Journal of IMO 2010 Kazakhstan

This journal describes the IMO adventures of the 2010 Canadian team: Robin Cheng, Pinetree Secondary School (Coquitlam, BC); Alex Song, Detroit County Day School (Detroit, MI); Hunter Spink, Western Canada High School (Calgary, AB); Chen Sun, A.B. Lucas Secondary School (London, ON); Yuqi Zhu, University Hill Secondary School (Vancouver, BC); and Jonathan Zung, University of Toronto Schools (Toronto, ON). The team was accompanied by team leader Adrian Tang, and deputy leaders Victoria Krakovna and Alexander Remorov. Each of the entries is written by one of the leaders.

Training camp (Victoria)

The 2010 training camp was held at the Wilfrid Laurier University in Waterloo, the same location as in 2008. This year’s camp was only one week, so the training was especially intense, and there was quite a bit of pre-training happening over e-mail before the camp. On most days of the camp there was a morning mock competition, an afternoon lecture, and a problem-solving session in the evening. However, since each of the three leaders gave two lectures, and there were only five days of training, by the Pigeonhole principle there had to be a day which contained two lectures. Even so, the students continued doing problems during meals, and worked in the classroom long after the problem-solving session officially ended - in fact, sometimes we had to chase them out of there. No worries, there was time for relaxation as well - the last evening was a movie night, and every day ended with a game of Mafia.

While the three of us were doing the training, Christopher Small and Edward Wang were around to help out and give the team valuable advice and encouragement. Two IMO alumni came by as well - Elyot Grant and David Rhee, who now study mathematics at the University of Waterloo. They enjoyed working on contest problems with the team, and I had a match of the card game SET with David just like in the good old days (David won, as usual). Adrian had to leave for Kazakhstan quite soon after the beginning of the camp, which was particularly unfortunate because the leaders kept being separated from the students during the IMO.

One day Dr. Small brought a very pleasant surprise - a new moose! For a year, the team had been grieving for the previous version of Canmoo, which was dishonourably lost in the Frankfurt airport (thankfully, it happened on the way back from the IMO). The new Canmoo is a cute miniature moose from the McMichael art gallery near Toronto, who shows his Canadian pride by wearing a red sweater that says “Canada”, and, more subtly, with a small Canadian flag tattooed on his foot. May this new mascot stay with the team for many years!

The ample supply of drinks and snacks in the classroom (thank you Dr. Wang!) gave rise to a new fad. Whenever you get bored of the problems, you take one of the empty water bottles lying around, and twist it until the remaining drops of water heat up under pressure. Then you open the bottle, and steam comes out! Thanks to the tireless efforts of Chen, Hunter and Alex Remorov, there soon was a lineup of artistic-looking bottles on the desk (besides those lying on the floor all over the place). The water bottle abuse did not stop there - the row of bottles looked suspiciously like targets, and so people started throwing stuff at them.

Another fad, started by Alex Song, was to replace expressions like “oh crap”, “this is stupid” or “this didn’t work” with “FAIL!”. Alex himself would say it around a hundred times a day. The word was repeatedly used while solving problems, playing cards, or just discussing things, and even made it into the mock olympiad solutions:

The team did not feel like the customary outing for Canada Day fireworks (since they were late in the night, which would add to the already significant undersleep factor), so this was replaced with seeing a movie on the last evening of the camp. The movie was “Knight and Day”, and everyone enjoyed it a lot, some even too much - if anyone is wondering whose loud hysterical laughter was heard throughout the whole movie, it was Victoria and David. Afterwards, a lot of Mafia was played back at the residence. The gem of the evening was from Hunter: “I’m the doctor, last night I slept with myself!”.

Next day at the airport, the team also had some opportunities for fun. At the gate, there were some statues of pumas, originally meant for kids to play with, but who says we are not kids? Also, Hunter bought a toy otter on skis - not just to keep Canmoo company, but also to annoy Chen. Apparently, rubbing the otter against Chen’s neck caused him to be paralyzed...

One of the ways we passed the time in airports and planes was playing a word game called Radar. One person thinks of a five-letter word, and the others give guesses, also five-letter words. The person with the word announces a score for each guess. The score is the number of letters which were correct and in the right place, e.g. if the word is “apple” then the guess “maple” has only a score of 2, since ‘a’ and ‘p’ are not in the right place. We gradually extended the game to words of variable length (generally sticking to 2-6 letters).

