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The idea of mathematical competitions goes back a long way. In the 16th century various mathematicians would challenge each other in cubic equation solving competitions. In this century, certain Eastern European countries, notably Hungary, saw mathematical competitions as a way of encouraging mathematically talented young people. Competitions were organised for different age-groups at the secondary school level. The Hungarian Eotvos competition began in 1894 and has helped Hungary to produce a galaxy of mathematical stars foremost of whom is probably Professor Paul Erdos, one of the world's best known mathematicians.
The idea spread and the first International Mathematics Olympiad was held in 1959 in Romania with seven countries participating. Every year since, an International Mathematics Olympiad has been held in places as far apart as Havana, Canberra and Beijing, with an ever-increasing number of teams participating. Ireland participated for the first time in 1988, when the Olympiad was held in Australia.
Many countries have a structured training programme which tries to identify able students early in secondary school and nurture them over the years. In Ireland, a training programme operates for specially chosen pupils in their final two years of secondary school. Able students are brought together on Saturday mornings or weekday evenings in various centres around the country, including the University of Limerick. These sessions tend to concentrate on geometry and number theory, topics which are not covered extensively in the Leaving Certificate Mathematics course.
Also important is the teaching of techniques for problem solving applicable to any problem. Around May of each year these boys and girls attempt the Irish Mathematics Olympiad, from the results of which a team of six is chosen to represent Ireland in the year's International Mathematics Olympiad. Competition for places is very high with Dublin schools usually providing most of the team. Last year Michael Sharpe from CBS, Roscrea became the second pupil from that school to make the Irish team.
At the International Mathematics Olympiad, the contestants sit two papers, each with three questions, on two consecutive days. The remainder of the time is taken up with sight-seeing trips and other social activities organised by the host nation. On the final day, gold, silver and bronze medals are awarded to the top half of the contestants. Ireland's sole medal to date was won by Andrew McMurray (The High School, Dublin) in 1990 in Beijing, although several others have come tantalisingly close. Only a handful of the competitors are able to solve all the problems. In recent years one the stars has been the Russian girl Eugenia Malinnikova, who first took part at the age of 14 and won gold medals in three consecutive Olympiads, losing only one mark in the process.
Here is a problem from the 2nd IMO for you to have a go at:
Determine all three digit numbers N having the property that N is divisible by 11, and N/11 is equal to the sum of the squares of the digits of N.Now a problem from this year's Olympiad in Moscow-
Find all integers a, b, c with 1<a<b<c such that (a-1)(b-1)(c-1) is a divisor of abc-1.
Gordon Lessells is a lecturer in Applied Mathematics at UL. He describes himself as being fanatical about bridge and an inveterate crossword puzzle solver.