Brian Zhao: IMO 2021 Report

The 62^nd IMO was held in Russia-Auckland. It was truly exciting to travel so f a r from home and be among so many talented young mathematicians on Discord, Zoom and Telegram. The legendary members and staff of the New Zealand Team, Ross, Josie, May, Rick, Hamish, Phillip, Brena, James and me, assembled at St Cuthbert College to launch our attack on the hardest year of the hardest high school maths competition in human history.

Pre-IMO training: 14^th July – 18^th July

14^th July

“Your name is NZL-6.” -Ross Atkins

15^th July

“hahahahaha” – James Xu

Cough cough the mock cough

16^th July

“I look forward to the day when someone solves a question that no one else can solve and says ‘That was trivial, what are you guys talking about?’” -Ross Atkins

17^th July

“It is always possible that we are all wrong and just haven’t noticed it yet.” – Ross Atkins

The combinatorics lecture was truly omnithink. We went over chase and evade problems, caught Rick on the forbidden grassland and James on the forbidden tetrahedron. What amazed me the most was the generalisation of one problem, which led to the conclusion that the number of points on a circle is strictly larger than the number of positive integers. Ross also presented multiple fake solutions for one famous problem and thoroughly confused us on whether his final solution was correct.

Late into the night, looking at my gigantic stack of polynomials and F.E. practice, a fear crept up my back. It was so subtle, so imperceptible against the overwhelming shadow of my anxiety, that at first I failed to name it. Ah, yes, it had a name: inequality. I did not prepare for inequality, at all.

As it turned out, no one did.

[foreshadowing music plays]

18^th July:

“I want to starve you [of maths] so that during the actual IMO you would go after the questions with vigour.” -Ross Atkins

The proper way to prepare for the IMO is to play Clash Royale with your hommies on the day before. We created a NZMOC clan and played so many games that I went from arena 1 to arena 5. In the evening we went to escape rooms and had a lot of fun. Everyone was smiling, laughing, relaxing, and pretending not to notice the approaching storm…

IMO exams

Day 1:

“Inequality is the root of social evil.” -Pope Francis

As the limit of time approaches 19:30, my fear overwhelmed me, as if I had been climbing a mountain all year long and suddenly looked down into the abyss below my feet. I reassured myself that the IMO was nothing but a game, and the questions were nothing but friends in an adventure to explore mathematics.

However, I realised that Q2 and Q3 were not my friends the moment I flipped over the paper. Inequality. Geometry. I almost laughed aloud at the audacity of the PSC to give Q2 inequalities for two years in a row. Unbeknown to me, Q2 would be forever branded into the memory of an entire generation of matheletes for its difficulty and outrage.

Luckily, I was able to solve Q1 after an embarrassingly long time. I checked my solution five times out of paranoia, while Q2 stares at me through the page, laughing at my long-lost dream of a silver medal.

Day 2:

“May the odds* be ever in your favour” -The Hunger Games

Knowing that I would get at least 1 mark for my Q1, I was determined to troll Day 2. After all, my goal was just a non-zero score. Sure enough, Q4 geo smiles at me like a clown to a clown. I was expecting an easy victory, a decisive battle that would seal my dominance over q1/4 geo once and for all.

I was wrong. Q4 involved length results that rendered Angle Chaser** useless and tangential quadrilateral that deterred any bashing attempts. The diagram was also hellish and took me 9 pages of roughwork to get it right. Unfortunately, my diagram was still not good enough for me to make that one crucial observation.

Defeated, I moved on to Q5. It was surprisingly easier and fell apart within an hour. How I wish that every question is combinatorics! Nothing else happened on that day. I mounted another assault on Q4, and another one on Q6, but yielded no further marks.

odds: odd numbers, integers that are not divisible by two.

Angle Chaser: my rubber duck mascot

Post-IMO

“Half of you will cry, and half will celebrate.” -Ross Atkins

We stayed up late every night, celebrating the end of the IMO and played more videogames. We also had two excursions, but I left early and only attended the ice-skating one. The highlight of post-IMO was Rick’s answer to “What’s your favourite number?” (69 because if you rotate it by 180 degree you get the same number). Unfortunately, the IMO committee was too shy to play it on the closing ceremony.

Overall, the mock and IMO questions were all really interesting and it was a bless to solve them. The lectures and excursions were also very interesting, for which I would like to sincerely thank Ross, Josie and May. I am also looking forward to IMO2022 in Oslo, Norway, hopefully not -Auckland.