Johnathan Leung: IMO 2018 Romania Report
The highlight of the day was going through missing a flight and having to do four flights in total as a result. I watched part of Lord of The Rings (2nd movie) on the first flight.
We were supposed to go from Los Angeles to Munich, to Cluj next. Unfortunately the AKL-LAX flight was delayed by one hour, so we only had 40 minutes to transfer to the next flight.
US Customs took a horribly long time because there were many people going through. The process is also quite complicated and I had trouble with the auto passport machine. Instead we missed the next flight, so we had to go from Los Angeles to Frankfurt, to Munich, to Cluj. On the Los Angeles to Frankfurt flight I only slept, watched documentaries, and stared at the flight map. I watched a documentary about Darth Vader and another about the rail tunnel through the Swiss Alps. Strangely enough you need email confirmation at Frankfurt airport, so I used my school email (which is useless), while William used firstname.lastname@example.org.
I began feeling tired towards the Munich flight, so I slept in the Munich terminal and then slept again on the flight to Cluj. We arrived at the accommodation at about midnight and slept after about 1am. We woke up at about 9am.
In the morning we went through the briefing of the IMO training, and then walked to the supermarket nearby (passing by the Avram Iancu square).
After breakfast/lunch we started doing geometry training from about 1-4pm, and then started doing a Mathex-style math relay. We got placed in three teams, and I was paired with Keiran (our team name was Rustic Potatoes), against the other two teams (An Arbitrary Team, email@example.com). Because both I and him are terrible at fast math, we fell far behind the other two teams.
For dinner we went to a burger restaurant which was just opposite our accommodation.
What become one of the running jokes of our IMO team was the phrase “rustic potatoes”, which was a menu entry in a Romanian restaurant menu (“Cartofi Rustici”). Later on I found out it simply means potatoes with the skin left on, and that this term is actually used in English too.
First day of training. I scored 7, 0, 0, (question 1 was an easy geometry, which appears to be my only strength). For the next few days, we mainly walked around the city after each mock IMO, and then did algebra training.
In today’s mock IMO, I got partial progress in question 1 and scored 3, 0, 0. Our training set today was on combinatorics.
There are many IMO signs around the city, like this one:
I scored only 1 mark in question 1, because I conjectured something important, thought I found a counterexample, and then wasted the rest of the time finding another approach. Sadly that “counterexample” was not one at all, so that was very unlucky. After lunch we finished our final training set, which was on number theory.
Firstly: a photo with our kiwi mascot, Tuffley Junior, High Priest of the Church of Ptolemy (aka. “Yiannis Fam”/”Rustic Potato”). I am on the far right.
We moved from our pre-competition accomodation to the official IMO accommodation (Hotel Victoria). In this year’s IMO, there are multiple hotels, and our one had about roughly about 20 countries. The wifi in our hotel is very unreliable, and sometimes you can randomly disconnect or not be able to connect.
I did mock IMO 4 today (though not under exam conditions), and managed to solve 1 (an algebra inequality) and 2 (a geometry which happened to be G4), although I didn’t time myself. My solution to question 2 only involved angle chases and some parallel lines, although apparently Keiran found a high-powered solution using poles and polars and radical axis.
Today was the Opening Ceremony. Interestingly, the Romanian president actually came (unlike some previous IMOs), showing the importance of the IMO in Romania. We also had the education minister, several politicians and Geoff Smith (IMO President) speak, and then the parade of the national teams. The ceremony was broadcast live on Romanian TV too.
In the afternoon we had a walk and explored the remains of the old city and parts of the Cit Wall, and then we visited an ice cream store. The real Hotel Transylvania:
Today was the first day of IMO! I solved the first problem (relatively easy geometry) in about 2 hours, although I spent half an hour trying to resolve an annoying diagram dependency, and then made partial progress on question 2, by finding the construction and writing the right conjecture. This made me quite confident that I would get an honourable mention.
After dinner, I played a (infuriating) game of Mao with students from other countries, and unfortunately I had forgotten some of the rules, so I accumulated a stack of cards which became the size of a whole deck.
Before the start of the IMO, people seemed to have a lot of fun in the hall. Firstly, many people laid down on their backs to form a line stretching through the middle of the hall. Later on, we starting running a circuit around the hall. Eventually people started walking while carrying their countries’ flags, forming an improvised flag parade. This could have been the official opening ceremony! (No photos because we can’t bring phones into the contest hall).
