IMO Shortlist 1974 problem 8


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2. travnja 2012.
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The variables a,b,c,d, traverse, independently from each other, the set of positive real values. What are the values which the expression S= \frac{a}{a+b+d} + \frac{b}{a+b+c} + \frac{c}{b+c+d} + \frac{d}{a+c+d} takes?
Izvor: Međunarodna matematička olimpijada, shortlist 1974