Gavan Reilly

thinking out loud

Tokyo, Part 1

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Due to unforseen circumstances I’m going to be offline and away from the world for the next few days… to keep up the pretence of daily blogging, a glorious re-run from an earlier post on Every Day is Election Day on my time as an international mathlete. Normal service will resume soon – thanks for reading.


Not so long ago, Alexia wrote a post about the places she’d most like to go to on holiday, and one of the places she listed was Electric Town in Japan. It didn’t take long to get me thinking that the fact I’ve been to Japan – and indeed to Electric Town – must be something worth blogging about. It being the Olympic time of year, too, it seems appropriate that I share some memories of a different type of Olympics.

Now, I’m not a physically big guy. I don’t have a huge amount of strength, or physical stamina, and aside from once having spun a yo-yo 5,500 times in succession on a bored Sunday, I do not have much physical skill to speak of.

But, believe it or not, I’ve been an Olympian in my time; not trading on the strength of my body or the agility of my muscles, but of calculating radians and solving for x.

I am an Olympian of a different kind, and this is my story.


My Olympic story, unorthadox as it is, begins in an even stranger place: my 5th Year English Class. It was a rainy November morning in 2002, and 31 young men were stooped in intense concentration, in a classroom to the rear of St Finian’s College in Mullingar, trying to figure out just how Macbeth was to be defeated should he be fallible only to ‘none of woman born’.

Our readings were interrupted by the familiar sound of heavy breathing over the intercom: it was the school principal, with the morning announcements, which were their usual nondescript selves. Under-17’s soccer training has been moved to Thursday afternoon instead of Wednesday, and the like. It wasn’t until the very end of the announcements that anything was unusual.

“Can Paul Riordan and Gavan Reilly come to the office, please? Thank you.”

An audible gasp arises in the rom. Uh-oh. You don’t get called to the office for behaving well, and everyone knows it. Silent but for our pounding hearts, Paul and I get up from our seats and leave the room. En route I ask him, “Any idea what this could be about?”
“I don’t know, did you get any results rechecked?”
“Oh, that’s it.” I had gotten 2 B’s in my Junior Cert results two months earlier and had sought second appraisals for each. How very wrong I was.

“Gentlemen,” said Fr Connell, as we arrived at his door in a collective cold, unsuspecting sweat. “I have news.” He handed us an A4 envelope each, and simply said, “Congratulations.” Together we smiled. We must have gotten a few upgrades. We opened the envelopes in the office, as was custom for exam results. What we received inside, though, surprised us. The letters didn’t contain the logo of the State Examinations Commission, or a harp anywhere. Instead, the letters were emblazened with the logo of NUI Maynooth. “These aren’t exam results,” Paul remarked, as if acting to shatter any remaining illusion.

“Certainly aren’t,” interrupted Fr Connell. “Congratulations, gentlemen, you’ve been invited to participate in the Irish Mathematical Olympiad.”

The what in the what now? We hadn’t time to ask for further questions, as we were ushered back to class – Finian’s protocol indicated that once your reason for classroom absence had been fulfilled, anything less than immediate apparition back at your desk resulted in a stern talking-to. Thankfully, the morning announcements were always made in the last few minutes of class preceding the 11am break, so there wasn’t long to wait to get to full grips with the content of this mysterious A4 missive. As I stood at my desk in the study hall a few minutes later, changing books at breaktime, I got to have a full look at the letter – however discrete, given the obvious pitfalls of being The Smart One in an all-boys boarding school.

It read that on the basis of my Junior Cert result in Maths, Paul and I – along with 298 other invitees, and 200 returning participants – had been invited to attend fortnightly maths lectures at any one of five training centres, beginning in January. The lectures would culminate in a national exam for the attendees – the Irish Mathematical Olympiad – taking place consecutively across the five venues, and with the top six results qualifying for the national team to take place in a parallel international competition. After consultation with my parents – who were as bemused as I about the notion of there being anything competitive about maths – I elected to go to the lectures in NUI Maynooth (the other venues being UCD, UL, UCC and NUI Galway) as it was only 20 minutes from home, and hence particularly conducive to ensuring the attendance of a just-turned-16-year-old at 9.30am on Saturday mornings in January.


