Stars make Madrid Olympiad count

By Burkard Polster and Marty Ross

The Age, 6 October 2008

Have you heard about IMO, the International Mathematical Olympiad? Just as in the “real” Olympics there are many different events. For example, there is the 100 Count. We all know how to count from 1 to 100, but here the aim is to get to 100 the fastest. Then there is the 200 Count, the 400 Count, the 800 Count and the Marathon Count. And then there’s Counting Backwards events, Counting in Twos, and the Counting Relay Race.

Of course, we jest. No mathematician would spend time training on something as mindless as counting from 1 to 100. In fact, the IMO is a yearly event in which secondary students from around the world compete against each other in the solving of very difficult maths problems.

Each country’s team consists of up to six students and their coaches. The competition is over two days, the students having 4.5 hours per day to solve three problems. The best problem solvers are awarded gold, silver and bronze medals.

This year’s IMO was held in Madrid. Similar to the just completed Beijing Olympics, the Chinese team dominated with Russia coming second, and the USA third.

Unlike in Beijing, Australia’s 19th placed them ahead of Great Britain in 23rd place. Clearly Kate Ellis, the Federal Minister for Sport, should have been betting on Australia’s math wizkids instead of our athletes. And in future Australia can strive to be first. Calls for increased funding for maths, anyone?

To give you a flavor of the IMO, here is a problem (one of the easier ones) from a previous year. Feel free to use your calculator:

Twenty-one girls and twenty-one boys took part in a mathematical contest. It turned out that each contestant solved at most six problems. And, for each pair of a girl and a boy, there was at least one problem that was solved by both of them. Show that one of the problems was solved by at least three girls and at least three boys.

We’ll give you all the time you wish to solve this problem. You can send us a solution to check. And as always, if you want help, just email your QuizMathsMasters.

By the way, the Michael Phelps of the Mathematical Olympiad is the Australian Terry Tao, who we wrote about recently. Terry won a bronze medal when he was 11 years old, a silver medal when he was 12 and a gold medal when he was 13. Terry was then ineligible, as he had started attending university. Now at the age of 31 Terry is one of the recipients of the Fields Medal, the “Nobel Prize for Mathematics”. In our eyes Terry’s achievements eclipse anything that Michael Phelps has done, or ever could do.