Wednesday 1st August 2018

William Han: IMO 2018 Romania Report

Introduction

I was privileged to have been selected as part of the team that represented New Zealand at the 59th International Mathematical Olympiad that was held in Cluj-Napoca, Romania in July 2018. In this report, I have sought to provide a detailed and comprehensive account of my experience at the IMO.

Background

The IMO is the premier Mathematics competition for secondary school students around the world. It is an annual event held in a different country each year in July. Each country may send up to six contestants, who compete individually. This year, 594 students out of delegations from 107 countries attended this competition, the oldest and most prestigious of the Science Olympiads. The IMO is a competition renowned for its exceptional diculty. This year, the most common score attained was 0 points.

The competition itself is over two consecutive days, with four-and-a-half hours to answer three challenging problems each day. Each day consists of an easy, medium and hard problem, with Problems 1 and 4 being the easy problems, Problems 2 and 5 being the medium problems, and Problems 3 and 6 being the hard problems. The problems chosen are from various areas of secondary school mathematics, broadly classifiable as geometry, number theory, algebra, and combinatorics. They require no knowledge of higher mathematics such as calculus and analysis. No calculators are allowed.

Each problem is marked out of 7 points, so the maximum total score for each contestant is 42 points. The marks of each competitor are agreed upon in a process called coordination, which happens in the days immediately after the competition. The Leader and Deputy Leader from each country meet with Coordinators provided by the host country. Coordination consists of both discussion regarding the merits and flaws of the solutions of each contestant, and a more adversarial process as the Leader and Deputy Leader attempt to secure extra marks for the contestants of their country.

Medals are awarded to the highest ranked participants, with slightly fewer than half receiving a medal. The cutoffs, which are the minimum scores required to receive a Gold, Silver or Bronze medal respectively, are then chosen so that the numbers of gold, silver and bronze medals awarded are approximately in the ratio 1:2:3. Participants who do not win a medal but who score 7 points on at least one problem receive an Honourable Mention.

Aside from the competition, the IMO also provides an opportunity to meet other talented young mathematicians from all over the world. Some of the most enjoyable experiences at the IMO are simply being able to interact with other people who share the same passion for mathematics. Additionally, the opportunity to travel and to experience a foreign country is definitely an upside. It has truly been an honour to be able to participate in the IMO and to represent New Zealand whilst doing so.

The Team

The NZ IMO team of 2018:

Accompanying the team this year was Team Leader Ross Atkins (Verizon Connect), Deputy Leader Peter Huxford (University of Auckland), and Manager Phil Truesdale (Papanui High School).

2018 NZ IMO team: Johnathan Leung, Andrew Chen, Ishan Nath, William Han, Tony Wang, Keiran Lewellen.

Results Summary

The results obtained by the NZ team this year:

NameP1P2P3P4P5P6TotalAward
Andrew Chen11072011Honourable Mention
William Han77077028Silver Medal
Johnathan Leung72020011Honourable Mention
Keiran Lewellen72041014Honourable Mention
Ishan Nath72072018Bronze Medal
Tony Wang65072020Bronze Medal

Overall, New Zealand obtained a silver medal, two bronze medals, and three honourable mentions, with a total score of 102 points, an improvement from the 94 points obtained last year.

This places New Zealand 45th out of 107 participating countries, an improvement of one place from the 46th place obtained last year.

Full results are available at the IMO official site: https://www.imo-official.org/year_info.aspx?year=2018

Diary

July 1

The team meets at Auckland Airport in the evening to commence our 17500km journey to Cluj-Napoca. The first leg of our journey will take us to Los Angeles, but before we depart we have to go through all the tiresome procedures that come with air travel. Apparently travelling to the US now requires additional security measures, because in addition to the usual procedures, I am confronted by a woman who asks me questions such as “Did you pack your own bags?", “Do you own everything in your bags?", and “Is it possible that someone may have put something in your luggage without you knowing?" I manage to answer these rather pointless questions correctly. After some waiting around, our flight leaves an hour behind schedule.

The team about to depart.