We were pleasantly surprised. It was 11.10am; break time, and although the lecture theatre – Callan Hall, on the south campus – had been deathly cold, the morning had been much more palatable than we had anticipated. After some warm-up problems of the vintage seven-litre-and-three-litre-jugs variety, we’d moved onto some chessboard problems that, as we would learn, form a staple foodgroup of the mathematical diet.

An example: take a chessboard, 8×8, and take off squares from two opposite corners, so that there are 62 squares remaining. Is it possible to lay dominos across the board, each domino covering two squares, so that the entire board is covered?

The answer is a definitive no. Picture a chessboard in your head, and remove the squares from two opposite corners. These squares will always be the same colour, and so – let’s say the squares you remove are black – your board will have 32 white squares and 30 black ones remaining. Laying a domino on a chessboard will mean it covers one black square and one white, and because the number of white squares remaining exceeds the number of black ones, having laid 30 dominoes the board will be left with two exposed white pieces, which cannot lie beside each other, and hence the board cannot be covered.


Heartened by what we understood of the first day’s classes, Paul and I continued to return each fortnight, as the attendance slowly diminished around us. From the first day where about 120 people from the midlands and north-east had attended, the group slowly diminished to under 100. While the hassles of early Saturday transport may well have played a role in the dropout rate, what was more likely to see them staying at home was the frightening pace at which the material being covered became more difficult. The first week, it seemed, had been coercive in its ease: by the third week we’d gotten to the theorems of Fermat and beyond; by the fifth we were dealing with advanced combinatorics.

Around March, the exact nature of what we were dealing with was finally revealed to us. The Olympiad competitions, it was explained to us, were only open to pre-University students, and the syllabus up for examination, therefore, was an amalgamation of the second-level maths syllabi of each participating country. This it seemed, unintentionally favoured particular countries: Ireland, with its 40-minutes-a-day, often only four-days-a-week maths teaching, can only ever hope to cover a certain amount of material. China, on the other hand, teaches its teenagers for six-and-a-half days a week, and hence can cover much more. The end result was that while we learned rudimentary probability and basic integration on weekdays, our Saturdays slowly became consumed with advanced inequalities, game theory and optimisation. We were also made subtly aware of an analagous fact: because there was so much material to cover, and because pre-University students who competed in the national Olympiad were invited back the following year, it usually took two years’ worth of attendance to stand a real chance of making the international event, so that while the 2003 event in Tokyo would be out of reach, if one had the resiliance to make it through two years’ training. And all the while, the crowd grew thinner and thinner, ultimately leaving us in a room of twenty on the top floor of Logic House on the old campus of St Patrick’s College in Maynooth.

Ultimately it came to May, and the Irish Mathematical Olympiad. In the end 22 people – myself and Paul among them, though we’d probably both admit to being more interested in the company than the teachings – sat the papers in Maynooth; we heard rumours on the day that only UCD had mustered more entrants, and that only nine had stayed the pace in Galway. The papers, we had earlier been told, would take most of the day, and so it proved: the Irish Mathematical Olympiad, or IrMO as it was usually known, was spread over two papers. Each paper was three hours in length, and contained five problems. We had also, somewhere in between, been broken to the harsh truth of the difficulty: on average, participants scoring 30% would stand a great chance of making the national team, and anyone managing 40% was effectively guaranteed of securing international competition.

As we finished the day, jaded after the intensity of a days’ work that definitely outranked the Leaving Cert in difficulty, I didn’t want to engage in much of a post-mortem afterwards. Truth be told, I remember very little about the day’s problems, other than the fact that the four months’ extra tuition had proved quite fruitless, in that ultimately I had used none of the new techniques I had armed myself with in attacking the questions before me, and had resorted to rudimentary Junior Cert techniques with the occasional advance in mental logic in breaking down the decade of tests. While I felt a couple of questions had been brought to a fair conclusion, surely my inability to apply what I had been taught would put pay to any hopes of a big finish.


“Thank God it’s over,” I thought, as we left the church. It was a Friday night a few weeks later and the children’s choir that my mother had now run for three years was finishing up in advance of the end of the school year. As the most ably equipped next-of-kin, having studied piano for twelve years by then, I had no choice but to act as the keyboardist/organist for the choir – a joyless job that I quickly took to hating, What teenager, having spent a week at boarding school, would want to kick off his weekend spending 90 minutes with shrieking children playing music he quite despised? The summer break could never come quickly enough.

