Suppose I have 8 teams $A_1,\ldots, A_8$, competing in different 8 games $X_1,\ldots, X_8$. For example $X_1 = soccer, X_2 = basket ball, \ldots,$ . In the morning there are 4 games $X_1,X_2,X_3,X_4$ take place, with 16 matches. In the afternoon there are another 4 games $X_5,X_6,X_7,X_8$ take place with 16 matches again. Can I schedule (I can freely choose any game) such that:
a) Every team participate in 4 different games in the morning and 4 different games in the afternoon.
b) Every team has a change to meet with another 7 teams?
c) Each games need two teams to play in one match?