James Xu: IMO 2021 Report
The 62nd IMO was held this year at USA Russia Auckland. We were lucky (comparing to last year) to be able to have all 6 of us (Brian, Hamish, Philip, Rick, Brena, and I) together at St Cuthbert’s College from the 14th July to the 24th July, accompanied by Ross, Josie, and May, our leader, deputy and manager.
Pre-IMO training: 14th July – 17th July
14th July:
The Auckland students all arrived at St Cuth around 5:00pm on the 14th of July. Ross, Josie, May, and Hamish were already there waiting for us. We first got our team uniform, and went off to dinner together. At dinner, Ross decided to rename all of us. I was called NZL-5. :/
After dinner was our first mock with the team together in our exam room. As we made our way to the exam room, Ross realized that he did not prepare any paper before hand, so we had nothing to write on. Desperate for paper, all of us searched over the things we bought to St Cuth. As it turns out, there were just barely enough paper for everyone after 3 of us shared our stack of paper among the team. As we finished the mock, at 12am, we all stayed awake for 2-3 more hours, and then went to bed.
17th July:
This was the last day of mock IMO for 2021. As usual, we headed out for a 1 hour exercise, involving various random sports we invented, i.e. using soccer ball to play tennis. But today was a bit special. Instead of normal sports, as it was raining, Ross decided to make us do a team relay with math/non-math questions. We had to run 2 laps around the 2nd floor of the building we were in every time we submit an answer. One of the questions asked “what is an opinion without 3.1415926…” The answer was… “onion”
We also had daily lectures. Today was Geometry lecture, and we had this wonderful diagram from Josie:
“ABNC cyclic”
At dinner, Ross also told us many things to do/not do in the exam, including trying all the problems in the first 30 min, as that is the only time that you can ask questions. When I flipped over the question paper, I saw that Q1 was geo, Q2 was algebra and Q3 was Combinatorics. In the first 30 minutes, after trying Q1, 2 for a bit, moving onto Q3, I immediately decided that it was too hard and I would take too long to understand the problem. So I completely ignored Ross’ instructions, and decided that it would be wise to just work on problem 1 and 2. (Thankfully I wasn’t the only one to do so, so I escaped Ross’ wrath). As it turns out, my geo was particularly trash, and was unable to make much progress on the problem. So I decided to move onto Q2. After working on Q2 for 30 minutes, I made ε progress, apart from guessing the function. Now with 3 hours on the clock, I had no choice but to tackle Q1 again. Q1 on mock 4 was the worst nightmare in all of my mocks. After all these fruitless tries, I decided that it might be more productive to co-ordinate bash this problem (ISL2020 G1). Unknown to me, there exists a simple angle chase solution…….
I bashed the problem twice, as I made a mistake on my first try. After using some sneaky trick, I was able to bash/sneak my way through and produce a solution with a total of 16 pages. Because I was so desperate in time, I did not label my pages, and therefore, I couldn’t put them in order. So thanks Ross for reading my badly written and ordered solution.
18th July:
This was the last day before the IMO. Knowing that I’ve co-ordinate bashed Q1 on mock 4, it was a bit worrying when the results were about to come out. When I received my script, I found a 6 marked on my Q1, “6 is the most embarrassing mark you can ever get.”- Ross 2021. As I asked Ross what brought my solution down to a 6, it turns out to be that co-ordinate bash was fine, but I did not write out my angle chase, which I did to make my bash a bit easier, in full. :(
After finishing math on the No-Math day following the IMO tradition, we had dinner and went to escape room. We had 2 groups, “Ross sucks” including Josie, Brena, Rick, and Philip. My group had Brian, Hamish and May. Both of our groups finished the escape room, but sadly, the batteries they provided didn’t work so well so we couldn’t open our final door. :(
The IMO exams (19-20 Julys)
Day 1:
On day 1, I started the exam pretty excited. In the first 30 minutes, I did as Ross told me to, trying all 3 problems, despite giving up on Q3 in 10 seconds. At first, Q1 felt hard. It offered no clear way of tackling. After 30 more minutes of struggling, I solved Q1, after remembering Ross telling us to think simple ideas.
Moving onto Q2, unknown that it was extremely hard that only 16 people ended up getting full marks this year, I produced a fake solution, which was almost true, except it was weaker than the question required. In the exam, I knew Q2 would not be as easy as the way I solved it. Highly doubting the validity, I checked multiple times after the exam, eventually proving that it was a fake solve. As I “finished” Q2, I attempted Q3, but it was useless. Completely directionless, I made no more progress, and finished the exam in the exact same state.
Day 2:
Knowing that I fake solved Q2 was quite a shock to me, and didn’t put me in the best position for day 2. As I flipped over the contest paper, even worse, the first question was geometry, my worst topic of all. Then, I looked at Q5, a Combinatorics. This was also a surprise to me, as I thought that Q1 was Combi, and knowing that Q1,2,4,5 are usually A,C,G,N in some order tells me that Q4,5 must be Geometry, and Number Theory. I was relatively confident in Number theory, so I knew I had a chance at solving another problem on day 2. However, as Q5 turns out to be a Combi problem, it terrified me a bit. Knowing that both Q4, 5 are not my favorite topics was a bit scary.
After spending 30 minutes trying all 3 problems, I thought my best chance was Q4. This turns out to be false, as I made little progress after spending another hour on Q4. With 3 hour on the clock, I was scared. After a quick thought, I decided that the best method might be co-ordinate geometry again. However, after estimating the time taken from calculations, I found that the time left was far from enough. I therefore decided that Q5 was better. To my surprise, Q5 fell apart quite easily, after trying the idea I just happened to come across. When I finished off Q5, there was still more than 1 hour on the clock. Despite my best effort, I was unable to get any more marks, off Q4 or Q6.
Post IMO activities: 21st-24th July
After finishing the IMO, most of us stayed up late, celebrating/moaning as written on our official schedule. We had 2 excursions, one on the 22nd and one on the 23rd July. We first went to ice skating. However, as expected, since none of us have sufficient prior knowledge, most of us fell over pretty badly. Although there were many struggles, the excursion was mainly fun. On the second night, we went to play pool, and karaoke. Just as we arrived, we received a message from our guide that they are hosting a post IMO activity right now. After 20 minutes of watching, we all decided that it was boring and moved on to playing what we originally intended for the night. During a duel with Ross, both of us achieved a historical record of sinking 2 balls each for the other person unintentionally.
Overall, the post IMO activities were fun, with some events targeted to help us social internationally. However, sadly, as IMO is remote this year, we were unable to communicate as well, and meet with people from other countries.