# Flooded Floors

Algebra Level 4

$\displaystyle f(x) = \sum_{i=1}^\infty \bigg\lfloor \frac{x + 2^{i-1} } { 2^i } \bigg\rfloor$

A function $$\displaystyle f : \mathbb{R} \to \mathbb{Z}$$ is defined as above. Evaluate: $$\displaystyle f(20.14)$$.

Details and Assumptions:

• $$\displaystyle \lfloor x \rfloor$$ denotes the greatest integer less than or equal to $$x$$.

• It is $$20.14$$ and not $$2014$$.

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