2017 IMO Problems/Problem 5
An integer is given. A collection of soccer players, no two of whom are of the same height, stand in a row. Sir Alex wants to remove players from this row leaving a new row of players in which the following 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.
Show that this is always possible.