# IMO 2014 – Part Four – Coordination and Close

Thursday 10th July

At last year’s IMO, a discussion arose concerning which of the seven members of the UK delegation at lunch was most likely to be the deputy leader. I placed rather low down the list. Despite the fresh-faced nature of the 2014 team, I’m taking no chances this year and now have a fairly full beard. However, today we have the first of our meetings with the coordinators to agree the UK team’s marks, and it may be necessary for Geoff and I to play good cop/bad cop. I prefer to play bad cop and feel this is a role best approached clean-shaven. In any case, there is a clash of timings so after signing for a vector of zeros on Q6, I end up playing solo cop on Q2.

We start with Frank, who has tried to prove something more general in one place, which is unfortunately false, but would be true in the special case. He then uses this in the second part of the problem, referencing the false bit, but using only the bit which is actually true. His habit of putting bold circles round sections he thinks are dubious is heart-warmingly honest, but I wonder whether it might have made more sense to use the time at the end of the exam to un-dubify them, rather than operating a series of nested post scripts? In any case, rather by an accident of the markscheme, we are offered 4, which is what I was hoping for, but definitely more than I was expecting. We also agree a 7 on Warren’s solution, and after coordinator Robert dramatically waves a diagram of a common counterexample to Harvey’s final argument at me, we agree a 5 for him.

The others are more tricky. Joe has done both parts of the problem fundamentally correctly, but has written down the final answer incorrectly. Since this step is genuinely trivial, it seems harsh to dock it a mark. Especially since the coordinators didn’t notice until we pointed it out to them. Hopefully this should be squashed overnight, though ultimately it is likely that several students will have done this, so consistency is all one can ask for. In any case, I regret my cavalier assurance straight after the exam. Freddie is offered 7, but also has a tiny mistake that they have not noticed. In fairness to them, this is very hard to spot, with the construction of an extra point in an extremal argument failing only in the case (2,2) out of $[1,n]\times [1,n]$, but they insist it has to be a 6. Coordinator Santiago reminds me that a proof is not a proof if it contains a mistake. This is a true statement. We will reconvene tomorrow.

The team have got back from their own excursion to Cape Point and seem to have enjoyed themselves, even the extended musical lunch. It would be nice to be able to give them more information about their marks, but they will have to bide their time. Perhaps in preparation for IMO 2015 in Chiang Mai, we return for a fifth visit to the Thai Cafe in Rondenbosch where both sides give a fuller exposition of their activities during the day. Afterwards, I see the team appropriating one of the giant Google cubes that have appeared round the site. They reassure me that they are still taking the medication for kleptomania, and in fact they intend to use it to distribute the UKMT playing cards as gifts to the other contestants.

Friday 11th July

Again I spend much of the night wading through slicks of combinatorial vomit, now including Q5, perhaps ambitiously described as Number Theory. After Geoff gets exactly what we want on Q1 and Q4, I’m raring to go for an early fourth session on Q2. The French leaders have a student in a similar position to Joe and have threatened to take his case to the jury. They get the extra mark, and in the spirit of Agincourt and Trafalgar I’m only too happy to coast in on their wave. Gabriel, from whom there were plans to drop two separate marks for the same mistake, gets his 6, and after successfully countering yesterday’s counterexample, so does Harvey. Freddie’s appears to be still under discussion, and I find myself saying “With respect…” several times, before it transpires that actually they are trying to offer 7, which of course we take. While it’s easy to criticise, I should emphasise that this question a) was an absolute nightmare; b) had a harsh markscheme, but this was certainly consistently enforced; and c) ultimately if the students hadn’t made mistakes none of this would have been relevant. Our coordinators knew the scripts well, were reasonable and fair, and I can only imagine how difficult it must be to do it all over again in Uzbek.

Question 5 proceeds much more smoothly, starting with our observation that Warren’s script looks identical to the official solution, including the location of the page break. He and Harvey get 7s with no real debate, and after a brief examination of the Chinese characters in Frank’s rough it turns out we are in agreement on the other four marks too. This was a very well-constructed markscheme for part marks. It is sensible to be both generous and sub-additive and it felt like there was not much room for ambiguity, though I’m glad we didn’t have any almost-complete solutions.

We are finished rather earlier than expected, with a nice bunch of scores between 20 and 28, and a team score of 142 looking likely to place the UK in the high teens. This is a strong team performance. The ‘easy’ (of course, this is relative) questions 1 and 4 have been dispatched and we have scored well compared to other similar countries on the medium questions. This is what we train for, and it is excellent to see it bringing rewards. Our younger students will have more practice and experience and will earn more marks on the hard questions in years to come. In any case, Geoff and I are very pleased. I am thus able to join the team for a second, sunnier attempt at Table Mountain. I arrive in time to see the end of the team’s latest instalment of ‘play a round of bridge in unusual places’, and even get to see a group of dassies sunning themselves on the cliff edge. Some of the group are tired or nervous about medal boundaries, but the remainder head for a walk to Maclean’s Beacon, the highest point on the summit. It goes without saying that the views were beyond comparison.

