EGMO Diary Part 1

Introduction: European Girls Maths Olympiad (EGMO) is a mathematical contest similar to the International Maths Olympiad. It takes place every year in April and it aims to inspire more girls to participate in Olmpiads and take pleasure in exploring the world of mathematics. This year EGMO took place in Kyiv, Ukraine.

7th of April

So, here we are again, at the 8th rendition of European Girls’ Maths Olympiad!

We set off on the 7th of April, top of the morning. The flight wasn’t too bad, we exchanged at Amsterdam and the total time we spent in the air was no more than 4 and a half hours. We were lucky, compared to other teams from Australia or India where after spending 30 something hours in the air they still have to solve the problem of jet lag before going to solve the problems in the maths contest.

We arrived at Kyiv late that evening, starving and falling asleep. The hotel was marvellous, with 22 floors, which is the tallest building some of us have been in, and the bag we got was amazing and full of goodies. My favourite thing in the bag was a hair band with flowers on it, following the Ukrainian tradition for girls to wear wreaths on their heads.

8th of April

Today we got up late and enjoyed the bright morning sunshine in Kyiv. The opening ceremony in the morning was very enjoyable, the speeches were not long at all and it’s very interesting to see all the countries. After lunch, our guide Halyna, offered to take us to the city centre. She is really kind and incredibly eager to tell us all about Ukraine and learn about Ireland. We also kind of adopted another guide, Ivan, who is a friend of Halyna’s, and he has something to tell us about everything in Ukraine.

We went to a few shopping centres, visited the central square the Maiden, and experienced the deepest underground railways station in Europe. (whole 3 minutes on the fast moving escalator!)

We got back relatively late, around 8, and we are positively exhausted. Which is not necessarily a bad thing, because tomorrow is the exam and we need a lot of sleep.

We packed all our stuff, did a last minute review of some generaal tops, and went to bed at 9:30. A good night’s sleep, that’s what is the most important part of the maths olympiad preparation.

9th of April

Exam day No 1!

Exam starts at 9:30 and last until 2 o’clock in the afternoon. We got assigned breakfast time, and ours is the earlier shift, 7 to 8. I thought this was unfortunate, because it meant that we would get less time to sleep. However as later event turns out, this hour actually has its advantages.

Because of this time to burn, we went back to our room after breakfast and deliberately did nothing but sit there and controlling our breathing. It helped me calm down, empty my mind and oil the machineries in my brain. Later on we did stretches in our rooms, and it calmed my nerves immediately. When I met our leader in the hallways, she said the minute she saw me: “You look more relaxed.” Indeed, I had never been this relaxed while walking into the exam hall, and I think this state of mind actually helped in my exam.

I opened the paper, and found that either the first nor the second problem is a geometry, which in normal circumstances might cause me to freak out a bit, but that day I was relatively calm and just started reading the question.

Question 1 was algebra, my worst area, really. I think the most difficult part of algebra is that the letters and the computations are so abstract it’s often hard to truly grasp what’s happening in the full picture. You’ll have to keep your mind open and try every single possible technique, and along that line it’s easy to lose your way or go further and further down the wrong track. Sometimes by the time you realise that you are on a crooked path, you don’t have much time left.

For the first hour and a half, I was jotting down equations, manipulating them, changing their form by using factorising, observing patterns and symmetries. It’s easy to make a mistake and sometimes small things like writing “c” instead of “a” can have devastating effects. And after all that time I didn’t seem to be making much progress. All calculations I tried led to three symmetric equations that were neat but weird at the same time. They were concise enough, but I was not sure how to use them. And my work quickly became very messy, I had no idea where one led on to the other and it takes me awhile to even find the sheet I was just writing on. That’s when I decided to turn to geometry.

Granted, this was a risky thing to do, maybe it was a bit reckless of me, because the geometry was at the position of a question 3 — the hardest problem in the paper, and it was there for a reason. What gave me the courage, I think, was that geometry is my strongest and I have managed solved a EGMO geometry question 6 before (And I have hung up the draft paper proudly on my wall). So I drew the picture, and jotted down a few ideas that immediately came to my mind.