We also had a game of questions and answers that Alex Song came up with. One of the players tries to think of a question that everyone knows the answer to, but a particular person will be the first to answer. For example, if the target is Jonathan then it makes sense to ask about physics, and if it’s Alex then the question could be a mental calculation. These games were nice to play on the move, since they didn’t require any materials. I particularly liked the questions and answers game, since it required thinking about the interests and qualities of the other players. On the other hand, Radar required less focus, so that’s what we played most of the time.

Vienna (Victoria)

On our way to Kazakhstan, we had a 12 hour transit in Vienna. Though many of the students did not have a good sleep on the flight, they were eager to explore the city. We were in such a hurry to get out of the airport, that we did not consider leaving the carry-on luggage in some kind of storage facility, and ended up dragging it around with us in Vienna. Getting to and around the city was easy, thanks to Gertrud Jeewanjee's instructions and the generally good navigability of the place. The Schnellbahn ("Fast Train") took us directly into the core downtown area, surrounded by a circular road called (unsurprisingly) the Ring.

After hanging out for a while in a souvenir shop (the students were particularly excited by the rich variety of music boxes), we headed for the central downtown square, the site of the majestic St. Stephen's Cathedral. We arrived there during a mass, and so had a chance to enjoy the excellent acoustics of the cathedral. In front of the cathedral there were people in 19th century costumes inviting everyone to a concert happening in the cathedral that evening (which we unfortunately couldn't attend), and lots of horse-carriages!

We continued walking around, making several stops for ice-cream and refreshments due to the hot weather and tiredness (the heavy luggage didn't help either). When we walked into a pleasant air-conditioned museum, the students just sat down on the floor near the entrance, putting down their bags all over the place. They were so relaxed that it took me ten minutes to drag them out of there, and head for a more appropriate location. That in fact existed nearby, and in an unexpected place too - the fancy park next to the Hofburg Palace, which looked funny with crowds of people sunbathing everywhere. In front of the Palace there was a statue of Mozart, which allowed Chen to show his statue-mimicking skills.

The main entrance of the Palace led into a large courtyard, with beautiful architecture and statues. The last stop was the Parliament building - we did not go inside, but had a good time hanging out on the front steps in the company of great philosophers. When it was time to head back to the airport, everyone was quite tired but pleased with the excursion.

Problem selection in Almaty (Adrian)

I arrived in Almaty at midnight local time, where I nearly ignited an international crisis when I knocked out two customs officers. Just kidding. But I was detained by customs officers after they placed his box of CMS calculators in the x-ray. After questioning the contents of the box, they claimed that I can only take two calculators (out of 100) with me. “Come Again?” I told them that the calculators were not for resale and that they were gifts. Their English skills seemingly vanished. Leading nowhere, they said that I had to pay them to bring the calculators in.

Welcome to the world of bribery. I refuse to even ask them how much money I had to pay.

At this point I had 200 USD and 200 CDN on me. There was zero chance I was taking out my wallet. Instead, I was getting help. Leaving my luggage behind, I burst out to the greeting area to find someone in charge. To fight my battle with the customs officers, it was either a young not-so-tall guide in her early 20s who spoke no English, or a tall gentleman in a leather jacket, who can speak English, who was telling leaders where to go, and in order to make Kazakhstan look good, will be on my side. Bingo! The gentleman came with me and I cannot exactly described what happened next, as 10 minutes of Kazakh, with the occasional ‘matematika’ thrown in there, were exchanged between the gentleman and the customs officers. It could have been Russian I suppose. Through my uneducated ears, the exchange was a mumble jumble of sounds, with more “r”, “s” and “v” sounds in the sample than any other sound. I smiled like a bystander, and when I saw the customs officers laugh and smile, I saw a small ray of hope. The gentleman told me “how many calculators can I give them?”. Oh no. I suppose I could not answer zero. Before I could say anything, I was asked “How about four?”. I blurted out a pathetic counter-offer of “three”. Adrian, you idiot. Don’t you know the law of haggling? If your offer is x, and their counter-offer is y, your next offer is always less than or equal to (x+y)/2. Hence, I should have said one or two. (I could have said zero, but that would also be the probability that they agree.) Too late. I blurted out three. More Kazakh was exchanged before they accepted and let me go with 97 calculators. It could have been worse. I had six small bottles of ice wine on me that went undetected. Oh well, for the next several days, this would be the end of the bad news, except I still can’t but feel my manhood shrink after this episode. No matter. I was now in Kazakhstan, with all my belongings minus three calculators. Life is still good.

