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The Mandelbrot Problem Book
This elegant volume contains all individual and team tests that were given during the years 1995 through 2002. Full solutions accompany every test, with additional answer keys provided for quick checks, all laid out in a handsomely designed format.
Individual Test questions are excellent training for the AMC and AIME contests, and the Team Test questions are excellent training for students first learning how to tackle challenging proof problems. This author is a past US International Math Olympiad team member.