During the contest, I spent all 4 ½ hours trying to, but not fully, solve question 4. This problem was a “find the maximum possible K” involving a 20x20 board. I managed to prove the case 100 was possible (checkerboard coloring), but showing higher values would not work was quite nasty for me. I tried to find pairing strategies, but the correct way to go about the problem was to chop up the 20 by 20 board into 4x4 boards and then finding the “cycles”. I felt quite annoyed at myself for not going back to the 4x4 case and then doing this approach. Despite this, I thought that an Honourable Mention was still likely for me.
We went on an excursion to the Turda salt mines, which was about an hour away.
It was cool inside the salt mine, which apparently is more than 100m below ground. However, the bus AC was broken (or it may have no AC), so the bus was extremely hot and stuffy on the way back.
Today we learned that the marking of the IMO was under way. The preliminary results (for the candidates’ solutions that had been marked) were posted on the AOPS website, and my marks were 7, 2, 0, 2, *, 0. (* = not marked). However. I submitted nothing on question 5 anyway, so that was effectively my final score.
Today’s excursion was to the town of Alba Iulia, which is a few hours south of Cluj Napoca. We went into the old city area. A small group of soldiers, including a marching band and horseback soldiers, marched towards the city gate, and presented to us a show of the Changing of the Guard, which included a few cannons firing. Later on we stayed in the old city area, where I was surprised to find that the public bathrooms had a fee of 1 leu(!).
After lunch, we were treated to a 3 hour bus journey, and it was very stuffy and hot inside the bus again. Sadly, we also got trapped in major traffic jams in Cluj, which slowed the ride down even further. I was finally relieved when we were let off the bus for the IMO Conference. The results for everyone were confirmed today, and our team got one silver (William), two bronze (Ishan, Tony), and the other three students, including me, got Honourable Mentions. I was satisfied with my result but slightly disappointed that I couldn’t get more in question 4.
At night I went to a park and then went on a hill which overlooked the city. I went together with Ishan and our guide Paula, and met the Austrian team too. I took some photos of the city during this time.
Cluj Napoca at night time:
The IMO came to a close today at the Closing Ceremony. The hall was very hot, and this was worsened because we had to wear formal attire. After more speeches, people received their medals. One time, the camera zoomed up to a Mexican bronze medallist, who was doing a geometry problem while waiting to go on stage, and his math work was displayed on the screen for all to see.
After this, there was a video showing a preview of the next IMO in Bath in 2019, and then a performance by a Romanian dance group, complete with violins and shouting girls. Finally, there was a “surprise” laser light show.
We had dinner in a large hotel, which for some reason had a DJ, which turned the “farewell banquet” into something more like a party.
Tuffley Junior at the closing ceremony:
My first IMO was a great experience for me, and my result this year was good also. This experience is great, not only because of the math we do, but because of the social atmosphere. I get to meet people from all over the world, who, just like me, have strong interests in math, and that’s special because I normally can’t do this back in New Zealand.
This means I get to have stronger social bonds with these like-minded people. I also have an opportunity to explore the world, and experience a very different Romanian culture. I get to become more independent, because it is my first time travelling overseas without my family, and the IMO is a preparation for my future life, when I will spend more time studying possibly in the USA or some other country.
The IMO is valuable preparation for the math I want to do in the future. While the topics covered in IMO papers are very different from university math, it helps me extend my problem solving and logical thinking skills, which are important skills in university study. I also find Olympiad math very intriguing, as it is very different from the repetitive, mechanical nature of school math. Instead, I need insight and deep thinking to solve Olympiad problems. I get to discover new ideas, and I feel a sense of satisfaction when I finish a problem. I am pleased that I found out about the IMO, because it greatly changed my perception about math, and otherwise I would have nothing else to do as a high school student! I feel inspired by the IMO to pursue math further, because the thinking required is a preview of what’s to come next.
I am looking forward to next year’s IMO, which I will hopefully qualify for, as this year’s event was amazing for me. Thank you to the people who helped organize the trip for the NZIMO team, so I could have the opportunity to go to the IMO. Especially Chris Tuffley, Ross Atkins and Peter Huxford for providing valuable training for us for preparing for the IMO. Also to Phil Truesdale for working behind the scenes to make sure our trip ran smoothly.
Also, a huge thank you for the Royal Society of New Zealand and the New Zealand Mathematics Enrichment Trust for helping to fund and support us.