Problems for the Mathematics Olympiads: Please donate generously

摘要

About once in three years the Senior Problems Committee of the Australian Mathematical Olympiad Committee (AMOC) turns to our mathematical community with an appeal for problem donations that can be used in national, regional and international senior-secondary-school mathematics competitions. The latest appeal [2] provided examples of competition problems that had been set for various contests in Australia and in the Asia-Pacific region between 2008 and early 2010. The present article is to repeat this exercise with problems from competitions held between 2010 and early 2013. Problems chosen for these competitions are from 'pre-calculus' areas such as geometry (with a strong preference for 'Euclidean' geometry), number theory, algebra and combinatorics.