Wednesday 1st August 2018

Xutong Wang: IMO 2018 Romania Report

Questions & Answers

How has attending this event demonstrated greater knowledge of available career paths in science and technology?

When I went to the IMO last year, I found it quite incredible to be among so many other talented mathematicians. At one point there was a lecture from a Brazilian Fields Medalist where he talked about other Fields medalists and what they were currently researching right now. That was a wonderful opportunity to explore many of the different areas of maths that one can specialise in. After last year’s IMO, I decided to pursue mathematics as a career, and I was also inspired to apply to Cambridge.

This year, there was a lecture on the various applications of mathematics in business, economics, communication, and many more fields. This allowed me to better appreciate the influence mathematics has had (and will have) on our society. Although I think I will still work primarily in pure mathematics, I feel it is very important to keep applications of mathematics in mind–after all, it is from its applications that much of maths research receives its funding.

How has attending this event enthused or inspired you to pursue science and technology careers?

The two years that I have been to the IMO have changed the direction of my life. I had not been thinking about applying to the UK before, but after my first IMO, I decided to apply to Cambridge and am now waiting for my final result from them to see whether or not I get in. I also changed my focus from physics to mathematics–undoubtedly I will still take physics courses in maths, but they will likely be very maths-heavy.

Has attending this event changed about how you feel about science or technology?

Yes, and greatly so. I mentioned this in my report last year but I had never attended such a large gathering of mathematicians and students aspiring to be mathematicians. It gave me a better sense of just how large and supportive the mathematics community is around the world. Much awareness has also been spread in these past two years about gender inequality in mathematics and in the sciences. I now recognise that many women are not receiving the same opportunities as men when in comes to science education at all ages. If this is happening, then we may be wasting half of the human potential for advancement in science and maths.

How has attending this event and participating with like-minded students been of benefit to you?

For an aspiring mathematician, there is no better event to attend than the IMO. This year I have made many friends from Hong Kong, Ireland, Australia, the Netherlands, Austria, Latvia, Kosovo, and more. I have developed my maths skills during the NZ training and also over the course of the IMO with the other contestants. Winning a bronze medal this year was also a big achievement for me that will open up many paths in the future.

Now that you have had time to reflect about your experience what have you learnt about yourself?

Probably one of the most important things I’ve learnt about myself at this IMO is that I should sometimes give myself a little bit of space to clear my thoughts. Last year, and sometimes in the mocks this year, I often found myself too fixated on one particular approach to a problem that didn’t work. I believe the approach played a big part in the solving of Q1, though I think I could have definitely taken more time to step back and gather my thoughts on Q5.

What did you enjoy about your experience?

I don’t think there was a single moment I didn’t enjoy. What I enjoyed the most was getting to know people from other countries, the tour to the Salt Mine, playing Catan with the Kosovo team, Mao with the Austrian team, Mafia with a lot of teams, and of course, receiving my bronze medal at the closing ceremony. I’ve written more about the experience below.

Some serious thoughts

This year was my second year at the IMO, and also my last. I did not feel the same way after the IMO last year, but now I feel very sad that I will never be able to compete in the IMO again. I intend to keep myself involved with the IMO in whatever way possible, including helping out at camp, composing problems to send to the IMO (which is apparently possible even at my age), and perhaps even to go as a leader or deputy leader in the future.

I also somewhat regret not preparing myself enough for the IMO this year. Although I did better than last year and was able to win a bronze medal for NZ, I did have hopes of winning NZ’s second gold medal. However I became too busy with academics and this severely limited the amount of training I was able to do (to almost nothing compared to the previous year).

Some not so serious thoughts

Personally, I enjoyed this year’s IMO more than the last. Perhaps it was because it lasted longer (we stayed in Romania for just under two weeks!), but I think it was more because I met more people and more unexpected things happened. I’ll talk about them in the diary.

Note: I may allude to my journal from last year at random intervals.

Day -2

It’s 5pm. As per tradition, I show up at the airport with my violin. That violin has been with me to four camps and two IMOs now. I also show up with luggage that is about twice as small as everyone else’s–I guess I never realised how big the average luggage is.

While waiting for the plane to depart, we chuck each other maths problems while Phil chucks us our bags of souvenirs that we must get rid of before we get back.

We are tasked with naming our mascot kiwi this year. “Chris Tuffley Jr.” and “Ptolemy” are thrown around, but ultimately we cannot decide.

The plane (Air, not Cartesian) is delayed by about two hours, which is quite bad because our next connecting flight was supposed to depart about two hours after us arriving in LA.

