding and then 1 hour wandering in the park. It made me feel that Spain was a paradise to live in.

12-13 July

We got along with the Netherlands team really well. During our afternoon break on the 12th, we played soccer. Of course, we got beaten, but not by much. The sad thing was Jed injured his right foot, because of not wearing shoes, and a sharp object went in. Unlucky things tended to come in a bunch. On 13th, when I was having a shower, my glasses broken in the shower room, and one leg of the frame went down the drain.

4. Living in IMO Resident Hall

14 July

The real IMO started on 14th. We checked out from our training camp and moved to our IMO resident hall. We met so many contestants from all parts of the world: Malaysia, Germany, Canada and so on. I just thought it would be an unforgettable 8 days living here. In the afternoon, I went to the local shopping mall with our guide Juan and our team manager May. I found out that everything in Madrid market was on special: from clothing to footwear. You could name it, they got it on sale. I went to an “Optica” shop, where I got my glasses reframed for €55 and the reframing was done in an hour, much cheaper and faster than I expected.

15 July

The next day morning, the Opening Ceremony started. Sadly, only one contestant from each country can cross the stage. So I had given up my chance to Ben. In this ceremony, the speaker spoke in English and Spanish alternatively. All speeches were about the importance of mathematics, being glad to have you here and should keep working hard in maths. Then the show started. It was a very good performance. The best one was the 2 female performers dance on the 2 vertical cloths. After the ceremony, we had a lunch in the park with all the contestants from 96 countries. It was amazing to communicate with people from all parts of the globe. I talked and took photos with contestants over 40 countries.

2008 New Zealand and Australian IMO teams pose. (Source: Thomas Li)

In the afternoon, I went to swim with 2 guides (NZ and Germany), So-Young, Tom and Jed. Well it was cool to cool you down a bit in a temperature of 35 ˚C. The pool also have water jet at the side, it was so relaxing just in the pool. After that I had a nap, and then had a dinner. The following day was the first day of the competition; I was nervous and excited at the same time. I was looking forward to it.

5. The Contest

16 July

16th was the first contest day. I was nervous as everyone else. The test centre was in a university in Madrid with a very big room that would fit every contestant. The table and the chair were not as comfortable as expected. The table was in an angle of about 25 degrees which was slippery so that my paper kept slipping down. The chair was a high stool which was really not comfortable for four and half hours. Beside that, everything was fine. We were given muesli bars and mineral water.

Contest room. (Source: Thomas Li)

The exam started. After reading all the problems, I spent one and half hours in problem one, but no luck. Then I used one hour in question 2 to do some expansion of the bracket for the inequality and to try some substitution which helped me to find one solution for the equality. Then I spent the rest of my time in question 1, no luck until the last 20 minutes. At last I simplified the problem into a very simple algebra question, but with one calculation error.

17th of July

Day two of the contest, before it started, I was walking in the contest room. I saw a USA contestant had prepared everything to the last detail. His pencil, pen, ruler, protractor were placed on the table in order. So prepared and planned! Then the contest started. I looked at question 4, which is a functional equation. My brain went to blank because I have only done 2 functional equations in the last 6 months. I made some progress in question 4, but it was not enough to solve it. Therefore I started to pray for inspiration. Then luck went my way in question 5. After reading question 5, I got two ideas: one was a normal idea to find M and N individually then divided it to find N/M and the other was to find the ratio of N/M straight away. I tried the first idea which turned out to be too hard. When I tried the second idea, amazingly it worked perfectly. Everything just fitted together so nicely. Near the end, I tried question 6 and 4 again, and got no luck. Soon the contest was over.

After the contest, members of all the teams had a dinner party in a park, where a band was playing. We had lots of fun time during the party: we were dancing, clapping and jumping around. It was fantastic!

6. The Excursions and Free Time

18th of July

Our excursion started. We went to Segovia and Escorial.

Segovia is an old Spanish town, with a lot of historical buildings and aged trees. There were a lot of hard walk for this trip, but it’s worth it because of the good view. It’s a very lovely place. Everyone was lost in the wonderful colour and brilliant scenery. We had seen the water bridge: the way Spanish people transport water near the centre of Segovia. This was followed by a 30 minutes uphill walk to the top the mountain with a palace on it. Unfortunately we couldn’t go in, but it was significant on the outside. It was the most amazing palace I had ever seen.

