The UK was invited to send a team to the Romanian Master of Mathematics competition, held in Bucharest for the seventh time in 2015. This is a short account of what happened. There are moments when I wasn’t present, for which Joe reports on behalf of the students.
A pdf version with more details about the organisation of the contest, statements of the problems and a brief summary of results can be found here. Background and reports on similar competitions can be found here, including links to more comprehensive registers of hosted elsewhere.
Wednesday 25th February
We have spent the night at a hotel close to Luton Airport, so we can proceed to our flight on foot. Walking in front of a bright red sunrise to a bright orange terminal to depart on a bright pink plane leaves me with a sense of colour overload not experienced since I last watched South Pacific. The three hour flight to Bucharest is unremarkable. Sam has fallen asleep with pencil poised halfway through a long expression where every other term is 
Soon afterwards we arrive in Romania and get lifts to the Moxa accommodation complex of the University of Economics where the students will stay. There are clearly mild cultural differences concerning what levels of privacy middle-aged adults might expect to enjoy, but the organisers have done a good job, and all is resolved satisfactorily. Of the students, Harry and Sam will share with two Brazilian boys who are due to arrive in the middle of the night, and the remaining four have a dorm to themselves, complete with precarious looking upper bunks.
Joe writes: Slightly surprisingly, we have been given seven guides, an entire Year 11 class at the Vianu school. Four of them take us on a walking tour round the central area of Bucharest, including the imposing Victory Square, and Herastrau Park. A sign informs us we should not toboggan down the brief slope between the path and the lake. We heed this advice.
Later in the evening, James and I diverge for the first leaders’ meeting. Old friendships are renewed, and the proceedings are informal and brief, allowing as much time as possible to get to grips with the questions. A proposed pair of papers is circulated by chief problem selector Ilya Bogdanov, and we get to work in James’ room. Our immediate impression is that we like them a lot, and this is reaffirmed over the coming hours as we explore them further.
Thursday 26th February
The leaders get to work finalising the papers. My confidence in the quality of the questions has grown even stronger overnight, and so I am not surprised when these are approved fairly rapidly. I propose swapping questions 3 and 5 based entirely on my own prejudice regarding their relative difficulty, and it turns out that others feel similarly, and this is approved.
Next, we must finalise a definitive wording of the questions before they are translated into languages for 14 other countries. Various people have strong views on commas, how many times one should use the word `let’ in a given sentence, and whether `open’ or `interior’ are more likely to be found ambiguous by students. Perhaps unexpectedly, a question submitted by the UK, courtesy of Lex Betts, causes the most problems for wording. In the end, it seems easiest to avoid ambiguity by completely rephrasing it in terms of the blackboard setup that will now appear as Q3 on the paper, accompanying Q2, the work of our own Jeremy King.
Joe writes: Meanwhile we enjoy a more comprehensive tour of Bucharest, past the old city and the Palace of the Parliament, then on to an excellent lecture by Calin Popescu. He tells us about topological dimension, and we learn that triangles are two-dimensional, though unsurprisingly the real challenge is deciding precisely what `triangle’ and `two-dimensional’ actually mean.
The opening ceremony is a well-organised affair in the grand university hall with several generous speeches from the mayor and other local dignitaries, and representatives of Tudor Vianu school. On the way home, the students examine their goodie bags, featuring various stationery and an RMM polo shirt. The leaders have not been missed out, though I wonder whether their guesses at sizes may have been informed by my predecessors? Certainly I will have to eat a lot of the omnipresent potato salad to run any danger of fitting into this item before the end of the competition…
After our winter camp in Hungary, the students are now connoisseurs of Eastern European cuisine, and remain unfazed by even the most remarkable display of gherkins. While James and I catch up on work, they relax before tomorrow’s festivities by starting another round of the card game which I am apparently not allowed to name. Suffice it to say, it has a similar quality to The Archers, offering a nonsensical background murmur which proves surprisingly supportive to research productivity.
Friday 27th February
Harry reports over breakfast that he spent some of the night helping dismantle a hyperactive burglar alarm, but it seems everyone is feeling well-prepared for the first day of the contest. James and I have carefully assembled a selection of fruit for the UK team’s refreshment, but, after Snow White themed questions regarding our intentions, the apples prove substantially more popular with the Hungarian students.
After approving answers to a handful of questions, mostly about the nature of the `first turn’ in Q2, we are free, so I return for a walk around the serpentine Herastrau Lake. The boundary of the lake seems to have Hausdorff dimension slightly greater than 1, but in any case, it is pleasant to stop halfway round its seemingly infinite perimeter to work on some problems about multitype branching processes. I also stop at the orthodox cathedral, from which my own college chapel could learn plenty about how a solemn space can be gold without being gauche.
Our students seem unsure whether to be upbeat or not, but we have a complete set of solutions claimed for Q1, and some cautious reports of progress on Q2. To avoid wasting time worrying about the recent past, some of the guides scoop up the Russian, American and UK teams for a walking tour of Bucharest old town and the stylish Cismigiu park. As in 2008, I observe that Bucharest enjoys a surfeit of excellently-equipped playgrounds almost everywhere, but a total absence of children using them. On this occasion, the younger members of our team are reluctant to rectify this.
I get started on the Q2s after dinner, and in a pleasing reversal of what often happens at some competitions, our two students claiming partial solutions have actually done rather better than they suggested. Sam in particular has been very clear about what he can and cannot do, and might even end up scoring seven. James and I convene at his hotel to discuss the challenging Q3 which seems to be equally clear-cut, so it is a hard-working evening, but a lot less drawn-out than it might have been. It is good to see that our recent active efforts to encourage the students to improve their write-up style are paying dividends.
Eventually Almost Everywhere 