\documentclass[a4paper]{article}
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\title{European Girls' Mathematical Olympiad \\ an unofficial UK student report}
\date{Murray Edwards College, Cambridge
  \\ \smallskip 10\textsuperscript{th}--16\textsuperscript{th} April 2012}

\begin{document}
\maketitle

\section*{Introduction}

Once upon a time, in a galaxy far, far away, in Cambridge, the final
frontier\ldots

So, you've all heard about EGMO 2012, the inaugural Olympiad solely
for those with a higher than average number of X-chromosomes, which
took place in Murray Edwards College, Cambridge, the final frontier.

We are the Egmoids of UNK:
\begin{center}
\includegraphics[width=120mm]{team.jpg}
\end{center}
\begin{itemize}
\item Natalie Behague (like `behave' with a `G'), UNK 1
\item Katya Richards (also on this year's IMO squad), UNK 4
\item UNK 2, Lizzy Lee (who dislikes excessive commenting on her
  rather long hair, so we won't mention that here)
\item UNK 3, Ella Mi (half of the twins Ella and Emma, although there
  are scurrilous rumours of a third twin Enna Mi. Perhaps
  unsurprisingly, she is never talked about\ldots), and last
  but not least\ldots
\item Emily Bain (who dislikes excessive commenting on her pink hair,
  so we won't mention that here either), the reserve.
\end{itemize}
Our leader was the lovely Alison Zhu, and our deputy leader the
equally lovely Jo Harbour.

\section*{Tuesday 10\textsuperscript{th} April}

The Egmoids arrived at Murray Edwards College in dribs and drabs on
Tuesday afternoon. The pink-haired reserve arrived late, unfortunately
delayed by a body on the line. She claims this had nothing to do with
her.

Most of the afternoon was spent lonely and alone in the Dome. Teams
were supposed to socialise here, but our sole companions were the
muffins, who, incidentally, were very tasty. We were disappointed to
discover that the EGMO rucksacks given to us on arrival were neither
psychic, nor could open doors. However, they did contain a number of
small gifts, the most exciting being the UKMT freebee Frisbee. This we
used for sophisticated experiments on the nature of aerodynamics and
gravity.

Eventually, we were joined in the dome by the Luxembourgeois, whom we
taught to play cheat. In retrospect, we are not entirely certain
whether this was the best idea. At around 6:15 all the other teams
magically appeared, just in time for dinner.

After eating, we headed down to the games room were we were greeted by
an awesome 1000-piece MC Escher jigsaw puzzle. Some bemoaned the lack
of colour; others were put off by the high proportion of plain white
pieces; and some disliked jigsaws altogether. But we are the Egmoids
of UNK, and we are up for any challenge, and so an evening of ordering
various grey pieces of cardboard began.

Natalie and the one with pink hair were the first to grow weary of
this cardboard sorting, and joined a group of Poles and Luxembourgeois
for a game of anarchic Jenga, otherwise known as Mikado, Morocco or
pick-up-sticks. The term anarchic Jenga was coined by none other than
James Cranch, who, to ensure that EGMO wasn't left a single night
without first aid cover, rushed all the way from Sheffield to
Cambridge at a moment's notice. Travelling by foot. Barefoot. In the
rain. We appreciated his heroic efforts, and also his conversation,
learning in the course of the evening that he is both UNK avuncular
and has no friends, at least according to his lanyard.

\section*{Wednesday 11\textsuperscript{th} April}

We were up bright and early Wednesday morning, resplendent in our
rather fetching subtle pink T-shirts, ready for the opening
ceremony. Whilst the T-shirts clashed horribly with both our green
lanyards and the Union flag in our team photograph, the one thing they
didn't clash with was the Polish leader, the Poles having adopted the
convention of girls in blue, boys in pink. In fact, the two pinks went
so well together that we adopted the Polish leader,
Micha\l\ Pilipczuk, into the UNK fold for the rest of the day.

After a blissfully short opening ceremony, we spent the afternoon
participating in various sporting activities. This was more fun than
it sounds and, after giggling our way through a blindfolded obstacle
course, boules, rounders and ultimate frisbee, we felt we had
fulfilled our sports quota for the entire year. Whilst enthusiastic,
we must admit we were slightly lacking in skill, especially when
compared to members of the Hungarian and Ukrainian teams who could
hula-hoop and hula-hoop and just keep on hula-hooping -- useful in
everyday life, and invaluable in the obstacle course where precious
seconds were deducted for every hoop revolution.

