Organizing a chess tournament

Six players are participating in a chess tournament. In the first phase of the tournament, each player plays against three other players. By double counting, there are \( \frac{6 \times 3 }{2} = 9 \) games that are held.

How many different possibilities are there for the set of 9 different games to be played?

Details and assumptions

The order the games are played in does not matter, just which pairs of players compete.

As an explicit example, here is a possible set of 9 games: Player \(i\) plays against player \( i-1, i+1 \) and \( i + 3 \), where calculations are done modulo 6.


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