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I have 16 total teams in a competition. In this competition, each team will play every other team (15 teams) once and only once. In each match in this competition, there are 4 teams (ie. A vs. B vs. C vs. D).

I know there should be a total of 20 matches in this competition. In each match, a team plays against 3 different opponents - so a team needs a total of 5 matches to play all 15 opponents. This is essentially the same as having 5 "rounds" in the competition. With 16 teams, each round will have 4 matches (4 teams per match x 4 matches = 16 teams involved).

What are the 20 different combos here of match-ups where no team plays another team more than once?

Also, if I have 25 teams where each match has 5 teams per match, what would the matchups be? I know that with 25 teams, I would have 30 total matches (6 rounds x 5 matches per round).

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