July 1 (Again)

We land in Los Angeles in the afternoon, having somehow travelled back in time a few hours. It seems that crossing a random line in the Pacific Ocean is the easiest way to time travel backwards. It is my first time in America, and my entire time here will be spent trying to get through the terribly designed LAX airport. Instead of being able to proceed straight to the departure gate as is with most other airports, we are forced to collect our luggage and proceed through customs and immigration. This process is slow and inefficient, and by the time that we finally complete this, we have managed to miss our connecting flight to Munich. We can lay the blame on a combination of our first flight being delayed and the inefficient design of LAX airport. Phil manages to get us booked onto another route, although unfortunately this one involves an extra flight and sees us arrive in Romania after midnight. Eventually, our flight to Frankfurt leaves, but not before we pass through another round of aviation security.

July 2

We land in Frankfurt after a flight in which I was seated beside a Trump-supporting American who kept checking Trump's tweets. Travelling for long enough by air tends to put you into a state of limbo in which time and date lose any meaning. Certainly, I have no idea what the actual time is. The idea that I am now also in Europe for the first time is equally as disorientating. We may be `just' 1000km from Cluj now, but we still have two flights to go. The first is a short hop to Munich in which we are only in the air for half an hour, and then after a long wait in Munich and another two-hour flight we finally arrive in Cluj-Napoca. After a taxi ride through the night, we arrive at the house that we have rented for our pre-IMO accommodation. We notice that there is only a single bathroom that all nine of us will have to somehow share, but we are too exhausted after 40 hours of travelling, and immediately go to sleep.

July 3

Despite sleeping at 3am local time, I somehow wake at 6am, which is a waking time that I will have until after the IMO contest days. Our first morning in Cluj is spent walking to a local supermarket and buying food for the next few days. We return to our accommodation and have lunch, discovering in the process that there is no cutlery to be found. After lunch, we do a geometry handout that Ross has created. It becomes quite clear that my ability in geometry is still lacking when it takes me a lot longer to solve many of these problems than several of the other team members.

Eventually we decide to head out to a nearby restaurant for dinner, thus sparing me from having to endure more geometry. Phil attempts to impose a 10pm curfew time for our stay at this place, however he never quite manages to succeed in doing so. As it gets darker, we also notice that the light in the hallway keeps switching on and off, seemingly of its own accord. We may be in Transylvania, but surely only the foolish would suspect the supernatural. Closer inspection eventually reveals that the cause is a malfunctioning motion sensor, and we are able to go to bed in peace.

July 4

We wake ready for the first of our Mock IMO tests. It is intended that these tests resemble an actual IMO, however this effect is partially ruined by the use of an overturned cupboard as one of our tables. It turns out that the house lacks tables, as well as bathrooms and cutlery. I am dismayed to see that the first question of our mock is geometry, and even more dismayed when I take a full three hours to solve it. This is as long as I took to solve the geometry Problem 4 from the IMO last year, and taking so long to solve an easy geometry problem does not bode well for the actual IMO. For today, it means that I lack sufficient time to attempt the next problem, a number theory problem, and only make a little progress.

After lunch, we head out for a walk around Cluj, which is warm and sunny in contrast to the weather we have just left at home. Meanwhile, Ross leaves to perform the duties associated with being the Team Leader. One of his main responsibilities will be helping select the questions that will appear on the IMO. Because of this, we are forbidden from contacting him and we will not see him until after the IMO contest days. Following our walk, we have our scripts returned. I obtain 7 points for my solution to the first problem and 2 points for my progress on the second problem, a total of 9 points. Overall, it is not a very good performance, but I suppose I have a few more mocks to come. We spend the afternoon going over the solutions to the mock, then doing a combinatorics handout. It is a welcome relief from geometry.

For dinner, we head to Piata Unirii (Union Square), the main square of the city, and a protest is taking place. An internet search later reveals that the protest is against the weakening of anti-corruption legislation by the Romanian government. A pity that we could not join in.

The team doing a mock.

July 5

Today we have the second of our Mock IMO tests. After breakfast we begin the four-and-a-half- hour test. The first question is an interesting algebra problem that I solve and write up in an hour and a half, and the second problem is a game involving number theory. I soon solve this problem as well. As the third problem is a hard geometry problem, I make little progress on it in the remaining time. Following lunch and another walk around Cluj, we have our scripts returned. I obtain 7 points for both the first and second problems, a total of 14 points. It is a satisfactory performance.

