I have 5 arenas and 15 players. There are 5 game rounds, and each player should be at 1 arena per round. Every player should pass all 5 arenas after 5 rounds, but the sequence doesn't matter.
This creates 5 groups of 3 players, which shift every round between an arena.
Now, I also want each player to see as many different players as possible.
My solution with 5 groups of 3 players that shift between arenas checks all boxes, except the last.
From my understanding, it is impossible to have unique groups every round whilst also meeting the other requirements, but I'd like to have the best possible solution for this problem.
This is a solution I came up with myself, but as you can see these are just 5 static groups that shift around between the different arenas (player 1, 6 and 11 stay together at all times).
Is there an existing algorithm to solve this problem? Or can someone give me kind-of a flowchart?