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 Question from Andrea, a teacher: I need to organize 8 teams. Each team has to go through 8 games against another team, but not against the same as before.

Andrea,

Can you clarify: are you asking for a schedule where each team plays each other team once? With 8 teams there are only 7 possible opponents. A schedule to do that over 7 "game days" is possible.

--Victoria

Andrea replied

Yes that's what I meant!!

Ok, here is a schedule that should work for you. The teams are the 8 positions in each sequence, and the numbers indicate the games. For example, on Day 0, team 1 plays team 2 in game 0, team 3 plays team 4 in game 1, and so on.

Day 0 : (0, 0, 1, 1, 2, 2, 3, 3)
Day 1 : (0, 1, 0, 1, 2, 3, 2, 3)
Day 2 : (0, 1, 1, 0, 2, 3, 3, 2)
Day 3 : (0, 1, 2, 3, 0, 1, 2, 3)
Day 4 : (0, 1, 2, 3, 1, 0, 3, 2)
Day 5 : (0, 1, 2, 3, 2, 3, 0, 1)
Day 6 : (0, 1, 2, 3, 3, 2, 1, 0)

--Victoria

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