Tuesday 1st August 2017

Xutong Wang: IMO 2017 Brazil Report

The Journal

Day 0

We depart for Argentina for a transfer flight to Rio. The flight there was 12 hours long, and the flight from Argentina to Brazil 3 hours long, not too much happened on the flights, except for watching movies and perhaps attempting the occasional maths problem (which is usually more common in less cramped spaces). We arrive in Rio on a fine Brazilian evening, and I happened to catch my first glimpse of the Christ the Redeemer statue.

After our arrival at the Sheraton (the place we were staying for the first leg of our journey), I was rather tired and feel asleep almost immediately.

Day 1

We were told that our rooms at the Sheraton came with a complimentary breakfast. However, this was not the case as we found out in the morning. Instead we resorted to a nearly bakery, where we would have lunch at too.

For the most part of the morning we were at the beach which the Sheraton over-looked. A stroll and some fun at the beach later I was back at the Sheraton. I decided I didn’t like the beach that much (not that I particularly liked beaches to begin with) because the sand was too harsh on my bare feet.

In the afternoon, we finished off the last problem set that we were supposed to do before our flight back in NZ. It was also about the fourth time I had solved a question of the Q3/6 difficulty level without any hints (albeit with a small amount of group effort).

We had dinner at the Sheraton. It was expensive but looking back this was our only chance at some fancy Brazilian cuisine so I guess it was worth it.

The evening was not too productive because of the jetlag. We slept early instead.

Day 2

This was supposed to be the first official day of the IMO, and was the day we checked out of the Sheraton, into the official accommodation provided by the IMO: the Windsor Oceanico. The walk was conveniently only a few hundred meters.

I was very excited to see so many other contestants at the venue. As everyone wore nametags it was possible to identify which country each team was from by looking at the displayed flag. I happened to know a lot of flags – even many of the lesser-known countries - so I could identify where most contestants came from. As it turned out I would become quite adept at doing this.

We met our guide – a Brazilian who had studied at Auckland Uni earlier in the year. She was very friendly and seemed to be overall a great guide.

In the official IMO bags we all got we discovered an IMO notepad, an IMO shirt, and an IMO zip-lock sleeve.

We were also assigned rooms. We were told three of us were staying in the same room and the other three would be staying in separate rooms with two roommates from other countries. I secretly wanted one of the separated ones (not because I don’t like the rest of the NZ team, mind you! I just want to meet more people), and it turned out I was! When I went up to my room my two roommates had not yet arrived so I thought I’d leave them a message telling them I was from NZ, since I was sure they’d want to know.

We had lunch at a nearby restaurant (which we walked back past the Sheraton for!) I ordered chicken with rice and French fries, which was delicious. We happened to meet the Swiss team there, and we exchanged some souvenirs – I got a Swiss cap. It was a good opportunity since I have plans to go to ETH Zurich University for my post-grad studies.

When I got back to my room that afternoon I found that there had been some additions to the paper note I left for my roommates, though they themselves were nowhere to be found. It turned out they were from Portugal and had a great sense of humour. I was looking forward to meeting them! (I attach a picture of the paper to the right)

I had dinner at the Windsor – it was the first official IMO meal. The dining hall was huge. You could see that it could be partitioned into 12 decently sized expo rooms. 5 long buffet tables were placed around the outside of the room. The dinner itself was quite nice - there were many different dishes to try out, and we all got a complementary can of Guarana, the L&P of Brazil.

After dinner, I went back up to my room. I was walking along the corridor when I first met my roommates. The entire Portuguese team walked past me when someone recognized the NZ flag, whereupon they asked me where Tony was! I told them I was Tony, and exchanged high-fives with their team.

I planned to study some maths during the evening, but I accidentally fell asleep instead – it was only when my roommates came back into the room that I realised I had fallen asleep! We were all quite tired, so we slept at 10.

Day 3

Tomorrow is the day we sit the first paper in the IMO, so today there was a maths embargo on the NZ team. It’s traditional. The idea is that we’re not allowed to talk about any maths for the entire day so that when we do go into the exam hall tomorrow, we’re all ‘hungry’ for maths.

