**Thursday 18th July**

The third practice exam again proceeds smoothly. The first problem is a nice exercise by John Conway, on classifying sets of points which obey some intersection property. There were various ways to misread the problem, of which some students took full advantage, and an almost limitless number of ways to classify the satisfactory configurations. As a result the marking, which I chose to do outside, took ages, though at least I had the company of a few passing green lizards and a brief visit from an eagle.

The resort where we are staying, and in fact where the IMO itself will be held, is actually about 10km outside Santa Marta itself, so we decide to venture in to explore the town once marking is complete. The historical centre, though modelled on a grid, is very Mediterranean, with narrow streets wending their way underneath exposed municipal wiring down to the seafront. We pause outside the Cathedral, where Mass is just starting. The dry heat clearly not enough to discourage a very full and colourful set of vestments.

On the way down to the sea we pass a park featuring yet another statue of the most famous man to live (and in fact die) in Santa Marta. Our guide Maria looks horrified as one of the students asks “Simon Who?” Dinner ends up al fresco, where we are treated to the accordion playing and fire-juggling in the town square. How does some one take up fire-juggling one wonders? Are there beginner kits with just lightbulbs on the end? Very few of the party receive the meal they think they ordered, but all are satisfied nonetheless. The convoy of taxis departs into the night. I am in the second one and it is clear that the driver has no idea where he is going, and his dedication to staying within sight of his leader is admirable if occasionally terrifying.

**Friday 19th July**

To mix things up, today each team has set an IMO-style paper for the other to attempt. The UK team then has to mark the Australian scripts during the afternoon and vice versa, before co-ordinating the results with Ivan the Australian deputy leader and myself. It’s always a profitable exercise to have to struggle with poorly worded solutions as perhaps it will encourage everyone to avoid such things in the actual exam. Questions which fall into the realm of the combinatorial essay are always particularly at risk of large blocks of waffling prose, and each Q2 produces exactly that. Hopefully the students found the exercise useful as well as time-consuming.

Meanwhile, it seems that the UKMT-branded frisbees we ordered to distribute as gifts at the IMO have been held up somewhere in the intricacies of Colombian customs. Initial attempts to speak on the phone are hindered by my non-existent Spanish, and even an attempt to spell out my email address is fraught with the challenges of differing vowel pronunciations. I fear we may have to resign ourselves to being the stingy delegation at this competition…

I take advantage of a relatively free afternoon to sample the resort’s various pools and catch up on what’s been happening in the cricket. Our own version of the Ashes is taking place tomorrow, so hopefully the demolition happening at Lord’s is a good omen. Geoff and his brother are attempting to get the hashtag #otherashes trending. So far we have one tweet (by me) and a mention in the Guardian cricket feed. From tiny acorns…

**Saturday 20th July**

And so to the final practice exam of this pre-IMO camp, the Mathematical Ashes. I was a student in 2008 for the inaugural competition, the only time the UK has lost, and so in keeping with the cricket tradition the ceremonial funeral urn is filled with the ashes of UK mathematics, including a geometry question in my handwriting. (In fact, the pyre formed during an excursion after the IMO in Madrid got a bit out hand, and so it probably contains a comparable amount of Australian material.)

As for the other exams, we are using questions from last year’s IMO shortlist, that is, problems that were considered for inclusion by the jury, but not selected. The first two chosen are at the easier end of the IMO difficulty spectrum, while the third is really very awkward indeed. Post-exam, the teams compare notes and it seems that it will be tight, so Ivan and I divide up the questions, devise brief mark schemes and get going. Three hours later we feel happy with our conclusion: UNK 82, AUS 81. In reality, by far the most pleasing aspect is that both teams have demolished the two easier questions with such aplomb. This bodes very well for the IMO itself next week.

A wager is placed that less than 10 minutes will elapse between emailing Joseph Myers, custodian of the IMO Register and the BMOS website, and the results appearing on the latter. The placer of this wager turns out to be rather wise. We await a flood of hits on the OtherAshes blog. Meanwhile, we pay our final visit to the Santorini resort restaurant, who have accommodated our various dietary specifications and comical Spanish with elan. I order at random from the fish and seafood section and end up with a steak topped with guacamole. Definitely not complaining. Everyone heads back feeling understandably excited for the start of the main event tomorrow.