6 teams randomly arranged in groups of 3

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Question from Anthony:

im trying to make a game scheduled for 6 teams using a 1vs2vs3 ; 4vs5vs6 format.
all 6 teams randomly arranged in groups of 3. each team will play all teams at least twice, im trying to see how to make the number of times each team play another the same.
schedule should be arranged as such 1vs2vs3 4vs5vs6 so that (1vs2, 1vs3, 2vs3) and (4vs5, 4vs6, 5vs6)
i am limited to having only 2 sets of 3 at a time with 6 teams.

Anothony,

The schedule below has the property that every pair of teams are together exactly twice. The way to read it is that the positions in each sequence are the teams and the numbers indicate the groups.

1 : (0, 0, 1, 0, 1, 1)
2 : (0, 1, 0, 1, 0, 1)
3 : (0, 1, 1, 0, 0, 1)
4 : (0, 0, 1, 1, 0, 1)
5 : (0, 1, 0, 0, 1, 1)
6 : (0, 0, 1, 1, 1, 0)
7 : (0, 1, 0, 1, 1, 0)
8 : (0, 1, 1, 0, 1, 0)
9 : (0, 1, 1, 1, 0, 0)
10 : (0, 0, 0, 1, 1, 1)

I hope this is what you are looking for.
—Victoria

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