Sets Problem!
Let be a set with 8 elements. Then the maximal number of 3-element subsets of ; such that the intersection of any two of them is not a 2- element set is
Find
If anyone has a nice solution to this problem, please do post it:)
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1 solution
With a little experimentation, it isn't hard to find eight such sets, for example, ( 1 , 2 , 3 ) , ( 1 , 4 , 5 ) , ( 1 , 6 , 7 ) , ( 3 , 4 , 8 ) , ( 5 , 6 , 8 ) , ( 2 , 7 , 8 ) , ( 3 , 5 , 7 ) , ( 2 , 4 , 6 ) . There cannot be more than eight such sets since no number can appear in more than three. Thus the answer is 6 4 .