A Riddle of Sorts

[Jinn]

My brother is a teacher and is putting field day together. He came to me with the issue and we were able to solve it to a point by breaking some rules, if you even want to call them rules.

Rules?:
There are 4 activities.

There are 4 classes, each class is split up into an A team and a B team making 8 teams total.

The A and B teams from each class cannot play each other.

Each team must play all other teams once.

Each team must play each activity once.


Our biggest issue was trying to fit this into a 4x4 bracket, we determined this was impossible and were only able to accomplish the above rules by fitting it into a 4x6 bracket.

He's wondering if it's even possible to fit this into a 4x4 bracket with following the above set of rules.

[Byrthnoth]

My brother is a teacher and is putting field day together. He came to me with the issue and we were able to solve it to a point by breaking some rules, if you even want to call them rules.

Rules?:
There are 4 activities.

There are 4 classes, each class is split up into an A team and a B team making 8 teams total.

The A and B teams from each class cannot play each other. Also, teams cannot play themselves. This leaves 6 opponents.

Each team must play all other teams once.

Each team must play each activity once.


Our biggest issue was trying to fit this into a 4x4 bracket, we determined this was impossible and were only able to accomplish the above rules by fitting it into a 4x6 bracket.

He's wondering if it's even possible to fit this into a 4x4 bracket with following the above set of rules.

These rules make a 4x6 bracket necessary. The "Each team must play each activity once" makes the system of rules impossible.

[Kanriel]

If the rule was "Each team must play a different team each round" then 4x4 would be possible.