Afterwards, the team leaders were immediately greeted warmly by local organizers. Most did not speak much English beyond “Welcome to Kazakhstan”, but their warm smiles assured us that they will make our stay enjoyable. Kazakhs have a very unique look. They are oriental except some have darker skin than others. Many could pass for a Chinese. Conversely, I was mistaken for a Kazakh on a few occasions on this trip. For an introduction, here are some simple Kazakh phrases:

Salem - Hello (informal)

Saubol - Good-bye (informal)

Rahmet - Thank you

Menin atym - My name is

Salem, our dear readers.

A one hour bus ride took us to our hotel. Unable to see the hotel’s surroundings in the darkness, I saved my midnight stroll for another night. I checked into his comfortable room, showered and promptly fell asleep.

Upon waking up, I discovered that the hotel was in fact a relaxation and wellness centre, with mineral water baths and a beautiful park in which people could ride bikes, paddle boats and exercise. My balcony overlooked a (golfing) driving range surrounded by beautiful greenery, with a scenic mountain backdrop. It was a beautiful sight to wake up to in the morning.

I received the shortlist problems, from which six problems were to be chosen for the competition. Our job was to judge the beauty and difficulty of as many problems as we could over the following two days. I gathered with fellow team leaders to solve and discuss the problems. I promptly solved the easy problems and kept my two favourites in mind, a functional equation and a geometry problem. At the jury meeting, a leader’s job is to support beautiful problems that appear favourable to his/her team. The Canadians had a thorough session on functional equations and are overall quite strong in geometry. Hence, my choices for favourites were clear. There was one easy problem that I was vehemently against. I called it every bad word possible, until I realized that the problem is a Canadian proposal. Oops. But I stood my ground.

We took an afternoon excursion to Medeo, the site of the future Asian Winter Games in 2011. Although still under construction, the skating rink facilities appeared to be at a world class level and the mountains were glorious. We hiked up the steps to the top of the mountain and soaked in the picturesque views from the top.

A jury meeting was scheduled on this evening at 8pm, to eliminate problems from the shortlist that were previously known. However, the German leader spoke up and reminded the jury that the Germany vs Argentina World Cup game was at 8pm that evening and proposed to shift the meeting to 6:30pm. This was met with thunderous applause from everyone, including me. Even the jury chair jokingly apologized for his “scheduling over this important event”. Priorities became World Cup > IMO Shortlist. The game was projected onto the big screen in the jury meeting room and roughly 100 leaders and observers gathered to watch the game. Watching with an international crowd was a very unique experience and definitely made the game far more exciting.

The shortlist problems were of very high quality. Just in case Hunter and Alex can read my soul and absorb subtle hints in my writing, I will say nothing else about the shortlist problems. Consequently, the jury had many choices for the medium and difficult problems. I was particularly enamoured with the following combinatorics problem:

Problem 5. In each of 6 boxes B₁, B₂, B₃, B₄, B₅, B₆, there is initially one coin. There are two types of operation allowed:

Type 1: Choose a non-empty box B_j with 1 <= j <= 5. Remove one coin from B_j and add two coins to B_j+1.

Type 2: Choose a non-empty box B_k with 1 <= k <= 4. Remove one coin from B_k and exchange the contents of B_k+1 and B_k+2.

Determine whether there is a finite sequence of such operations that results in boxes B₁, B₂, B₃, B₄, B₅ being empty and box B₆ containing exactly 2010^{2010^2010} coins.

We ask you, the reader, to play around with this fun problem. Go ahead. Come back in an hour after you’ve played with it.

Okay, you are back. Do not read this paragraph if you do not want spoilers. Would you believe that the answer is yes? Would you believe that you can obtain far more coins than what is asked in the problem? Would you believe that you can obtain 2 x 2^2^2^2 ... ^2 coins, where there are 2^2^2^2^2^2^2^2^2^2^2^2^2^2 twos in this tower? Yes, it’s a huge number. And yes it can be done. This result is absolutely mind-blowing. We strongly recommend you to share this problem with the students in your math clubs, math circles or math classes. We promise you it will be worthwhile.

A majority of the jury also loved this problem and this problem was selected. I was happy that all six chosen problems were amongst my favourites. The next stage was the translation of the problems. Formulating the wording of the problems in English and the subsequent translations into over 50 languages was traditionally a hassle. Thankfully this year, the English version required only some minor tweaks in five of the problems and the creation of a cleaner scenario in the aforementioned coins problem to complete the English translation. It is amazing that certain English words cannot be translated easily into some languages. For example, a certain language apparently did not have a word for “stack”. My shameful lack of Chinese skills did not allow me to aid with translating the paper into Chinese. I thank the Chinese leaders for handling this matter. I read over and approved the Chinese translations of the paper.

