Question 5
Fix $N \ge 1$. A collection of $N(N+1)$ soccer players of distinct heights stand in a row. Sir Alex Song wishes to remove $N(N-1)$ players from this row to obtain a new row of $2N$ players in which the following $N$ conditions hold: no one stands between the two tallest players, no one stands between the third and fourth tallest players, …, no one stands between the two shortest players. Prove that this is possible.