Let F be a function from the interval [0,1] to itself
having the following 3 properties:

F is increasing, i.e., x <= y implies that F(x) <= F(y)
F(x/3) = F(x)/2
F(x) + F(1 - x) = 1

Find the following values:
F(1/13)
F(Sqrt[1/2])
 

(thanks to Ajit Thyagarajan <ajit@brookmoor.com>
for introducing this puzzle to me.   PDA )