Question 50
Juku has the first 100 volumes of the Harrie Totter book series at his home. For every $i$ and $j$, where $1 \le i \lt j \le 100$, call the pair $(i, j)$ *reversed* if volume No $j$ is before volume No $i$ on Juku's shelf. Juku wants to arrange all volumes of the series to one row on his shelf in such a way that there does not exist numbers $i, j, k$, where $1 \le i \lt j \lt k \le 100$, such that pairs $(i, j)$ and $(j, k)$ are both reversed. Find the largest number of reversed pairs that can occur under this condition.