There were other orders of business for the leaders at this site, including the election of a new chairman and two new members. I felt severely uninformed and voted entirely on impression moreso than merit. Nazar Agakhanov, the Russian leader, was elected chairman. József Pelikán’s efforts will not be forgotten, as the success of the IMO today is primarily due to his vision and hard work. We all owe József a lot of gratitude. (To students reading this, it may surprise you that organizing an IMO either locally, or on a year-to-year basis, requires a tremendous amount of work all year round. It is due to visionaries like József and others that the IMO can even come into fruition. For this, we should all thank him and all past chairmen and members.)

Arrival to Kazakhstan and opening ceremony (Victoria)

When we landed in the Astana airport, some of us were concerned that we would be taken to the contest location (a kids' camp) right away, meaning a 4-hour bus ride right after the tiring flight. Fortunately, that was not the case, - the newly arrived teams were taken to the luxurious hotel Duman in Astana. After a lengthy check-in at the reception, a whole day of relaxation was ahead. The hotel was packed pretty much to maximum capacity - it was funny to see fancy rooms lined with little wooden beds that were obviously put there just to accommodate the sheer numbers of students. For some reason, the Internet room was only going to open the next day, when it was already time for the opening ceremony and the departure for the contest site.

Astana (literally meaning “capital”) was a very modern and futuristic-looking city, with golden towers, artistically shaped skyscrapers, a huge castle that turned out to be a fancy apartment complex, all this built only in the past 12 years since the capital was moved there from Almaty. The opening ceremony took place at the Palace of Independence (a blue-and-white building shaped like a truncated rectangular pyramid). There, a grandiose welcome awaited the IMO participants - people in national costumes outside the building, and an orchestra (also in national costumes) inside. During the ceremony itself there were lots of performances - singers, folk dancers, drummers, you name it, even the famous rock band Ulitau. The Kazakh organizers obviously put lots of effort into the entertainment part of the IMO, and the performers were really great.

Usually, as the teams walk across the stage, they have a chance to put up a bit of a show, or throw goodies at the audience. For example, in 2006 the Italians played soccer on stage, the Hong Kong team brought cameras and took pictures of each other, and some members of the Canadian team did a moonwalk. This year, unfortunately, the teams were marched across the stage way too fast to do anything cool. Somehow, the screen managed to switch even faster, and so it introduced the Canadians as the Chinese team! (In fact, we could almost pass as the Chinese team, especially if you remove the deputy leaders from the picture...)

After the opening ceremony and lunch, we were peacefully sitting in the hall outside the cafeteria, when some guys from the Cyprus team came up to us. “Well, guys”, they said, “we have a tradition. Every year, we steal your moose. So, you might as well hand it over.” When I replied that the Canadians, in turn, have a tradition of protecting their moose well, the Cyprus guys decided that it’s time for brute force, and attempted to tear Canmoo out of my hands. We maintained our tight grip on Canmoo, and suggested the Cyprus team to steal the Singapore teddy bear instead. After a few more fruitless attempts, the moosenappers departed with the final words, “In a few days, when you let down your guard, the moose will be ours!”.

Opening ceremony and contest days (Adrian)

We departed at 3am on July 7th, for Astana, Kazakhstan’s capital, for the opening ceremony and the coordination site. To my recollection, this is the first time the team leaders are flown from the leaders’ site to the coordination site. Imagine the shock of the airline check-in counter when 200 people arrive simultaneously to check in. The check-in was smooth and the team leaders and observers were promptly boarded.

The opening ceremony took place at the Palace of Independence in Astana. We were greeted by a group of lovely Kazakh musicians, before being escorted to a designated rest area. I admired the murals of the Astana 2030 project, a plan by President Nursultan Nazarbayev to transform Astana into a futuristic-looking metropolis by 2030. The opening ceremony would coincide with the anniversary of Astana being the nation’s capital and the President’s birthday.

The team leaders were separated from the students and deputies during the opening ceremony. However, me and my team still exchanged waves of hellos with our proud Canadian flags. The opening ceremony performances began with children coming on stage wearing t-shirts with math symbols on them. It was an adorable sight that melted the audience to go “awwwwwww...“. The Kazakhs went all out to provide lively musical and dance performances for everyone to enjoy. During the introduction of countries, the Canadian team walked across the stage proudly, waving the maple leaf flag and holding onto our team mascot, Canmoo, the moose that gives us strength, loved by all and stolen by many.