After some algebra from yet another handout, we head to Piata Unirii again for dinner. A number of protesters are still protesting, and although the protest is rather subdued, a few police officers are nearby watching it. Phil becomes rather worried when I walk through the protest, although I maintain that jaywalking across busy city streets is clearly more dangerous than walking through a gathering of people who can barely even be described as chanting. For some bizarre reason, Phil seems happy to do the former but not the latter.

The team at Piata Unirii.

July 6

Our third Mock IMO test commences after breakfast. The first question is an easy but interesting combinatorics problem that I solve and write up within an hour. The second problem is an algebra problem, which I solve and write up after another two-and-a-half hours. I then try the third problem, a number theory problem, for a while. When I check my solutions to the first two problems, I realise that I have overlooked something in my solution to the second problem. Because of this, I have to spend the last half-hour frantically rewriting my solution to the second problem. Thankfully, I finish with just minutes to spare.

Following lunch, it begins to rain, so we cannot go out for another walk. Instead, we pass time playing a few card games while Peter marks the scripts. When he finally returns them, it emerges that he has awarded me only 5 points for the first problem and 7 points for the second problem, a total of 12 points. It is difficult to take the deduction for the first problem seriously, considering that it was for asserting without proof something that was clearly obvious. Moreover, I could see a ‘7' that had been scribbled out on my script, indicating that he had been about to award 7 points. Eventually, I get Peter to admit that had this been the actual IMO, he would have argued for 7 points in coordination, and that the point of this deduction during practice was as a warning to be more careful in general. Interestingly, when we go out to dinner that evening, Phil chooses to take us in the opposite direction of Piata Unirii.

The team with our mascot Tuffey Jr. II, High Priest of the Church of Ptolemy “Yiannis Fam/Rustic Potato”. The name is a concatenation of a number of inside jokes and references.

July 7

Today we are scheduled to move into the official IMO accommodation. Therefore we are unable to have the fourth Mock IMO in the morning. Instead we pack all of our stuff, and clean and restore the house to its original state. This, of course, includes righting the cupboard we have been using as a table. We depart just before midday, saying goodbye to the house and its single bathroom, its lack of furniture and cutlery, and the malfunctioning light in the hallway that kept turning on and off randomly. Obviously we hope the official IMO accommodation is equally as good.

It turns out that our accommodation is at the Hotel Victoria, which is located in the middle of the city. We also find out that not all the other teams will be staying at the same hotel as us. In fact, only about 15 teams will be staying here. This is not ideal, as it means we will barely get to meet many of the other contestants. We find out that the teams from the Netherlands, Australia, Canada, Austria, Norway, and Ireland are among the teams staying here. After receiving a bag filled with sponsored items, we head to our rooms.

Andrew and I are assigned the largest room on our floor by random chance. It has a large bedroom, two bathrooms and a lounge with sofas and tables. Most of the other rooms only consist of a bedroom and a small bathroom. The only downside to this arrangement is that our room becomes both the de jure meeting room for team meetings and the de facto common room for the other members of the team. Following this, we head down to a buffet lunch at the hotel restaurant. The food served here is decidedly average and unexceptional, however we do get to sample some local cuisine.

After lunch, we decide to sit the fourth Mock IMO unocially that afternoon. The first problem is a nasty inequality question poorly disguised as a polynomial. The other team members seem to be able to solve this problem extremely quickly, but nothing I try seems to work and I remain stuck on this problem after more than an hour and a half. Then suddenly an extremely simple solution hits me in a blinding flash of obvious, and I am done. I move onto the second problem, which unfortunately is geometry. As is often the case with harder geometry problems, I end up staring at my diagram for long intervals of time, with short intervals in between where I will observe something and note it down. I somehow manage to observe the right things eventually, and solve the problem after several hours.

