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2001 AMC 10 · #20Angles & Polygons

A regular octagon is formed by cutting an isosceles right triangle from each of the corners of a square with sides of length 20002000 . What is the length of each side of the octagon?

2000 AMC 10 · #20Algebraic Manipulation

Let AA , MM , and CC be nonnegative integers such that A+M+C=10A+M+C=10 . What is the maximum value of A⋅M⋅C+A⋅M+M⋅C+C⋅AA\cdot M\cdot C+A\cdot M+M\cdot C+C\cdot A ?

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