Water bridge in Segovia. (Source: Thomas Li)

Then we went to Escorial to visit the monastery. This monastery is one of the historical places in Spain, which got lots of beautiful paintings to show the history of Spain.

Still in Escorial, we went to swimming. It was so cool and relaxed to swim in a hot weather. We also played the IMO soccer tournament. We were paired up with Coast Rica (the best team), but we still lost. Also, we played basketball with other teams. Well it was fun to be mixed with other team. The only thing that went wrong was that the dinner queue was a bit long: it took us nearly an hour to get our dinner.

19 July

In the morning of 19th/July was activity day. We worked with our team members in a group of 6 people. There were 6 events: World map, Diana (darts), Sudoku, Sack racing, Memory and Tectonic plate (making balloon into shape). Our team did really well in Sudoku and World map thanks to everyone in our team. But we were late for the Memory game and did really poor. However the Sack race was the most interesting game. Four people (Everyone except Tom and So-young) were in a sack trying to jump forward. We nearly cross the finish line in time. But the fun thing was that we fall lot of times.

In the afternoon, Heather, Ben, Dr Albert and I went to a modern art museum when the rest of the team came back to the resident hall. (The sad thing was that Jed’s wallet got stolen on the way back.) Those modern arts were not only beautiful, but also imaginary. There were a lot of fascinating works of art from different countries. It was one of the best museums that I have been to. Out of museum, we had some ice-cream. I had the mint-chocolate biscuit, which is chewy and indulgent.

In the evening, we had a dinner party at CM Aquinas. We had lots of fun during the party. We talked to most of the contestants from the Commonwealth countries, especially our neighbour Aussies.

In the same day, we found out what mark we got. Ben got the highest mark in our team which is 14. We all hoped that was good enough for a bronze, but it seemed unlikely for this IMO.

20 July

In the morning of 20th of July, we had some free time, which was seldom in IMO. We played Hearts (a card game) together. In the afternoon, we went to Toledo, a town. At first, we had a tour on bus, after that we tackled it by foot. Toledo is one of the oldest towns in Spain, which is over 2000 years old. We had seen a lot of different historical places.

Tower, Toledo. (Source: Thomas Li)

Then, more bad news came: my camera’s LCD was broken, and Tom broke his IPOD screen.

21 July

Today was our second last day in Spain, but also the day for the closing ceremony of IMO. Surely I had a great time, and the time was going so fast. It’s the closing ceremony in the afternoon, followed by a farewell dinner. In the morning, we bought some present for Juan (our guide), and some souvenirs for ourselves. We had a fun time wondering around Sol (central area of Madrid). We went on the subway for 2 last times. I still thought it is a very cool transport. Sol is much busier than any NZ city centre. There were a lot of people passing around you. It’s a fantastic experience to be in the flow of people.

7. Coming Home

22 July

Today was our last day in Spain, and we would be in New Zealand very soon. After having a breakfast at the resident hall, we left for the airport. At the airport, we said: “Good bye” to Juan, also gave him our team mascot “Kiwi bird” and some other present our team prepared to show our thankfulness. We checked our bags in, and had a sandwich at the airport café. Still thinking about the wonderful time that I and all my team members had in the last few weeks, the trip was nearly over. I had another look at the busy airport terminals and some of the other airplane takeoff before boarding our plane. I was thinking that I would be in New Zealand in 30 hours, and 4 hours more I would be beside my parents, or even have a rest at home.

Then our plane took off, carrying all of our team members on board with happy memories. We flied to Munich, then Hong Kong, then Auckland, and finally I got to my town Christchurch. We had a stop over in Hong Kong for 3 hours. On the way back, I had a few sleeps. When I was awake, I was still thinking about the fun time that I had in this IMO and thinking about the wonderful problems that I had solved.

24 July

“The plane is about to land,” the Captain said: “Welcome to Christchurch.” I went and picked up my luggage, and my parents were already waiting for me. I went home, and went to rest.

When I woke up at home, I thought about the things I learnt in this IMO. Firstly, never give up and keep your confidence: if I had given up after the first day of IMO, I would only get one point. Secondly, prepare everything you can: I was inspired by the USA contestant 2.