Dinner interrupts shortly afterwards, and I only manage to finish writing up my solutions after dinner. It is not clear to me how much time I have used for this paper, however it is likely to be longer than the four-and-a-half hours allowed. Geometry has proven to be my stumbling block again, and the appearance of a medium geometry problem in the IMO would be terrible for me. I can only hope that this will not happen. When Peter returns my scripts later that evening, he awards me 7 marks for the first problem and 6 marks for the second problem, a total of 13 points. He points out that I have overlooked an extremely minor point in my solution to the second problem. Once again, it seems like I must be careful, especially with regards to geometry, where similar issues could quite possibly recur.

July 8

As the opening ceremony is scheduled to take place today, we dress in our formal team uniform and board buses to head to the Sala Polivalenta (Polyvalent Hall), the location of both the opening ceremony and the two contest days. We notice that we have an escort of police cars marked with the word ‘Jandarmeria' on them. An internet search reveals that this is the military police force of Romania, tasked with high-risk and specialised law enforcement duties. As it happens, Hafez al-Assad, the son of Syrian dictator Bashar al-Assad, is attending the IMO and is staying in our hotel. Perhaps this explains the police presence following us everywhere.

The ceremony will be broadcast live on local television channels, and a number of politicians will be in attendance, including the President of Romania, Klaus Iohannis. Because of this, we have to undergo a security screening, and we are expressly forbidden from bringing a number of items, including ‘knapsacks’ but also water bottles for some reason. Apparently this is due to the threat of liquid explosives. How anyone could obtain them is a question we are unable to answer.

After we arrive, we wait two hours before the ceremony begins. Why we had to arrive so early is another question we cannot answer. Once the opening ceremony nally begins, we listen to the Romanian and EU anthems, watch a video about Romania, and then listen to a succession of speeches from politicians, dignitaries, organisers and sponsors. Many of the speeches are in Romanian, which is actually a Romance language in the same language family as French, Spanish and Italian. Due to this, the meaning of some parts of the speeches can be inferred without resorting to the translations displayed on screens around the hall. The speeches become rather repetitive after a while, and so it is a relief when we nally move on. The Romanian team takes the IMO Oath on behalf of all the contestants, and then we move to the Parade of Nations. This involves each of the teams parading onto the stage in succession. This year, the organisers have provided every country with a flag to parade with. Every country except Taiwan, that is, who only receive a copy of the IMO flag. It turns out that Romania does not recognise Taiwan at all. Following the parade, there are a few musical items before the ceremony concludes.

Afterwards, we are driven back to the hotel, and immediately after lunch we agree to go around Cluj with our guides, Paula and Iarina. Unfortunately it begins to rain once we begin the journey, however we opt to continue and get to see several landmarks around Cluj, including cathedrals and fortresses dating back to medieval times. Upon returning to the hotel, we immediately head by bus to the Sala Polivalenta again, for a look at the contest venue. Local volunteers have spent the afternoon transforming the room into a huge contest hall, and we arrive to see over 600 desks arranged neatly into rows and columns. After locating our designated seats, we head back to the hotel for dinner. Shortly after dinner, we organise our stuff for the contest days and head to bed at 9:30pm.

The team after the opening ceremony.

July 9

It is the morning of the first contest day. I head to breakfast, feeling a mixture of both anxiety and anticipation. Following breakfast, we bus to the contest venue, undergo the mandatory security check to ensure we are not bringing in prohibited items, and are let into the contest hall. Unfortunately, there is over an hour until the contest starts. With time to kill, we mill about inside. The upside to this is that we get to meet other contestants and have a chat with them. It occurs to many of us that someone could have already ripped open the envelope with the questions in it and thereby obtained an extra hour, however we hope that the other contestants are all above cheating.

Eventually, we are called to take our seats and the contest finally begins. I open the envelope and remove the questions, and notice that the first question is geometry. I am relieved since this means that there will be no medium geometry question, but obviously I have to ensure I actually solve this easy geometry question, and in a reasonable time frame too. Fortunately, the problem proves straightforward to solve, and within an hour and a half I finish it. I then turn my attention to the second problem, an algebra problem involving a sequence. It does not take long for me to determine a viable method of approaching the problem, but figuring out the actual details needed to complete the solution takes me a long time. By the time I manage to solve and write up this problem, there is less than an hour left to go. I attempt the third problem, a combinatorics problem, for a while, however I do not make any substantial progress. With the thought of deductions from the mocks in my mind, I spend the last few minutes checking my solutions to the two problems that I had solved. Then the invigilator announces that the first day of the IMO is over.

