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Summary: Some of the best problems ever created
Review: Problems that are used in the mathematical Olympiads are a very select set. They must of course be challenging, but not too challenging. Since they are to be taken by high school students, most areas of mathematics are off-limits, severely restricting the range of solution techniques. Subtleties can be used in the problem, but only to a well-established point. I enjoy reading them, because these restrictions make the writing of such problems an art form.
This collection contains the six problems used in the 2001 United States of America Mathematical Olympiad (USAMO), the nine problems used in the 2001 International Mathematical Olympiad (IMO) American team selection test and the six problems used in the 2001 IMO. It is designed as study material for those preparing for possible competition in future Olympiads.
The problems themselves take up only the first seven pages of the book. Hints to the solutions take up the next four pages and formal solutions the remaining eighty-eight pages. Problem credits, a glossary of key theorems and previous Olympiad results complete the book. Reading these problems is an exercise that all mathematicians should engage in. They are some of the best ever written, sometimes knowing that the solutions require only "simple" mathematics makes them all the more difficult to find. I often think of potential solution strategies, only to reject them as using techniques officially out of bounds. I encourage everyone to take a look at these problems.Published in the recreational mathematics e-mail newsletter, reprinted with permission.
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