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Among his \(2018\) guests, Keith chooses a random subset of people to attend his super secret mathematics-themed party. Let \(X\) be the number of people Keith chooses. Also, let ...

Two players \(A\) and \(B\) play the following game:

\(A\) divides an \(n \times n\) square into strips of unit width (and various integer lengths). After that, player \(B\) picks ...

Suppose that \[ x + \frac{1}{x} = \frac{1 + \sqrt{5}}{2}. \] Compute \(x^{2000} + x^{-2000}\).

Let \(0 \leq x_k \leq 1\) for all \(k = 1, 2, ..., 2018\). Maximize \[ f(x_1, x_2, ..., x_{2018}) = x_1 + x_2 + ... + x_{2018} - x_1x_2...x_{2018}. \]

Define the function \[ f(x) = \prod_{n= 1}^\infty \cos \frac{x}{2^n}. \] Compute \(f(1)\).

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