Heading out of the contest hall, I meet up with the other team members. I soon find out that I am the only team member who found Problem 1 straightforward. The others all seem to be of the opinion that the problem was unusually hard for an easy geometry problem. I maintain that the problem was at worst no harder, and quite possible easier, than a usual easy geometry problem. My opinion is clearly in the minority though. Many of the others spent two or three hours on the problem, preventing them from having an adequate amount of time to attempt Problem 2. Andrew did not manage to solve the problem at all.

After heading back to the hotel and eating lunch, we opt to stay at the hotel and relax rather than go out for the afternoon. It seems like many other contestants have the same idea, as a large number of contestants gather in the designated recreation room, playing a variety of card games and board games. It is even possible to spot someone doing maths. After a late dinner, it is soon time for bed at 9:30pm again.

The contest hall.

July 10

It is the morning of the second contest day. After breakfast and the usual bus ride, we arrive at the contest venue an hour beforehand again. To occupy the time before the contest, many of the contestants opt to remove their national flags from the display stands lining one side of the hall, and join in a flag parade around the contest hall. Several of the UK contestants can be spotted waving the EU flag. No Brexit supporters can be seen anywhere. The chief invigilator finally calls everyone to order, and the contest soon begins.

The first problem, Problem 4, is a nice combinatorics problem involving a game. I solve this problem in half an hour, and move onto the next problem. This problem, Problem 5, is number theory. As time ticks away, I attempt to solve the problem using a variety of methods. However, nothing I try seems to be working. With around 40 minutes of the contest left, I am beginning to accept that I will not be able to solve the problem within the allocated time. Hoping for a few partial marks, I am about to begin writing up my progress, when a method of solving the problem that I had not considered earlier hits me.

Throwing caution to the wind, I begin frantically working through the details, and to my surprise, I produce what appears to be a solution. A glance at the timer reveals that there are 15 minutes to go. Oh dear. So I write with a speed that I have never written with before, my handwriting degenerating into an almost indecipherable scrawl. I complete my write-up with just two minutes to go. Quickly scanning through my solution, I realise that I have forgotten a certain case. Oh dear. I find that I have dealt with this case in my rough working, and with not enough time to properly amend my solution, the best I can do is to write a note on my solution referencing the page of rough working. As the invigilator calls time, I can only hope that I have not left out anything else. In fact, I have to hope that my solution even holds in the first place, with no fatal flaws that could nullify it. I can barely spare a thought for poor Ross and Peter, who will have to go through my script and coordinate it. Following lunch, we again opt to relax at the hotel. However the thought of Problem 5 remains at the back of my mind.

July 11

I have to drag myself out of bed to get ready for our first excursion. Today the IMO organisers have planned for us to go to Salina Turda, a salt mine located in the nearby city of Turda, 35km away. Once we get there, we are taken for a tour around the mine. We are shown the machinery that was used to mine salt since the Middle Ages, and we descend down to the bottom of the huge underground halls that extend over 100 metres underground. The mine has been converted into a tourist attraction, and features a subterranean museum and recreation centre deep underground, which has basketball courts, a mini-golf course, a Ferris wheel, and an underground lake.

After a couple of hours underground, we head back to the surface and into the buses, which take us to a restaurant in the centre of Turda. Following a three-course meal, we head back to Cluj in the bus. It is extremely sunny and hot outside, and the lack of air conditioning inside the bus means that the interior of the bus is stifling and unbearable. It is a relief when we finally step out into the comparative coolness of Cluj, more than an hour after boarding the bus. It turns out that instead of heading back to the hotel, we are instead going straight to the Casa de Cultura a Studentilor (Students' Cultural House) in order to attend the IMO Conference. We listen to lectures given by Ciprian Manolescu and Victor Nistor, two mathematicians who were former IMO gold medallists.

