Can a Round Robin Schedule Accommodate n Players and n-1 Rounds?

[mangaferret]

Hi. I was tasked with organising a tournament with the following set up:
8 players
7 rounds
each round, each player is paired with another, and plays another pair; so each round has 2 games played (ie, a&b vs c&d ; e&f vs g&h)

However there were the following constraints:
Each player must be teamed up with each other player exactly once.
Each player must oppose each player exactly twice.

I was able to come to a solution, but it got me thinking: is it possiple that such an arangement could be organised for n players & n-1 rounds?

 

[Valkarie]

Yes, it is possible to organize a tournament with n players and n-1 rounds. The way to do this is to create a round robin schedule, which assigns each player to one opponent in every round. This ensures that each player plays each other player exactly once and opposes each other player exactly twice. To do this, you would need to organize the schedule such that each player plays two consecutive games against two different opponents in each round. For example, if there are 8 players, the following could be one possible schedule: Round 1:A vs B, C vs DE vs F, G vs HRound 2:A vs C, B vs DE vs G, F vs HRound 3:A vs D, B vs CE vs H, F vs GRound 4:A vs E, B vs FC vs G, D vs HRound 5:A vs F, B vs EC vs H, D vs GRound 6:A vs G, B vs HC vs F, D vs ERound 7:A vs H, B vs GC vs E, D vs FThis way, each player plays each other player exactly once and opposes each other player exactly twice.