Aaron, Brian, Calvin, Daniel and Peter are going to divide \(n\) coins among themselves knowing that:
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Everyone receives at least one coin.

Aaron gets fewer coins than Brian, who gets fewer coins than Calvin, who gets fewer than Daniel, who gets fewer than Peter.

Each person knows only the total \(n\) and how many coins he got.

What is the smallest possible value of \(n\) such that there exists at least one possible configurational distribution of the coins such that nobody can deduce the number of coins received by each of the others without more information?

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