The flight is long so I sleep and ...

Day -1

wake up in time to land in LA. I’m actually not too sure what to call a day anymore but I suppose they will just be somewhat arbitrarily defined.

We have about an hour to catch our connecting flight but due to what we think is a design flaw in the LA airport, we must go through security checks to enter the US before we then leave. Our baggage was also in need of claiming and reloading onto the next flight. The security, and the airport in general, turned out to be more challenging to get through than this year’s IMO paper, and so we missed our connecting flight and had to find a new path from LA to Cluj. The new path turned out to pass through the vertices Frankfurt and Munich, and arrived in Cluj 6 hours later than the original path.

We wait a while at LA for our flight to Frankfurt. During this time we come up with more names for our mascot such as “Yiannis Fam” and the title “High Priest of the Church of Ptolemy”, but none of them stick.

We catch our flight to Frankfurt which was about the same length of 12 hours as the one from Auckland to LA. I watch a few movies on this one but surprisingly also sleep for the last half of the flight.

Day 0

After arriving in Frankfurt, we settle at a few coffee tables overlooking the terminals, do some maths (I attempt Keiran’s “Happy city problem”), and wait two hours for our flight to Munich.

The flight is about an hour long. During our wait in Munich we make great use of the chequered floor tiling by solving some chess-related maths problems on it. Of course, we also stood on it when necessary. Some people start falling asleep. Me and a few others are reminded of Ross’s (our leader) “Snaggletooth” puzzle game that’s now on the Play store and start playing the game, which turned out to be quite a good time killer.

I think I may have slept on the flight but I can’t remember. I probably did.

Day 1

We finally arrive in Cluj. We required four edges to get from vertex Auckland to vertex Cluj. It took us 40 hours; for some it was more than that! Since it’s about 1am, we take three taxis to our accommodation. Rooms are assigned and we promptly sleep.

Upon waking up, we look around the unit. We find that there seems to be enough sleeping space for 12 people, but cooking and dining space for 2. We are 9 people, so we’ll have to eat out quite often, though we’ll get plenty of sleep. There also seems to be a lack of tables, which is somewhat worrying since training for the IMO typically requires tables. We find two tables, one of which is from outside, and four chairs. Phil (the manager) then comes up with the genius idea of turning a wardrobe onto its side and using bedside tables as chairs. All of this is set up in the psuedo-living room, which is also where my bed is.

Because of the delay in our arrival time, we had already decided not to have a mock IMO today. Instead, we go on our first excursion, which is to the nearest groceries store! We buy sandwich ingredients and 15 litres of water, as well as other snacks and drinks. When we get back we have sandwiches for lunch.

The afternoon begins with a geometry handout from Ross. There are seven problems and we soon discover that the last three all seem to be somewhat similar, but requiring independently difficult proofs. Ross confirms this and, seeing as Andrew is already beginning to discover “dark side” geometry, a part of which was a common theme to the problems, promises a lecture on it after dinner.

At some point Phil brings back a menu from a restaurant across the street that we’ll apparently be having dinner at. One of the items on the menu is “cartofi rustici”, which is translated by Google translate into “rustic potatoes” (correctly, as far as I know), but for some silly reason it becomes an instant meme that sticks with us for the rest of the trip.

Next we had a maths relay in the style of Mathex, or Cantamath, or whatever it’s called in your region, except we had 41 questions, unlimited time, and *ahem* actually correct model solutions and actually good markers. I was in a team with William and as “an arbitrary team” we were neck to neck with Andrew and Ishan’s team “a@a.com” for most of the relay. Of course, the final team, consisting of Keiran and Johnathan was “Rustic Potatoes”.

In the end a@a.com ended up finishing the 40th question a few seconds before us, and nobody ended up solving the 41st question in time, so their team won some chocolate. Everyone else also won some chocolate, it was just chocolate that was not as premium.

At some point Phil made a Facebook post about the kiwi, and so we were forced to come up with a name. Our final name? Tuffley Jr. II, High Priest of the Church of Ptolemy "Yiannis Fam/Rustic Potato"

The post in question >

Dinner was indeed at the restaurant across the street. I order bolognaise, but it turns out they don’t have it and I was given a plate of carbonara instead. I am slightly disappointed, but it turns out, I would like it so much as to order carbonara whenever available for the rest of the trip!

Seated with Ross, Kieran, and Peter (the deputy leader), I am introduced to projective geometry and various other interesting geometric ideas including the 41st question which was about dividing a pizza.

