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Question: Question from another pocket

Question:Question from another pocket

Markiyan Hirnyk 7799
logic set
January 19 2013
0

We have 12 sets S[1], S[2], ..., S[12] and the listlist LL:=[[2, 4, 5, 8, 10], [1, 3, 6, 7, 11], [2, 5, 6, 9, 10],
 [1, 5, 6, 9, 11], [1, 3, 4, 7, 12], [2, 3, 4, 8, 12], [2, 5, 10, 11, 12], [1, 6, 10, 11, 12], [3, 4, 10, 11, 12], [1, 3, 7, 8, 9], [2, 4, 7, 8, 9], [5, 6, 7, 8, 9]] which means that the set S[1] does not intersect with the sets
S[2], S[4], S[5], S[8], and S[10] (PS. but S[1] intersects with S[1], S[3], S[6], S[7], S[9], S[11], S[12]) and so on. What is the maximal number of nonoverlapping sets
from S[1],...,S[12]? Such problems appear in logic
(for example, see http://www.maplesoft.com/applications/view.aspx?SID=3509).
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