Following the conference, we are taken back to the hotel, where we congregate in the recreation room once again. By now, partial results of coordination can be found online, and I find out that I have received 7 points on each of Problems 1, 2, and 4. In fact, Ross and Peter have finished coordinating all the problems except Problem 5, which will take place the following day. Regarding my solution to Problem 5, I am informed by Ross that my solution holds, and at worst there could be a deduction of one or two points. This news is a welcome relief to hear.

Deep underground at Salina Turda.

July 12

Once again I drag myself out of bed for the second excursion. Today we are going on an excursion to Alba Iulia, a city located 100km away from Cluj. After a two hour bus ride, we arrive at Cetatea Alba Carolina (Alba Carolina Citadel), a fortress built in the eighteenth century by the Habsburg Empire to protect against the military efforts of the Ottoman Empire. We tour the fortications, and witness the changing of the guard. In this ceremony, three traditional cannons are fired. The noise created by these antiques is startling. After roaming the fortications for a while longer, we head to a buffet lunch in central Alba Iulia.

After lunch, we are once again roasted inside the buses while we head back to Cluj. The bus journey back takes close to three hours, and as we are approaching the outer limits of Cluj, a number of contestants find out that the IMO results have been released online. I find out, much to my pleasant surprise, that I have somehow gotten 7 points on Problem 5 as well. I can only wonder how Ross and Peter managed to pull that off. This puts my nal score at 28 points, which means I have managed to obtain a silver medal. The medal cutoffs are 16 points for bronze, 25 points for silver, and 31 points for gold. In particular, the cutoff for a silver medal is the highest it has been in over 20 years.

Cetatea Alba Carolina.

July 13

This morning, most of the team opts to go shopping for souvenirs. Phil takes us on a walk to a local mall where inexpensive souvenirs can be found. After buying a few, we head back to the hotel for an early lunch. After lunch, we dress in our formal uniform ready to depart for the closing ceremony, which is held at the Sala Sporturilor Horia Demian (Horia Demian Sports Hall). Unfortunately this ceremony will also be broadcast live on local television channels. Once we eventually make our way in after a long wait, all the medallists head for the reserved seating in the centre facing the stage, while non-medallists and everyone else is seated around the sides of the hall.

The ceremony gets under way, beginning with a long series of speeches, followed by the names of all those who achieved honourable mentions being displayed on a screen. Then the actual medal ceremony begins, in which I receive my silver medal along with all the other medallists. Following the awarding of all the medals, the IMO flag is passed between the Romanian delegation and the UK delegation, who will host the next IMO in Bath. After this, a traditional folk dancing group performs. Unfortunately the noise that this group makes is excessively loud, to the point where the screeching noises of the singers is physically painful to listen to. Combined with the stifling heat of the poorly ventilated room and the blinding white lights of the hall, making it through this item is almost a feat of endurance. Eventually, this item finally finishes. Suddenly, all the lights in the hall are switched off, and a light show begins. This involves lights of many colours being shined onto the walls of the hall in order to make various recognisable figures. After this concludes, and without warning, confetti is sprayed into the seating area of the medallists. I sit and watch as confetti rains down and covers me and my surroundings. Once this ceases, and after I brush off hundreds of pieces of confetti from myself, we head outside for a succession of photos. It is remarkable that some people never seem to tire of taking photos.

After a bus back to the hotel, another bus takes us to the Grand Hotel Italia for the closing banquet. This is a splendid buffet meal catering to all those involved with the IMO. While some people enjoy the loud party music that plays throughout the evening, I find it preferable to escape the noise in order to chat with various people. While doing so, I find out about allegations of cheating during this IMO. It turns out that three contestants from Uzbekistan were disqualified after the jury strongly suspected them of cheating. Apparently the three students, all of whom went to the same school, produced solutions to the difficult Problem 6 that were almost identical to each other. A number of other pieces of circumstantial evidence was also brought to the attention of the Jury, and this seems to have resulted in the disqualification of these students. Their names and any evidence that they attended this IMO have been wiped from the IMO website. As the Jury operates under a great deal of secrecy, the full story is unknown and we can only speculate at what actually happened.

The team at the closing banquet.

