Ireland wins two medals at International Mathematical Olympiad in Rio

By Oscar Michel, Masters in Journalism, DCU

Anna Mustata (5th year at Bishopstown Community School, Cork) and Cillian Doherty (6th year at Coláiste Eoin, Booterstown) have won Bwonze Medals at the international Mathematical Olympiad (IMO) in Rio de Janeiro.

The International Mathematical Olympiad (IMO) is the World Championship Mathematics Competition for High School students and is held annually in a different country. The first IMO was held in 1959 in Romania, with 7 countries participating. It has gradually expanded to over 112 countries from 5 continents this year.

Ireland joined the competition in 1988 and won a medal for the first time since is entrance.  Ireland’s team score was also the highest score ever achieved by an Irish team in the competition.

The Irish team will arrive at Dublin Airport this afternoon (Monday, 24 July).

Ireland’s four other team members received Honourable Mentions. They are: Antonia Huang (Mount Anville Secondary School, Dublin); Mark Heavey (Blackrock College, Dublin); Mark Fortune (CBS Thurles Secondary School, Tipperary); and Darragh Glynn (St Paul’s College, Raheny, Dublin).

The Irish team was led by two scientists. Dr. Mark Flanagan, an Associate Professor at the School of Electrical & Electronic Engineering at UCD and a researcher with CONNECT, the Science Foundation Ireland Research Centre for Future Networks. Anca Mustata, a lecturer in the School of Mathematical Sciences in UCC, was Deputy Leader.

Example of the problems past during the competition:

Problem 2. Let R be the set of real numbers. Determine all functions f : R ? R such that, for all real numbers x and y,
f (f(x)f(y)) + f(x + y) = f(xy).

Problem 3. A hunter and an invisible rabbit play a game in the Euclidean plane. The rabbit’s starting point, A0, and the hunter’s starting point, B0, are the same. After n?1 rounds of the game, the rabbit is at point An?1 and the hunter is at point Bn?1. In the n th round of the game, three
things occur in order.
(i) The rabbit moves invisibly to a point An such that the distance between An?1 and An is exactly 1.
(ii) A tracking device reports a point Pn to the hunter. The only guarantee provided by the tracking device to the hunter is that the distance between Pn and An is at most 1.
(iii) The hunter moves visibly to a point Bn such that the distance between Bn?1 and Bn is exactly 1.
Is it always possible, no matter how the rabbit moves, and no matter what points are reported by the tracking device, for the hunter to choose her moves so that after 109 rounds she can ensure that the distance between her and the rabbit is at most 100?

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