Real life problem.
I have 8 different musical instruments and 14 players of each instrument. There will be 9 sessions where the players are placed into 14 bands (each band has 1 of each instrument). So if each instrumentalist was labeled 1-14 for their respective instrument, the first session could be band 1: all instrument 1s, band 2 all instrument 2s etc.
Is it possible for each band in each session to be unique? I.e. Trumpet 1 doesn't play with clarinet 1 more than once (and doesn't play with any other instrumental person from other instruments more than once). I am able to brute force this with 3 or 4 sessions but past that it gets difficult.
While I have a math degree and took some combinatorics classes, I am definitely not an expert. I think this might fall under Combinatorial Design but I am not really sure.