2017 IMO Problems/Problem 5

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.

solution

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