Problem #2






Let F be a function from the interval [0,1] to itself having the following properties
  1. F is increasing, i.e. x ≤ y implies that F(x) ≤ F(y).
  2. F(x/3) = F(x)/2.
  3. F(x) + F(1 - x) = 1.
Find the following values:

Source: Nordic Mathematical Contest



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