Monday 1st August 2016

Yiannis Fam: IMO 2016 Hong Kong Report

Introduction

The 57th International Mathematical Olympiad 2016 was held in Hong Kong and we were hosted by the Hong Kong University of Science and Technology (HKUST). This year there was a record number of contestants at the IMO (602) and I am glad to have had the opportunity to meet a number of them.

Over the two days of competition (3 questions and 4.5 hours each day) I managed a score of 16 which, fortunately, was enough for a bronze medal. The New Zealand team also produced a silver medal and two honourable mentions to come 53rd out of 109 participating countries - congratulations in particular to Miles for his silver medal. It was truly an honour to represent New Zealand in an international olympiad and to compete alongside such talented mathematicians.

Training in Auckland

From 3-8 July, an IMO preparation training camp was held in Auckland.
I was billeted by Andrew and his family to whom I would like to express my thanks. Mock IMO tests and lectures were held in the University of Auckland.

Over the duration of the camp, we were given four mock IMO tests - using problems from the 2015 IMO Shortlist - for which I scored 8, 8, 13, 7. I was certainly comforted by my consistency in completely solving one problem in each test, and reproducing this on the IMO would get me at least an honourable mention - which was my goal before the exam. However, the only ‘medium difficulty’ question I could solve was a geometry problem, and the lack of such a medium question in recent years put doubt over my hopes of a bronze medal. Lectures were largely on combinatorics, given by our leader Michael, which I found useful given it was my weakest area. The training, which was a highly enriching experience, was interspersed with interesting and entertaining discussions with our deputy leader, Stephen, about studying maths in future and about how mathematicians eat corn (analysts eat in spirals and algebraists eat in rows). It was also an opportunity to collaborate with the rest of the team, a luxury somewhat lacking when living with the minority in Wellington (although I would like to thank Stephen for holding discussion sessions every week online). This was very valuable in learning to think about problems differently and seek different solution methods (including bashing geometry problems with Miles using complex numbers).

Arrival and the competition

We arrived in Hong Kong on 9 July after a long, sleepless flight, and were warmly greeted by our fantastic guide, Joanna. One scenic bus ride later and we were settled in at HKUST. Although the view from the 6th floor was excellent - including a large expanse of water which lit up beautifully to several hundred lightning strikes on our first night there - it came at the cost of being located on something of a cliff. This meant crossing between buildings (occasionally in heavy rain) and taking 3 or 4 elevators to get to the food court. It was worth it, however, as the catering was excellent and I thoroughly enjoyed the comfort food, that was somewhat nostalgic. The day before the exam we took a minibus into the city to take our minds off the test, where we visited the velodrome and wandered around the park.

The first day of the exam began with an immense rush of nerves. My excitement/fear left me somewhat incapable of thinking, made worse by the sound of 600 Velcro folders being opened at once. It took 30 minutes to comprehend the geometry question 1 and realise that an angle bisector meant equal angles. This, and another silly observation, put me under considerable pressure since geometry was supposed to be my strongest area. After (several) deep breaths I was able to finally gather my thoughts and solve the rest of the problem in 20 minutes. It then took me a painful 45 minutes to write up several versions of the solution before I was satisfied. With this came relief as I was fairly confident of an honourable mention. This relief was immediately flushed away with the appearance of combinatorics as question two. Knowing full well that the best I could hope for was one or two marks, I spent the remaining two hours failing to find what was eventually a simple configuration that could have gained partial marks. Overall, it was pleasing to solve one problem but disappointing to have made no progress on the second (the third was completely inaccessible).

The second day of the exam went much better with high partials on both question 4 and 5 (4 and 5 marks respectively). This time I alternated between work on both questions which seemed to work better, although in both problems I only made significant progress towards the end of the exam. As a result, my solution to problem 4 was rushed and skipped the working for the last part of the proof (which I wrongly thought was obvious enough to state), which cost 3 marks. It was a painful way to learn a lesson but I’ll keep it in mind for future problems. In contrast, I was very fortunate to score 5 marks on problem 5 after finishing the exam convinced that my solution was flawed. It turns out that it was, but not a major flaw as the ideas are extended to all cases with only some work. My working and configuration was right, however, which got me a number of marks. Ending the exam expecting at most 2 points I was ecstatic to score 5. It was great to see Michael after the exam.

I thus ended the IMO with 16 marks which was just enough for a bronze medal. This meant a lot to me and I was proud to receive my medal representing New Zealand at the closing ceremony. I hope to be in the team for Rio next year to continue my quest to overcome my eternal foe in combinatorics.

