how to create a schedule for 9 teams playing x number of games no team can play same team twice no team can play same game twice

Question

I am setting up a minute to win it challenge for a party. I have 9 teams of 5 players each. Each round will be head to head challenge with one team idle per round. All games are played simultaneously. there will be stations set up with a different game at each station. Teams will rotate through each station/game. Rules: no team will play the other team twice, no team will play the same game twice How many games do I need to do this? How do I determine the schedule per round?

I am not a mathematics person so simpler answers or equations would be appreciated. Some of the answers I have read are over my head or are displaying complete graphs which I cannot interpret.

Answer 1

Here is a $9$-round schedule. This is optimal because there are $\binom 92=36$ pairs of teams, and each round takes care of four pairs.

${}$	G1	G2	G3	G4	G5	G6	G7	G8	G9
R1	3/5	7/8	2/6	1/4
R2		4/6	8/9	3/7	2/5
R3			5/7	9/1	4/8	3/6
R4				6/8	1/2	5/9	4/7
R5					7/9	2/3	6/1	5/8
R6						8/1	3/4	7/2	6/9
R7	7/1						9/2	4/5	8/3
R8	9/4	8/2						1/3	5/6
R9	6/7	1/5	9/3						2/4

I found this using the idea presented in Anders Kaseorg's solution to a similar scheduling problem, together with brute force search to find the parameters which work.