IMO Shortlist 1979 problem 12


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2. travnja 2012.
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Let R be a set of exactly 6 elements. A set F of subsets of R is called an S-family over R if and only if it satisfies the following three conditions:
(i) For no two sets X, Y in F is X \subseteq Y ;

(ii) For any three sets X, Y,Z in F, X \cup Y \cup Z \neq R,

(iii) \bigcup_{X \in F} X = R
Izvor: Međunarodna matematička olimpijada, shortlist 1979