Monday 1st August 2016

Miles Lee: IMO 2016 Hong Kong Report

This year, the 57th International Mathematical Olympiad was held at the Hong Kong University of Science and Technology (HKUST).

As our team took the first steps off the plane, we were hit by a puff of hot air which had infiltrated the gap between the plane and jet bridge.
We had arrived in Hong Kong.

On the other end of the airport, we met our guide, who later led us out the airport and into the heat. Thankfully, our walk to the bus was only about 10 meters, and we spent the rest of the journey to the University in the presence of air conditioning (an important aspect of our lives for the next few days). On the way to the University, we past Hong Kong’s vast ports piled with thousands and thousands of shipping containers, and towering residential skyscrapers. I tried a functional equation question on the bus but soon felt carsick as we weaved through some hills. Parts of Hong Kong were quite built up, others were still full of greenery and nature. It was quite a beautiful place, what a pity there was some smog though.

After arriving at the University, our team was assigned to floor 6 of Hall VII, which had a spectacular north-east view over parts of the University and Clear Water Bay. The rooms were simple and also very hot, but after we got the air conditioning running they were rather comfortable. Kevin and I shared a room next to Andrew and Keiran. The four of us had to share the rather spacious bathroom, but we never really needed to use it at the same time. I spent some of the first afternoon exploring the campus (and burning my bare feet because it would have been too stuffy to walk around in shoes) before trying the same functions question then giving up and looking at the solution. It was then time for dinner.

Meals were fun. For the event, we were given vouchers of values 10 and 20 HKD to spend on campus to purchase meals. As we were not given change for our vouchers, we would try to maximise the “efficiency” of our meals, by getting the values of meals to be as close to a multiple of 10 from below as possible. Also, due to the inequality:

Where is the value of our meal in HKD and denotes the smallest integer larger than , eventually we tried to minimise the value of the vouchers that we wasted by ordering together. There was a time when five of our team (Andrew didn’t join us because his meal was 0 mod 10) put our orders together, which we calculated to be 9 mod 10. However, somehow we miscalculated and ended up with a remainder of 2 (I still have no idea where I messed up). We then ordered 2 more drinks for 3 HKD each, resulting in a remainder of 8. As a result, we only wasted 2 HKD among the 5 of us, and also had two extra drinks. Someone took one, and we decided to assign everyone a one digit number and give the last drink to whoever had the first number after the decimal point on the random number generator. Our deputy leader won it, and he kindly shared some of it with Keiran.
Anyway, the majority of us decided to have Asian food (often rice or noodles), and most of our drinks were iced (either fruit or milk tea) so we could cool off from the heat outside. Even at night, it would fell shocking to walk outside and still be hit by a temperature far higher than inside.

Our first dinner was quite lively, with us sharing maths puzzles, jokes and advice for the upcoming exam. We headed back to our rooms early, as we were tired after our flights. We spent a little more time doing a bit more maths before our traditional embargo; Yiannis and I collaborated to solve a number theory shortlist problem from the year before. Later, somehow I decided my hair was too long so I tried to cut it, then I messed up, so Kevin helped me. We quit and headed for bed when we decided not to mess it up anymore. There was quite a large lightning storm.

The next day was the day before the exam, and the opening ceremony. It has been a tradition in the NZ team not to do any maths the day before the exam, so that we can be “hungry” for maths the next day.

We had a lot of waiting time after being seated for the opening ceremony and so we found our leader Michael sitting with the rest of the team leaders and waved to him. I also spent some time with the Australian team by confusing them with The Lanyard Trick, a variation of a stunt in which I “strangle” myself that I showed them when I attended their camp December last year. I came up with it on the bus ride to the opening ceremony, and it involves a special knot hidden under the collar to give the illusion of rope passing through neck. I’m sort of proud of it. I showed Andrew but later he messed up and ruined his lanyard a few days later. Oops.

The opening ceremony itself was spectacular, with a fantastic orchestra performance, another musical performance but with drums made of plastic water tanks, and a speech from Professor Shum Kar Ping who delivered it in his native language: Cantonese. As the teams crossed the stage, some of them started throwing treats from their countries to the audience. I was then fortunate enough to try some of Kazakhstan’s chocolate (but honestly I couldn’t taste the difference). After the closing ceremony, the contestants started throwing paper planes around. From our team, it was mainly Andrew and I who joined in. The staff tried to stop us for some reason (safety?) by telling us not to and by picking up and keeping our planes, but we only did when the two of us ran out of paper. It was fun. A few members of the Korean team sitting behind us joined in as well.

I made a terrible mistake and left our mascot on the bus back from the opening ceremony. Tuffley Jr was never found.

