Friday 1st August 2014

Peter Huxford: IMO 2014 Cape Town Report

On the 30th of June, at Auckland Airport we gave our hugs and goodbyes to our families, and headed off to our destination: Cape Town. What followed was around 30 hours of travelling time: including stopovers in both Perth and Johannesburg. In all honesty I was exhausted by the end of it all, having only managed a couple hours of sleep throughout, between sampling the various movies Air New Zealand and South African Airways had to offer, or sitting idly in airport lounges. Although there was some interesting banter of some simpler maths problems, our efforts to just mark difficult questions from our previous mock IMO between flights offered little success. Despite this, I had felt nothing but excitement and nervousness since leaving New Zealand soil, and was very much looking forward to the challenges ahead.

By the time we had arrived at the place we would be staying in Cape Town for the first week, it was around 2pm in the afternoon. Driving from the airport was a surreal experience for me, as there were many large differences in South Africa in comparison to New Zealand, most notably the obvious gap between rich and poor, and the presence of barbed wire, as well as other security measures, on many storefronts and homes in the city. We had been told to be wary of thieves during our stay, and while I may have been a bit too paranoid, it was a relief when we finally made it to our temporary home.

Only after an hour or so of rest, in an effort to battle the jet lag we decided to do some afternoon training, so that we might stay awake until a reasonable bedtime. If I recall correctly we were looking at a very interesting Dutch handout discussing methods of grouping (in a combinatorial sense), to prove divisibility facts, but perhaps that was the day after. The training continued during the week, including the next day, where Malcolm’s arrival from the USA brought some new problems and resources to study. Our team leader Chris had to leave part way through the week, so that he and the other team leaders could secretly decide on that problems, so Malcolm held the training after that.

Interspersed with the training, were several mock IMO’s. To emulate the conditions of one of the test days, we usually started at about 9:00am after breakfast, and sat a 3 question test for 4.5 hours, finishing at 1:30pm. From what I and the others could tell, the questions (which were taken from the 2013 shortlist) fairly closely matched the difficulties of actual IMO questions. I believe I ended up with an average of 7/21 marks per test, which would result in a score of 14 at the IMO. However I knew my score was likely to be lower than that unless I got lucky, because there would very likely be an easy geometry problem, and my skill in geometry is quite poor in comparison to the other parts of Olympiad Maths, most likely leaving that question out of reach.

In that first week, we sampled many of the foods Cape Town had to offer, as we were not catered prior to the IMO. Highlights were eating an Ostrich Burger, and the Springbok Stew: which were very tasty and well prepared at the restaurant we went to (although I personally couldn’t distinguish them from other meats we eat here). Throughout our meals Malcolm gave us interesting maths and logic puzzles to solve: it was difficult to tell if they were trick questions, or simply required some clever insight to solve. For example, one question was

“If you are blindfolded, and given 100 coins, 10 of which are heads, and the remaining coins tails, how can you split the coins into two piles in such a way so as to maximize the probability that both piles contain the same number of heads.”

Once we had established that the way in which a coin was facing up could not be ascertained by touch alone, we began to try to solve the problem. We then came up with a method by which it would be possible to compute the answer, however it wouldn’t be feasible to perform the computation in the restaurant.

After having discussed the problem for most of dinner, we managed to get the solution out of Malcolm: you make a pile of 10 coins, and put the remaining 90 in the other pile, the flip all the coins in the pile of 10. This will always give the same number of heads in each pile (hence 100).

After what felt like a relatively short time, we left the backpackers we were staying, for the accommodation provided for us at the University of Cape Town. We were immediately struck by the beauty of Table Mountain – I felt like some of the scenery greatly surpassed what I had seen in New Zealand, but perhaps I don’t explore here as much as I should. We also met our guide Paul, who was going to take care of us during our stay at UCT.

It was a great relief arriving in our quarters: having a double room to myself as opposed to all 6 of us being in the same room, like we were at the backpackers. For some reason my room quickly became the place to “hang” and do random maths problems from obscure Russian Olympiads up until the competition’s start.

It was the next day where we were all arranging our ties and shirts, for it was the opening ceremony: where we would be able to show off our flag, stuffed Kiwi, and incredible dress sense. It was great to see all of the other countries at once, to see such a diverse range of people, all here for one purpose. That being said, during some of the talks I think a few of us were wondering why we couldn’t just go back to our rooms and sleep in preparation for the next day.

The next day was Day 1 of testing. Entering into the sports center where the test would be held I was incredibly nervous. This was a moment I had spent many hours training for, and I really didn’t want to mess up. I tried to just relax and enjoy whatever problems came up. Thankfully Problem 1 was relatively easy (and more importantly not geometry), although I probably spent an hour longer than necessary nutting out the finer details of my cumbersome proof. Problem 2 was an interesting chessboard problem. I felt like I had made significant progress: I had found a lower bound which turned out being at most 1 away from the true answer, moreover I believed the proof of my lower bound could be tightened slightly to reach the true answer.

By the time Day 2 came around, I was just hoping that I could repeat my success of the previous day. Just solving one problem fully would give me a decent shot at bronze. Unfortunately the easiest problem that day (Problem 4) was geometry (as expected), which is easily my weakest point. I spent a long time trying to make headway, and had a couple of observations which would be useful, but to be honest no real direction. The second problem of that day I made what I considered to be absolutely no progress, essentially just rough working of small cases.

If you totalled up my scores from the 2 days, I ended up with a total of 11 – definitely not a bronze medal, but since I got full marks on Question 1 I would receive an honorable mention. What I was surprised about, was that Malcolm and Chris had managed to get me 1 mark for my “useless” working out of small cases in Problem 5 – arguing that it contained the kernel of an important idea in the proof of the problem, while my arguably more significant work on the chessboard problem (Problem 2) also only received 1 mark.

The next several days were a lot of fun. One of my favourite things we did was an excursion to Cape Point, where we had the opportunity to see one of the most breathtaking views I had ever seen. Along with this, were celebrity lectures from certain famous mathematicians. I found it interesting to hear about current research in mathematics, as it is something I hope to pursue in the future. While some of the latter parts of the talks went over my head, I had reasonably good understanding of what was being discussed.

Finally, we had some of the best games of ‘Mafia’ in the last few days in Cape Town. Massive games involving members of the NZ, USA, South Africa, various Nordic countries, and many more were organised, with ordered pizza and soft drinks, some of us staying up well past midnight. It was great to be in the company of such a large number of mathematically inclined students of similar ages, and I think we all made some great friends.

Soon enough though, it was the end. The closing ceremony where awards and medals were handed out, and where we exchanged souvenirs with many other countries, marked the final major event, and the very next day we left the UCT campus, to stay one final night at the backpackers we stayed at initially. We had all had had an amazing time in South Africa, and I hope that next year’s team can have an experience which was just as enjoyable as our own.

I would like to express my gratitude towards the New Zealand Royal Society for their generous donations. It has been an honour to represent New Zealand in this competition, and I understand that without this contribution it would be very difficult to source the money to send a supervised team overseas to compete. I would also like to thank everyone who is currently involved in the running of the New Zealand Maths Olympiad program, including but not limited to Ivan Reilly, Alan Parris, Chris Tuffley, May Meng, Malcolm Granville. This experience has been a highlight of my life, and I am happy that myself and other students have this opportunity available to them.