Combinatorics struggles I am stuck in combinatorics problem that there must be a solution to but every experiment is leaving me stuck.
I am needing to build a bracket for a some games at a graduation event:


*

*There will be $8$ teams doing eight events. They will complete against each other in each event. The eight events will be in two different time blocks.

*So events $1$-$4$ will happen simultaneously and will be repeated for a total of four times, then events $5$-$8$ will happen simultaneously and will be repeated for a total of four times.


$\textsf{My goal}$ is to have each team face all the other teams.
I realize each team will have to repeat one event and face one team twice. It is quite similar to a round robin tournament but I cant figure out how to keep them from repeating events. 
Help would be greatly appreciated.

For any one team, there is a maximum of $7$ distinct pairings with other teams for the various events. Since you have $8$ events, you must have at least one pairing repeat. Another way of thinking about this would be the fact that there are only 28 distinct team pairings and you are trying to uniquely assign 32 events, which is impossible.
The easiest solution would be to eliminate one of the events.
For example Teams $1-8$ competing in Events $A-G$ could be matched up as follows:
$$
\begin{array}{c|cccccccc}
 &1&2&3&4&5&6&7&8\\ \hline
1& &A&B&C&D&E&F&G\\
2&A& &C&D&E&F&G&B\\
3&B&C& &E&F&G&A&D\\
4&C&D&E& &G&A&B&F\\
5&D&E&F&G& &B&C&A\\
6&E&F&G&A&B& &D&C\\
7&F&G&A&B&C&D& &E\\
8&G&B&D&F&A&C&E&
\end{array}
$$
If you insist on $8$ events, assign the pairings for event $H$ the same pairing of event $A$. Now you'll want to run events $A,B,C,D$ as your first group of events and $E,F,G,H$ as your second group of events.
