Question 19
Let $n$ be a fixed positive integer. Initially, $n$ $1$'s are written on a blackboard. Every minute, David picks two numbers $x$ and $y$ written on the blackboard, erases them, and writes the number $(x+y)^4$ on the blackboard. Show that after $n-1$ minutes, the number written on the blackboard is at least $2^{\frac{4 n^{2}-4}{3}}$.