Wednesday, November 17, 2010
7th Australian Mathematical Olympiad Problems 1986
A1. Given a positive integer n and real k > 0, what is the largest possible value for (x1x2 + x2x3 + x3x4 + ... + xn-1xn), where xi are non-negative real numbers with sum k? A2. What is the smallest tower of 100s that exceeds a tower of 100 threes? In other words, let a1 = 3, a2 = 33, and an+1 = 3an. Similarly, b1 = 100, b2 = 100100 etc. What is the smallest n for which bn >
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