That evening, dinner was almost silent. Everyone was too nervous for the exam the next day. Again we headed back to our rooms quite early. Again I messed around with my haircut and a pair of scissors before heading to bed.

Breakfast the next morning was different. The maths embargo had been lifted, so some of us bombarded Stephen with the last questions before the exam. We lined up for a pre-exam photo and after a team huddle and roar of “Hail Ptolemy” (our team deity and ancient Greek geometer) we headed into the hall.

I guess I was somewhat nervous, but not too worried. Being a returning team member who missed the silver cut in 2015 by 1 mark, I did not have the silver curse (where a returning silver medallist of the NZ team performs worse than previously), and would be content with any coloured medal. Someone promised me two tickets to Switzerland if I obtained a perfect score of 42/42, but he didn’t specify if they were return tickets, so I couldn’t really be bothered. I had a goal to beat some of the Australian team, as Angelo (their leader) did say that I would have made their team if I was Australian. I guess I didn’t put myself in a lot of pressure.

I solved the first problem in the first hour and a half but then somehow ran out of brainpower to solve remaining two. I had the right idea for the second question, but failed to extend it to a full solution (mainly because I failed to construct the n=9 case and took an unsuccessful path). I was also somewhat annoyed at the fact that halfway through the exam when I had used up over 15 pages and asked for more, they only gave a mere extra 5 pages for the remaining two hours or so, so I had to ask for more again.

After the exam 4 of us were happy to have solved the first problem and we got Yum Cha for lunch. It was quite an enjoyable meal due to the variety of dishes, and we were all sharing our thoughts or solutions to the problems. Later, we went to find solutions from the other teams, and some of us worked on a bit more maths. Again, we went to bed early that night, but this time I stopped messing with my haircut.

The next day, the second day of the exam felt similar. Once again I solved the first question in a reasonable time, then felt stuck on the second. I had simplified the problem down to a single inequality that I failed to prove and in fact I was convinced that I had oversimplified to a now incorrect inequality. So I backtracked and tried some other methods, all to no avail.
When I walked out of the exam hall, it felt impossible to get a silver, as generally two complete solutions is not nearly enough, perhaps only just enough for bronze.

The following 2 days were spent in great suspense, which was only mildly mitigated by our activities.

My nights were spent socialising with members of other teams: playing Mafia with the Finnish (they are either very good or very bad, sometimes it’s easy to tell, sometimes it’s very difficult), Australians and Canadians; playing table tennis with the Indonesians; watching movies with either the Aussies or collectively with many other teams; attending the cultural nights to see the performance of the face changing. I also found it quite sad that I might not ever use Olympiad Geometry again, so decided to spend some time on it as a farewell. Some people must think I’m crazy for staying up to 2am doing Geometry. I don’t blame them.

My days were occupied with excursions to Disneyland and a local school. Some of the rides at Disney were exhilarating, although the queues were massive. I guess the fast rides helped take the heat away, but otherwise the heat was still quite unbearable. Overall it was very enjoyable though.

I wasn’t just on roller coasters at Disney, but also on roller coasters of emotion whenever Michael brought us news from coordination for our marks. My expected maximum mark for Problem 2 was a 3, which at some point looked like a 5, plummeted to a 2 (but still, not too bad). As for my Problem 5, it escalated slowly to a 6. With a final score of 7+2+0+7+6+0=22, I was no longer certain that I couldn’t get a silver.

The night before the closing ceremony, the results were revealed and I was to become the 10th New Zealander to receive a Silver. I expected to feel overjoyed, but at the same time, it felt so sad that my IMO career had come to an end.

On the morning of the closing ceremony, I, along with many other contestants, attended Professor Frank Morgan’s lecture on tiling. I will forever remember the question that Wilson Zhao of the Australian team asked about the most inefficient tiling and his subsequent face palm. The lecture focused on Geometry, and it gave me hope that perhaps I could indeed use my knowledge in the area beyond the Olympiad. The future looked bright.

The closing ceremony was great, with some more musical performance from a marching band and drum group. Medals were finally given out, and our team helped the Australians give out (clip) Clippy Koalas (on)to (unsuspecting) other teams.
The closing dinner was delicious too.

That night I joined the Americans, Israelis, British, Australians and Canadians, who put together their remaining food vouchers and bought a mountain of food. It seemed like the Americans were in charge because all of it was McDonalds, but another explanation was that only McDonalds was open at that hour. We socialised to a late hour, playing a card game Coup, Frisbee and some gun game. Eventually I said my goodbyes to the other teams.

On the day of our departure, our team put together our food vouchers for a final Yum Cha. We soon left the University, and caught a flight back home.

I would like to thank the following: