USA and International Mathematical Olympiads 2003.

USA and International Mathematical Olympiads 2003 Titu Andreescu and Zuming Feng Published by The Mathematical Association of America xvi+85 pages, soft cover ISBN 0-88385-817-7

This book contains the problems in the USA Mathematical Olympiad, the USA Team Selection Test and the International Mathematical Olympiad (IMO) from the year 2003. There are 18 problems, six from each, divided into two 4 hour papers. There are one or two line hints for each problem in a 'Hints' section and then one, or more, detailed solutions for each problem in the 'Solutions' section. There is a short glossary of useful definitions, theorems and identities.

The creators of the problems often involve the number of the current year in an imaginative way. For example, here is problem 6 from the 2003 USA Olympiad, from page 2 of the book:
At the vertices of a regular hexagon are
written six non-negative integers whose sum
is 2003. Bert is allowed to make moves of the
following form: he may pick a vertex and
replace the number written there by the
absolute value of the difference between the
numbers written at the two neighbouring
vertices. Prove that Bert can make a
sequence of moves, after which the number 0
appears at all six vertices.

The book closes with a summary of the performance of the US team over the last few years. An interesting table in this section gives a ranking of high-performing IMO teams, ranked in terms of the total scores obtained out of a maximum of 1260. In this table, China leads with 1048 points, followed by Russia (964), Bulgaria (918), USA (889), Korea (841), Vietnam (823), Romania (741), Taiwan (733), Belarus (713), Iran (680) ... with Australia (544) ranked 20th. As the editors remark, 'The competition is getting tougher and tougher. A top ten finish is no longer a given for the traditional powerhouses.'

These problems are useful for exceptionally keen mathematics students in Years 9 through 11. Similar collections for the Australian Mathematics Olympiads, for example Lausch and Taylor (1997), can be obtained from the Australian Mathematics Trust.

Deborah J. Street

Reference

Lausch, H. & Taylor, P. J. (1997). Australian Mathematical Olympiads. Belconnen: Australian Mathematics Trust.
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