## IMO 2017 problem -5

Discussion on International Mathematical Olympiad (IMO)
samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### IMO 2017 problem -5

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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### Re: IMO 2017 problem -5

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?
You cannot cross the sea merely by standing and staring at the water.

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

### Re: IMO 2017 problem -5

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.