We departed for the luxurious hotel Duman in Astana, in preparation for the meeting to approve of the marking schemes for the problems. Here is a tip for everyone: never create and discuss marking schemes when you are sleep deprived. Our day began at 3am and it was decided to continue the jury meeting on following day after everyone has slept. However, this did not deter me and many of the leaders from watching the Netherlands vs Uruguay World Cup semi-final game that night at 12:30am.

The next day began with the Question and Answer period. Students’ questions are faxed to the leaders’ room and each student’s leader proposes answers to return to the student. We braced ourselves that no embarrassing questions come from our own students. Gems from past years (not from Canadian students) included “What is a grasshopper?” and “I cannot draw the diagram (described in the problem). Can you do it for me?” This year’s questions were fairly straightforward and uneventful, to the relief of everyone.

The team leaders went on an excursion to downtown, the site of the Baiterek Tower, the symbol of Astana. Downtown Astana encapsulated a futuristic look, with gold-coloured buildings and modern architecture that rivalled that of Dubai. At the base of the tower was a square with an impressive display of bear statues, one for each country in the world. The bears symbolized love and unity amongst nations. The bear representing Canada was disappointing, since it was blue and white in colour and appeared pixelated. I did not see why this represented Canada. Other bears were more colourful and symbolic of their representing countries. At the top of the tower was a small platform with the handprint of the President of Kazakhstan. Visitors were encouraged to place their hand in the handprint and make a wish. I did, and wished that the Canadian team would have a wonderful time in Kazakhstan.

Another order of business was the APMO Meeting. Yuji Ito, the current chair of the APMO, hosted the meeting. The details of the meeting are lost on me, but the main points are:

1) The first problem of APMO 2010 was far too easy. The mean of Problem 1 is higher than 6, to my recollection.

2) Please submit problem proposals to the APMO. In APMO 2010, there were only seven problem proposals. (How they came up with a good contest from seven problems is beyond me.)

3) There *may* be a fee to participate in the APMO. This is odd since the APMO is working on a surplus.

4) Ideas as to what to do with the surplus are welcome.

Many new countries wanted to participate in the APMO, although these countries are neither Asian or touching the Pacific. Looking at the countries present, I hereby rename the Asian Pacific Mathematical Olympiad (APMO) the Non-European Mathematical Olympiad (NEMO).

(Okay, before you frantically cry foul on Mathlinks or AOPS, the previous statement is a joke. :) )

Adventures at the contest site (Victoria)

One thing that the organizers didn't seem to have worked out was providing us sufficient information about what's going on. The participants were given a program, which was extensive but still incomplete. After the opening ceremony, the students and the deputies boarded the buses heading for a kids' summer camp called Baldauren, where the contest was to be written. When we arrived to the police checkpoint in front of the camp, the students had already gotten there, and gone inside. The deputies tried to follow suit, but apparently the police thought otherwise. It turned out that not only we were staying in a different place from the students (a resort a half-hour drive away), but that we were supposedly not allowed to see the students at all. Naturally, the program did not mention any such thing...

So, we are sitting in our bus, having just been told that we are not supposed even to get off the bus, which will soon be taking us to our resort. However, since most of the deputies on the bus were quite angry, we left the bus after some arguing with the guides, and started crowding around the police checkpoint. This is the part where having two Russian-speaking deputy leaders is more than useful. After quite a bit of arguing, and the police calling up their superiors, the chief guide decided to take us in. Even then, the policeman was running alongside us, and kept telling us to stop. At this point, people were barely listening to him, and I was later happy to learn that many of us simply sneaked around the checkpoint during the arguing. Still, because of this, only the most persistent and angry deputies got to see their students and wish them good luck before the competition, which I believe is a disadvantage for their teams... To return to the theme of misinformation, even our team's guide was surprised to hear that we would not be staying with the students.

The next day the situation improved - the organizers arranged some buses to take us to the students' camp after the first day of the contest (the original plan was to have an afternoon excursion). However, even after the buses brought us there with the express purpose of seeing the students, the police were yet again unwilling to let us in. We had to wait for a while at the checkpoint for the policeman to receive the appropriate instructions, and then we were finally admitted into the camp.

