IMO 2017 problem -5

Discussion on International Mathematical Olympiad (IMO)
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samiul_samin
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Joined: Sat Dec 09, 2017 1:32 pm

IMO 2017 problem -5

Unread post by samiul_samin » 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.

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M. M. Fahad Joy
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Re: IMO 2017 problem -5

Unread post by M. M. Fahad Joy » 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?
Math is the main inspiration of my life.

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samiul_samin
Posts: 1004
Joined: Sat Dec 09, 2017 1:32 pm

Re: IMO 2017 problem -5

Unread post by samiul_samin » Sat Feb 17, 2018 10:06 pm

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.

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