# Maximal Value of $$n$$

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Let $$A= \left \{a_1, \dots , a_n \right \}$$ and $$S(A)$$ be a set of some subsets $$D \subset A$$ such that

• each subset $$D \in S(A)$$ contains at most $$n-1$$ elements
• each element of $$A$$ belongs to exactly $$4$$ distinct subsets
• any unordered pair of distinct elements $$a_i, a_j \in A$$ belongs to exactly one subset $$D$$.

Determine the maximal possible value of $$n$$.

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