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Playing 4 on 4 basketball with up to 12 players (three teams) is easy to manage. But when player thirteen shows up, is there a way to work everyone in such that no one sits two games in a row?

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    See my solution, I think you need to add more conditions to your questions. Because my solution means that players 11,12,13 keep playing all the games.2011-03-29
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    As long as there are $16$ or less players, then no one has to sit more than $1$ game in a row. For example, call the players $x_1 , \dots , x_{16}$. Then players $x_1 , \dots x_8$ play the first game, $x_9 , \dots , x_{16}$ play the second game, and then they alternate. I suspect, however, that this may not be the intent of your original question.2011-03-29

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