As we set foot inside the door at home – myself still lugging bags brought home from school, having not had a chance to get home for a brief respite first – Dad seemed to be smirking. “You’ve just missed a call.”


“Yeah. Do you know anyone called Gordon?” I didn’t. “He’s just after calling now, you just missed him, he said he’d ring back, but he said that he was from the college, in Limerick, and that he was organising the maths thing, the Olympiad, and he said that he’d marked your paper, and that you did very well,” – and at this point he could contain the smirk no longer – “you made the team to Tokyo.”

The only reaction I can remember having is dropping the coat I was carrying to the floor, and saying, “Fucking hell!”, as Mum yelped, and then yelped again.

After Gordon – Lessells, who worked in the Maths faculty at the University of Limerick – had called back and I’d confirmed that yes, I’d quite like a trip to Tokyo, thanks very much, we made the usual phone calls: both sets of grandparents, Fr Connell, and so on.

The next time we heard Fr Connell’s breathing over the intercom preceding the daily announcements, we were again in English class, and my only recollection of the announcement is that another classmate – now a senior inter-county footballer – thought the notion of pride in someone qualifying for an international competition in maths so ludicrous that he guffawed loudly, and couldn’t stop himself until long after whatever congratulatory message my Principal was making was long finished.


Having sinced read Angela’s Ashes, I know that the rain we had in Limerick that June is not atypical Shannonside. At the time, though, I feared the apocalypse.

The University of Limerick had invited the six qualifiers – I, of course, had come sixth – to the International Mathematical Olympiad to a week’s training on-campus, aimed at giving us the further leg-up we would need to stand any real chance of competing. Some of the other promising entrants, who had scored well in the IrMO and would stand a chance of making the following year’s international team, were also invited for the first two days’ classes. Again as it turned out, they needn’t have bothered, as the material explained went far over my head. While the first two days’ tuition was bearable, in that I could hide somewhat anonymously amongst a larger group, the latter days came close to breaking me altogether.

I nearly quit in Limerick. I remember getting a call from home, who were still all delighted at their teenage son getting to represent his country, and nearly cracking into tears. My distinct words were, “I don’t think I’ll do it again next year.” I felt scared at being caught out; of revealing that I’d bluffed my way through the IrMO and that while I was taking extensive notes in the classes, I wasn’t understanding any of it. My five fellow contestants, all male, thought I was merely playing up my youth by cheekily admitting I’d cleared the IrMO by only using Junior Cert material. It seemed nobody seemed prepared to accept that I may not have deserved my spot. Diarmuid, who had made the team to the 2002 IMO in Glasgow, reassured me that if I’d finished sixth in the IrMO then I deserved my spot, because IrMO could not be bluffed through. Hugh, a rookie whose father happened to be the team organiser for the year (and who, it would later transpire, had just completed a perfect Leaving Cert of nine 9 A1’s), assured me that having managed the IrMO with Junior Cert maths was a sign of tremendous potential and of great natural ability to tackle problems without needing further education in how to do so.

I was still unconvinced. While I enjoyed the comfort of hanging out with five lads, all of similar intellect and age to myself, it was the times where – on their own initiative – they would huddle down over past IMO problems that made me feel most inadequate. It wasn’t that I didn’t want to learn more and do well; I just couldn’t understand the material. There seemed to have been a mystery time, within which I was apparently visiting cryogenia, in which the other five had been taught things like the identity of ‘pfi’ and other such numbers you could otherwise only encounter when getting change for a 100 Drachma note.

Though I was edgy about my mathematical pedigree, I couldn’t stay down for every long. There was, after all, a free nine-day trip to Tokyo coming soon.


Part two will be posted here tomorrow.

Written by Gav

January 27th, 2009 at 12:00 pm

2 Responses to 'Tokyo, Part 1'

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  1. […] following is the final part of my Tokyo diaries – read parts 1 and […]

  2. I always kind of regret not going back and giving it another chot in 2003.

    You never know, we could have met each other a few years earlier….


    3 Feb 09 at 5:12 pm

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