For the special case where the number of venues is one less than the number of players, it might be asked whether we can arrange it so that each player plays exactly once at each venue; such a design is called a Room Square. This is not possible if the number of players is odd, nor if the number of players is 4 or nor 6. That leaves 8, but the 8-player Room Square violates the above “no venue idle twice consecutively” constraint. Subject to this, the formats chosen have each player either once or twice at each venue; or twice at one venue, no times at another, and once at the others. << - excessive quotation removed - >>
What are you reading about? What are the players playing? A card game? Is it a real game, or an imaginary game made up to prove a point?
Also, what is the source of this quotation. Not only do the rules require it, but knowing the source may help us in some way to understand this and enable us to be more helpful to you. Which is what we would like to do.