At some point between the ceremony and the sports, whilst playing
cards in the walkway, the UNKs were approached by Ceri Fiddes, the
competition organiser. She wished to know if any of us would be
willing to join her at an interview for BBC Radio Cambridgeshire after
the sports. Natalie, na\"ive excitement in her eyes, leapt at the
chance. Suffice it to say that with questions such as `Is Maths
geeky?' and `Are you a clever-clogs?', the interviewer was clearly no
Mathematician.

\section*{Thursday 12\textsuperscript{th} April}

Thursday's second most important event, was, of course the first
exam. It is tempting to follow the lead of a certain other student
report, and skim over the questions very briefly:

Question 1 was a geometry problem, solved by only one UNK but a large
number of other participants. Natalie surprised herself by actually
finishing a geometry question, something never achieved in practise
papers.

Question 2 concerned the possible number of rows of a table with n
columns, such that the maximum difference between some two
corresponding elements in different rows is exactly one. Every UNK
claimed this question, but all bar Katya had, sadly, made one of a
variety of fatal flaws.

Question 3 contained a fun equation. Not much to say here.

Question 4 was the first of three tricksy problems posed by the
Romanian leader, Dan Schwarz (the others being 6 and 8). Only two
contestants scored any marks on this question.

Katya decided to name the questions after \sout{rabbits} fish:
adorable, fluffy, huggable and sick-making, respectively. This
bijection seems entirely appropriate given that ``f's look just like
huggable dinosaurs!'' according to Lizzy.

So, onto the most important event of Thursday: cake! Yes, today was
Natalie's eighteenth birthday and therefore there was an abundance of
cake. Chocolate cake and cupcakes at lunchtime, and another birthday
cake, of which more later. A chocolate bar with an appropriate UK
Olympics wrapper was a gift from the guides; this was also given not
so appropriately to Elise, the Belgian contestant whose birthday was
on Thursday too.

Lunch was spent discussing all the exciting possibilities open to
Natalie now that she is eighteen, such as getting a mortgage, buying a
lawnmower, marriage -- all suitable things to do in the middle of an
Olympiad.

Our yearly quota of vitamin D was provided by an afternoon spent
playing cards in the sunshine. Here is a brief step-by-step guide to
Egmoid card games:
\begin{enumerate}
\item Work yourself up into a suitable hysterical state;
\item Take great glee in burning cards (games are accompanied by
  general pyromania and other insane tendencies);
\item Keep playing until Natalie loses.  Jake, the college cat, made
  several attempts to sit on the cards, but was successfully
  distracted by an EGMO egg. These UNK mascots were prizes awarded in
  the quiz at the pre-EGMO (Pregmo) camp, and were priceless genuine
  polystyrene. Lizzy's egg made a great sacrifice and was left with
  telltale battle scars after Jake was through with him.
\end{enumerate}

The only other vaguely notable event was an attempt by Ross Atkins,
the semi-bearded Australian staff member, to interview us for the
daily bulletin. As our answers were punctuated with shouts of
`cheat!', he felt, surprisingly, that another team would make better
interviewees, and left to find one.

A while later, after dinner, the UNKs roamed the walkway, likened unto
the 4 Egmoids of the Apocalypse: War, Famine, Pink and Cake. The cake
in question was a large birthday cake, slightly squashed from a
journey on the London Undergound, and innocent passers-by were
accosted and given an impossible choice: Cake? Or death?

When the supply of cake had run dry, a group of British (and an
Australian) convened in the walkway, and talked late into the
night. Or at least until about half past nine, as an early night was
needed before the second exam.

\section*{Friday 13\textsuperscript{th} April}

So, Friday dawned and brought the second exam with it. This time Lizzy
named the questions: paper-waster, badly-worded, annoying and
impossible. She evidently liked the paper.

5 was a number theory question that needed careful handling. Some UNK
marks were picked up here. Question 6, concerning friendships on the
famous social-networking site, Mugbook, prompted the wonderful comment
from Katya, `best friendship is like a directed graph.' Jo agreed that
among the girls in the class she teaches, that is most definitely the
case. Question 7 was more geometry and question 8 was indeed
impossible.

In the afternoon it had been arranged for all of the students to enjoy
the touristy delights of Cambridge. This began with an absolutely
amazing mock courtroom scene in Cambridge's tourist information
centre. The hi-tech animatronic puppets were incredibly lifelike and
the whole experience was fascinating and not in the least bit
patronising.