Upon arrival, the first thing we heard out of the students was "FAIL! We did so bad!". Upon further questioning, it turned out that each of the six solved at least one problem, and some solved two, so not a bad day at all. There was also an unpleasant surprise - it turned out that Hunter no longer had either of his insulin packages. One of them he broke by accident, and the other one, apparently, simply disappeared from the bathroom counter! This was a private bathroom adjacent to the Canadian team's room, so the bottle was removed by the camp personnel - either discarded, which was unlikely since it was a labeled half-full bottle of medicine, or stolen. Thankfully, I had an extra package back in my room at the resort - an emergency one that we were hoping to never open. As outraged as we were, the first order of business was to deliver the last package to Hunter as soon as possible, since he needed an insulin shot every day. So I went down to the camp reception, told them about the problem, and requested that I be taken to the resort and back to pick up the package.

First, they suggested that Hunter goes to their medical office and gets some insulin there. I patiently explained that he uses a special kind of insulin, and that I am certainly not going to give him some obscure medicine. So I asked again, "How can I get back to the resort?" "We don't know!" said they. "You should probably call a taxi". After some more insistence from me, they said that they will call the taxi, but I have to pay for it. "How do I pay for it?" I asked. "Go and exchange some money at the counter over there." "What is my resort called, exactly?" "We don't know... it's probably Shuchinski, but we are not sure." They were acting as if they have nothing to do with the whole thing, even though it was their personnel who screwed up in the first place. I understand why the receptionists might not know some of these things, but they should definitely be able to summon someone who does, and who can take care of the issue. Naturally, the whole exchange happened in Russian, since these folks didn't speak much English. I was ok with that, but for a non-Russian-speaking leader such a situation would have been awful.

So I borrowed some US dollars from Robin, exchanged them for Kazakh tenge, and came out to the police checkpoint. To my relief, instead of a taxi, there was a policeman who kindly volunteered to drive me. This was quite handy, since at the entrance and exit from the resort, there was also a police checkpoint, and this way I didn't have to explain anything to them, since I was in a police car. The trip there and back went without any adventures, except that up until we got there I was still not entirely sure we were going to the right resort (there were lots of them in the area). Luckily, it was indeed Shuchinski, we just drove into it from a different, unfamiliar side. So Hunter got his insulin in time, and thankfully he was careful with the last package, which lasted him until the end of the trip without any further issues. Unfortunately, by the time I got back with the insulin, we were so tired of this incident and happy that it was resolved that we did not put further demands on the organizers to investigate what happened.

After this disgraceful episode was over, we enjoyed a lengthy discussion with the students about their results. When we came down to the reception, all the buses back to the resort had already left, but the people said that a bus will come for the remaining 10-15 deputy leaders. We went outside, and there was indeed a bus - but no driver. After standing around for at least half and hour, we went back and continued waiting at the reception. We waited for another hour, and at some point the reception people announced that a bus is waiting for us, and we should go back outside immediately. So we waited outside for another half-hour, and then finally the bus came.

Back at the resort, everyone was having a party! There was an orchestra playing in the dining hall, and in between their great numbers, a very energetic woman was trying to get everyone to dance and sing. Most of the audience preferred to sit back, listening and enjoying the food, but a few people did come up to the stage - we heard Hungarian, Ukrainian, African, and other songs. Several people also showed some cool dancing skills in the exciting Georgian dance "Lezginka". On the program this was called the "Night of Surprises". I thought that the surprises began the previous night, and this should be more accurately called the "Night of Pleasant Surprises".

The next day, we had an excursion in the morning, and then it was time to head back to Astana, dropping by the students' camp on the way. The excursion to Burabai National Park was awesome. First we climbed a small hill with a good view of the surrounding mountains, and interesting rock formations on the top. The next stop was a picturesque open field surrounded by hills, with a memorial in the center. There were also some locals with eagles that you could hold on your hand! They had a wolf too - unfortunately, a stuffed one.

Later, the students visited the same place. Does anyone else get the impression that Hunter is running away from Chen?

Back at the camp, Alex and I found out that almost all of the team got Problem 4, but most got tripped up by the non-standard Problem 5. However, most of the other contestants also went down the wrong path for Problem 5, so this was going to even out. In the end, everyone solved at least 1-2 problems, plus the Canadians had someone who completely owned Day 1 and someone who completely owned Day 2, which was awesome. Great work team!

Coordination (Adrian)

After Day 1, many members of the Canadian team showed their usual modesty proclaiming they "failed” on the first day. Leaders often have to remind students that their performance is always relative to other countries and to trust the leaders in their job of obtaining as many marks for each student as possible. I received the Day 1 scripts and was delighted to know that Robin seemed to have a perfect Day 1. On Problem 1, Canada had three perfect solutions, one solution with a minor flaw, and two incomplete solutions which were still worth five (out of seven) points. On Problem 2, Canada had two perfect solutions, but a plethora of part marks amongst the other four solutions. The problem was a tricky geometry problem, and hence, the Canadian leaders were content with this result. Canada had one perfect solution to Problem 3, a difficult number theory problem disguised as a functional equation, and also three solutions with partial progress, which eventually yielded us part marks. Hooray for garbage marks!

