Poker Math Question

[dawkdawkins]

Can you answer this Poker/Math Question?
I have 20 players

They are going to play in 20 Tournaments 10 people at a time so that each person plays in 10 Tournaments.

Players are labeled here: (EACH LETTER IS A PLAYER)

A B C D E F G H I J K L M N O P Q R S T

Tournament 1:

ABCDEFGHIJ

Tournament 2:

KLMNOPQRST

I need the participants for Tournaments 3 through 20, so 18 more total.

My Question is:

it is possible to divide players such that each player plays 14 other players 5 times, and 5 other players 4 times.

I am having trouble figuring out how to fill in the 18 remaining tournaments.

Thank you

 

[DrMike]

You may be able to do it this way.

Call the players 1..20

Now, arrange the numbers 1..10 on a 10x10 chessboard, so that
* each row contains all the numbers from 1 to 10
* each column contains the numbers from 1 to 10
There are lots of ways to do this. Not all will work for what follows.

Next - make two copies of your chessboard. On one, add 10 to all the white squares, on the other, add 10 to all the black squares.

Then, the rows of the chessboard are your tournaments. There are 20 players, 20 tournaments, each player plays in 10 of the tournaments. Whether this meets your other conditions depends on how you arranged the chessboard to begin with.