July 14

Today most of the teams are leaving, however we will be staying an additional night in Cluj. After breakfast, we head with our guide Paula to the Gradina Botanica Alexandru Borza (Alexandru Borza Botanical Garden). We roam about inside the gardens, trying to cope with the blistering summer sun. It must be said that I am not usually a fan of botanical gardens, however in this case the visit was pleasantly relaxing.

Following this, we head to VIVO Mall, the largest shopping mall in Cluj. We have lunch at the food court, and I take the opportunity to visit a bookstore. Among other purchases, I decide to buy a copy of Dracula. We are in Transylvania, after all. Once we head back to the hotel, we find it devoid of people. Everyone has already departed, leaving just us in the hotel. We head to Piata Unirii for dinner, finding it devoid of protesters. Our final Romanian supper is taken outside, however we have to move indoors for dessert once it suddenly starts raining. After dinner, we opt for an early night in preparation for departure tomorrow.

July 15

We wake, eat breakfast, and begin packing. The process of trying to fit objects into a suitcase that seems to have shrunk since the start of the trip takes up my entire morning, except for an interlude for a debrief. Having finally managed this exceptionally difficult task, we take a walk to a local supermarket for some food for a quick lunch.

The afternoon rolls around and it soon comes time to leave for the airport. We are braced for a long trip and an endless succession of queues, checks and waits. A two hour flight takes us to Munich. At Munich, while passing through a security check, a security officer demands to know why I have a large piece of metal in my bag. I panic because I cannot remember having such an object in my bag, but eventually the officer works out that it was my silver medal. Oops. Following a short stop in Munich, we board a flight to Hong Kong.

July 16

We land in Hong Kong, pass through a few checks, and then wait a few hours. Once again we have entered the strange world of plane travel, a monotonous world seemingly detached from reality in which time makes no sense. At least this time the journey is smooth and without delays or missed flights. We board our final leg of travel to Auckland, about to complete a circumnavigation of the world.

July 17

We land in Auckland in what seems to be the morning. Immediately I notice the cold. Apparently it is actually winter here in New Zealand, something that I had almost forgotten in the hot summer of Europe.

It appears that we have managed to travel around the world in just 16 days, with spare time to experience an entire IMO in between. And this has definitely been quite an experience.

Conclusion

Thoughts

After talking with contestants from other countries, it is impossible not to notice the lack of support that we in New Zealand receive compared with other countries. An Iranian person who achieved the same score as me told me that after being selected for the IMO team, the team members attend a training camp lasting six months in replacement of their ordinary schooling. Of course, the very thought of this is unheard of in New Zealand. The Dutch team tells me that rather than having to pay or seek sponsorship to attend the IMO, everything is paid for completely. In fact, their reserve also travels with them to the IMO. Furthermore, if they win a medal at the IMO, they receive a prize of several hundred Euros. The Australians run a well-organised training program with many staff members and volunteers involved. These are but a few examples. In light of this, it seems remarkable that we are able to compete and hold our own with the best in the world. Of course, this is not a justifiable excuse for not fixing the glaring and very serious problems within the current system in New Zealand, which I shall avoid explicitly detailing. It is my hope that the system will be reformed in the near future to ensure not only a more extensive and comprehensive system, but also a fairer one free from cheating.

Something that has struck me recently is the frequency with which I label problems as `trivial'. This word, as used by mathematicians to describe something as being extremely simple to the point of being self-evident, is a favourite word among Maths Olympiad participants. We are quick to brand any problem that we solve without much difficulty with this label. I was quick to call Problem 4 of this year trivial, but later I found out that the average score attained for this problem was among the lowest over the last 10 years for an easy problem. I had almost forgotten over the last year or so how difficult the IMO actually is from an objective point of view. Each year, countries send their best young mathematicians to compete, students that would presumably ace the national mathematics courses in their countries. But at the IMO, so many of these students fail to achieve a result that could even be called respectable. This year the most common score was 0 points, after all. This lack of success, rather than being a reflection of the ability of these students, is far more a reflection of the difficulty of the IMO. Quite simply, it is in a completely different league from the mathematics taught in schools. This also made me think back to a couple of years ago, when I was beginning Maths Olympiad. Back then, doing even the easiest problems was an immense struggle, and to me, the IMO was this competition with impossible problems that I had no chance of ever going to. How things have changed. It made me appreciate how far I have come, and how the progress and achievement I have attained has only been possible through spending a great deal of time and effort.

