Question 26
Let $n$ be a positive integer. A train stops at $2n$ stations, including the first and last ones, numbered in order from the first to the $2n^{th}$. It is known that on a certain car, for each pair of integers $i, j$ such that $1 \le i \lt j \le 2n$, exactly one seat has been reserved for the trip from the $i^{th}$ station to the $j^{th}$. Find the minimum number of seats that must be available in that car.