IMO is a really good program for improving my maths skill, as well as make me become passionate about this fun and enjoyable subject.

Acknowledgements

I would like to thank my parents for their mental and financial support during my study in Maths.

I am grateful to all the IMO and other maths teachers who made this trip possible. Special thanks to Dr Albert (NZIMO team leader), Heather Macbeth (NZIMO team deputy leader) and May (NZIMO team manager) for their help during this trip.  I wish to express my thanks to Alan Parris, Mr. Robert Long and Mr. Brian Wood for their helping with IMO training.

Thanks all the sponsors, especially to the Royal Society of New Zealand for their funding.

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.

Training in Auckland. (Source: Heather Macbeth)

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.

A lecture with the Dutch team. (Source: Heather Macbeth)

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.

Eating out in Madrid. (Source: Heather Macbeth)

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.

New Zealand team after opening ceremony. (Source: IMO08 archive)

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.

El Escorial excursion. (Source: IMO08 archive)

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.

The trip to the IMO itself began with a flight to Hong Kong, where we stayed for several hours before finally flying off to Vietnam. Unfortunately during our stay in Hong Kong we were only given the option to explore the wonders of the airport rather than of the city itself. Shortly after, we left for Hanoi, the capital of Vietnam and our final destination. When we arrived and I took my first step into Asian territory, the heat was already just about enough to make me second guess whether the trip was a good idea. However we all quickly adjusted to the new climate and began exploring the hotel and the general vicinity in which we stayed to discover that there really is an enormous gap of cultures between New Zealand and Vietnam.

On the evening of the second day was the opening ceremony to the 48^th International Mathematical Olympiad. The show was spectacular with a wide variety of traditional dances and other performances, followed by insightful speeches given by the head figures of the organizers of the IMO. The following day (giving us only one and a half days to adjust to our new environment) the contest began and the sweat really started to pour. After the two days of competition we finally felt like we could relax somewhat and socialize a little more with the other teams. Almost every day the guides took us to different historical and natural sites, including Halong Bay (a fantastic natural wonder sculpted by nature and time over millions of years) and a superb silk market where I acquired a fabulous green tie to take back home to New Zealand.

Halong Bay. (Source: Jingcheng Bian)

The results from the Olympiad eventually started to arrive and I remember the feeling I got when one of my team mates rushed into my room and said I won a bronze medal. I was shocked, surprised, overjoyed and relieved all put together. As a whole, the New Zealand team did relatively well, winning a grand total of three bronze medals and two honorable mentions; a performance worth congratulations in my opinion.

So overlooking the few bumps we had along the way, the entire experience was extraordinary and without a doubt an amazing one. I do pity the fact that I will no longer be allowed to compete next year, but I hope I will be given the opportunity sometime to pass on any knowledge that I acquired to future contestants who are just as eager about mathematics as the members of our team were. It really is a shame to say goodbye to Olympiad mathematics, as I grew quite fond of this fun version of math, and I hope that the future participants of this competition will enjoy it just as much I did.

The team selection process began from September of last year, where we did a problem set called the September Problems, and 25 people from all over New Zealand were selected for a residential training camp held Christchurch in January. At the camp, we were lectured and sat two exams, and the top 10 were selected to be in the IMO Training Squad. The squad members received assignments, and were able to participate in the Asia-Pacific Mathematical Olympiad. Our performances determined the final selection for the team of 6 representing New Zealand at this prestigious event. The team and the two reserves received further training in the four areas of mathematics, namely number theory, combinatorics, geometry and algebra, before our departure for Vietnam.

When we arrived at Hanoi airport on July 23rd, we were greeted by our guide Tham, and a red banner with “Warmly welcoming contestants of the 48th IMO” written in block letters. We were then taken by a bus to our hotel. The hotel was air-conditioned through out, which was needed when the temperature was always around 30 degrees, even at night! Hanoi was a very lively city, with roads full of motorcycles, and relatively few cars, whose horn honking can be heard well into the night.

On the next day we attended the opening ceremony, where the Vietnamese prime minister officially declared the start of the Olympiad. I was surprised that our bus fleet was escorted by police, and ran almost every single red light. Besides that, there were some brilliant performances from Vietnamese artists, and Cuba once again got the biggest cheer for their one-man team.