Post-IMO activities

Our first day of break from maths was a trip to Disneyland. This began with a one hour wait for the bus, although we were fortunately sheltered from the rain. With nothing else to do we broke our fast early and played some maths games to pass the time. Eventually we arrived at Hong Kong Disneyland with a welcome lack of rain and queued up with hundreds of other people to get in. Surprisingly, the team did not come up with a strategy to optimise the number of rides we went on, but it was nice to just explore as we wished. After an enjoyable excursion, highlighted by a ride through Mystic Manor in which a cannon was fired at Miles and we were attacked by a swarm of insects, we returned to HKUST, overheated and in good spirits.

The next day we took a bus to visit The Peak - the landmark building that was the inspiration for the IMO logo - that had a beautiful view of foggy Hong Kong. While exploring the shopping options and enjoying another maths game of Contact we ran into the Australian team, which promptly joined us. We then took a bus to St Stephen’s College where we walked the heritage trail through the school. After learning more about the fascinating history of the college, which was used in WWII as a makeshift hospital, we walked into the town of Stanley. Unfortunately, the high temperatures and lack of shade made walking around somewhat unbearable, so we eventually camped out in McDonalds for the remaining few minutes before boarding the bus back. The skinny, winding roads made for a few issues with traffic for which the bus driver was impressive in manoeuvring around.

Closing ceremony day began with day 3 of the IMO, kindly organised by Miles. We then attended a lecture on pentagonal tilings of which I understood little, but found interesting nonetheless. Half of the team then went to play a round of table tennis where I was thoroughly beaten by anyone who had any experience whatsoever. One mocha coffee from Starbucks later - to help stay awake after watching a movie with most of the Australian team and some of the New Zealanders the night before - and we were off to the closing ceremony. We arrived at least an hour early and took the time to hand out a multitude of souvenirs and receive a fair share back - the Australians clipped mini koalas on to unsuspecting contestants and team leaders alike - as well as take some pictures with other teams. It was a great experience in receiving my medal and I was reasonably confident that I was holding the flag the right way up. This was matched by an excellent IMO dinner, although I would have rather preferred more authentic food than smoked salmon and chicken roulade. We were entertained by a harmonica group and a rather unconventional lion dance that performed to Gangnam Style, and had the IMO theme song thoroughly drilled into us - approximately sqrt(2016) times. Rather emotional thanks were passed round the table and those of us eligible (and ineligible) expressed great interest in (hopefully) returning for next year’s IMO in Rio.

Finally, we prepared to fly back to New Zealand. With time to kill until the afternoon flight, the team decided to splurge the hundreds of Hong Kong dollars worth of vouchers we had remaining on a delicious meal at HKUST’s ‘Chinese Restaurant’, in which the sweet tofu dessert was particularly nice. We then headed back to the rooms to retrieve our bags - Stephen rushed back to pack and compress his belongings so that the convex hull of his items lay entirely within the convex hull of his (tiny) suitcase. We then took some more pictures and gave out some more souvenirs, where I also got some souvenir coins from Uzbekistan, then boarded a packed bus back to the airport. The flight back was uneventful, demonstrated through a familiar lack of sleep although I was fortunate to manage an exceptional 15 minutes of it. We arrived at Auckland airport where we were greeted by the families of the Auckland half of the team. Again I would like to thank Andrew’s family for their kind hospitality. We took some pictures (some of which were with traded medals - mine is bronze not silver, unfortunately) and said farewells and the Wellington half ^ Phil departed for our domestic flights.

I thoroughly enjoyed this adventure from camp through to the IMO, and the experience of meeting mathematicians from across the globe, as well as build stronger relationships with those in New Zealand. I'd like to wish Stephen, Miles and Kevin well as they move on to bigger and better things (although it's hard to improve on the quality of this IMO). I'd also like to thank Stephen and Michael and all my other tutors along the way for exposing me to the beauty of mathematics, as well as the other contestants at the camp, squad and team for showing me new ways of think about maths, and for the moments of laughter and encouragement. Thanks also to manager Phil and our guide Joanna for ensuring that the IMO ran smoothly and was a truly enjoyable experience.

Finally, I would like to thank the sponsors of NZIMO, in particular the Royal Society of New Zealand, for enabling this IMO experience to be a reality. The maths competitions I've trained for have served as inspiration for me to work harder to achieve things in mathematics I could never have before and has convinced me that this is the field where I believe I belong. I hope to make next year’s IMO team for the competition in Rio and will work hard to perform as best as I can, there and along the way.