6 teams, round robin, 5 stations

[dpuneil]

Hosting a corporate event where we will have 6 teams and 5 different games/stations. Each game can accommodate only one match per round.

We would like each team to play each other once and play each game/station once.

Fiddling with Excel it seems impossible - true?

[Ian Wakeling]

It is indeed mathematically impossible to construct a schedule like this.  But other similar schedules exist.  The best option is probably to drop one of the stations:

(C D) (---) (F E) (A B)
(---) (A F) (C B) (E D)
(B F) (C E) (A D) (---)
(A E) (D B) (---) (C F)

The square is symmetrical, so rounds and stations could be assigned either way around to rows and columns, but note that the teams play only 4 out of the 5 possible opponents.  The smallest example that will work as you intended it would be 8 teams, 7 stations and 7 rounds.

(---) (G B) (C A) (F D) (---) (E H) (---)
(---) (D E) (---) (C G) (H A) (---) (B F)
(C B) (---) (H F) (A E) (D G) (---) (---)
(A D) (C H) (---) (---) (E B) (F G) (---)
(E F) (---) (---) (H B) (---) (C D) (A G)
(---) (---) (G E) (---) (C F) (B A) (D H)
(G H) (F A) (B D) (---) (---) (---) (C E)