This was followed by a chauffeured punt trip down the river Cam. With
bright, if cold, weather and supplies of chocolate, this was quite
enjoyable, marred only slightly by our jaded punter. The
contradictions between his stories and those of nearby punters raised
his and our eyebrows on several occasions. The one thing that
impressed him was us responding to `some past students have put
traffic cones on top of King's College Chapel' with `yes, we know one
of them!'

On arriving back at Murray Edwards, we were ushered into a talk by a
woman from HP (the company, not the sauce or fictional wizard). She
was enthusiastic and interesting, explaining algorithms for spotting
patterns in data.

During dinner, James regaled us with stories of encounters with
various dubious characters, while Jo chastised the UNKs for laughing
-- ``You'll only encourage him.'' We were also informed that whilst we
were being pushed along a river, Andrew Carlotti had turned up at
Murray Edwards, clearly having forgotten that he was no longer Andrea,
the UK's emergency reserve.

The evening's entertainment was a high-energy Ceilidh, which left
everyone feeling happy but thoroughly exhausted.

Heart-warming fact of the day: the beautiful flowers left in the
public areas of Murray Edwards College were freshly picked every day
by the gardeners for the benefit of EGMO. These flowers were as good
as or better than any found in a professional arrangement.

\section*{Saturday 14\textsuperscript{th} April}

On Saturday, we woke up at 7.30 to no food. The plan had been a lie-in
followed by brunch, but unfortunately we skipped the first part. No
matter, because today was Ross Atkins's birthday and he had come
prepared for cake! Well, in truth, he had just been that morning to
`some strange supermarket where everything was organic and expensive'
(i.e. M\&S) and bought cake ingredients there, but that was
preparation enough. We headed to our tiny student kitchen, pilfered
some student kitchenware, and got baking. Well, microwaving.

Recipe for Cross Catkins Cake:
\begin{enumerate}
\item Find a suitable vessel or two.
\item Break eggs on (different) convenient surfaces and pour in.
\item Add flour, baking powder, sugar, cocoa powder, milk and oil (to
  bowl as well as worktop).
\item Observe the dollops of mixture on the floor.
\item Add more cocoa powder.
\item Remove bits of eggshell from mixture.
\item Add fingers to taste.
\item Stick in microwave for a while until nicely gooey.
\item Meanwhile, mix milk, sugar and cocoa powder to make icing. The
  consistency should be somewhere between gravy and custard. If you
  are not sure, add more cocoa powder.
\item Ice half the cake (for obvious reasons).
\item Et voila! Now go and feed people.
\end{enumerate}

And feed people was what we did! Once more, (and not for the last
time), we roamed the corridors giving people cake. People were
slightly more suspicious of this cake, which closely resembled
waterlogged soil, but all it took was one taste of the warm,
chocolatey goodness for people to be converted. This was not just any
cake. This was an M\&S cake. (We apologise to all the people who ate
the cake and, after reading the recipe above, are now regretting it.)

Whilst all this was happening, the pink haired one had been out in
Cambridge with the Irish team, and, ignorant of the cooking going on,
returned with another two cakes. These were carefully topped with
melted chocolate and walnuts to create Ross's likeness, and proudly
presented to him after brunch.

Today was also co-ordination day, and in an effort to prevent
contestants working themselves up into a frenzy staring at the live
results, we all headed off on a mathematical tour of
Cambridge. Sally-Anne, the UNK guide (or GUNK), took the UNKs and the
Irish, who were fast becoming the best of friends. One of the most
interesting sights was actually on a slight detour from the prescribed
route, to visit the zoology department and Sean Finnegan, the
magnificent Finback whale skeleton.

And then back to Murray Edwards for more -- you guessed it -- cake! We
seemed to be developing quite an obsession. Lemon drizzle cake this
time, and a considerably less chaotic cooking style. We did, however,
somehow manage to put it in the wrong part of the oven so it failed to
cook. Realising our mistake an hour or so later, we transferred it to
the right part and headed off to a talk.

The talk, by Romanian leader Dan Schwarz, was genuinely fascinating
(as opposed to the \textit{fascinating} courtroom show). He discussed
two Olympiad problems: the infamous windmill problem from IMO 2011 and
another combinatorial question of his own. Watching the windmill
problem being solved, a good few months after first hearing it, was
particularly satisfying.

