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I am scheduling a games tournament for my girlfriend's cousin's 21st birtday party.

There will be 8 teams.

There can be either 7 or 8 different games.

The briefing I have been given is:

  • Each team must play every other team at least once;
  • Each team must play every game (they do not need to play every team at every game);
  • Each game requires 2 teams to play.

I have worked out that there needs to be a minimum of 7 rounds, so that each team can play every other team. I have designed a schedule which states who plays who in each round.

However, I only have 1 version of each game, so each round has to have 4 different games being played.

Can anyone find a schedule which satisfies the above criteria?

Mark
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  • if you have 8 games then you can assign each game to one team and this is like scheduling round-robin tournament with home and away game. Each team will play each game once and it will play every other team twice (14 rounds). – Vasili Dec 05 '17 at 14:23

1 Answers1

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On the wikipedia page on the Room square, there is an example given which works for 8 teams. Assign your 8 teams a number from 0 to 7, associate to each row of the table a type of game and associate each column with a game round (7 rounds suffices). Now you can read of which pair of teams plays what game at what round from the table.

Room squares exist also in the sizes 1, 9, 11, 13... for resp. 2, 10, 12, 14... teams. So the only (odd) sizes where they do not exist are 3 and 5.

5th decile
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