Team, before opening ceremony. (Source: Shaun Harnett)

July 25th and 26th, were the two days when we had 2 four-and-a-half hour exams in the mornings. Each exam consisted of only 3 problems, in rough order of difficulty. I felt calm when I walked into the exam room, because I had participated in last year’s IMO, and I knew that stress and panic wouldn’t do me any good in this extremely difficult exam. On the first day, I spent the majority of my time attempting to solve the first problem, however a mistake in the understanding of the problem cost me the chance to solve it. I was also unable to solve the more difficult number 2 and 3, and I felt quite disappointed about this. I did better on the second day, fully solving number 4, but making little progress in number 5 and 6. Overall I was quite happy, because my complete solution for number 4 would earn me an “honourable mention”.

After the exams are finished we had plenty of time to socialize with other contestants, exchange souvenirs, and get to know each other and each other’s country. Apart from our normal “friends” from English-speaking countries, I had a chance to talk to the Montenegro team, learning that they’re the youngest country in existence. We were also taken on 2 excursions out of Hanoi, one of which was the beautiful Ha Long Bay. The limestone caves and the amazing landscape that formed over billions of years were truly spectacular. Also we had a chance to shop in the CBD of Hanoi, where we all picked up on the methods of haggling. I had the impression that the people of Vietnam were very friendly, despite the fact that verbal communication was made next to impossible by the language barrier.

It was evident that this event was taken very seriously in Vietnam. During our stay, news about the Olympiad could be seen on major newspapers, and state television. According to Shaun and a member of the Canadian team, I was shown on TV twice! Additionally, en route to the closing ceremony, I was lucky to be interviewed by the Voice of Vietnam.

Kiwis get interviewed. (Source: Shaun Harnett)

The closing ceremony, much like the opening ceremony, contained many entertaining performances by Vietnamese artists. As a team, we did rather well this year. Ilya, Ronald and Rupert each received a bronze medal, while Emily and I were awarded with honourable mentions.

I thoroughly enjoyed this unforgettable experience, and would like to take this opportunity to voice my thanks to the New Zealand Mathematical Olympiad Committee, for their support and organization of this trip, the Royal Society of New Zealand for providing me with funding, thus make this trip possible. I would like to especially thank our team leader Michael Albert, deputy leader Heather Macbeth, for giving us trainings, and arguing hard with the competition coordinators for partial credits in my incomplete solutions. And last but not least, our team manager Shaun Harnett, for accompanying us in this long journey. Thank you.

And eventually it came. On Sunday 22 July we left Auckland airport late at night. The mathematical side of the preparation was now over, and now we just had to focus on being in the right state of mind mentally. It was my second IMO, and this year I felt a much larger weight of expectation on myself. At the 2006 Olympiad in Ljubljana, Slovenia I had exceeded my personal expectations, winning a bronze medal. I felt like I should be aiming for the next step – the silver medal, only ever won by a New Zealander four times in our history of competing which goes back almost 20 Olympiads. However, at the same time I considered the nature of the competition. The IMO is a contest where you can’t really count on anything. Often students with high expectations do abysmally badly, and in general, on average around one person per team will perform far worse than they had hoped for. Therefore I resolved to think positively about my chances, but at the same time I knew that I should not take for granted that I would be able to repeat my 2006 medal-winning result.

After a minor ticketing crisis in Hong Kong airport we arrived in Hanoi. We all felt a sense of relief that we had truly made it there. We met up with our Vietnamese guide and several of the other teams that had come through on our same flight. One of the great things about the IMO is the social side. Last year in Slovenia we had got to know similar people from all over the world, and we made good friends with a lot of them. This is an essential part of the IMO experience.

That first bus trip from the airport to our hotel was amazing. I had never in my wildest dreams considered that the city would be so different from what I had previously seen in other countries. The most notable differences were motorists’ habit of using their horns every three seconds (this is an exaggeration, but only slightly!), the ad hoc approach to electrical wiring, and obvious disregard for any kind of building permit system. It was amazing how disorderly everything was, from the traffic to the architecture. It was truly chaotic. But at the same time this sense of busyness had a real charm to it, and this is now what I love Hanoi most for.