The lecture on dark geometry is delivered as promised and while it was completely optional (seeing as originally we had nothing planned for the night), everyone attends and is sucked in by the powers of dark geometry. We start off with the incredibly powerful poles and polars which trivially solves all three problems we were stuck on and eventually reach discussions involving duality on a projective plane which is super overpowered despite being of almost no use in the Olympiad. However, we quickly degenerated to memeing about the legendary Cayley–Bacharach theorem shortly afterwards. (Apparently, pivot theorem, radical axis theorem, pascal’s theorem, pappus’s theorem, desargues theorem, and more are just special cases of the Cayley–Bacharach theorem)

Day 2

Today we wake at 7:00 in time for our first mock IMO from 8:30 to 1:00. I spend too long on an approach that turned out to not work on the first geometry problem, but I solve it eventually. It turns out to be quite a nice geometry problem involving inscribing a circle in a pentagon. However, I am left with not enough time for the second problem, a number theory problem, which I also waste time on with a wrong approach.

While we were doing the paper, Phil went out to restock on deconstructions of sandwiches. Immediately following the paper we have lunch and then Phil takes the team out for a walk while Peter and Ross mark our scripts. We were going to visit the Botanic Gardens which was close to where we lived but it required an entry fee and we didn’t have any Romania leu on us.

I end up doing quite poorly and only scoring 6, 0, 0. When I see the solution to problem two I was quite surprised at how short and elegant it was and also a little frustrated that I didn’t think of it.

Ross leaves to go to the leader’s conference and help pick the problems that will be in the paper.

In the afternoon we are given a combinatorics handout from Peter. There were 11 questions, but none seemed too challenging. My favourite problem on it (and I think one that I will remember for a while) is “Prove that the number of ways of partitioning a number into odd numbers is the same as the number of ways of partitioning a number into distinct numbers.”

For dinner we go to a slightly fancier restaurant bordering a large square with a cathedral we passed on the way to the market. I order carbonara again. I think it’s better than the carbonara yesterday. We have an interesting discussion about maths education in New Zealand with Phil.

In the evening I play cards with the others. At first it’s Set but after a while some people leave and we play Spades. After some more time, it’s just me and I play violin.

Day 3

Today the mock IMO has a rather easy Algebra P1 that I manage to solve within an hour. I move onto P2, which is number theory, and solve it in under three hours, it’s a rather nice problem. I move onto P3 for about an hour but don’t manage to make any substantial progress apart from noting a particular known configuration and what it has to do with the problem.

After having lunch, we go out for a walk again - same as yesterday. During the walk we discuss the mock IMO I find out I missed over half of P2! I solved one case but because I misquoted a theorem, I had missed the other case completely. I think if I had actually known about the other case, I would have been able to solve the problem completely.

It takes a while for Peter to mark the scripts, so he gives us the number theory handout to work on while he continues marking. When we get our results back, I am quite disappointed to see that I got 7, 1, 1. I do think I would have gotten more marks on P2 in the actual IMO - I did make quite a lot of progress and the other case isn’t too difficult once you get the first one.

So with a 6 on the first day and 9 on the second day, I’m not doing too well, and am a little depressed that I seem to be doing about the same in the mocks last year as I am this year - I definitely feel like I have gotten better, and it has already shown in my BMO and APMO results.

For dinner we walk around and end up at a ribs restaurant. Most of us get ribs with chips on the side. I order a spicy variant, but I only do so because there was no carbonara. The evening is spent in much the same way as the previous night. Before we sleep Andrew and I have a deep conversation about our lives and futures.

Day 4

The third mock IMO involved a combi P1 which I solve in about 2 hours. I think my solution is rather nice as it involves bijecting a string to paths on a cube. I move onto the algebra P2, which I don’t think I can solve, as I consider algebra my worst area. Rather surprisingly, I think I manage to solve it in 1.5 hours. I am very careful this time with my solution and check it to see if I have made any errors, but it appears that the solution is very much legitimate. I think it’s a rather strange question and was somewhat easy for a P2. I move onto problem three, which is a number theory problem. It’s one of the problems where you are not told whether a statement is true or not, and that you must either prove it or disprove it. I made a conjecture that the statement was true, and tried proving it for the remaining hour, but to no avail.

Interestingly enough, Andrew and William conjectured that the statement was false for large enough n. Peter then comes and confirms that it is indeed false! It turns out the statement was false and that actually n = 3 is a counterexample–I wasted an hour trying to prove the wrong thing. I am mildly annoyed though I didn’t think I would be able to solve it even if I had made the right conjecture.

