IMO Shortlist 1994 problem C2

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Dodao/la: arhiva
2. travnja 2012.
In a certain city, age is reckoned in terms of real numbers rather than integers. Every two citizens x and x' either know each other or do not know each other. Moreover, if they do not, then there exists a chain of citizens x = x_0, x_1, \ldots, x_n = x' for some integer n \geq 2 such that x_{i-1} and x_i know each other. In a census, all male citizens declare their ages, and there is at least one male citizen. Each female citizen provides only the information that her age is the average of the ages of all the citizens she knows. Prove that this is enough to determine uniquely the ages of all the female citizens.
Izvor: Međunarodna matematička olimpijada, shortlist 1994