Breakfast and lunch were both early, partly because the Opening Ceremony was to begin at around 1pm. It was a very nice opening ceremony (albeit slightly disorganised) compared to last year’s opening ceremony it was much less showy (so I heard) but there was some music in the background as each country was led onto the stage. After all the counties had been on stage there were a few musical items by a brass band that could be somewhat described as funk.

Straight after the opening ceremony, when we exited the doors that we had entered, everyone was greeted with a huge white board with the words “leave your message here” on it. I left a couple of messages on it, including a rather large Ptolemy diagram, a maths pun, and several other maths quirks (as well as several other things not related to maths at all!). You could see about half the board was filled with maths - an interesting observation. You could see geometry diagrams and maths jokes scrawled all over the board. Of particular interest (well, for entertainment purposes, really) was how the interactions between rival countries played out.

Dinner was similar to the day before really.

After dinner we visited the exam hall, just so we would know what it was like. It was unsurprisingly a very large room - split into 6 sections based on contestant number. There were more than 600 desks, each desk sufficiently separated from those that surrounded it. In the evening the NZ team discovered the recreation room, which contained tables of chess sets, a table more of games like Monopoly and Jenga, 6 table tennis tables, 3 foosball (table football) tables, 2 karaokes, a row of laptops for general use, and 4 TV stations complete with Xbox and Netflix. After playing a couple of chess games and playing table tennis I hung around the foosball tables with Yiannis Fam. In the following days I would meet quite a few people from many countries in the ‘foosball squad’, many of whom were quite adept at the sport.

I slept later today, which was good – it meant I was getting used to the time zone. I tried to secretly do some maths but unfortunately didn’t do much before it got late.

Day 4

The first day of the IMO!

We were instructed to put all items (including food and drinks) that we were bringing into the exam hall into the official IMO plastic zip-lock sleeve we were given the first day. With possibly the smallest bag of all the contestants I went down to the first floor – which took quite a long time since I was on the 15 th floor and the elevators would stop at every floor – to meet the rest of my team. It was very crowded here. We lined up to get our zip-lock bags checked by invigilators, and then we were in! I waited at my table, both anxious and excited, for the first paper of the IMO to begin.

I examined the various things at my desk. A plastic folder labelled DAY 1, and a white envelope were present. Opening the plastic folder I found 3 plastic sleeves - one for each problem - 5 cards for signalling, 3 question sheets, and around 20 sheets of paper with fancy borders and instructions not to write on the other side. The chief invigilator briefed everyone on how to use the cards and the question sheets. (Using the cards we could request paper, water, a toilet break, and general help, as well as submit a question about the problems.)

After he finished we were given the signal to begin. That was the start of our four-and-a-half hours. I eagerly ripped open the envelope and, as I was hungry for maths, devoured the first question. Actually, I chewed on it for 10 minutes, by which point I knew I had the general gist of the proof. Only it took me another 90 minutes to actually write the proof up rigorously – it ended up taking 2 pages and I had to iron out some minor problems I ran into while writing it up.

Oh, and I also had a nosebleed about an hour in, which took me 10 minutes to fix.

So after I solved the first problem I immediately turned to the second problem. It was a functional equation, and I hadn’t done much work on functional equations until quite recently. Still, I was determined to solve it.

For 2 hours I made steady progress on it. I had so much progress after the 2 hours that I thought I must have missed something somewhere that was entirely obvious and would help me finish the proof. Then I found it! Of course! If we used one of the identities I proved was true, we’re done. Hastily, I wrote up my solution in 5 minutes (it was about 6 lines long this time) and so I finished the first day of the IMO with mixed emotions. I wasn’t entirely certain that my proof was correct (since there were some abnormalities I found during some of my other work which I neglected in my final proof), but I was quite sure I would at least get some partial marks on the question for my progress.

When we were released from the exam hall, I quickly rushed out the door and found the rest of my team. I quickly learned that my proof for Q2 was indeed wrong, all because of an exception case I had missed (which had something to do with division by 0!). Somewhat depressed, I went to have lunch with the rest of my team. It was there that I also learnt that I had overlooked one of the main ideas of the functional equation – which was that it had 3 solutions, not 1! There were 3 people who had made this mistake in the NZ team. Ahh! If only I had done the simple calculations to get the other two solutions, it might have saved me an hour of feeling confused about the abnormalities I talked about earlier!