Whenever I talk to laypeople about maths, I always notice a few major misconceptions about it. Some people have the rather dumb misconception that maths is simply arithmetic, and mathematicians just compute large and complicated arithmetical operations. These people are the ones who invariably ask me to add or multiply large numbers when they hear that I have a talent for maths. Equally invariably, I am hopeless at doing so. After all, many mathematicians are quite poor at arithmetic, myself included. Maths is about far more than just arithmetic. A somewhat more intelligent misconception held by many is that maths is simply a tool used to assist science, and as such, it only involves logical and analytical thought. But in reality, contrary to the impression given by rote learning formulas and mindlessly applying them in school, maths actually requires creative thought as well. It takes a great deal of creativity to come up with ingenious solutions to problems. After all, when faced with an actual maths problem, there is no rote learned method that can be applied. It is this synthesis of logical and creative thought that makes maths so appealing. Indeed, the mathematician does not do maths because it is useful, but rather because it is beautiful.

Reflection

The opportunity to attend this prestigious event means a lot to me. I have had the opportunity to meet and interact with like-minded students who enjoy doing maths as much as I do. Being able to connect with these people over our shared passion was a truly profound experience, one that cannot be replicated here in New Zealand. This trip has also allowed me to experience being in an environment that challenged me intellectually and encouraged me to think deeply, in sharp contrast to my daily life at school. Also, this trip has really influenced me to consider the possibility of pursuing mathematics as a career path. Definitely, after meeting so many talented young mathematicians, I believe the future of mathematics looks very promising.

After my performance at the IMO, when people notice my silver medal and my position at the top of the NZ team, unfortunately they are quick to credit intelligence and talent as being the main factors of my achievement. This is a judgement that lacks depth. To have attained these results, I have had to spend a great deal of time and effort, and I believe that my results are a testament to this. During my entire time doing Maths Olympiad, I have really learnt the value of perseverance. Each problem can require many hours of perseverance to solve, and it is often only after many failed attempts that I finally solve it. On a larger scale, it is only because I persevered and did not give up that I am here today. Through this experience, I have discovered my own capacity to persevere, to continue when the easiest thing to do is to quit.

When people talk about the IMO, they often only talk about it in terms of the contest. And yes, while the contest is at the heart of the IMO, ultimately the IMO is also an experience. And this year, the IMO experience was also a highly enjoyable and worthwhile experience. From getting to know people from all over the world, to exploring the culture, history, and cuisine of another country, being able to experience the IMO in a place like Romania has been a truly unforgettable experience for me. In twelve months time, the 2019 IMO will be held in Bath, the United Kingdom, and I am looking forward to it.

Acknowledgements

I would like to express my appreciation to everyone involved with organising the 2018 IMO, for helping make the IMO the successful event that it was.

Thanks to everyone I had the pleasure of meeting at the IMO, for making it such an enjoyable experience.

Thanks to the Royal Society, the New Zealand Mathematics Enrichment Trust, Macleans College and the Howick RSA for your funding of this trip. It is only because of your generous support that I could attend the IMO.

I would like to express my gratitude to Ross and Peter, our Leader and Deputy Leader, for your contributions in our training and your excellent job in coordination in making sure we got the marks we deserved.

A massive thanks to Phil for accompanying us, and for being the best Observer C we could wish for. I have no idea where we would be without your excellent job `observing'.

And finally, to the rest of the NZ IMO team, Andrew, Johnathan, Keiran, Ishan, and Tony, thanks for being such wonderful teammates, and for the excellent result we achieved together.

Official Photos

2018 NZ IMO team: Manager Phil Truesdale, Deputy Leader Peter Huxford, Keiran Lewellen, Ishan Nath, William Han, Tony Wang, Andrew Chen, Johnathan Leung, Leader Ross Atkins.

2018 NZ IMO team: Keiran Lewellen, Ishan Nath, William Han, Tony Wang, Johnathan Leung, Andrew Chen.

Medallists: Ishan Nath, William Han, Tony Wang.

William Han