1991 OIM Problems/Problem 3

Problem

Let $f$ be an increasing function defined for every real number $x$ , $0 \le x \le 1$ , such that:

a. $f(0) = 0$

b. $f(x/3) = f(x)/2$

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

Find $f(18/1991)$

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.