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.
IMO 2017 problem -5
- M. M. Fahad Joy
- Posts:120
- Joined:Sun Jan 28, 2018 11:43 pm
Re: IMO 2017 problem -5
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?
You cannot cross the sea merely by standing and staring at the water.
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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
Re: IMO 2017 problem -5
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?