Impossible schedule ? 6 teams, 5 courts, 5 rounds.

[Yann_D.]

Hello !
I'm looking for a way to get a tournament schedule with the following rules:

"6 teams. 5 days. Each day, each team challenges another one in 5 fields.
They can't fight the same team two times or play twice in the same field."

(it basically means that each round, 3/5 fields are being used, 2 are empty.
and teams 1/2 - 2/1 is the same, obviously.
also, teams' number of players and winner/loser stats won't matter here).

When I try to get the schedule, I can get n-1 good rounds with n rounds/fields,
but then the n round has either: - A team that already visited it once.
-I use a couple of teams that has already been done.
So that's where I was wondering: Is this particular cubic setup impossible to realize,
or is there a single solution (or more) ?
If this is impossible to complete, I'm also interested in any clues to demonstrate it.
-It may be obvious, I haven't fully checked yet.  :-/
I've also looked some existing threads, those two in particular:

Court Balanced Round Robin and
10 teams, and 10 games

Thanks for your answers  

[Ian Wakeling]

Hello,

You are looking for a Room square of side 5, but if you look at this Wikipedia page on Room squares it states that the order 5 square is known not to exist.   I have not seen the Wallis reference, but I am guessing that would explain why it is impossible.

Hope that helps.