Monday 1st August 2016

Andrew Chen: IMO 2016 Hong Kong Report

Introduction

The International Mathematics Olympiad, widely regarded as the most prestigious mathematics competition worldwide for pre-university students, was held in Hong Kong this year from the 6th to the 16th of July, 2016. Participating countries are permitted to send up to six contestants, all of which would have previously partaken in an intensive training and selection process.

Participating in the IMO this year was an excellent experience for me for many reasons. Firstly, we were able to meet, converse, and become friends with some of the top mathematics students from around the world. Secondly, it allowed us to experience the cosmopolitan metropolis of Hong Kong, a genuine “world city” home to over 7 million people. Lastly, as the youngest of the six contestants of the New Zealand team, and one of the youngest participants, I am eligible to participate two more times, making this year only the beginning of my journey in Olympiad mathematics. Overall, the invaluable opportunity of participating in this year’s IMO has not only strengthened my interest in mathematics, but also inspired me to do more in this area in the future.

Contest Structure

The contest itself consists of six questions spread over two days. On each of the contest days, we received three questions, and had four and a half hours to work independently on them. Each question is marked out of 7, making scores out of 42. Gold, silver and bronze medals are awarded, as well as honourable mentions for contestants who completely solved at least one question but did not receive a medal. I scored 2, 1, 0, 7, 0, 0, a total of 10, gaining an honourable mention. New Zealand placed 53th of 109 participating countries.

Living in Hong Kong

We arrived in Hong Kong on the morning of the 9th of July. Before even stepping outside of the airport, we felt the hot, humid air which characterised Hong Kong’s summer. Daily temperatures always reached the mid-30s, and did not drop much lower at night. Thankfully, air conditioning in buildings and buses was commonplace.

We at HKUST (the Hong Kong University of Science and Technology), where most of our activities, including the competition took place. A guide helped each team around, showing us where things were and detailing our activities. During our free time, we played card games with other teams, and of course, discussed mathematics, having fun and creating friendships.

Upon arrival, we were given a large amount of IMO themed items, including a bag, two shirts and a hat. We were also given over HK$700 of food vouchers, which we used for breakfast, lunch, and dinner at cafeterias and restaurants around the campus. There was a large selection of Asian and European style foods available, resulting from Hong Kong’s predominantly Chinese population and history of being a British colony. We enjoyed a variety of foods, and were pleasantly surprised at the speed at which we were served – at some places, food came a few seconds after ordering.

Pre-competition Mocks

Before leaving for Hong Kong, we had a week of training in Auckland. We did four IMO style mocks, consisting of the 2015 IMO shortlist questions, which were considered for the 2015 IMO. This was very helpful because it gave me an idea of what to expect during the actual competition. In the mocks, I scored 13, 7, 3, 7, a total of 30, one of the highest totals in the team.

I found that generally, I could solve the first question each day, but algebra (especially functions and inequalities) and geometry questions were more difficult for me. Also, I could solve a combinatorics question two if I had enough time. My scores averaged 15 over a two day period, showing I had a good chance of getting a bronze medal. (The cut-off for bronze varies from 14-16.)

The Competition

In short, day 1 went terribly. Despite questions 1 and 2 being geometry and combinatorics respectively, meaning I had a chance at solving two questions, but I did not solve any. Question 1 had a complicated diagram which took a long time to draw. Within 1.5 hours I thought I had a full solution, but as soon as I started writing it up, I realised it was seriously flawed and I had assumed many things I couldn’t prove in my ‘solution.’

As the three questions on each day are ordered by difficulty, question 2 is generally a lot more difficult than question 1. Therefore I spent a lot of time trying to complete my proof to question 1, but with no success. This wasted around 4 hours of my time. However, after not very long of working on question 2, I came up with the right idea for a solution. Unfortunately, there were only a few minutes left so I had no time to write it up properly.

Afterwards, everyone else in the New Zealand team claimed to have solved question 1. I felt very miserable, but I told myself that it is how we deal with failures that shows who we truly are. What has happened has already happened, and no-one can change it. It does no good to dwell in the past, nor does it do any good to feel sorry for yourself. Instead, learn from the past, live in the present and create a better future. I did not let what happened that morning get me down. I spent that afternoon relaxing with other teams, and thinking. I vowed to target one question on day 2 and solve it completely. Question 4 (The first question of the 2nd day) was a number theory question. This was good, because I was definitely better at number theory than algebra. After experimenting for around 40 minutes, I found the right idea. I then pushed it through and solved the question within another 40 minutes. I felt great relief.

