Question

A badminton coach invites players for a practice tournament. Every player shall play exactly 2 games. Each game is between two players. He knows all players well enough to rank them from best to worst where a stronger player would always beat a weaker player. To have a balanced tournament, he wants to minimize the number of players that win both games. How low can he get this number of double winners by careful planning the pairings?

Answer 1

Given : A badminton coach invites players for a practice tournament. Every player shall play exactly 2 games. Each game is between two players. He knows all players well enough to rank them from best to worst where a stronger player would always beat a weaker player. To have a balanced tournament, he wants to minimize the number of players that win both games.

To Find : How low can he get this number of double winners by careful planning the pairings?

Solution:

Person with Rank 1 is expected to win  both games.  

and last rank will loose both games.

Rest can be planned in such a way that they win 1 and loose 1.

Number of double winners by careful planning the pairings can be as low as 1

Here is one of the way to plan  , let say there are n players invited

Rank      of players playing against    and who  won

                           Winner

1            2                1

2            3               2

3            4               3

__          __           __

___       ___          _

n-1           n             n-1

1               n              1

Here only player  Rank  1 is winning  both games and Rank last is losing both game

Hence Number of double winners by careful planning the pairings can be as low as 1

Learn More:

A badminton coach invites players for a practice tournament.

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