After this brief interlude, we got back to our main occupation. The
cake was rescued from the oven and the burnt bits removed, before it
too was offered to the masses. Imre Leader, sighting the cake, gave
Ross a `nice person stroke' in a subtle attempt to obtain a
slice. Lizzy suggested the introduction of the EMCSO (the European
Maths, Cake and Singing Olympiad), a competition the UNKs would surely
win, with all the practise they'd been getting.

Saturday ended with craft activities in the dome. The UNKs chose to
use their time wisely and make origami dodecahedrons, items that
turned out to be very difficult to safely transport back home. It was
during this period that we received the happy news that Katya and
Natalie were both EGMO bronze medallists. The Polish team won overall,
beating the Romanians by a hair, and the UNKs managed their objective
of beating a country!

\section*{Sunday 15\textsuperscript{th} April}

We blearily pulled ourselves out of bed early Sunday morning, for this
was the day of the great EGMO expedition to Bletchley
Park. Unfortunately, Jo had to go home to prepare for the start of
school on Monday, and Alison, understandably, felt her time would be
better spent revising for her upcoming exams. The UNKs were just
planning all the things we would get up to without adult supervision,
when James stepped in with a sinister giggle (yes, such a thing does
exist) and volunteered to be our replacement leader. Jo left us
reluctantly with stern warnings not to laugh at James's jokes
(although we were free to laugh at him).This didn't seem like it would
be too hard when, after a cursory `UNK UNK UNK UNK UNK?' to check we
were all present and correct, James strode off and got on a completely
different coach.

For those of you who don't know, Bletchley is not some minor ailment
(as in, `I wouldn't if I were you, I'm feeling a bit Bletchley') but
the former home of British code-breakers. Our tour guide for the
section of the Park focused on the Second World War effort was less
than satisfactory: he knew less about the workings of an Enigma
machine than us, and what is more, was utterly dull. In complete
contrast, the guide to the computer museum also on the site was
enthusiastic and knowledgeable, giving us a whistle-stop tour of
computing from Colossus to the present day.

The weather began to turn nasty, with some UNKs claiming it was even
snowing. For this reason (and because we're lazy), we used the time
after lunch not particularly productively, not even moving from the
spot where we were sitting. Lizzy and Katya spent a good hour simply
doodling.

Back at Murray Edwards, everyone spruced up for the Gala dinner and
closing ceremony. Alison sneakily handed out UKMT thermos flasks to
the other leaders from a box secreted under the table, and the UNKs
presented Sally-Anne with a photo of us as a thank you gift and
memento. The ceremony went smoothly, the only hitch coming at the very
end when the time came for us to hand over the EGMO flag to the
Luxembourgeois, who will be hosting next year. The UNKs came up to the
stage and looked bemusedly around for the flag. It transpired that the
flag was the piece of fabric with the EGMO logo on it, right in front
of our noses.

It was at this point that Ella had to go home, as her parents were
unable to collect her the next day. After a number of team
photographs, we said a fond farewell, and went back to the party,
which continued late into the night. So late, in fact, that the staff
began clearing tables and turning lights on and off as subtle hints
for us to leave. The Irish and the pink haired one took great delight
in sprinkling James's hair with little sequin stars, but eventually
tiredness won out over even such great amusement, and we retired to
bed.

\begin{center}
\includegraphics[width=80mm]{sparkles.jpg}
\end{center}

\section*{Monday 16\textsuperscript{th} April}

The last day.

A mood of gloom hung over Murray Edwards as people began slowly to
depart. This was relieved slightly by the giving of birthday cake to
Sally-Anne (the second lemon drizzle cake made on Saturday). The
remaining UNKs hung on as long as possible, not wanting to leave. We
sat on the floor in the hallway, playing cards and giggling at amusing
web pages until the arrival of parents or train reservations meant we
could stay no longer.

We'd like to take this opportunity to thank everyone involved in EGMO:
the organisers, and particularly Ceri Fiddes for dreaming it up; the
coordinators; the guides, including our GUNK Sally-Anne Bennett;
Alison Zhu and Jo Harbour; and anyone else we've not mentioned. We all
had a wonderful, wonderful week, filled with good cake, good maths,
and lots of laughter. Long live EGMO!



\vskip 20mm

\textit{Written by Natalie Behague, with considerable input from
  Elizabeth Lee and Katya Richards.}

\textit{Disclaimer: All efforts have been made to ensure that this
  EGMO report is completely factual. If reality does not match up to
  what is written here, reality has got it wrong.}

\end{document}
