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Math Help - 3-fold triples

  1. #1
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    3-fold triples

    A 3-fold truple system is an ordered pair (S,T). S is finite set and T is collection of 3-element sets called triples of S such that every pair of distinct elements of S appears in exactly 3 triples.

    Show that a 3-fold triple system of order n(cardinality of S) exists if and only if n is odd.
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  2. #2
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    I am having trouble coming up with a 3-fold triple system for S=\{1,2,3\}. The only possible triple seems to be S itself, so it is not clear how the pair \{1,2\} may be a subset (is this the meaning of "appears in"?) three different triples. Provided " T is collection" means " T is a set", so that, for example, a multiset T=\{S, S, S\} is not allowed.
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