I wanted to tag this question with tournaments, but we don't have that, so I thought oh, I'll tag it with block-designs, but we don't have that either. What do we have that fits?
I was presented with this problem at work. Say you have $24$ people and $8$ tables in a room. You want to set people at these tables in groups of three such that during each new round (where people switch tables and partners) no one meets someone twice and by the end everyone has met everyone.
A...