Geometry in my opinion, is really like a scavenger hunt. (well, all olympiad problems are, but geometry I think is especially like this) You wander about in the unfamiliar landscape noticing things and gathering clues. Once you get something, use that as a landmark and try extract more things from it. Our amazing geometry teacher (also our leader) like to use the metaphor of someone lost and trying to find their way back… you have to look for a clear noticeable thing in your field of vision, like an overhead power line. There would be cities at the end of the line. Then you work your way across the desert and across swamps but keep your eyes on the line.

So I noticed a few things, some obvious, some not so much, and then somehow after 45 minutes I thought I had a solution.

In retrospect, alarm bells should have been going off there—45 minutes for a question designed to challenge the gold medalists? But I guess I was under pressure and didn’t think much. I was happy, of course, thinking that I have one problem under my belt, so even if I don’t solve question 1, it won’t be too bad a result from day 1. Calmer and reassured I went back to solve question 1, this time employing the technique our leader advised us to use, which is using one separate sheet of paper to track all our progress. This is like drawing a map for yourself, tracking all the steps, writing down all possible things to try at each step, and if one doesn’t seem to work, you can use this to find the last place you stopped at and try another. And I also tried to be careful and probe a bit more before diving into one method of manipulation, just in case it won’t work out.

And chocolate, of course! I took one chocolate break, and I can almost feel my energy level pump up, much like the advertisement you see on TV, where someone stuck in a dismal situation takes a bite out of a bar of chocolate and suddenly there’s flowers and summer breezes and there’s golden light and magic and rainbow and he’s completely energised… that is exactly what happened to me.

All things combined my stress level had decreased, and suddenly I looked up from one line of equation and there’s the solution staring right at me. I gave a mental high five, looked up, and it was 45 minutes left.

I wrote out my solution neatly, arranged everything, and went back to looking at question 3. I noticed halfway through that I have made a mistake, classic mistake of too much wishful thinking and assuming something right. Shots of adrenaline went through my bloodstream, and I struggled to write down any other observation that might lead to a solution, that might get me a few marks down the road.

The last 20 minutes went by so fast. I spent it all trying to find a solution to the problem, to no avail. Frankly I walked out feeling quite disappointed with myself, because although solving question 1 was good, I spent way too long in that question.

I was comforted soon enough, by eavesdropping on the contestants sitting around me talking. Israel 1, India 1, … all saying that they got 2, maybe 3. These were world class problem solvers, and if they think that they only got two problems, then me getting 1 and maybe a little more does not sound entirely too pathetic.

Ah well, no one knows for now and we’ll know soon enough. We went into the shopping mall in search of a hot beverage, and slept or read or done nothing for the afternoon.

Around 5 in the afternoon just before dinner, we went down the hall with a box of games our leaders brought for us and went in search of people from other countries to play games with. We found the members of the Australian team and the Danish team, and we started playing the classic game of Avalon together.

Historical note 1: Avalon the game is a variant of game The Resistance, first released in 2012. In Avalon, the game features Arthurian Knights against evil minions of Modred, and it is a game of deception, lies and manipulation. First introduced by our team leader at her house during one of the training camps, it has now become the standard game for all Irish maths olympians and mischief lovers. Study shows that it is also popular among maths enthusiasts all around the world.

It was an amazing bonding experience, we made new friends among the two teams and got to know each other well.

After dinner, a girl from the UK team approached us and invited us to play a game of Irish Snap.

Historical note 2 (according to the UK team): Irish snap, also called Chinese snap, is a poker game involving reflection time and slapping on tables. You also have to be good at remembering rules as new rules keeps appearing and disappearing, and it’s easy to lose track. The game never ends.

Have to say, we have 4 members in the Irish team, with quite a few Chinese descent, none of us have heard anything with relation to the Irish snap/ Chinese snap. Just as well, it was a great game which became heated in the end before we switched to Avalon. We played till 8 in the evening (Avalon can often drag on forever) and at that point we decided to go back to our room. Another day ahead of us!