HMMT November 2010 U27

Let $f(x)=-x^{2}+10 x-20$ . Find the sum of all $2^{2010}$ solutions to $\underbrace{f(f(\ldots(x) \ldots))}_{2010 f \mathrm{~s}}=2$ .

Dataset text NuminaMath olympiads. Quoted with source.

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5 \cdot 2^{2010}

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