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IMO 2017 problem -5

Posted: Wed Feb 14, 2018 10:14 am
by samiul_samin
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.

Re: IMO 2017 problem -5

Posted: Sat Feb 17, 2018 9:32 pm
by M. M. Fahad Joy
samiul_samin wrote:
Wed Feb 14, 2018 10:14 am
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.

Can you solve this?

Re: IMO 2017 problem -5

Posted: Sat Feb 17, 2018 10:06 pm
by samiul_samin
M. M. Fahad Joy wrote:
Sat Feb 17, 2018 9:32 pm
samiul_samin wrote:
Wed Feb 14, 2018 10:14 am
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.

Can you solve this?
No,Need expert to solve this and IMO problems are very high level problems.So,try easier problems first.