I have $N$ guests and $M$ tables with $L$ seats each ($N\leq M\cdot L$). My task is it to distribute the guests for $N\geq D\geq3$ rounds such that no guest will sit on the same table, and he will never meet the same guests again.
As example: I have four guests, and two tables, with two seats each. Then I can distribute my guests as following:
In the first round: T1: [1, 2] T2: [3, 4] In the second round: T1: [3, 1] //Already a problem! T2: [2, 4] //Already a problem!
I tried to find an algorithm, but until now I failed. My initial approaches were either using the distribution of the guests in a matrix, and then using the columns, rows, and diagonals for at least three rounds, but that approach failed in the third round already. The other approach was using a "labyrinth-solving" approach by using a recursive function. But is there a mathematical approach how to solve that problem?