Although the Mathematical Olympiads are for high school students, the problems that appear on the exams are unusual and challenging enough to provide mathematical exercise for college students and professional mathematicians. One of the advantages of using these problems is that you know up front that the problem has a solution that involves only "elementary" mathematics. Therefore, with some proper direction, the problems can be used in classes in mathematical research and problem solving at the college level. If the goal is research, giving the student an appropriate Olympiad problem would be an excellent starting point and if the point is to solve challenging and doable problems, there are none better than those found in this and similar books. The problems in this book are those appearing in the USA Mathematical Olympiad and International Mathematical Olympiad competitions in the year 2005. The problems are stated in the first section, hints for solution appear in the next section, followed by the formal solutions.
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