I spent the next one and a half hours carefully writing up my solution. It was carefully structured, claims and lemmas being numbered and referred to later on. Each step was explained in detail. Calculations were shown in full. Care was taken to deal with every single case. I wrote 8 pages, and by the time I was done the time was nearing 3 hours. But I did not care, for I had fully solved an IMO question. I then read through my solution numerous times to ensure the markers had no excuses to take off any marks. I then worked on questions 5 and 6.

In coordination, where the team leaders and deputy leaders argue with the coordinators, our marks were determined. I was surprised that my work on question 1 was worth two marks – one mark for a very minor result and a second for having a plan as to which theorem to use. However, my badly written solution to question 2 was only worth 1 mark, because it was only recognized as progress. My solution to question 4 was “just perfect” and worth 7 marks, but my work on questions 5 and 6 wasn’t worth any marks. In total, this was 10 marks, placing in the top 400 in the world and receiving an honourable mention.

Later, I worked out the details to my solution for question 2 and wrote it up fully in less than one hour. This was bittersweet – if I had only spent less time on question 1, I would have solved question 2 and gained a bronze medal, but I knew I definitely had the ability to solve two questions and gain bronze, also evidenced by my scores in the mocks.

A few things became very apparent to me after participating at the IMO. Firstly, I learnt the hard way that my geometry skills are very shaky. It is perhaps a result of going from someone who had never previously made it to the camp to someone on the team within a year that my basic knowledge in many areas is rather incomplete. Before the next IMO, I must ensure my basic skills in geometry and algebra are solid, and to a lesser extent, number theory.

My experiences at this year’s IMO have inspired me to work harder for the next one. I have already set an ambitious goal – a silver medal. To achieve this, I will do a number of things. As already stated, I will revise the basics and make sure my basic knowledge is complete. This will allow me to consistently solve question 1s and 4s. I will also work to bring my ability in number theory (and hopefully algebra) up to a level where I can solve such question 2s and 5s. Lastly, I will work on raising my combinatorics ability to where I can solve combinatorics question 3s and 6s. All of this will require countless hours of hard work, which I am determined to put my mind to.

Excursions

During our time at Hong Kong, we also left the HKUST campus many times. The opening ceremony was held at a stadium in the city centre. The closing ceremony was held at the Hong Kong Convention and Exhibition Centre, and followed by the IMO dinner. Over 700 contestants, team leaders, deputy leaders, observers and organisers were seated together in a giant hall. There were performances, speeches, and the top contestants were interviewed. The meal itself was very extravagant – with over 5 courses, it was the fanciest I have ever had.

During the two days of coordination, the contestants also went on excursions. The first day we went to Disneyland. Although I have been there in the past, and I am 15 already, I can confidently say that Disneyland never loses its magic. It was a great day, and the perfect way to relax following the contest. On the second day, we went to a number of places. First we went to The Peak Galleria, a shopping mall with a distinctive design which the logo for this year’s IMO was designed after. Unfortunately, it was a rainy day, so views were limited.

We then went to a heritage trail at St. Stephen’s College. To say it was boring would be a severe understatement. A total waste of time, I doubt anyone been there before would go again. I strongly recommend anyone visiting Hong Kong to make the most of the city and avoid the hellhole. I am still dumbfounded as to why we even went there. It was blistering hot, the docents waffled on and on, showing indifference when everyone was clearly bored. The tour was more propaganda (though not very effective) for their school than anything else. They even tried (although unsuccessfully, which is unsurprising) to sell souvenirs at the end. It is without doubt that it was my least favourite part of this year’s IMO, and almost certainly the least worthwhile place I have ever visited. We then explored the Stanley Bay Markets, and recovered in heavily air conditioned buildings.

Conclusion

Participating in the IMO is a truly remarkable experience which will stick with me for the rest of my life. Such a worthwhile trip would not be possible without funding, so we must thank our generous sponsors and in particular the Royal Society of New Zealand. We hope for your continued support so more New Zealand students can have the highly rewarding opportunity to attend the International Mathematics Olympiad. For me, meeting like-minded students (which there are too few of in New Zealand), and getting to know them was a definite highlight. It was also very beneficial that the competition opened my eyes as to the abilities of the top contestants, while still recognising my own abilities. Lastly, the skills I have developed for and at the IMO will stand me in good stead for the future, with mathematics and logical thinking becoming increasingly applicable in all areas of study and all areas of life.

As my journey through the world of Olympiad Mathematics has only begun, I look to the future, now inspired to do better next year, and knowing with enough effort, I can and I will.