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Richard Rusczyk (/ ˈ r ʌ s ɪ k /; Polish: [ˈrustʂɨk]; born September 21, 1971) is the founder and chief executive officer of Art of Problem Solving Inc. (as well as the website, which serves as a mathematics forum and place to hold online classes) and a co-author of the Art of Problem Solving textbooks.
The American Invitational Mathematics Examination (AIME) is a selective and prestigious 15-question 3-hour test given since 1983 to those who rank in the top 5% on the AMC 12 high school mathematics examination (formerly known as the AHSME), and starting in 2010, those who rank in the top 2.5% on the AMC 10. Two different versions of the test ...
The AMC 8 is a 25 multiple-choice question, 40-minute competition designed for middle schoolers. [4] No problems require the use of a calculator, and their use has been banned since 2008. Since 2022, the competition has been held in January. The AMC 8 is a standalone competition; students cannot qualify for the AIME via their AMC 8 score alone.
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For years, the idea of extending the training program for the U.S. IMO team was discussed. During the 2004–2005 school year, U.S. IMO team coach Zuming Feng directed the Winter Olympiad Training Program, utilizing the Art of Problem Solving (AoPS) site for discussion purposes. The program was short-lived, lasting only that year.
The outer coin makes two rotations rolling once around the inner coin. The path of a single point on the edge of the moving coin is a cardioid.. The coin rotation paradox is the counter-intuitive math problem that, when one coin is rolled around the rim of another coin of equal size, the moving coin completes not one but two full rotations after going all the way around the stationary coin ...
Replace some a i by a variable x in the formulas, and obtain an equation for which a i is a solution. Using Vieta's formulas, show that this implies the existence of a smaller solution, hence a contradiction. Example. Problem #6 at IMO 1988: Let a and b be positive integers such that ab + 1 divides a 2 + b 2. Prove that a 2 + b 2 / ab + 1 ...
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