MHB Creating theorems for an axiomatic system

[malloryjohn]

I have the axioms:

Axiom 1: Each game is played by two distinct teams
Axiom 2: There are at least four teams
Axiom 3: There are at least six games played
Axiom 4: Each team played at most 4 games.

And I have come up with the theorem: If there are exactly 4 teams, then there are at most 8 games.

I need to come up with two more theorems. I'm pretty stuck on where to go from here, so any advice would be greatly appreciate

 

[Deveno]

How many teams can there be, if there are exactly six games played?

If each team plays only once, how many teams can there be (if only teams that play games count)?

The general idea is: fix ONE of your variables, and determine limits on the others.