During lunch I find that it seems that only William and I claimed to have solved P2, which is strange since I thought it was quite an easy problem.

Yiannis Fam, a team member in 2016 and 2017, then arrives. We’ve been expecting his arrival, and invite him in to have some deconstructed sandwiches with us. He chooses to construct the sandwiches anyway. His dad was apparently in Romania with work for a few weeks, so Yiannis popped down and had planned to visit us this afternoon.

We all go out on a walk, which today was around the other side of the Botanical gardens. I think there is an unspoken consensus of disinterest in the botanical gardens. On the way back we take a small detour to take a picture with a huge IMO advertisement that we spotted on the way here.

I am happy to see that I managed to get a 7, 7, 0 today, which puts me at 29 for three mocks, the same as about 19 for an IMO on average. That’s pretty much a guaranteed bronze and the only year it would have been any different was probably last year where 19 was actually the silver cut-off. But of course, actual performance in the IMO can vary wildly compared to results. At this point I’m still not sure if there’s another mock IMO tomorrow, since it’s the day that we move into the official IMO accommodation, but if there isn’t we’ll still be given it unofficially and it will be interesting to see how well I do on that.

Our handout today is on algebra–there are a couple of functional equations, some analysis questions, and other stuff. But with Yiannis here, we go off track and start discussing what life was like at Cambridge and what he’s doing there! Of course, he also shares some really nice problems that he got from his courses.

Anyway, Yiannis leaves and we go to have dinner. Today it’s at a restaurant that does wood-fired pizzas. I order carbonara anyway. I didn’t know I would like carbonara this much! I also ate some pieces of leftover pizza at the end. I talked about university life with Peter, and learnt that he also wanted to do his post-grad studies at Cambridge! The night is spent also like the previous night.

Day 5

It turns out we won’t be doing the final mock IMO today. We’ll be given it in the afternoon, perhaps. We pack, clean up, and in general decrease the entropy of the unit. While we wait for our transport to arrive, I get out my violin and strum on it like a guitar, an art in which I think I have become increasingly proficient over the past few days. I figure out a couple more chords and I can even get a four bar chord progression going. The transport arrives, so we leave a thank you note in the accommodation and leave. The car ride is about 4 minutes, which is surprisingly short. We are dropped off at Hotel Victoria.

When we get there I’m very excited to finally be able to meet the other contestants. (I had actually thought we were going to arrive in Cluj early to train with the Netherlands team, as we sometimes do, but I was somewhat disappointed this didn’t happen.) However we are one of the first to arrive. We gather in the lobby, meet our guides, Iarina and Paula (for some reason there are two this year), take a few photos with our flag which we grab from the row of flags, and go up to put our luggage in our rooms. For some reason two of the beds are king beds and they expected two people to share it but Phil wasn’t happy so it used his genius to persuade the Hotel to give us another room. That room was 203 and it turned out to be my room (shared with Ishan).

Because the first two floors consisted of a function room, reception, restaurant, etc. we were actually on the fourth floor. We look out the window to see the beautiful view consisting of the tops of buildings, a bunch of pipes and that’s pretty much it.

We go down to the restaurant to have lunch. There are many rectangular tables arranged in the restaurant with about 8 chairs around them, and each country was assigned to a table. A quick look around told me that only about 15 countries were staying in our Hotel, which meant that accommodation was separated this year. I suppose that gave us less opportunities to meet different people but more time get to know the people staying with us. Notably, there was Australia, Netherlands, Ireland, and Canada–we knew each other quite well from previous IMOs.

Lunch is served, and it’s very nice. Waiters served us a bowl of soup to start, which was quite delicious. Next was the main–a chicken dish–with coleslaw as a side dish, and after that there was dessert. It was a very nice meal–in my opinion, better than last year’s meals.

At some point I went to help myself to the drinks. There was a very wide selection of identical glasses to choose from, all neatly arranged in a grid-like fashion. Once you choose a glass of your liking you could go over and choose a drink if you so desired; the set of available beverages was {still water, sparkling water, pepsi, orange juice, grapefruit juice}, and one could choose an element in its power set to bring back to the table.

After lunch we went up to our rooms and that was when we first saw the Netherlands team–from the fourth floor we saw them sitting around on the third with their luggage. We went down to say hi and immediately someone called Nils said that he knew me from the Cambridge Maths Offers Facebook group chat! We have a nice chat about the mock IMOs (since the NZ and dutch team always work together when putting the mock IMOs and pre-IMO handouts together) and they give us a heads up on what’s coming for the fourth mock. “The first problem has a solution that’s this long,” they say, holding their thumb and index about 5cm apart “but you can’t find it.”