I received the Day 2 scripts the day after, and was happily reunited with my deputies Victoria and Alex. How I missed them dearly. We scoured the Day 2 scripts and were further delighted to know that Hunter seemed to have a perfect Day 2. Canada had five perfect solutions to Problem 4, two to Problem 5 and one to Problem 6. Unfortunately several students on the team thought the answer to Problem 5 was no. However, this misfortune was not only bestowed upon Canada, but on every other country. The leaders envisioned the yells of anguish from many contestants after Day 2, who spent most of the 4.5 hours proving a false claim. One contestant (not from Canada) allegedly used 150 pages for Problem 5, trying to prove the coin problem to be impossible. On an unrelated note, the organizers ran out of paper on Day 2. So to recap, all was not lost for Canada. Two of our students obtained partial marks on Problem 5. More hoorays for garbage marks!

Coordination was very smooth with the exception of one problem, namely Problem 1, where the coordinators insisted on going through every line for five of our students’ solutions. This is a warning to future team members: the coordinators were urged to deduct marks for minor things such as typos and bad notation on Problem 1. Hence, please write solutions to easy problems with extreme care. Canada narrowly escaped punishment this year, but other countries were said to be not as lucky. For the remaining five problems, we agreed on the scores with little to no disagreements. There was one incident where one student used the word “obvious” in his solution, which caused some minor headaches since his claim was anything but obvious. Oh no! The dreaded “o” word. Thankfully, this issue was cleared when Alex spent 20 minutes explaining (in Russian) why the student’s claim was obvious.

After coordination, our score was 129 out of 252 and we looked to be ranked amongst the top 20 countries. This itself would be a great success for Canada already. Robin and Hunter seemingly had gold medals secured with scores of 35 and 32, respectively, and Yuqi had his bronze medal secured with a score of 19. Jonathan received an honourable mention, with a performance worthy of recognition. Chen’s score of 21 and Alex’s score of 15 were dancing on the edge of the silver cutoff and bronze cutoff, respectively. In each of the past three years, Canada had at least one student who was one mark short of a cutoff. Oh please let the universe balance itself and give Chen and Alex the desired medals! The jury meeting began and the medal gods responded. The gold, silver and bronze cutoffs were determined to be 27, 21, 15, respectively. Hi-five! Silver for Chen and bronze for Alex! It is worth noting that Alex is only 13 years old, which makes his bronze medal achievement even more astounding. This made a total of 2 golds, 1 silver, 2 bronzes and an honourable mention for Canada. More exciting news arrived, as we discovered that Canada was ranked 13th! Thinking 20th and receiving 13th set off all sorts of fireworks in our heads. Percentile-wise, this is Canada’s best performance ever! The Canadians could not handle any more news, until they realized that individually, Robin and Hunter ranked 7th and 11th, respectively, out of all 517 contestants. Wow Wow Wee Wow! Smiles and hugs were shared amongst Victoria, Alex and me, as we celebrated, laughed and giggled throughout the night. We emailed the results to the students and to interested parties back in Canada and could only imagine the elation and glee from everyone.

Alex, Victoria and I decided that there was only one mature way to reward our awesome team - make fun of them. Or at least make fun of one team member who happened to have won a gold medal. Names will be hidden to protect the innocent. HUNTER SPINK has fairly illegible handwriting, which caused both confusion and hilarity during coordination. Most of his words are readable, but other words and symbols are often in some foreign ambiguous alphabet. His b’s, f’s, t’s and + sign look identical. The leaders lost all sense of professionalism and took snapshots of highly ambiguous and unreadable portions of his solutions to create the game “how well do you know Hunter?”. In the end, none of our team can correctly identify any of Hunter’s Martian-like symbols and Brownian-behaved squiggles. Hunter correctly identified three sigma symbols (which pairwise looked nothing alike) on his paper but could not identify several other symbols. In the end, only Hunter knew Hunter, but only somewhat.

Various quotes from the coordination time

While preparing for coordination,

Adrian: “I think we are taking up more than multiple desks...”

While discussing problem 5 at the dinner table,

“It would be interesting to have these kinds of twists in other areas of mathematics. For example, if you were asked to prove that three lines are NOT concurrent.”

Later in the same conversation about problem 5,

A deputy leader: “Well, in the first hour when the deputy leaders tried the question, they also thought it was impossible.”

