There have been 9 problems before this, and this is the 10th. To celebrate, let's have a fun problem before we carry on with normal, serious ones!

Let \(a_{i}, i=1, 2, 3, 4, 5, 7, 8, 9, 10\) be the answer to Problem #\(i\) in the set Easy Problems. (The link can be found below.)

There exists a unique triple of distinct positive integers from 1 to 10 \((m, n, p)\) such that \(a _{m}+a_{n}=a_{p}\). Find \(m+n+p\).

Hint: solve systematically!

This problem is part of the set Easy Problems

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