Six teams playing five games

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Question from Aidan, a student:

I have six teams that will be playing five games.
I want each team to play each game once and each team to play each other team once.
Is this possible or should I add an extra round and let some teams play each other twice?

Aidan,

I think it works out. The schedule of matchups is

16, 25, 34
26, 13, 45
36, 24, 51
46, 35, 12
56, 41, 23

To schedule the different games, use this array:

6 1 2 3 4 5
1 6 3 4 5 2
2 3 6 5 1 4
3 4 5 6 2 1
4 5 1 2 6 3
5 2 4 1 3 6

When team i plays team j, they play the game whose number is in row i and column j of the array.

--Victoria

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