IMO 2017 Problem 5

IMO 2017 Problem 5

Proposed by: -
Verified: no
Verdicts: FAIL + FAIL
Solve time: 15m44s

Problem

An integer $N \ge 2$ is given. A collection of $N(N + 1)$ soccer players, no two of whom are of the same height, stand in a row. Sir Alex wants to remove $N(N - 1)$ players from this row leaving a new row of $2N$ players in which the following $N$ conditions hold:

($1$) no one stands between the two tallest players,

($2$) no one stands between the third and fourth tallest players,

$;;\vdots$

($N$) no one stands between the two shortest players.

Show that this is always possible.