After seeing the eland on Wednesday, I feel obliged to branch out and try one of their steaks, but in fact the kudu was marginally nicer. Marginals are up for grabs after dinner, as it’s time for the final jury meeting, featuring the confirmation of UK as host of IMO 2019, and the all-important medal boundaries. First there is discussion of various administrative matters, and thanking various people involved in the five official languages. There are long delays while the microphone is carried round the room. Geoff makes several speeches. For these the lack of microphone proves no problem. Eventually the flashy software brings up the crucial bar charts, and the boundaries are decided. A decision has to be made about whether to award medals to 47% or 53% of contestants. Either way, the boundaries are lower than I had expected, leaving us with 4 silvers and 2 bronzes. It is a shame for Frank and Freddie to miss out so narrowly, and perhaps a surprise for Warren that he ends up only one mark off a gold, but of course these things will happen, and it is no reason not to enjoy the festivities into the night.

Saturday 12th July

While the previous night featured slicks of mathematical vomit, last night offered a digression onto genuine vomit. No hard feelings Joe. We’re now even given that I hit him over the head with a punt paddle the first time we met. I have too many spotty socks anyway, and certainly couldn’t have dealt with another night of combinatorics. While he sleeps off whatever it is he’s caught, Jill and I get mildly stressed, and the team head off on an excursion to the Waterfront. Free entrance to the aquarium is by some margin the best feature, with a remarkable collection from both the oceans that converge on the Cape Peninsula. The team debate whether the Coriolis effect or some form of social self-reinforcement process is responsible for all the fish swimming clockwise, while they play yet another round of bridge (four clubs in case you were wondering) in front of the shark tank. Geoff makes the mistake of offering to wait for us while we obtain lunch, in a further demonstration that South Africa doesn’t really understand the first word in the term ‘fast food’, while Gabriel wants me to verify that a watch he’s planning to buy is genuine. I feel there do exist things which fall outside the deputy leader remit.

I’m definitely catching Joe’s affliction, so I sleep while the team get ready for the closing ceremony. By the time I wake up, the Google cube is already dressed in the Union Jack, filled with the fetching playing cards, and providing everyone with a good core workout as they manoeuvre it onto the bus. I enjoy what I see of the closing ceremony, in particular the excellent and strident youth choir. No mewling Anglican tenors on show here. A traditional ‘praise singer’ comes onstage and shouts about maths for about three minutes, which is less impressive, but equally entertaining. Our master of ceremonies returns, wearing the exact chromatic inverse of his outfit at the opening ceremony, and guides the medal presenters and recipients through their steps. Initially this is tricky, as there are substantially more bronze medal presenters than room on the stage.

The UK team are consummate professionals of course, managing the task (found tricky by many of their competitors) of getting the medal in front of the flag, and orienting the latter correctly. Harvey positions himself well so gets his medal presented by Geoff. Gabriel does not position himself well, so disrupts the linear ordering to get his medal presented by Geoff. Photos are taken in huge quantities. The team’s plan to distribute the cards to contestants as they leave the stage is to my astonishment a) working and b) not hugely annoying the organisers.

I make a brief run down the mountain to check on our sleeping silver medallist. On returning it seems the organisers are grateful for his absence, as they ran out following the unexpected boundaries, evinced by Warren’s prize, which does indeed appear to be a spray-painted bronze. I have missed Geoff being presented with a vuvuzela in recognition of his maximally numerous contributions to the jury. Like a toddler on Christmas morning, I suspect his new toy may ‘get broken’ at some point fairly soon. This is more of a reception than the usual sit-down affair, and the remainder of our team seem to be happily mingling, so there is time to say all the requisite goodbyes, and reflect on an excellent competition. Gabriel chooses 12.45am as the moment to ask US leader Po-Shen the question about probabilistic combinatorics he’s been brewing all week. Let it never be said that social convention stood in the way of good mathematics.

Sunday 13th July and Conclusion

I need to be in France, and Frank needs to be in North-East China, so we are leaving earlier than the rest of the group. Joe appears to be operational again, and receives his silver medal in front of a small but adoring crowd at breakfast. Muffins are again served with grated cheese, goodbyes are said, the final Rand are changed back, and we are off.

My journey to Paris via Dubai was highly unpleasant, and my view of the Emirates was mainly through the bottom of a paper bag, so I won’t dwell on that at all.

What I should dwell on is what an enjoyable year and an excellent IMO we’ve experienced together. I understand why peers and colleagues might well ask why I choose to come to the olympiad rather than take a conventional holiday, but this was a great event to be a part of, and a great group of people to travel with. I hope I’ve given a flavour of the students’ enthusiasm for problems in this report. It was entirely infectious, and we of course enjoyed all the other possibilities which two weeks in Cape Town offered us.

For me, there was a particularly pleasing cyclicity to lead a team at the IMO including Freddie and Gabriel, who were junior students at the first summer school I taught at, and though they are perhaps disappointed not to have made a bigger splash in the competition, they and Frank have been entirely excellent people to know over the past few years, proving exemplary models to their younger colleagues both mathematically and generally. We will miss them as students, but equally look forward to working with them as colleagues in the future, should they wish. While we missed the starry heights of 2013, this was nonetheless an excellent team performance, and with young team members, young reserves, and plenty of talented and keen students getting involved at all levels, the future seems bright for UK maths. I hope that our activities through the year to come will be as enriching for everyone as it has been in 2014.