It's an event so tough that if you are a winner, you may well prove to be a serious contender at world level: welcome to Australia's longest-running and toughest test of young mathematical minds, the UNSW School Mathematics Competition.
Indeed, with the annual competition marking its 50th anniversary at a prize-giving ceremony tomorrow (Friday 16 September), three of the students in last year's competition went on to win medals for Australia at the recent Mathematical Olympiad, held in Amsterdam.
They are among tens of thousands of junior and senior secondary school students from NSW and the ACT who have sat the demanding three-hour exam since its inception in 1962. At its peak, some 1,200 students pitted their wits against the examiners each year: although less popular today, the competition still attracted almost 600 of our brightest and best entrants this year despite – or perhaps because of - its toughness.
"The purpose of the Competition is to test mathematical insight and ingenuity rather than ability in routine mathematical applications," says the competition's director, Associate Professor Bruce Henry, of the UNSW School of Mathematics and Statistics. "The problems are very difficult. They are not multiple choice and full proofs are required. Most of the problems are essentially original but we put in some classics too.
"Typically, about 85% of students receive less than half the possible total marks, and most of these students would be in the top 1% for maths in their year."
In this year's junior division (to Year 10) for example, none of the 332 entrants scored the maximum possible 30 marks and a quarter of them got no better than four marks.
"At a time when our average performance at Year 9 is lagging internationally, it is crucial to cater for the extremely able mathematical minds who will become the driving force behind Australia’s increasingly technological future," says Professor Tony Dooley, Head of the UNSW School of Mathematics and Statistics.
"The standard of questions has remained challenging throughout the competition's 50-year history, and I am happy to be able to report that the standard of the winning answers is as high as ever."
Cash prizes of up to $250 are awarded for place-getters, Distinction and High Distinction passes, along with certificates for Credit passes and participation.
Top of the 2011 Senior Division were: Equal First - Edmond Cheng ( Newington College) Declan Gorey (Sydney Boys High); Equal Second - Timothy Large (Sydney Grammar) and Jinghang Luo (James Ruse High); Equal Third - Nancy Fu and Allan Zhang (both James Ruse High)
Declan Gorey and Timothy Large won silver medals at the International Math Olympiad in Amsterdam this year and Nancy Fu won a bronze.
Top of the 2011 Junior Division were: First - Seyoon Ragavan (Knox Grammar School); Second - James Chen (Sydney Boys High School); Third - William Wang (Sydney Grammar School).
Tony Dooley - firstname.lastname@example.org
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Example question from the 2011 competition, Junior Division:
You flip one hundred coins on a table top with your eyes blindfolded and you are reliably informed that thirteen landed heads up and the remainder landed heads down. Supposing you remain blindfolded, how can you sort the coins into two groups so that there is the same number showing heads up in each group? You may turn the coins over but you must not discard coins.
Select thirteen coins at random and move (slide) them into a separate group. There will then be n, less than or equal to thirteen, coins heads up and thirteen minus n heads down in the separated group, and there will be thirteen minus n coins heads up in the remaining group.
Now turn all coins over in the separated group to have thirteen minus n heads up.