Creating theorems for an axiomatic system

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The discussion centers on formulating theorems within an axiomatic system based on specified axioms regarding teams and games. The established theorem states that with exactly four teams, there can be at most eight games played. Participants are encouraged to explore additional theorems, particularly focusing on the implications of having six games and the constraints on team counts when each team plays only once. The approach recommended involves fixing one variable and analyzing the limits on the others.

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malloryjohn
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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
 
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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.
 

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