Inspired by Andrei Golovanov
Probability
Level
4
Given 7 elements, what is the most number of 3 element subsets that we can pick, such that any two subsets have exactly one point in common?
9
5
7
4
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1 solution
[This is not a complete solution]
Many people are likely to think that the answer is 2 9 − 1 = 4 , where the sets share one element in common.
However, we can get 7 sets, by using the 7 points in the Fano plane (projective space), in which every 2 lines intersect at exactly one point.