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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.