Set $X$ has $56$ elements. Determine the least positive integer $n$ such that for any 15 subsets of $X$, if the union of any $7$ of the subsets has at least $n$ elements, then 3 of the subsets have nonempty intersection.
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Tags: combinatorics unsolved, combinatorics
Set $X$ has $56$ elements. Determine the least positive integer $n$ such that for any 15 subsets of $X$, if the union of any $7$ of the subsets has at least $n$ elements, then 3 of the subsets have nonempty intersection.