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 )