### Mathematical Olympiad Challenges - comments

*By Johannes Tang Lek Huo*

This is quite good, but not comprehensive. Despite the title, the book has drawn problems from various sources, including the Putnam exam.

The book covers some topics not usually found elsewhere 2.2 Look at the Endpoints (discusses the role convexity and linearity play in solving maxima and minima problems), 1.8 Tetrahedra Inscribed in Parallelepipeds (solid geometry is less popular than plane geometry in IMO, but you may get something out of this), 2.7 The Abel Summation Formula, The Mean Value Theorem, 3.3 Repunits, 3.6 Equations with Unknowns as Exponents (this is good, as many other authors assume that every Olympian knows this, well this may not be true!).

You may use this as a supplement to Arthur Engel's Problem Solving Strategies. This book was written by two Americans of Romanian descent, so the book has a rich blend of American and Romanian problems, and many problems were composed by the authors themselves.

But at times I notice that the authors had been bogged down by unnecessary details, as can be seen in 2.5/Problem 1. Just add the three equations and if we know that log can't be negative, we are done. And one more thing about Olympiad books: many adopt the 'skip it' approach, namely, they don't usually include the Problem 3's and Problem 6's of the IMO. They should actually help the reader to solve easier as well as harder problems.

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© John Scholes

jscholes@kalva.demon.co.uk

2 Mar 2003

Last updated/corrected 2 Mar 2003