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

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

.

.

.

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

Show that ,

**this is always possible**.

- samiul_samin
**Posts:**1007**Joined:**Sat Dec 09, 2017 1:32 pm

An integer $N\geq2$ 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 $N$ condition holds:

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

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

.

.

.

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

Show that ,**this is always possible**.

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

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

.

.

.

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

Show that ,

- M. M. Fahad Joy
**Posts:**120**Joined:**Sun Jan 28, 2018 11:43 pm**Location:**Dhaka, Bangladesh

samiul_samin wrote: ↑Wed Feb 14, 2018 10:14 amAn integer $N\geq2$ 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 $N$ condition holds:

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

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

.

.

.

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

Show that ,this is always possible.

Can you solve this?

- samiul_samin
**Posts:**1007**Joined:**Sat Dec 09, 2017 1:32 pm

No,Need expert to solve this and IMO problems are very high level problems.So,try easier problems first.M. M. Fahad Joy wrote: ↑Sat Feb 17, 2018 9:32 pmsamiul_samin wrote: ↑Wed Feb 14, 2018 10:14 amAn integer $N\geq2$ 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 $N$ condition holds:

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

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

.

.

.

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

Show that ,this is always possible.

Can you solve this?