# Figure-It-Out Function! - Part 1: For 4 years

Algebra Level 5

A function $$f:\mathbb{Z}\rightarrow\mathbb{Z}$$, has the following conditions

• $$f(n)=\frac{f(n-1)+2f(\frac{n}{2})}{2}$$, if $$n$$ is even

• $$f(n)=\frac{f(n)+2f(\frac{n-1}{2})}{2}$$, if $$n$$ is odd

If $$f(1)=2$$, find $$\frac{f(2011)f(2012)f(2013)f(2014)}{f(3)f(4)f(10)f(12)f(18)f(52)f(60)f(502)}$$

This problem is part of the Figure-It-Out Function! series

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