A leader: “That’s why they are deputies!”

After coordination,

Alex: “We should bring more chairs.”

Victoria: “For the jury meeting or the soccer game?”

Adrian: “Of course, the soccer game. Priorities, Victoria, priorities!”

After coordination, or Let the games begin! (Victoria)

After our last coordination, it was time to sit back and have some fun. Thankfully, the hotel had some great facilities for that. There was a bowling alley, and a go-cart track outside, which we enjoyed with some fellow leaders. There was also a memorial with an enormous flag of Kazakhstan (supposedly the flag sheet was 15x30m).

Indeed, it turned out we were not completely harmless - two people crashed into each other, and one of the carts was broken. Conclusion: beware of leaders who are chilling out after a lot of hard work!

After some excursions to the President’s Cultural Centre and the President’s Museum, the big day arrived. We were going to see an equestrian performance of Kazakh national sports - along with our students, who were just arriving from Baldauren! Unfortunately, yet again they were seated separately from us, but at least after the show we would have some time to hang out together.

The equestrian show was really amazing. The performers did all sorts of mind-blowing acrobatics on horses - riding two horses at once, riding the horse with their legs in the air, swinging off the horse at full gallop to pick up a handkerchief from the ground, and so forth. They competed in horseback archery, tried to wrestle each other off their horses, and played a soccer-like game with a goat carcass instead of a ball (thankfully, for practical purposes the carcass was fake). There was also an adorable game where a guy chases a girl on his horse, in the attempt to hug and kiss her while in full gallop. If he fails, then on the way back she chases and whips him!

After a thunder of applause to the acrobats for their amazing performance, we went outside to reconvene with our students. An eager exchange of stories took place - the students had some good times with the other teams, fun excursions and concerts, and of course Canmoo got stolen. Also, apparently, Jonathan and Hunter ventured out for a nighttime hike, which involved climbing some hills and the flashlight falling down the hill into the bushes... Anyway, they got back to the camp safely, so it’s all good. We administered the Hunter quiz, and enjoyed the students’ confusion and wild guesses about his spelling. Then, unfortunately, it was time for us to part again, since the students were to stay in a different hotel (understandably, since our hotel was rather full), and to go on separate excursions (now this part is less understandable). In this sense I was even looking forward to the trip home, when it would be just us and the team again.

Closing ceremony (Adrian)

We arrived at the Palace of Independence for the closing ceremony. The students were given the red carpet treatment, literally, as they marched on a red carpet into the Palace to a majestic fanfare performed by Kazakh musicians. The leaders followed soon after and the closing ceremony began. Victoria, Alex and I cheered on as the Canadians proudly went up on stage and received their medals. The gold medalists were further rewarded with laptops, courtesy of the main sponsor of this IMO, ExxonMobil.

After the ceremony, we celebrated our glory and achievement this year. We bussed back to the leaders’ hotel to gather for the farewell dinner. We sat together and were joined by the Canadian guide, Zauresh. She did an amazing job taking care of our team. The Canadians loved her, and she loved the Canadians. We proudly signed our names onto a Canadian flag and presented the flag to her as a gift. Zauresh’s eyes lit up in happiness. The dinner consisted an assortment of Kazakh cuisine, which we feasted on to our hearts’ delight.

After the closing ceremony (Victoria)

We also found a somewhat unconventional way to pour out our joy about our glorious results. Namely, we took turns putting on a Canadian flag as a cape, running around the ceremony hall and screaming. We even got Adrian to do it, and he spent a lot of time afterwards mumbling to himself, “Dr. Small, I can explain...”. In the end, the bravest of us went outside, to show the Canadian pride to a wider audience.

When we got back to the hotel, it was time for the farewell party! The students were also transferred to Duman, which had a fancy and spacious dining hall. After enjoying a sumptuous selection of Kazakh dishes, the teams were hanging out outside the hotel. The Australians were sneaking around pinning little koalas onto people (see below for a particularly severe case of koala infestation), and Canmoo once again became the focus of major attention.

After the party, it was soon time for us to leave for the airport, for our 5am flight. Goodbye, Astana!

Farewell (Adrian)

An event is only as wonderful as the people who were there to share the experience with. We said farewell to our friends and colleagues, who filled our experience in Kazakhstan with happiness, laughter and life-long friendships. We will certainly see them again at a future IMO or through other endeavours. The Kazakhs were wonderful hosts, who made the strongest effort to please out of all the hosts we have ever encountered. Rahmet Kazakhstan, for a lovely IMO 2010.