When we are given the last mock IMO from Peter to do in whatever manner we want. Ishan and I decide to give ourselves a quiet four-and-a-half hours in our room to attempt it independently. The first is an algebra problem which I manage to solve in under an hour but using a very bashy method which is definitely not the intended solution. The second problem is a geometry which, funnily enough, Ishan recognises as part of a training set of problems that Ross gave us about a month ago for IMO preparation. He pulls out the pdf on his phone and sure enough, it’s the third problem in that set. Neither of us remember the solution (I don’t even remember the problem!) so we attempt the problem anyway. About two hours in I have managed to prove that a triangle is isosceles but that’s about it. We are interrupted by Keiran knocking on our door and instead of continuing with the mock IMO Ishan and I decide to gather in Andrew and William’s lounge and see how everyone else is doing. Keiran boasts a solution to problem 2 using poles and polars, and I immediately see it and facepalm. (Such is the power of dark geometry)

After a while we return to our own room with Keiran, and before dinner comes along we try solving problem 3 together. Again, it is a problem in which we must make a conjecture about some formula. Our initial formula turns out to be completely wrong (though we don’t know that until tomorrow) and so of course, our attempt of proving our conjecture is thwarted.

We go down to have dinner at about 6pm. By this time a few more teams have flown into Cluj and we see them at their tables. Dinner seems to be in a buffet style, which makes sense because there are going to be a lot of people, though I am also a little sad that we won’t be able to have proper three course meals anymore (did I mention lunch was really good?). There’s all the normal stuff in a buffet, but there’s also things like fried cheese. I don’t take one at first, but after hearing from everyone else at the table that it’s really nice, I went to get one. It was actually pretty nice.

After dinner we take our ties that Phil gives us every year to wear with our white shirt and black trousers onto the stage at the opening ceremony, which will be held tomorrow. Ishan and I then head back to our room and we continue trying to solve P3, but give up in favour of playing violin. At some point we go downstairs and play a game of Monopoly in the games room.

Day 6

Today was the day of the opening ceremony. I get into my formal wear and meet our guides and the others downstairs. It is also the day of the maths embargo–the traditional 24 hour period of mathematical fasting. The idea is that we’re not allowed to do maths today so that we’re “hungry” for maths during the Day 1 paper tomorrow. I very much doubt, however, that this rule will be enforced by anyone who isn’t hypocritical – I certainly will be doing maths today!

We see many more people in the lobby, and strike up a conversation with the Irish team. Unsurprisingly, we are asked about how our trip was, and we launch into a rant about how it took some of us 50 hours to get to Cluj.

While this is happening, I see the Australians in their green blazers out of the corner of my eye. William suddenly announces that he has been koala’d. Of course! Clip-on Koalas. What the Australians are famous for. They’re small koala toys that have a clip inside them. You might turn around and suddenly see one on your bag straps or jacket or pants or really just anywhere. Apparently in 2016 they could be found randomly climbing trees. Anyway, this year we were prepared–not in the sense that we had anti-aussie spray or anything but in the sense that they were about to be kiwi’d. We had accepted their challenge.

Eventually the teams were called out one by one to board their designated bus. We shared a bus with the Netherlands, Latvia, and Lithuania. On the ride there we played a Dutch card game and got to know them a little better.

The bus trip was rather long in distance but took only about 10 minutes, probably because we were escorted by police cars on both sides. We arrive at the venue and pass through security, where they confiscate any bottles of water (really??). We enter what looks like a redecorated oversized basketball arena. There’s a four-story tall IMO banner hung at one end and a podium at the other. We sit on the right side of the podium, and it seems like leaders and other guests sit on the left. The empty space in the middle is spotted with living embodiments of the many many media partners that are on the IMO banners across the city.

We’re one of the first to arrive so there were few other people. We find our designated seats and settle in. Slowly the arena becomes more filled and we start seeing contestants from other countries. In from of us is Nepal, behind us are Norway and Netherlands.

As usual, the deputy leader begins receiving many problem booklets from other countries that they used this year in national olympiads. NZ generally don’t come up with our own problems, so these booklets are apparently a very good source of national problem income–we can then spend them on camp and squad selection tests (shh don’t tell anyone!) Despite a maths embargo and the supposed confidentiality of these problems, we persuade Peter to give us a look at the booklets and preoccupy ourselves with the problems.