It was too late to worry about it now – I guess I just need to learn my lesson and not make the same mistake tomorrow.

I spent the rest of the day doing maths and playing foosball, nothing particularly eventful happened.

Day 5

This morning was mostly the same as yesterday.

The IMO paper was different, however. It took me 2 hours to get Q4, which was a geometry question (a rather nice one at that) and I had 2.5 hours left for Q5. But it was a very confusing question to think about (it was combinatorics, but just not the particularly pleasant type to think about). I tried a completely irrelevant approach and tried to biject between two sets. It didn’t work. I think I should have been more open to other approaches. The reason I tried what I tried was because, from experience, the problem seemed like one I could approach with a very general solution, instead of going into the details and doing all sorts of casework.

Because today was the last paper of the Olympiad, we were allowed to see our leader, who told us that Q5 was actually about pigeonhole principle and induction. Well, that meant I probably got a 0 for Q5, disappointing as well. I can only hope for some partials on Q2 now.

At this point the bronze cut-off was very uncertain; the NZ team reported seeing many of our desk neighbours still drawing geometry diagrams at increasingly alarming times throughout the paper. Based on rumours there were apparently many other countries that found Q4 difficult. The swiss team purportedly had only 1 solve out of 6 on Q4, which was rather shocking, seeing as everyone from NZ claimed to have solved it.

After lunch we went to visit a mall and a Lego expo at that mall with a few of other teams, most notably the Mexicans. I didn’t particularly like exploring around the mall even though it was an extremely posh one (you wouldn’t even see anything as luxurious in NZ) – I’m generally not a fan of shopping. However, the Lego expo was something rather different. And it was very interesting too!

After we came back to the Windsor the NZ team had dinner together and then we each went off on our own ways – Keiran to play cards with his roommates (the Canadians) and others, Yiannis and I to foosball, and the rest I’m not too sure.

In the evening I found out my Portuguese roommates had done about the same as me.

At this point I was predicting a 15 or 16, and the bronze cut-off at 15.

Day 6

Today we went to the sugarloaf in the morning (that’s the mountain which this year’s IMO logo was based on). It was an independent trip – just the NZ team and our guide. Actually we met the UK team at the sugarloaf, which was a pleasant surprise.

In the afternoon there was a live talk show about the role of women in mathematics. (More on this in the questions section) Although it was interesting I think the lecture tomorrow to be given by a Brazilian field’s medallist will be more engaging.

In the evening I played some foosball, but also Mafia - at first with some people from Botswana and Niger I think. At some point an Australian called Matthew Cheah came along and single-handedly beat everyone (literally: 1 hand vs. 4 hands and he still won). Someone had to play with him to mak e it more even! I also started stacking Jenga blocks and making tall structures with them. After an hour or so I went up to the rooftop where there was a pool and a bar, and discovered that some Australians, Canadians, and Kieran (and a few others) were playing a large game of Mafia. It was however the last game they played, as everyone went off to their rooms shortly after. So instead I joined a nearby group of people playing a game called Mao, which I was familiar with. I remember that there were around 3 or 4 Irish people and someone from Trinidad and Tobago.

Day 7

Today was the day of the official planned tour. We visited the Lagoon as well as a couple of other tourist attractions. During the tour, however, Michael, the team leader, texted us our predicted scores. I was very disappointed to learn that neither Keiran nor I were able to get any partial marks on Q2 or 5, which meant we both had a total of 14 points. At this point I was also quite convinced that the bronze medal cut-off was going to be higher than 14, so I was quite depressed for the rest of the day. Yiannis was hoping for 19, but instead he got 18, so he was depressed too (he thought the silver cut-off was going to be 19). So the three of us were in a rather suboptimal state to enjoy the remainder of the trip. We visited some football stadium, but since I’m not very interested in football I don’t remember that much of that (especially with that 14 hovering over my head).

The medal cut-offs were due to be released that night at 10pm, but I wasn’t particularly anxious. I was mentally prepared for an honourable mention already.

