Camp team challenge assignments

[littleviolin]

Object:
I have 10 teams attending youth camp. We have 9 (1vs1) games at camp that every team will play. Each game is a point based thing with highest total points for a team winning the grand prize so no need for a bracket or playoff.
I want each team to play any other team only once.

I don't know how to even write this out in a mathematical question so this may not be the right thread for this.
I have tried figuring this out for about 11hrs and have gotten no where with it. If you have any idea how to calculate this please help my poor brain. Thanks Joshua

 

[Harry_the_cat]

Does each team play every other team exactly once for each of the 9 games?

If that is the case, each game will need to be played 45 times (ie \(\displaystyle \frac{10*9}{2}\)).

So there will be \(\displaystyle 9*45=405\) games played in all.

Is that what you wanted to know?