Motorcycles in Hanoi. (Source: Jingcheng Bian)

The IMO had a nice atmosphere to it. The entire competition (students and managers, that is, not leaders or deputy leaders) stayed in one compound, and it was sunny and summery the entire time – a huge contrast from the weather of New Zealand in July. But soon the reality of the whole thing sunk in. After a grand opening ceremony, featuring the President of Vietnam himself, we made final preparations and went to bed.

The contest itself was spread out over two massive rooms at Vietnam’s national convention centre. Everyone got to the exam room tantalizingly early and spent about half and hour sitting at our desks in apprehension. It was interesting to see the various nervous habits of the competitors, who were all dealing with their nerves in their own personalized way, either with repetitive fidgeting or a blank stare into space or anything in between. And then it began.

The first question was long, meaty and hard to get your head around, and had the potential to throw people’s confidence. Once I got into it, however, it actually revealed itself to be pretty straightforward. After momentarily going down the wrong track, I managed to work out the first part of the question, and followed that up with part two. I wrote up my solution to part a, and then, struggling to find the right wording for part b, I decided to leave writing it up until later. And I moved on to question 2. This turned out to be a big mistake – I never really got into the question mentally, because I always knew I had q1 part b to come back to, and in the end I rushed down my solution to part b in the last 15 minutes of the exam (and this solution wasn’t explained well enough so I lost marks for it). I was slightly annoyed, but resolved to focus on the second day of the contest.

The first question of day 2 was a relatively straightforward geometry problem. I got it out in about an hour, and wrote up my solution. Then, knowing that I probably needed a full solution for the second question to gain a silver, I attacked it with everything I had. In the end, I was beaten by a better question, but I was glad I had given it a good shot.

Contest examination room. (Source: IMO07 archive.)

As a team, we were all pretty happy with how we had done, and were now ready to relax and enjoy the IMO experience.

Unfortunately, I had to be back in New Zealand for duties at my school ball. And so I was whisked away to the airport within hours of finishing the second exam (again, the trip to the airport was slightly incredible: road laws in Vietnam serve only as a rough guideline to how you should get around in a mêlée of motor scooters and cars). Flying out of Hanoi, I felt a slight sense of sadness. I was missing what was really the fun half of the trip – the mixing and mingling with other teams, the tourism side of it, the closing ceremony and the highly illicit partying into all hours of the night (mathematicians indeed know how to party). Also I knew that my IMO career had come to an end. I had spent four years involved in the programme, and, correspondingly, many hours slaving over those seemingly impossible problems. The IMO has provided me with many new experiences, travel-wise, socially and intellectually, and has been a great thing to have been involved in.

I arrived back in New Zealand at 9:30 at night on Friday 27 July. Amidst of preparations for my school ball, I received update from Vietnam that I had scraped through to get a bronze, and that Ilya and Ronald had also got bronzes, while Jed and Emily had got honourable mentions – not a bad NZ showing by any standard!

It was very tough to get in to the NZ team. I had to do September problems in 2005, to go to the Christchurch team squad selection camp which was held in January. Then after various tests and assignments I was selected for the squad, and then after competing in the Asian Pacific Maths Olympiad with 20 other countries, I finally made into the team.

We had a week camp in Auckland before we left to Europe, training hard for the competition. First we went to Heidelburg in Germany for few days, by the time we got there, we were so exhausted by the long airplane trip. It was very necessary for us to spend few days before the competition to get over jet leg and recharge our energy. It was my first time in Europe and it was truly amazing. I’ve seen more parts of the world and I indeed learned so much as well as enjoying my time over there.

Then we went to Slovenia. It only takes an hour to get there from Germany. Slovenia was quite different from Germany but it was also very beautiful. There were people from over 90 countries. All the most mathematically talented teenagers from all over the world were there. It was such an awesome event to meet other people from other countries and get to know them. The competition was very hard. We did two 4 and a half exam over two days solving 6 questions in total. 3 questions per day. I managed to get a certificate of Honourable Mention.

It was the most amazing trip in my whole entire life. During this trip I have met some truly amazing people, I have learnt a lot of thing and set my new ambitious goal to be the best mathematician in the world and also I had a great fun. I really would like to compete again in IMO and get a medal for NZ next year. I will study harder than I ever have to achieve my goal.