HMMT 2018 U34

The integers $1,2,3,4,5,6,7,8,9,10$ are written on a blackboard. Each day, a teacher chooses one of the integers uniformly at random and decreases it by 1 . Let $X$ be the expected value of the number of days which elapse before there are no longer positive integers on the board. Estimate $X$. An estimate of $E$ earns $\left\lfloor 20 \cdot 2^{-|X-E| / 8}\right\rfloor$ points.