We have $n$ teams ($n$ is even) and $x<n$ types of games (basketball, volleyball...).
We have $x$ pitches, one for each game (one volleyball pitch, one basketball pitch...).
Each day, every pitch can be used at most once.
In our tournament:
- Every team must play each game exactly once
- No two teams should meet each other more than once
How does the minimum number of days needed $d$ depend on $n$ and $x$?
Many times you can be fully efficient and $d=x$ (such as when $n=6$ and $x=3$), but sometimes $d>x$ (e. g. when $n=4$ and $x=2$, $d=4$).