The talk the Brazilian field’s medallist gave today turned out to be more a talk about various mathematicians and their current area of research – not what everyone had expected, which was an actual maths lecture! But it was interesting and it did give me lots information regarding career paths in mathematics. I still would have liked to see an really maths lecture though – I didn’t really want to let such a good opportunity go to waste (Surely someone else could have talked about other mathematicians?)

In the evening I again went to play foosball until about 10pm, which was when the medal cut- offs were announced. Well, bronze was 16, and silver was 19. (Gold was 25 but no-one from NZ cared much about that!) In the NZ team, Keiran, Yiannis, Stacey and I were all quite disappointed.

Stacey, Yiannis, and I went to the rooftop and for a while sat around a table in silence, contemplating the meaning of life. There were surprisingly few people around, and the night sky hung over us as if it too were depressed. We walked around for a while, peering at the Brazilian night. We were approached by a group of two people - well it looks like we had some company – they also missed the silver cut-off by 1 point. After chatting with them for a while I went and looked at the official score distribution. I noticed that there were 2 people who got 15 and didn’t get honourable mention. The next highest honourable mention came in at 12 points. Wow. That made me feel slightly better.

I guess fate decided my entire room would miss bronze – my two Portuguese roommates scored a 15 and also received an honourable mention. They also told me that a person in their team scored 15 and didn’t get an honourable mention. Oh so one of them was in the Portuguese team! As disappointed as I was I must admit I felt sorry for that guy.

Day 8

Today was the last full day of the IMO, the day of the closing ceremony. Some traces of the depression from last night still hung in the air, but for the most part our scores had been accepted.

The NZ team independently visited Christ the Redeemer this morning. Unfortunately it didn’t really redeem me or anything, though I will say that the view was quite stunning. On the long trip there and back (the round trip took around 3-4 hours!) our deputy leader, Robin, was once again discussing very interesting maths and physics topics (particularly when the discussion becomes very philosophical!) with the team. It did a good job of distracting me from the previous night.

In the afternoon the closing ceremony was held. All the people who received an honourable mention were displayed on a screen. The bronze medallists were then called to the stage and presented with a bronze medal, followed by the silver and finally the gold medallists.

Right after the closing ceremony there was a dinner party in which the dining hall had been completely refurbished with food stalls around the outside and tables on the inside. At one point a group of dancers came in and danced to the music, however I had already finished dinner and the music was too loud (for me at least) so Yiannis and I resorted to the recreation room again to play one last night of foosball.

At 10 I decided that I had played enough foosball for the year’s IMO and went to the rooftop to check who was playing what. Sure enough, the same group of people I played Mao with 2 days ago was there today. I played until we decided to pack and head back to our rooms at 12.

I had been planning to sleep when I got back to my room, since I would have to wake up at 5:45 the following morning, but as it turned out the entire Portuguese team was camping in my room and playing a board game! They also told me that one of their traditions was that the team produce a comical ‘news report’ for their friends who didn’t make it into the team. It seems like every country has their own traditions!

After they finished the board game they invited me to play, but some of them also wanted to head back to their own rooms. In the end it was just me and my two roommates playing. Surprisingly enough, I won, after which I was 1am and I really needed to sleep, so we slept.

Day 9

We woke up early this morning and packed our bags and headed off to the airport. I couldn’t say a farewell to my roommates since they were still sleeping but I had already friended them on Facebook the night before.

Since we were flying to Argentina first and transferring to Auckland, the Argentinian team flew with us. I recognised one of their members as one Yiannis and I had conversed with in an elevator following the day 1 paper. He had claimed to have solved Q2 (which was indeed true) but we had no idea he would go on to win a gold medal!

Upon their arrival the Argentinian team were greeted with shouts and cheers, presumably from close family and close friends – Argentina did quite well this year.

The NZ team minus Stacey (her family had arranged to go on a holiday in Peru following the IMO) had to wait for 12 hours for the flight back to NZ! To pass the time we set the leader and deputy leader the traditional Day 3 problems and also played some Mao.

The flight back to NZ was rather uneventful – just the usual stuff.

When we arrived all our parents were waiting (but sadly there were no cheers and shouts…) for us already, and we said our final goodbyes and each went on our own merry way.

For accompanying us on this trip, I sincerely thank Phil, Robin, and Michael, without whose support this journey would have been impossible.

Questions