Let F(x) be a non-decreasing function for all x in [0 1], such that

2F(x/3)=F(x) and F(x)+F(1-x)=1

1. Find F(173/1993) and F(1/13).

2. If possible give a general algorithm to find F(x) for any x.

Other questions:

3. Is F(x) uniquely determined(in [0,1])?

4. Is F(x) continuous(in [0,1])?

Source: unknown