About half an hour after we come in, I spot the Hong Kong team. I had talked with someone from Hong Kong about meeting at the IMO (I knew him from the Cambridge Maths Offers group chat), so I go over and meet David, Alvin, and the rest of the team. They all seem very friendly and again, I go on a rant about how long it took me to travel halfway across the world. We also talk about how selection and training works in Hong Kong. I’m then called back to my seat

After the ceremony we go back to hotel to have lunch at about 2pm. After lunch we go to explore Cluj with our two guides. We start at Hotel Victoria, top right of image. The path goes clockwise. We visit things in blue.

We’re back by about 5:30 and at 6:30 everyone who wants to see the contest hall (which is in the same place as the opening ceremony) is taken on a bus over to the hall. I was invited to go along with the Irish team to a night food market, but I thought it was probably better to stick to the team for now and visit the exam hall. I find my seat and meet a bunch of people including Harvey Yau and the Hong Kong team again. We go back and have dinner at about 7:30

After dinner there’s a brief team meeting and then we return to our rooms. Ishan and I attempt some of last year’s questions that we didn’t get. I try P5 while Ishan tries P4. I eventually get P5 with a hint from Ishan but I don’t think Ishan solves P4.

We shower and sleep.

Day 7

First day of the IMO. We wake up at 7am. Have breakfast. Pack stuff for IMO. Leave at 8am. Arrive at the contest hall at 8:15. There’s some confusion as to whether the IMO starts at 9am or 9:30, but this is probably only caused by the fact that we’re there so early.

There’s a lot of time so we wait around until 9:30 talking with some other teams. At 9:00 we have to sit in our seats and wait for 30 minutes. During this time I am quite anxious to see what the problems are. We begin.

When I come out we talk amongst our team. William seems to have solved both. I hope for 5/6 on Q1 and partials on Q2. Andrew very surprisingly didn’t manage to solve Q1. Everyone else seems to be in a similar position to me.

In the afternoon, Ishan and I go back to our rooms and attempt to solve the Q3 from the fourth mock IMO again. I also play some violin, etc.

Day 8

Second day of the IMO. I think I may have gotten about 8 or 9 points yesterday. Getting the same amount today should get me a bronze. If I do well today, I may be able to get a silver. We show up at the same time as yesterday, which gives us a lot of time to kill. There are 600 teenage mathematicians in a single building with nothing to do for an hour.

The first thing that was different was the music. Someone had decided to put on some music through the arena. It was the sort of music you might expect at the end of some dramatic movie. I felt as if the ending credits were going to start rolling at any time. Well the music made for some interesting events.

At 9am we were told to sit in our seats. Although yesterday I felt anxious during the thirty minutes that followed, I felt surprisingly calm today despite the greater pressure.

Opening the paper, I see combi, number theory, and then geometry. And a very, very short geometry question at that. It almost looked easy. Except there was a Q6 right at the start of the question. No, the length of the question was probably a trap. It was probably very difficult.

Perhaps the calmness really was beneficial, because I solved Q4 in under an hour. 54 minutes, to be exact. I moved onto Q5, hoping to solve it and leave some time to try Q6. I make some substantial progress just by trying something that seemed quite straight-foward. But about an hour later I realise that I made a typo somewhere in the first few sentences, so actually my entire first page of working was incorrect. I become quite frustrated, panic a little, and the next 2.5 hours seem to pass in a blur. I try many different things but they were all centered on the same approach of splitting the problem into two cases. I never really take the time to let myself gather my thoughts and so I feel like I am trying many many things without really going anywhere.

In the end I manage to prove one of the cases, but have no luck with the other one using the same approach as I did for the first case. This meant I had also solved one-and-a-half problems on Day Two. We leave our papers on the desks and my sector is allowed to leave the arena first today. As I walk out, I am suspecting that my approach was actually entirely wrong. Indeed, it seems that William had again solved 2 problems, and his solution to Q5 didn’t sound like it used my approach.

I spent a while thinking about my scores over the two days. I should get a 6 for Q1 and a 7 for Q2 if I didn’t overlook anything major. But the marks from Q2 and Q5 could vary a lot. I was estimating anywhere from 3 to 8. This means my score range would be between 16 and 21. Depending on how easy the problems were this year, this should be a relatively safe bronze, and if the problems are difficult it may even be a silver.

Talking with the other teams outside the arena though, it definitely doesn’t seem like this year’s problems were anything like last year’s. We took the bus back to the hotel and had lunch, similar to the day before.