OIM 1991 Problem 3

Let $f: \ [0,\ 1] \rightarrow \mathbb{R}$ be an increasing function satisfying the following conditions:

a) $f(0)=0$ ;

b) $f\left(\frac{x}{3}\right)=\frac{f(x)}{2}$ ;

c) $f(1-x)=1-f(x)$ .

Determine $f\left(\frac{18}{1991}\right)$ .